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Developing animal-habitat models for management of high-elevation forests Huggard, David John 2000

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DEVELOPING ANIMAL-HABITAT M O D E L S FOR M A N A G E M E N T OF HIGH-ELEVATION F O R E S T S by DAVID J . H U G G A R D B . S c . University of British C o l u m b i a , 1988 M . S c . University of British C o l u m b i a , 1991  A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES THE FACULTY OF FORESTRY Department of Forest S c i e n c e s  W e accept this thesis as conforming to the required standard  T H E UNIVERSITY O F BRITISH C O L U M B I A February 2 0 0 0 © D a v i d Huggard, 2 0 0 0  In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the head of my department or by h i s or her r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n ' s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n .  Department of  fc/effTS<:/C^Cg5  The U n i v e r s i t y of B r i t i s h Columbia Vancouver, Canada Date  F£B.  /P.  Abstract I examined ways to develop better models relating animals to habitat features, forest harvest types and edges, using data on spruce grouse (Falcipennis canadensis) and small mammals (masked shrews, Sorex cinereus; montane shrews, Sorex monticolus; and southern redbacked voles, Clethrionomys gapped). The work was part of the multidisciplinary Sicamous Creek Silviculture Systems project in high-elevation Engelmann spruce-subalpine fir forest in southern British Columbia. Spruce grouse in winter selected knolls and areas with dense, small and short trees, dense canopy cover, and exposed rock. Grouse avoided forest within 510 m of cutblock edges. Occurrence of grouse in forests near open wetlands increased with increasing predicted habitat quality, but declined within 10-20m of the opening. Removing 3 3 % of timber volume with openings of 0.1, 1, or 10 ha reduced occurrence of grouse by a similar amount; uniform partial cutting reduced their occurrence by 6 9 % . Habitat relationships were less evident for small mammals collected in pitfall traps. A s a preliminary step in model development, I elaborated techniques that partition environmental and spatial variation in abundance to include variation due to habitat types, habitat elements, and shared variation, and also estimated measurement error. Unexplained variation was high, and equalled expected measurement error in half the cases. Relationships with habitat elements were confounded to varying degrees by habitat type differences and spatial patterns. The elaborated technique is useful to characterize variation observed in habitat relationship studies, and to guide further study and interpretations of results. I compared classification and regression trees (CART) and neural networks (NN) to linear additive models. The more complex NN and C A R T habitat models fit data better than linear additive models, but had equal or poorer predictive abilities with data from independent sites. The fit of a model and its predictive ability were unrelated across 14 data sets and the 3 techniques. However, C A R T and NN modelling have heuristic benefits, suggesting non-linear and contingent relationships for future study. I summarized effects of harvest types on small mammals using likelihood functions to facilitate applied interpretations and a Bayesian combination with literature estimates. Sorex cinereus and immature red-backed voles declined in clearcuts by 26 - 57%, while uniform partial cutting had smaller negative or positive effects. Sorex monticolus increased slightly in both harvest types. Edge response varied for the 3 small mammal species. The shrews showed weak positive associations with shrub, herb, or forest floor cover. Red-backed voles showed stronger positive, interacting relationships with canopy, shrub cover and coarse woody debris. Management implications are presented for maintaining spruce grouse and small mammal habitats.  Table of Contents Page  Abstract List of Tables List of Figures Acknowledgements Chapter 1. Introduction - context and concepts Background on the Sicamous Creek Silvicultural Systems project and faunal research Background on concepts underlying this work 1. Natural history and ecological theory 2. Indices of habitat quality 3. Model validation 4. Sources of variation 5. Multiple-scale effects 6. Spatial pattern 7. Integrating past knowledge  Chapter 2. Winter use of subalpine forest by spruce grouse: Effects of habitat features, edges and harvest treatments  ii vi vii ix 1 2 6 6 8 8 9 10 10 11  12  Chapter Summary 12 Introduction 13 Methods 15 Main study site and validation sites 15 Habitat m o d e l s - f i e l d plots 16 Habitat models - analysis 18 Edge effects - response to edges of openings 20 Treatment effects - use of preferred habitat in different harvest treatments 21 Testing assumptions of droppings as an index of habitat use 22 Results 23 Assumptions of the use index 23 Effective sample size with spatial autocorrelation 24 Habitat models - occurrence of grouse by topography type 24 Habitat models - characteristics of grouse-centred plots compared to systematic plots 26 Habitat models - characteristics of plots with grouse present versus absent 26 Habitat models - classification and predictive success 28 Edge effects 28 Treatment effects - grouse occurrence and habitat scores in different harvest treatments 31 Discussion 33 Using habitat choices as an index of habitat quality 33 Habitat use by spruce grouse 34 Edge effects 35 Effects of alternative silvicultural systems 36 Implications for maintaining spruce grouse winter habitat in managed high-elevation forests 38  Chapter 3. Developing animal-habitat models: partitioning variance due to habitat, spatial trend and measurement error Chapter Summary Introduction Partitioning environmental and spatial components of variation - theory and utility Elaborations for developing habitat models: Habitat "types" and habitat "elements" Elaborations for developing habitat models: Undetermined component and measurement error  41 41 41 44 46 49  Methods Partitioning habitat-element, habitat-type and spatial variance components Estimating expected measurement error C a s e studies - study areas Small mammal and habitat element data sets Results and interpretations Undetermined component compared to expected measurement error Habitat types and habitat elements Spatial components Discussion  Chapter 4. Comparison of alternative modelling techniques for animal-habitat models Chapter Summary Introduction Methods Data sets - 1. Small mammal abundance in pitfall traps Data sets - 2. Occurrence of spruce grouse Analyses - 1. Model fitting Analyses - 2. Model testing Results and Discussion Fit of models Predictive ability of models Relationship between model fit and predictive ability Heuristics - interpretability of the models Summary and Recommendations  Chapter 5. Harvesting effects and habitat models for shrews in a high-elevation forest Chapter Summary Introduction Methods Study area Sampling small mammals Habitat measurements Catch index, and combining age and maturity classes Treatment and harvest type comparisons Prior probabilities from the literature Relationships between small mammals and habitat elements Results Summary of small mammal collection Treatment and harvest type effects Habitat models Habitat model details - Sorex cinereus Habitat model details - Sorex monticolus Habitat model details - Red-backed voles Site series Discussion I. Field and analysis methods Pitfall captures as an index of habitat quality Interpreting weak effects II. Harvest effects and habitat relationships Treatment, harvest type and edge effects Implications of habitat models Appendix 5.1. Calculation of the small mammal abundance index  50 50 52 53 55 56 57 60 62 62  67 67 68 73 73 75 76 78 79 79 83 86 88 97  100 100 101 103 103 104 105 106 108 109 110 111 111 113 118 119 122 123 125 125 125 125 127 129 129 131 134 iv  Chapter 6. General Conclusions and Recommendations  136  Methods for improving habitat models Habitat relationships, treatment effects and edge effects Management messages  136 139 142  References  144  v  List of Tables Table 2.1. Discriminant function to separate systematic plots from grousecentred plots at Sicamous Creek  25  Table 2.2. Discriminant functions to separate plots with and without grouse sign  27  Table 2.3. Classification and predictive ability of discriminant functions  29  Table 3.1. Total captures by species, sex and maturity class  57  Table 4.1. Fit of the small mammal models  81  Table 4.2. Fit of spruce grouse models generated with linear additive, classification and regression tree (CART) and neural network (NN) techniques  82  Table 4.3. Predictive ability of small mammal models generated with linear additive, classification and regression tree (CART) and neural network (NN) techniques, tested with independent data  84  Table 4.4. Predictive ability of spruce grouse models generated with linear additive, classification and regression tree (CART) and neural network (NN) techniques, tested with independent data  85  Table 4.5. Step-wise regression for abundance index of red-backed voles at Sicamous Creek in August Table 4.6. Discriminant function analysis for occurrence of spruce grouse  89 90  Table 5.1. Total captures by species, sex and maturity class  112  Table 5.2. Fit and predictive ability of habitat models  119  Table 5.3. Step-wise regression models for S. cinereus  120  Table 5.4. Step-wise regression models for S. monticolus  122  Table 5.5. Step-wise regression models for red-backed voles  124  vi  List of Figures Fig. 1.1. The Sicamous Creek Silvicultural Systems study area  4  Fig. 2.1. Layout of 5.65 m-radius plots  17  Fig. 2.2. Percent occurrence of grouse droppings in 0.01-ha plots in 3 topography types  25  Fig. 2.3. Relative abundance of grouse at different distances into the forest from clearcuts  30  Fig. 2.4. Occurrence of grouse droppings in grouse-centred plots as a function of distance from cutblock and distance from open wetland Fig. 2.5. Occurrence of grouse droppings in preferred in 5 treatments  31 32  Fig. 2.6. Cumulative percentile plots of discriminant function scores for 0.1-ha plots in individual-tree selection and uncut control treatments Fig. 3.1. East Barriere Lake study area Fig. 3.2. Variance components for: East Barriere Lake spring; East Barriere Lake August; Sicamous Creek spring; and, Sicamous Creek August Fig. 4.1. Example of the peak cross-validation fit of neural networks for one small mammal data set, using networks with 2, 4 or 6 hidden nodes with 3 different, randomly-chosen subsets of the data used for training  33 54  58  78  Fig. 4.2. Relation of the fit of stepwise regression models for the 12 small mammal data sets to overall P R E of C A R T models, and fit of NN models  83  Fig. 4.3. Training and cross-validation fit of a typical NN model over 2000 iterations  83  Fig. 4.4. Relationships between the fit of a model to the original small mammal data set and its ability to predict with the independent test data for: stepwise regression; C A R T ; and, NN models  87  Fig. 4.5. Relationship between the fit of a model to the original small mammal data set and its ability to predict with independent data, within model types, for: C A R T models with different numbers of branches; and, different runs of NN models  87  Fig. 4.6. C A R T model for red-backed voles in August at Sicamous Creek  91  Fig. 4.7. C A R T model for occurrence of spruce grouse at Sicamous Creek  92  Fig. 4.8. Univariate plot of the behaviour of the NN model for red-backed voles in August at Sicamous Creek  94  Fig. 4.9. Univariate plot of the behaviour of the NN model for spruce grouse at Sicamous Creek  94  vii  Fig. 4.10. Bivariate plot of N N model predictions for spruce grouse at Sicamous Creek as basal area of subalpine fir trees and density of subalpine fir trees are varied from their minimum to maximum values  95  Fig. 4.11. Bivariate plots of N N model predictions for red-backed voles in August at Sicamous Creek as coarse woody debris and shrub cover are varied from their minimum to maximum values, at 3 levels of canopy cover  96  Fig. 5.1. Examples in which spring and August likelihood functions were not combined, or were combined  114  Fig. 5.2. Likelihood functions for the effects of 3 harvest types compared to contiguous uncut forest: S. cinereus; S. monticolus; red-backed vole females; and, red-backed vole males  114  Fig. 5.3. Likelihood functions for the effects of overall treatments compared to uncut control treatments: S. cinereus; S. monticolus; red-backed vole females; and, red-backed vole males  115  Fig. 5.4. Derivation of posterior probabilities combining Sicamous Creek data and literature values for: S. cinereus in clearcuts; S. monticolus in clearcuts; and, S. cinereus in partial cuts  117  Fig. 5.5. Behaviour of neural network model for S. cinereus in spring  121  Fig. 5.6. Behaviour of neural network models for S. monticolus  123  viii  Acknowledgements Everything in this thesis would have been indubitably, indisputably and inconceivably impossible without the Sicamous Creek Project, and that project would not exist without the efforts of Alan Vyse and Walt Klenner, still of the B.C. Forest Service. Putting together a successful operational, large-scale, multi-disciplinary project seems to be a remarkably thankless task (or worse) - so, from me, a huge "Thank you!"  The real work of this thesis - hauling heavy things up hills and back down again, enumerating innumerable balsam trees, peering at little tiny shrew teeth, and, of course, counting grouse "droppings" - was done by an army of field assistants who made a mockery of minimum wage laws. The main ones: Christine Chesson, Christine Chesson and Christine Chesson, Christine Ferguson, Bill Turko, Aaron Goh, Karen Gladders, Jared Hoobs, Andy Bennett, Tamsin Baker, Devon Haag, Kirsten Hannam, Catherine Henry, Tim Horton, Susan Pendray, Sarah Shima, Gillian Tumey and Sharilynn Wardrop. And thanks to Susan Dee-is-for-data and Russ Walton (for the beer, mainly...)  Thanks also to the other Sicamous Creek co-operators, and particularly the other researchers who make it such an interesting place to work (and were polite enough to avoid snickering at the ways of wildlife biologists).  A special thanks to my supervisor, Fred Bunnell, for allowing and encouraging research that is not "normal" (in the traditional, probably statistical, and hopefully Kuhnian senses of that word). Thanks also to my committee members Alton Harestad, Ken Lertzman and David Tait for their diverse inputs during this long process, and to Glenn Sutherland and the other CACB'ers who put up with my crazy ideas.  I gratefully acknowledge the funding for this work, provided by various regional and provincial sources in the B.C. Ministry of Forests (really, this is silviculture), and Forest Renewal B.C.  And, thanks especially to Kelly, for all her patience and help - I promise I will never, ever do another one of these things!  ix  Chapter 1. Introduction - context and concepts Forest management has become more complex. Foresters are required to manage for objectives well beyond the traditional silvicultural objectives of harvesting wood products and regenerating a new stand (Smith 1986). International agreements arising from U N C E D 1992, environmentally-aware markets, and well-voiced local concerns have made many other objectives equally important in forest management decisions. Long-term sustainability, efficient use of wood products, non-timber forest resources, water quality, maintenance of soil and soil productivity, terrain stability, visual aesthetics, conservation of particular species and maintenance of biological diversity - all are increasingly integral parts of forest management (Franklin 1989b, Hansen etal. 1991, Swanson and Franklin 1992, Haila 1994, Kohm and Franklin 1997). Correspondingly, the task of applied researchers providing information to forest managers has become more complex. The textbook model of scientific method - testing a prediction deduced from a general theory by carefully manipulating one or two critical factors and observing one or two response variables - is often of limited utility in applied forestry (Baskerville 1994). The applied researcher cannot freely choose the ideal system to test a question derived from a favourite theory, because actual issues in particular systems determine the important questions (Bunnell and Huggard 1999). The scale of applied research also is determined by the scale of operations, and often is much larger than scales chosen by researchers unconstrained by potential applicability of their findings and seeking abundant replication. At the same time, the wide range of values influencing forest management requires information on a similarly wide range of ecosystem components, all of which have their particular relevant scales and critical factors. No research program can address all, or even the majority, of these components in an ideal, optimally designed way, and yet applied research addressing only one or a few components is likely to have little influence on management decisions (Franklin 1989a, Rasmussen and Wright 1998, Larson 1996, Klenner  1  and Vyse 1999). One of the major challenges of applied research is therefore to develop diverse, creative and often non-traditional approaches to providing reliable information on the many issues relevant to managers. The research included in this dissertation explores some approaches to providing useable knowledge about relationships between wildlife species and habitat changes due to forest management. The work is one part of a larger faunal diversity research program, which is itself only one component of a large, long-term, integrated project at the Sicamous Creek Silvicultural Systems research site. Sicamous Creek is one of a number of large-scale experimental silvicultural systems projects that have recently been established in Canada and the United States, as one approach to meeting the increasingly complex information needs of forest managers (for other project sites, see Amott and Beese 1997, Cameron et al. 1999, Chambers et al. 1999, Franklin et al. 1999, Ritchie and Harcksen 1999). These projects provide several advantages, including the benefits of replicated, randomized designs, experimental variables that are simplified to provide interpretable answers but are still directly relevant to forest management, interactions between a large and diverse team of researchers, better prospects of long-term funding stability, and a high profile among managers, which promotes extension opportunities. This chapter is intended to provide 2 types of background information common to the chapters that follow: the details of the Sicamous Creek site, and some general conceptual issues that underlie the work presented here. These 2 sections are presented here to bring out some of the links between the different chapters, and simply to avoid repetition in each chapter.  Background on the Sicamous Creek Silvicultural Systems project and faunal research Management of high-elevation Engelmann spruce (Picea engelmannii) - subalpine fir (Abies lasiocarpa) forests is receiving increasing scrutiny, as both the importance to regional timber supplies and public and professional concerns about past practices intensify (Vyse  1999). Poor regeneration success in traditional large clearcuts, harvesting effects on supply and quality of water, and impacts on wildlife or biological diversity are primary factors leading to increased interest in alternative harvesting systems for these forests. The Sicamous Creek Silvicultural Systems project uses an active adaptive management approach (Walters and Holling 1990) to assess the effects of alternative management options on a wide array of forest components. The site is located 7 km southeast of Sicamous, British Columbia (50°50'N 118°50'W). The site is on a moderate north-facing slope, ranging from 1530 m to 1830 m elevation. In the hierarchical biogeoclimatic ecological classification scheme used in British Columbia (Pojar et al. 1987), the site is classified as the wet cold subzone of the Engelmann spruce - subalpine fir zone (ESSFwc2; Lloyd et al. 1990). Additional tree species are found in some other subzones of the E S S F zone, but only these two are found at Sicamous Creek, with 8 2 % subalpine fir and 1 8 % Engelmann spruce among canopy trees. The oldest trees in the stand are approximately 350 years old (Parish 1997). The understory consists of dense shrubs (Rhododendron albiflorum, Menziesia ferruginea and Vaccinium species) or herbaceous plants (Rubus pedatus, Valeriana sitchensis, Streptopus roseus, Tiarella trifoliata, Gymnocarpium dryopteris) and an almost ubiquitous moss layer. Soil moisture regimes range from subxeric in shallow soils on elevated topography to hygric sites in poorly drained areas. The site has been divided into 15 contiguous study units of 30 ha each (Fig. 1.1). Five treatments were assigned to the units, in a randomised block design (randomisation within lower-, middle- and upper-elevation blocks): 1.  Single 10-ha clearcut with surrounding 20-ha leave strip;  2.  Array of 9 1-ha patch cuts with 100-m wide leave strips;  3. Array of 55 0.1-ha patch cuts with 30-m wide leave strips; 4.  Individual tree selection partial cuts with 2 0 % uniform removal across the size distribution of the 2 tree species and complete tree removal along skid trails (33% total removal); and  5.  Uncut control. 3  Fig. 1.1. The Sicamous Creek Silvicultural Systems study area. Black areas are cutblocks of 0.1 ha, 1 ha, and 10 ha; grey areas are individual-tree selection blocks; white is uncut forest.  The treatments are current or feasible future operational harvest types for E S S F forests. With associated skid trails and roading, each of the 4 harvest treatments removed approximately 3 3 % of the timber volume from each study unit.  Harvesting with ground-based  machinery occurred in winter 1994-95. Four site preparation treatments have subsequently been applied in a split-plot design (30-m square plots) within each replicate unit, including controls: burned, organic layer removed, mounded with excavator (the standard operational treatment), and no site preparation. Other silvicultural options, such as natural versus planted regeneration, were also tested in small split-plot designs. Research at the site reflects the range of resources that forest managers must consider, with 38 primary researchers measuring: economics and logistics of harvest; performance of advanced, natural and planted regeneration; seed and tree pathologies and pests; windthrow; stand history; microclimate and hydrology; soil productivity and nutrient  4  cycling; ectomycorhyzzal and hypogeous fungi; vascular plants, bryophytes and lichens; and faunal diversity (Hollstedt and Vyse 1997). Eight primary researchers involved in the faunal diversity component of the Sicamous Creek project examined taxa potentially sensitive to forest harvesting that represent a range of body sizes and habitat associations. Priority in choosing faunal groups for study was given to groups that have been extirpated or seriously reduced by intensive forestry elsewhere, groups with documented keystone roles in forest systems, and highly diverse but little-known taxa (see Klenner and Huggard 1997 or Huggard et al. 1999a for rationale for indicator groups). Availability of efficient field sampling methods was also a criterion, given limited and unpredictable funding. Study organisms at Sicamous Creek included: pine martens and weasels, woodpeckers, spruce grouse, song birds, rodents, shrews, ground-dwelling invertebrates, aquatic invertebrates, and soil microarthropods. All studies at the Sicamous Creek site examine effects of the overall treatments, and many measure the effects of the edges that are a particularly prominent feature of the patch cut systems. Most of the faunal studies also relate the study groups to habitat features ("habitat models") at a variety of spatial scales. The Sicamous Creek site was designed to test effects of overall harvest systems, and allows simple direct comparisons of effects on operationally important variables (e. g., windthrow: Huggard et al. 1999b, marten winter use: Huggard 1999). The experimental design facilitates conclusions about even rare and unexpected organisms (e. g., grylloblattid insects, Huggard and Klenner in prep.). The site also allows easy study of edge effects, because the systematic placement of cutblocks does not confound the edge with the changes in forest type or topography that are typically encountered at the edges of operational cutblocks (Huggard et al. 1999b). However, the Sicamous Creek site is not specifically designed to allow easy development of habitat models - a reflection of the difficulty of designing one study site for the many spatial scales of variables that must be included in operationally-relevant forest research. Developing habitat models with the extensive data from Sicamous Creek therefore faces many of the same challenges as habitat modelling in other studies. Given the poor  5  performance of many wildlife-habitat models, these challenges appear to be serious (e. g., Laymon and Barrett 1986, Rotenberry 1986, Van Home and Wiens 1991, Morrison et al. 1992).  Background on concepts underlying this work Reviewing previous habitat models and the broader literature related to discovering reliable patterns in nature, I identified 7 general concepts to consider in improving our abilities to express relationships between animals and harvest treatments, habitat features, or edges. I review these concepts briefly here, and relate them to the 4 chapters that follow. They form much of the context and conceptual basis for the dissertation.  1. Natural history and ecological theory Ecological theory almost completely neglects the abiotic and non-dynamic biotic factors that compose habitat (Bell et al. 1992). [An exception is the very large scale of climiatic conditions combined with physiological limitations that determine the limits of a species' geographical range.] Theories of habitat selection at finer scales than geographical range generally rely on a priori designations of good and poor habitat, and are flexible enough to accommodate almost any pattern of habitat use (Rosenzweig 1985). Ecological theory therefore does not address the applied issue of predicting habitat relationships for individual species that are of management concern (Hansson 1992). However, our collective knowledge of the relationships between species and habitat features is vast - it forms the bulk of natural history. As Weiner (1995) pointed out, the natural history knowledge of field biologists provides far more testable predictions and a better basis for management decisions than any current ecological theory. The challenge is to capture intuitive natural history knowledge in a quantitative form that can be subject to scientific evaluation, assessed for generality ("patterns of patterns"; Bunnell and Huggard 1999), and communicated to those requesting the knowledge. Although many of our forest management practices are based on providing habitat features and managing edge (e. g., British Columbia Forest Service and British  6  Columbia Environment 1995), the relationships of particular species, even vertebrates, to these features are largely undocumented in western forests (Bunnell 1999, Kremsater and Bunnell 1999). Much of the faunal research at Sicamous Creek and much of this dissertation focus on providing quantitative natural history on these topics - habitat relationships, harvest and edge effects - for particular organisms (e. g., Chapter 2 for spruce grouse; Chapter 5 for shrews (Sorex cinereus and S. monticolus) and southern red-backed voles (Clethhonomys gapperi)). Ecological theory in this dissertation is therefore less a source of testable hypotheses, and more a tool to inform sampling, analyses, and interpretations. For example, theories of resource substitution and complementarity (Blackman 1905) suggested limitations to linear additive habitat modelling, and encouraged exploration of classification and regression trees, and neural network techniques (Chapter 4). Density-dependent patterns of habitat use predicted by theories of the ideal free distribution (Fretwell 1972) influenced the choice of an index to summarize multiple years of small mammal abundances (Chapters 3 and 5). Quantitative natural history can also be seen as the prime source of ecological theories (Franklin 1989a), particularly those of "limited domain" or mid-range generality that are most conducive to ecological progress and management (Weiner 1995). A s a simple example, two distinct habitat types preferred by spruce grouse suggested a common underlying pattern (Chapter 2), which led to further work on the morphology and foliar chemistry of individual spruce trees used by the birds (in progress). Another pattern common to at least 3 study groups at Sicamous Creek is a discordance between observed response to edges and overall effects of treatments with more or less edges (spruce grouse, Chapter 2; small mammals, Chapter 5; pine marten, Huggard 1999). Simple geometric calculations of edge effects do not predict the overall response well. As a natural historian might expect, the mechanisms behind this cross-scale disparity seem to differ for each group.  7  2. Indices of habitat quality Good quality habitat for a species ultimately means habitat in which that species can persist over at least intergenerational time scales. This is clearly something we cannot measure directly, and therefore we need to rely on indices of habitat quality. Relative density is the most commonly used indicator for habitat modelling, but Van Home (1983) pointed out that density may not be correlated with habitat quality, particularly when social interactions force subordinate animals into suboptimal habitat. Complete demographic measurements are often not possible because of logistical constraints, inability to measure critical demographic parameters such as overwinter survival or dispersal success, or a study scale inappropriate for demographic measurements.  In these situations, separate analyses of distinct classes of a  species can be used to examine and reduce the potential bias suggested by Van Home (1983) (e. g., small mammals in Chapters 3 and 5). The potential densities ("carrying capacity") and actual densities of species in a habitat type will never be exactly equal (Hobbs and Hanley 1990). Rather than a flaw in using density as an indicator, this inequality is a reminder that factors other than habitat contribute to variation in abundance. Partitioning sources of variation is a step towards resolving this difficulty (Chapter 3), although the details of interspecific interactions will undoubtedly remain unexplored in most applied habitat modelling research. When habitat features are small compared to the ranges of individuals, a comparison of used versus available habitats can indicate habitat quality. This index employs the assumption that the individual's choices are adaptive (i. e., they enhance fitness). The assumption is most likely to be true when conditions are most similar to those under which the species evolved. With the spruce grouse (Chapter 2), selection of habitat features within natural forest is likely to be a reliable indicator of habitat quality, while use of the overall harvest treatments, which may represent novel conditions for spruce grouse, should be viewed cautiously. 3. Model validation Habitat models often perform poorly when their validity is tested at different sites (Van Home and Wiens 1991, Morrison et al. 1992), yet most habitat models are presented without 8  validation, and are assumed to apply well beyond the site at which they were developed (Bunnell and Huggard 1999). Often management recommendations are made from these unvalidated models (e. g., 9 papers in Verner et al. 1986). This extrapolation is equivalent to making prescriptions with untested conceptual models (Conroy 1993), or making inferences from hypotheses without testing them. Validation at different sites was a critical aspect of the grouse and small mammal studies presented here (Chapters 2 and 5). Testing model predictions at other sites was most critical in the evaluation of different modelling techniques (Chapter 4), where it demonstrated that a models fit to the original data indicates little about its utility as a general predictive tool. However, aspects of the Sicamous Creek faunal research remain to be validated. Most notably, results from the overall treatments have not been validated directly, because harvest treatments other than clearcuts are almost non-existent in E S S F forests (Chapters 2 and 5). Specific relationships discovered in heuristic explorations of models produced by alternative techniques (Chapter 4) are also still to be validated (in part by other ongoing manipulations at Sicamous Creek; Craig et al. 1997, Vyse 1999). Further validation of the tested models remains desirable, particularly at sites representing a wider geographical and ecological range than could be studied here.  4. Sources of variation A major challenge in developing habitat models is that only part of the variation in the quality index (e. g., abundance) is related to habitat features. Other sources of variation include spatial patterns in the environment (Legendre and Fortin 1989, Borcard et al. 1992), sampling error (Link et al. 1994) and interactions with unmeasured biotic or abiotic elements (Hobbs and Hanley 1990). Two general problems that result are the risks of over-fitting or under-fitting models to the unknown proportion of variation that is explainable by habitat, and confounding habitat relationships with other sources of variation. Chapter 3, which is an elaboration of Borcard et al. (1992), resulted from struggling to understand these different sources of variance in the small-mammal data from Sicamous Creek. This approach to  9  partitioning variance can reduce some problems of model fitting and interpretation, and is useful as a tool to guide development of habitat models.  5. Multiple-scale effects Animal abundance is determined by factors operating at a continuous gradient of scales, from micro-site characteristics, through larger habitat types and landscapes, to broad biogeographic patterns (Ricklefs and Schluter 1993). Only some of these scales are amenable to management, but their interactions can make it difficult to discern or interpret patterns at any particular scale. The variance partitioning approach in Chapter 3 helps resolve some of the confusion about the inter-related scales of habitat elements ("micro-habitat") and habitat types ("stands"), and would be applicable to other cross-scale analyses. The small mammal models in Chapter 5 analyse, in part, residual abundances after incorporating effects of habitat types, to examine relationships with habitat elements within habitat types. The spruce grouse study (Chapter 2) benefits from a predictive micro-habitat model to examine edge effects, and to provide a more efficient way of surveying the larger-scale treatments.  6. Spatial pattern Contagious processes and spatial trends at all scales ensure that many ecological variables are more similar at neighbouring points than at points farther apart. This spatial pattern can be of interest in itself, but is more often a source of concern about confounded relationships (Legendre and Fortin 1989, Borcard etal. 1992), or spatial pseudo-replication producing unjustified confidence in fitted relationships (Clifford et al. 1989, Thomson et al. 1996). The interspersion produced by the randomized design at Sicamous Creek helps to ensure that treatment comparisons are not confounded by spatial patterns - a permutation test shows that 66.8% of all possible randomized block layouts at the site would have greater aggregation of treatments than the actual Sicamous Creek layout. Nonetheless, measuring and accounting for spatial pattern is still important, as it should be in any ecological field study with finite replication. For this work in particular, many relevant habitat variables showed natural variation beyond that created by the treatments, and could naturally show spatial trend 10  and autocorrelation. Concerns about the spatial nature of the data were addressed in several ways: 1) the component of variation in small mammal abundances due purely to spatial trend is estimated in the variance partitioning method, along with the potentially confounding component shared by spatial trend and habitat features (Chapter 3); 2) spatially detrended models were produced as part of this method (Chapters 3 and 5); 3) the method of Clifford et al. (1989) was used to estimate effective sample sizes accounting for spatial autocorrelation when spatially arranged data were used in significance tests (Chapters 2, 4 and 5); and, 4) surveys of treatment effects on spruce grouse sampled only preferred habitat types, partly because of the possibility that these particular habitats may have been over- or underrepresented by chance in a treatment. 7. Integrating past knowledge Various sources of variability tend to make individual studies of habitat relationships weak. However, in aggregate, the numerous studies on at least some aspects of many species may provide precise and useful relationships, but quantitative syntheses are rare in ecology (Arnqvist and Wooster 1995). Impediments to synthesis include our promotion of "novelty" rather than repeating previous work, an implicit belief that the particular system is critically important to results, and a tendency to look inwards for reductionist causal mechanisms behind observed patterns, rather than looking outwards for general "patterns of patterns" that may predict how systems will differ (Bunnell and Huggard 1999). Researchers also focus on tests of null hypotheses in their study designs and reporting, to the detriment of presenting the parameters themselves and their context (McBride et al. 1993, Cohen 1994). To explore one approach to alleviating these problems, a likelihood approach (Edwards 1972) was used to present responses of small mammals to harvest types, and Bayesian methods were used to combine these estimates with other quantitative estimates that are available in the literature (Chapter 5).  11  Chapter 2. Winter use of subalpine forest by spruce grouse: Effects of habitat features, edges and harvest treatments Chapter Summary Winter use of high-elevation forests by spruce grouse (Falcipennis canadensis) was measured in relation to habitat features and distance to edges of openings at the Sicamous Creek silvicultural systems site (SC) in south-central British Columbia, and tested at 5 other validation sites. The direct effect of alternative silvicultural systems was examined at S C , where 4 harvest treatments have each been applied to 3 replicate 30-ha blocks, in a randomised experimental design. Winter use by grouse was indicated by presence or absence of droppings in 0.01-ha habitat plots or2-m wide transects parallel to edges conducted shortly after snowmelt. The assumptions of using droppings to indicate absence or presence in different habitats or edge positions were assessed and their validity confirmed. Areas within 100 m of locations with high use by grouse were distinguished from areas available overall at S C by higher densities but lower basal areas of subalpine fir and Engelmann spruce, the presence of surficial rock and sparse shrub cover. Plots used by grouse within these high-use areas were distinguished from unused plots by these same habitat features, and greater canopy cover and higher density of relatively short trees. Knolls were highly preferred topography types, as predicted by this habitat model. Many features of habitats used by spruce grouse in winter suggest selection of sites that are poorer for conifer growth. Use of forest was considerably reduced within 10 m of harvested openings of 0.1 ha, 1 ha, and 10 ha. These habitat and edge relationships from S C were confirmed at the validation sites. Occurrence of grouse in forest increased with proximity to open wetlands, peaking at 20-35 m from the wetland edge, then declined nearer to the edge. Predicted habitat quality increased similarly with proximity to wetlands, but did not decline near the edge. Predicted habitat quality of most plots was lower in treatment units with 3 3 % of trees removed using individual-tree selection than in uncut controls. Winter occurrence of grouse on plots in preferred habitat types (knolls and areas 20-35 m from open wetlands) decreased from 5 8 % in uncut controls to 1 8 % in individual-tree selection units. Harvest treatments that removed 3 3 % of trees in arrays of 0.1-ha or 1-ha patch cuts, or with a 10-ha clearcut, produced a proportional drop in occurrence of grouse in winter, despite the high amount of remaining forest within 10 m of edge in the small patch-cut treatments. Recommendations to maintain winter habitat for spruce grouse in managed highelevation forests include designating reserves on knolls or other rocky, poor growing sites and around wetlands, retaining some reserve area around wetlands >10 m from an edge, and avoiding widespread use of uniform partial cutting systems.  12  Introduction Maintaining native species throughout their ranges has become an important objective in forest management, with particular concern expressed for forest-dwelling species that avoid the early-seral forest stages created extensively by industrial forestry ( F E M A T 1993, C S P 1995). Strategies to mitigate the fragmentation of older forests include establishment of reserves with corridors (Noss and Harris 1986, Thomas et al. 1990), and careful planning of forest harvesting in time and space (Gustafson and Crow 1996, Crow and Gustafson 1997). For many species, habitat loss and fragmentation can be reduced by maintaining features in the surrounding matrix of harvested forest that allow continued use by species associated with older forests (Franklin et al. 1986, Wilcove 1989, Franklin 1989b, Wiens 1995). Managing the matrix requires knowledge of features of forest stands that are critical to species of concern, and how these can be maintained in managed forests. Species most likely to benefit from knowledgeable management of the harvested forest are those known to be sensitive to habitat loss and fragmentation, but which are not entirely restricted to undisturbed old forest. Alternatives to large clearcuts, such as individual-tree selection partial cuts, green-tree retention or small patch-cut systems, are increasingly being recommended and used to maintain forest-dependent species (Franklin 1989b, C S P 1995). These alternative silvicultural systems may produce a matrix that is less hostile to many species associated with older forests, but because they disperse harvesting, they must also be applied to a larger area than clearcuts to obtain the same volume of timber, and they can create extensive edges, resulting in loss of forest interior conditions (Franklin and Forman 1987). To evaluate these alternative systems, we need to measure the trade-off between retaining forest structure in the residual stand, but affecting larger areas and increasing the amount of edges. The spruce grouse (Falcipennis canadensis) inhabits boreal and high-elevation forests and is a species of concern to managers, because harvest rates of conifers are increasing in these forest types (Braun et al. 1994). Although spruce grouse use openings such as wetlands, roadsides, and some harvested areas for breeding and foraging in summer (Pietz 13  and Tester 1982, Boag and Schroeder 1992), they are restricted to conifer forests for 7 to 9 months of winter, when their diet consists strictly of needles of coniferous trees (Pendergast and Boag 1970). Spruce grouse have been extirpated in areas where agricultural development has permanently reduced coniferous forest at the edge of their range (Fritz 1979), and they are rare in small, isolated patches of habitat (Whitcomb et al. 1996). A long history of intensive forest management is threatening the persistence of populations of the ecologically-similar capercaillie (Tetrao urogallus) in many places in Europe (Rolstad 1989, de Franceschi and Bottazzo 1991, Swenson and Angelstam 1993). However, spruce grouse can be abundant in young stands of lodgepole pine (Pinus contorta) or jack pine (Pinus banksiana) that have regenerated following wildfires (Szuba and Bendell 1983, Schroeder and Boag 1991). Ensuring successful regeneration and appropriate rotation lengths may be adequate to sustain spruce grouse in pine-dominated forests. The suitability of young stands is less certain in some boreal and high-elevation forests where pine species do not occur, and where slow regeneration combined with deep snowpacks can result in a lack of conifer cover during winter for several decades following harvesting. The association of spruce grouse with other habitat features in these forests, such as dense patches with greater canopy cover (Allan 1985, Boag and Schroeder 1992), suggests that retention of important stand elements may be a management option to mitigate effects of harvesting in forest types lacking pine regeneration. Effects of the edges of harvested openings and of different silvicultural systems are poorly known for spruce grouse. Edges of wetlands adjacent to forests are preferred for nesting and summer use in Minnesota, but this response changes in winter when grouse are using conifer trees (Pietz and Tester 1982), and may differ for harvested openings.  Siberian  spruce grouse (Falcipennis falcipennis) prefer areas near swamp edges in winter, but are expected to decline in extensively harvested landscapes (Andreev 1990). Capercaillie nest on clearcut edges (Storch 1991) and show little response to edges of natural openings in winter, but suffer greater mortality in areas fragmented by clear-cuts (Gjerde and Wegge 1989, Gjerde 1991, Wegge et al. 1992). Light thinning of forests does not affect capercaillie (Gjerde 1991, 14  Rolstad 1989), but heavy thinning or clearcutting has negative effects on winter use (Gjerde 1991) and on overall densities (de Francheschi and Bottazzo 1991). Scattered small openings are a preferred harvest system for capercaillie (Rolstad and Wegge 1987). The same system has been suggested for spruce grouse (Boag and Schroeder 1992), but is untested for this species. This study was designed to provide some of the information required to improve the suitability of managed high-elevation forests for spruce grouse. Objectives were: 1) to develop predictive models of winter habitat use that would identify important habitat elements for spruce grouse and allow the effects of different forest management options to be predicted; 2) to measure winter use by grouse of forest near edges of natural and harvested openings; and, 3) to evaluate directly the effects of alternative silvicultural treatments. The study focussed on winter use by spruce grouse, because forest management most directly affects the coniferous trees that the species relies on for the 7-9 months of winter conditions in high-elevation forests. Overwinter mortality has been identified as the key factor determining population size in a wellstudied population of red grouse (Lagopus lagopus) (Watson 1970). The energetics of overwinter survival (e. g., Thomas 1987) also suggest that constant access to suitable habitat in winter is critical for spruce grouse. A comprehensive strategy to maintain spruce grouse in managed forests must also include provision of breeding habitat and dispersal opportunities, because these are clearly also important to the persistence of spruce grouse populations (e. g., Boag et al. 1979, Boag and Schroeder 1987).  Methods Main study site and validation sites The main study was conducted at the Sicamous Creek Silvicultural Systems site (SC; see Chapter 1). The generality of habitat models and edge relationships from the S C study were tested at 5 validation sites located 10 - 90 km from the main study site. All validation sites were in forest >140 years old in the E S S F w c 2 subzone, with 54 - 9 0 % subalpine fir trees 15  (stems > 7.5 cm diameter at breast height) and the remainder Engelmann spruce. Slopes were generally <20° with variable topography and aspect. Clearcuts of 20 - 60 ha, from 3 to 20 years old, were scattered across the sites. These openings generally had sparse conifer regeneration < 2 m tall.  Habitat models - field plots Use of habitat features by spruce grouse was measured using circular plots of 5.65 m radius (0.01 ha). In each plot, observers recorded: percent canopy cover; percent shrub cover; the species, diameter at breast height (DBH), height, and decay class (following Thomas et al. 1979) of each tree or snag > 7.5 cm DBH; slope; topography in 1 of 6 classes (smooth slope, rolling slope, elevated knoll, side of knoll, ridge or gully); the presence of bedrock or large boulders at the surface; distance to the edge of the nearest cutblock; and distance to the nearest open wetland. Canopy and shrub covers were estimated visually, with all observers trained by one person. Tree heights were estimated, with estimates standardized to heights of 1 0 - 2 0 trees measured with a clinometer during training. Sampling of plots was conducted immediately after snowmelt, prior to the emergence of leaves on shrubs or herbaceous plants, generally between early and late June. Observers carefully examined the ground and logs in the 0.01-ha plot for grouse droppings (faeces composed of the dry fibrous remains of conifer needles, which are a distinctive cylindrical shape, 1 - 3 cm long, 5 mm in diameter). The presence or absence of droppings indicated the use or lack of use of the plot area by spruce grouse during the previous winter (see tests of this assumption below). Habitat plots used 2 sampling designs (Fig. 2.1): 1) Systematic plots were conducted every 100 m along parallel transects covering the study site at 250-m intervals. Every other plot (i. e., at 0 m, 200 m, 400 m, etc. along the transect) was surveyed in 1994 prior to harvesting; the other plots were surveyed in 1995 after harvesting. 2) "Grouse-centred plots" (GCP's) were centred on a location with high grouse activity. Early morning surveys were used during the spruce grouse display season prior to snowmelt to locate areas of spruce 16  grouse activity. Observers walked both the parallel transects and perpendicular transects forming a grid at 250 m spacing, recording the locations of any displaying male grouse, females heard or seen, tracks in the snow or concentrations of grouse droppings. Transect surveys were repeated 3 or 4 times per year in 1994, 1995 and 1996, with birds or their sign often recorded in the same location on each repetition. Incidental reports of spruce grouse from other biologists at the site generally corresponded to these same locations. A 5.65-m radius habitat plot was conducted at each of these high activity areas, and 25 m, 50 m and 100 m away to the north, east, south, and west. These 13 plots comprised one set of GCP's. Individual plots within a set of G C P ' s were occasionally not sampled, if they fell on roads or in standing water or were inaccessible because of cliffs. The central plots of sets of G C P ' s were separated by >100 m. This sampling design allowed 3 types of comparisons of areas used by grouse versus unused areas. Comparing individual plots with grouse sign to those without sign in  •  •  •  o  •  o  ofn i  • \  w  ^--100m  o 0  •  "•"  0  n  /  •  •G-  •  Fig. 2.1. Layout of 5.65 m-radius plots. Squares = systematic plots, circles = grouse-centred plots (2 sets of 13 plots shown within 100m (dashed line) of known area of high activity by grouse (X)). Solid symbols indicate plots with grouse sign. 17  G C P ' s indicated local habitat use choices in areas where individuals were known to occur within 100 m (Fig. 2.1; solid versus open circles). Comparing used versus unused systematic plots indicated both the presence or absence of a grouse in the general area, and the choice of the grouse to use a plot if it did occur in the area (Fig. 2.1; solid versus filled squares). Finally, comparison of habitat features in all systematic plots, as a sample of available habitat in the study area, to all the G C P plots indicated how habitat features in general areas where grouse occurred (within 100 m) differed from the study area overall (Fig. 2.1; squares versus circles). In 1997, 19 sets of G C P ' s were surveyed at the validation sites. The same methods were used, with sets of plots centred where spruce grouse or accumulations of their sign were observed at the different sites.  Habitat models - analysis Plots that fell in harvested openings (except individual tree selection units) or in untreed wetlands never contained grouse sign and were excluded from analyses. The proportion of plots with grouse droppings in each of the 6 topography types was compared using a Chisquared test, separately for the Sicamous G C P ' s and the validation GCP's.  Knolls and ridges  occurred too infrequently in systematic plots to allow topographic comparisons. Grouse use of knolls, which are relatively rare topographic features, was considerably higher than in non-knoll plots. Plots on knolls were not used in subsequent analyses, because these preferred habitats are readily identified, without the need for any further habitat modelling. If plots on knolls had been included, they would have strongly influenced the comparison of habitat features in plots used by grouse versus those not used. The resulting models would thus have been largely describing the difference in habitat features between knolls and non-knolls. Instead, the analysis is addressing the question, What habitat features distinguish plots used by grouse from those not used by grouse when they are not on knolls?  18  Fourteen variables were derived from the habitat plots: slope, canopy cover, shrub cover, the presence or absence of surface bedrock, the number of snags, the number of "relatively short" trees, and separately for subalpine fir and Engelmann spruce, the number of live trees, their basal area, their average DBH and the standard deviation of their DBH. "Relatively short" trees are those that are shorter than expected from the observed relationship between tree height and DBH of trees in systematic plots. This relationship was nearly identical for the 2 species, and the combined relationship was used: expected height = -24.61 + 32.87*logi DBH (r = 0.76, n = 741). Relatively short trees were suggested as a potentially 2  0  important variable for spruce grouse by studies of grouse foraging trees (Mueller 1993, Huggard unpub. data). All variables were examined for normality and transformed using logio(x+1) if this improved the distribution. The 14 variables were reduced to 9 for discriminant function analysis by eliminating the number of snags, which showed no apparent relationships to grouse use in preliminary analyses, and the average DBH and standard deviation of DBH for each species, which covaried almost completely with the number of stems and basal area of the species. Linear discriminant functions based on these 9 habitat variables were used to distinguish: 1) all grouse-centred plots at Sicamous Creek from all systematic plots at Sicamous Creek; 2) used from unused systematic plots at Sicamous Creek; 3) used from unused plots in grouse-centred plots at Sicamous Creek; and, 4) used from unused grousecentred plots at the validation sites. Discriminant functions were calculated using Systat 7.0. Because the habitat features in nearby plots may be similar (positive spatial autocorrelation) and the presence or absence of grouse may also be correlated in nearby plots, the 13 plots in a set of G C P ' s are not fully independent samples. The method developed by Clifford et al. (1989) to calculate the effective number of independent samples for correlations between 2 spatially autocorrelated variables was applied to the G C P data sets after the discriminant function analysis. The discriminant function score of each plot and the presence or absence of grouse were used as the 2 variables to calculate effective sample size. 19  Following Clifford et al. (1989), statistics to evaluate the significance of the discriminant functions were calculated with the entire data set, but evaluated using degrees of freedom based on the effective sample size. Numbers of observations in each cell of the Chi-squared analysis of topography types were reduced proportionally so that the total number of observations equalled the effective sample size. These procedures reduced the risk of obtaining spuriously significant results due to co-incidental spatial autocorrelation of the variables being analyzed (Clifford et al. 1989). The generality of the discriminant function habitat models was assessed by using each function to classify plots from one or both of the other 2 data sets and comparing with the observed presence or absence of grouse. The model based on Sicamous grouse-centred plots was tested with both the data from the Sicamous Creek systematic plots and the validation site grouse-centred plots. The model based on the Sicamous Creek systematic plots was tested with the Sicamous Creek G C P data. The model based on the validation sites G C P data was tested with the Sicamous Creek G C P data. The Sicamous Creek G C P function, based on non-knoll plots, was also used to classify plots on knolls at Sicamous Creek, addressing the question of whether the observed higher preference for areas on knolls could be explained by differences in habitat features alone.  Edge effects - response to edges of openings T o assess use by spruce grouse of forest adjacent to harvested openings at Sicamous Creek, transects were surveyed parallel to the 3 sizes of cutblocks at various distances into the forest: 5 m and 10 m from 0.1-ha openings; 5 m, 10 m, 20 m and 50 m from 1-ha openings; and, 5 m , 10 m, 20 m, 50 m and 100 m from 10-ha openings. Each transect was the entire length of the edge of the square opening being surveyed (32 m for 0.1-ha openings, 100 m for 1-ha openings and 316 m for 10-ha openings), except that parts of the transect were not used if they were closer to a road or another opening than to the adjacent opening being surveyed. Observers recorded the number of grouse droppings observed within 1 m of the transect. 20  Identical edge transects of 300 m length were conducted in 1997 adjacent to the larger clearcuts at the validation sites, at 5 m, 10 m, 20 m, 50 m and 100 m into the forest. For analysis, the set of transects adjacent to a particular edge was only used if grouse droppings occurred on at least one of the transects. The results therefore indicate edge use given that a grouse was at least somewhere in the area. The density of droppings per 100 m was calculated for each transect. This density was then transformed using log(x+1), because this improved the normality of the distribution and reduced the influence of extremely high values on the mean. The mean and standard errors were calculated for all transects at each distance from edges of each size of opening. Means and standard errors for each distance from the larger openings surveyed in 1997 were calculated in the same way. Edge responses at S C were examined in a second way, by plotting the observed presence or absence of grouse use in the G C P ' s against the measured distances to harvested openings or, separately, to natural openings caused by wetlands. A fourth-order polynomial regression line was used to indicate the form of the relationship between percent occurrence and edge distance. A fourth-order equation was used because it was flexible enough to indicate the main form of the edge relationship. The expected percent occurrence based on habitat features alone was plotted in the same way, using the expected presence or absence of grouse in each plot predicted by the Sicamous Creek G C P discriminant function. Only nonknoll plots were used for this analysis.  Treatment effects - use of preferred habitat in different harvest treatments Initial results from the habitat use plots showed a much higher occurrence of grouse sign on knolls and in the forest 20 - 35 m from open wetlands. To assess whether the different harvesting treatments affected the use of these preferred habitat types by spruce grouse, I conducted 5.65-m radius plots on each knoll or within 20 - 35 m of each open wetland in all 15 replicates at the site, recording the number of grouse droppings found in a careful search of  21  the plot. Three 5.65-m radius plots spaced 15 m apart were conducted on each knoll or adjacent to each open wetland, except on small knolls where only 1 or 2 plots would fit. To examine treatment differences in the proportion of plots used by grouse in these preferred habitats, I calculated the proportional occurrence of grouse sign in all the plots in each replicate, and then calculated the mean and standard error of these occurrence values for the 3 replicates of each treatment. This procedure weights each replicate of a treatment equally, regardless of how many plots were done in a replicate. I also assessed the potential effect of the ITS treatment by comparing the discriminant function scores for systematic plots in the ITS treatment after harvest with scores from plots in uncut forest. Because only 14 of the post-harvest systematic plots fell in ITS units, I supplemented the ITS data with discriminant function scores calculated for 18 5.65-m radius plots surveyed in ITS units with the same methods in a study of small mammals (see Huggard and Klenner 1997). Discriminant function scores for plots in ITS and uncut stands were compared using a Kolmogorov-Smirnov test.  Testing assumptions of droppings as an index of habitat use Relying on droppings to indicate winter use by spruce grouse involves a number of assumptions, including the assumptions that other grouse species are not present, and that droppings are not produced at substantially different rates in different areas. No other species of grouse have been recorded at the S C site in 6 years of nearly continuous field work by several crews of biologists. The low-quality, high-volume winter diet of spruce grouse results in a regular production of faeces (c.f. capercaillie, Klaus et al. 1986 cited in Gjerde 1991), with little likelihood of different rates of fecal production in the limited range of different habitats available in winter (Ratti et al. 1984), The method also assumes that grouse droppings are equally likely to be detected in different habitat types or in different positions relative to edges, and that they do not show different inter-annual persistence in different types. These 2 assumptions were tested directly. Droppings were collected from the snow in late winter, and 22  approximately 20 droppings were distributed on the snow at each of 30 sites, 10 sites in the forest away from openings, 10 sites 2 - 5 m into the forest adjacent to harvested openings and 10 sites in harvested openings. In forested sites, droppings were distributed on the snow both at the base of trees and under the outer branches. Sites were marked and revisited at snow melt (when plot surveys and edge transects began), 4 weeks later (when surveys and transects were finished), and at the end of the summer. The observer assessed whether the droppings would have been observed in a normal habitat plot or edge transect at each site. The assumption that droppings only represent one winter's use by grouse was also tested by looking for droppings at 4 sites in which grouse were recorded during display-season surveys in one post-harvest year but not the following year.  Results Assumptions of the use index Grouse droppings that I placed on the snow during winter were readily detected by observers at 10 of 10 sites in forest and edge locations at snowmelt and one month later. Droppings were visible in 8 of 10 sites in openings, and not visible at 2 sites, probably because of loss due to surface flow of melt water or disintegration caused by freezing and thawing in spring. By late summer, droppings could still be found at most sites, but they had decayed from their characteristic cylindrical form, and were only readily visible at 2 forested and 2 edge sites, because they were generally covered by conifer needles or leaves of shrubs and herbs. These observations support the assumptions that droppings are equally visible in different habitat types and edge positions during surveys immediately after snowmelt, and that very few, if any, droppings remain intact and visible enough to be counted in the following year's surveys. Examination of 4 previously occupied sites where grouse disappeared confirmed the latter assumption, with evidence of only highly decayed droppings, and no droppings that would have been recorded on surveys. The occurrence of grouse droppings in habitat plots  23  and edge transects conducted shortly after snowmelt is therefore likely to be an accurate indication of the relative occurrence of spruce grouse during the preceding winter.  Effective sample size with spatial autocorrelation For the Sicamous Creek GCP's, positive spatial autocorrelation of both discriminant function scores and grouse presence or absence resulted in an effective sample size of 328.5, reduced from the raw sample size of 415 (excluding knolls and open areas). With the validation GCP's, spatial autocorrelation was weaker, resulting in an effective sample size of 169.8, close to the raw sample size of 173. The systematic plots showed little spatial autocorrelation, probably because pairs of plots were at least 100 m apart. Therefore, statistics calculated for the S C and validation G C P ' s were evaluated using the effective sample sizes to compensate for the spatial autocorrelation, while the original sample size was used to evaluate statistics from the systematic plots.  Habitat models - occurrence of grouse by topography type Grouse droppings occurred in 19 of 165 systematic plots (11.5%) and in 204 of 503 individual plots in the G C P ' s (40.6%) at S C (including knolls and open areas). At S C , only 3 of the 165 systematic plots (1.8%) fell on knolls, because these occupy only a small part of the study area, while 32 of 503 grouse-centred plots (6.4%) were on knolls. The proportion of G C P ' s with grouse droppings differed by topography type at S C (x = 21.4, df = 5, p = 0.001). 2  Plots on knolls had a much higher occurrence of grouse droppings than plots in other topography types, with plots on ridges or benches having intermediate occurrence (Fig. 2.2). Grouse sign occurred in 93 of 242 G C P ' s (38.4%) conducted at validation sites, with knolls also showing much higher occurrence than other topography types (Fig. 2.2). Ridges and benches did not show intermediate levels of occurrence in the validation G C P ' s , but only 10 plots were in this topography type.  24  o 0) Q .  re  o o O 1-  0) Q. 0) (A _ 3 0) O 0_ O +C  < 1 > o  100 80 60 40 20  Knolls  Ridges  All others  Topography type Fig. 2.2. Percent occurrence of grouse droppings in 0.01 -ha plots in 3 topography types. Filled symbols = Sicamous Creek plots; open symbols = plots at validation sites. Error bars are binomial 95% confidence intervals.  Table 2.1. Discriminant function to separate systematic plots from grouse-centred plots at Sicamous Creek.  Variable  1  Co-efficient  2  Standardized co-efficient  3  Constant  0.244  LogSlope  -0.639  -0.253  0.229  0.088  LogShrub  -0.874  -0.484  Rock (0/1)  0.697  0.279  LogLiveB  1.825  0.541  Log LiveS  2.468  0.835  LogBAB  -0.287  -0.136  Log B A S  -0.681  -0.494  LogShort  -0.240  -0.083  LogCanopy  All variables are transformed as log (x+1), except rock presence/absence. LogSlope = slope in degrees, LogCanopy = canopy cover (%), LogShrub = shrub-layer cover (%), Rock = absence(O) or presence(1) of surficial rock, LogLiveB = number of live subalpine fir per 0.01 ha, LogLiveS = number of live spruce per 0.01 ha, L o g B A B = basal area of live subalpine fir (m /ha), L o g B A S = basal area of live spruce (m /ha), LogShort = number of relatively short live trees (see text) per 0.01 ha plot. Only trees > 7.5 cm dbh are counted. The discriminant function is calculated as the constant plus each of the variables multiplied by their coefficient. Values >0 indicate increased probability that the plot belonged to the G C P data set; values <0 indicate increased probability that the plot belonged to the systematic plots. T h e standardized coefficient is the coefficient divided by the standard deviation of the variable, and can be used to compare the relative importance of individual variables to the multivariate discriminant function. 1  10  2  2  2  3  25  Habitat models - characteristics of grouse-centred plots compared to systematic plots The habitat characteristics of all non-knoll grouse-centred plots differed significantly from the characteristics of systematic plots at S C (Table 2.1; Wilks' X = 0.88, approximate F = 8.53, d.f. = 9, 483, P < 0.001). Thus, habitat within 100 m of grouse high-use points, as sampled by the grouse-centred plots, differed from available habitat, as sampled by the systematic plots. Grouse-centred plots had higher stem densities of spruce and subalpine fir, but lower basal areas of these species, especially spruce. They also tended to have less shrub cover and lesser slopes, and more commonly had rock exposed at the surface. Canopy cover and the density of relatively short trees differed little between grouse-centred plots and systematic plots. The discriminant function identified 115 of 156 systematic plots (73.7%) correctly and 254 of 415 grouse-centred plots (61.4%) correctly.  Habitat models - characteristics of plots with grouse present versus absent The discriminant functions to separate plots with and without grouse sign were highly significant for the 3 data sets tested, indicating that plots with grouse present were not a random subset of all plots within the data set (SC grouse-centred plots: Wilks' X = 0.823, approx. F = 9.64, df = 9,318, P < 0.001; validation sites grouse-centred plots: Wilks' X = 0.757, approx. F = 5.82, df = 9, 159, P < 0.001; S C systematic plots: Wilks' X = 0.767, F = 4.93, df = 9, 155, P < 0.001). Standardized co-efficients of the individual variables in the discriminant functions based on the 3 data sets are presented in Table 2.2. The standardized co-efficients for the 3 data sets indicated increased probability of grouse presence with increasing stem densities of spruce and subalpine fir trees, and with the presence of bedrock at the surface. For the grouse-centred plots and systematic plots at SC, probability of grouse presence also increased with decreasing basal area of spruce and subalpine fir, despite the positive relationship with the densities of trees. The grouse-centred plots at the validation sites did not show this negative relationship with basal area. Increasing canopy cover and increasing numbers of relatively short trees led to increased probability of 26  r  grouse in the grouse-centred plots and systematic plots at SC, but the validation grousecentred plots showed only weak relationships with these variables. Sites with greater shrub cover had lower probabilities of occurrence of grouse in the systematic plots at SC, but there were only weak relationships with shrub cover within either set of grouse-centred plots, where shrub cover was generally lower overall. Increasing slopes increased the probability of grouse use in the S C systematic plots, but there was no relationship with slope in either set of grousecentred plots.  Table 2.2. Discriminant functions to separate plots with and without grouse sign.  Variable  1  Co-efficient SC GCPs Val. GCP SC Svst. 2  :5  Constant LogSlope LogCanopy LogShrub Rock (0/1) LogLiveB Log LiveS LogBAB LogBAS LogShort  -1.721 -0.132 1.625 -0.229 0.598 2.410 1.265 -2.325 -0.515 1.075  -3.251 -0.066 -0.364 -0.278 1.258 3.181 2.593 -0.193 0.568 0.246  -2.090 2.598 2.908 -1.375 4.952 0.600 7.219 -3.174 -2.674 1.607  Standardized co-efficient SC GCP's Val. GCP SC Svst. -0.045 0.540 -0.011 0.227 0.648 0.379 -0.999 -0.317 0.322  -0.020 -0.075 -0.112 0.480 0.536 0.573 -0.049 0.283 0.064  0.506 0.543 -0.351 0.588 0.079 0.961 -0.695 -0.929 0.247  Variables defined in Table 2.1. Values of the resulting discriminant function >0 indicate increased probability of grouse being present; values <0 indicate increased probability of grouse being absent. S C G C P = Sicamous Creek grouse-centred plots, Val. G C P = validation site grouse-centred plots, S C Syst. = Sicamous Creek systematic plots. 1  2  3  Habitat features distinguishing plots with grouse sign in the S C grouse-centred plots were similar to the features distinguishing the grouse-centred plots overall from the systematic plots, in particular there were positive relationships with the presence of rock and with tree densities, but a negative relationship with tree basal area. Thus, these features were selected at both the scale of locations of high-use areas and the finer scale of plot use within high-use areas. However, plots with grouse presence in the grouse-centred plots had greater densities of short trees and denser canopy, whereas these features were unimportant in distinguishing grouse-centred plots overall from systematic plots. Conversely, the lesser shrub cover and  27  slopes that distinguished grouse-centred plots from systematic plots were not useful in distinguishing used from non-used plots within the grouse-centred plots.  Habitat models - classification and predictive success The 3 discriminant functions correctly classified 67.2% to 71.1% of the plots in their respective data sets (Table 2.3). The 2 models based on grouse-centred plots were slightly less successful at predicting the presence or absence of grouse in the grouse-centred plots at the other sites, with overall success of 60.1 % or 65.1 % . The model based on the grousecentred plots at S C tended to err on the side of predicting that grouse sign would be present in a plot at the validation sites when grouse were actually absent. Conversely, the model based on the validation sites most often erred in predicting the absence of grouse from a S C plot in which grouse sign actually occurred. The discriminant function based on the systematic plots at S C predicted that grouse would be present in more S C grouse-centred plots than was actually observed. The discriminant function based on S C grouse-centred plots generally predicted correctly that grouse would be absent from most systematic plots at S C . The discriminant functions based on the habitat features in the non-knoll S C and validation site grouse-centred plots predicted that grouse would be present in 67.7% or 6 6 % of the plots on knolls at their respective sites (Table 2.3), and the predicted presence or absence was correct in 78.1% or 7 6 % of the cases, respectively.  Edge effects Transect surveys adjacent to the 3 sizes of openings at S C all showed considerably lower densities of grouse droppings 5 m into the forest than at 10 m from the opening. Densities at 10 m and further were the same (Fig. 2.3a). The transects adjacent to larger and older openings at other sites showed a similar lower density of droppings 5 m from edges compared to 50 m or 100 m into the forest, but intermediate densities at 10 m and 20 m from these openings (Fig. 2.3b), although error bars were much wider. 28  CD CM  — u re <D O  c> CM O  ^ - CO, CD,  l- o o  ^p  ^P  CM 00 00  T— T— O co T~ un CO,  s  CM  —•  —' M - CM m O CM CM  ^9 CD CO  00 CD oo CM  "CO ' o CM  m  CM  O in c o u c  3  4c re c u in  oi d 00 00  o >>  m o  ,—  o  CO 00  CM CD CO  ^p ^p  ^p ^p  c o CO CO CO CO CO CM CO  00 CO in oi CO  CO CD O CD m  m si  O  Q.  •a c re c o re u '55 in re O  CO n  re  CO  CD  ^p  CM m CO  o  CD CO CM  m CM  VP ^p  m CO CM CO 00, CO,  CO i n CD CD, co.  d CD, m  CD o o en T —  00 00 CM  T—  ^ o_ c o w re o. E o O  T—  in o  CL  •a  CD  ! c  CD O  vp ^p  I  CD CO 3 O  i_  a> II 0.  o O  in  CD  o o  0.  "o co O  =  i ECD O_ C In o  XL  o c  co 15 O O >  o  O O  o  CO CO  o o  o XL  co co i5 O  O CO 0.  c re. c E •c u u c  ^P  CM  CL  Q  vP  ^p  1^ o CO m CD CO T —  CO *J O  >  o  T— CM  , _  T3  2!  o  T3 d>  re  m T — o i CD oo  i n CD o 00 O o m CM  m CD CO m CM  re  m CM  ~9 ~9 CO m CO 00 CM CO CO un CM  CO m CO o i CO  .Q  ^P ^P  T  o 00 00 CM  m  c Q) (/>  ^P  o  VP  (A  m o  T— O  a> a>  —  00 CO  CD o CM  T—  Z  ^p CO LO 1^ d CO, CD,  >  X.  I  o  re >  >  CO  O CO  CD CD  co i5 Q  >  t_  O  O O  "o  CO  ^c  in  CO  CO  n  CO  o  co E CD CO CO  O  C73  E  CO  o CO II  O  CO  a) Sicamous Creek 2.0 x  0.1 ha  1 ha  510  510  10 ha  1.6  CD  "a  1.2  |)  0.8 0.4 0.0  20  50  510  20  50  100  Distance from edge (m) b) Validation sites 2.0 x  1.6  CD  E  1-2  .!>  0.8  (Ii  0.4 0.0  — 510  —//-  20 50 100 Distance from edge (m)  Fig. 2.3. Relative abundance of grouse droppings [log ((number of droppings + 1) per 100 m of transect)] at different distances into the forest from clearcuts at Sicamous Creek (a) and validation sites (b). The 3 opening sizes at Sicamous Creek are shown separately. Error bars are 95% confidence intervals. 10  The occurrence of grouse sign in Sicamous Creek grouse-centred plots was lower if the plot was within 10 m of a harvested opening than in more distant plots (Fig. 2.4a). The proportion of plots predicted to have grouse sign, based on the discriminant function, did not show a trend relative to distance from edge, which was expected based on the random placement of cutblock edges with respect to habitat features at the Sicamous Creek site, and the short time since harvesting for the habitat elements to respond to any edge influences. The predicted occurrence of grouse sign, based on the discriminant function from the Sicamous Creek grouse-centred plots, increased with proximity to marshes or other wetlands (Fig. 2.4b). The actual occurrence of grouse observed in the grouse-centred plots followed this predicted pattern, except at distances of < 15 m from the wetland edge, where observed proportions declined (Fig. 2.4b). The peak in observed occurrence of grouse sign was thus at  30  20 - 30 m from wetland edges, while maximum predicted occurrence based on habitat occurred at the wetland edge.  100 0)  u  c 22 3  80 60  O  u  o 40 c 0)  H 0) Q.  20  20  40  60  80  £100  Distance from cutblock (m) 100 u  c a o u  o c  +-> CD CD  Q.  20 40 60 80 Distance from open wetland (m)  >100  Fig. 2.4. Occurrence of grouse droppings in grouse-centred plots as a function of distance from cutblock (a) and distance from open wetland (b). Fourth-order polynomial lines (heavy line) and 95% confidence intervals (dotted lines) were fitted to the actual presence/absence data (data not shown). Distances >100 m from an edge were truncated to 100 m. Predicted occurrence, based on a fourth-order polynomial fitted to the presence or absence at each sample point predicted by the discriminant function model, is shown in (b) (thin line). Treatment effects - grouse occurrence and habitat scores in different harvest treatments Grouse sign occurred in 55.8% of all plots on knolls or in areas 20-30 m from open wetlands in uncut control blocks at SC. This occurrence is somewhat lower than the occurrence observed in G C P ' s in these habitat types, because the treatment surveys included all knolls and wetlands, not just those in general areas where grouse were known to occur. 31  Occurrence of grouse in the forested two-thirds of the 0.1-ha patch-cut array, 1-ha patch-cut array and 10-ha clearcut treatments was equal to or slightly reduced from the occurrence in the uncut control. Because grouse sign was never observed in the openings that occupy onethird of these treatments, the overall effect of these treatments was therefore to lower occurrence of grouse by one-third or slightly more, regardless of the size of the openings or leave strips (Fig. 2.5). The reduction in occurrence in the ITS treatment units was greater, with only 17.9% of plots in preferred habitat types having grouse sign (Fig. 2.5), a 6 8 % reduction in occurrence compared to uncut controls.  60 CD U  c £ u  u o  40  +J c  CD O CD  20  0_  UC  ITS  0.1-ha PCA  1-ha PCA  10-ha CC  Fig. 2.5. Occurrence of grouse droppings in preferred habitat (on knolls or in forest 20-35 m from open wetlands) in 5 treatments: UC = uncut control, ITS = individual-tree selection partial cut, 0.1-ha PCA = 0.1-ha patch-cut arrays, 1-ha PCA = 1-ha patch-cut arrays, 10-ha C C = 10-ha clearcut and surrounding leave strip. Error bars are 95% confidence intervals based on n = 3 replicate blocks. Dotted line is at 66.7% of the occurrence observed in controls.  Plots in ITS had lower scores calculated using the systematic plot discriminant function than plots in uncut forest (Kolmogorov-Smirnov D = 0.424, P < 0.001). Approximately 1 0 % of plots in both harvest types had very high scores, associated primarily with the presence of surficial rock in these plots (Fig. 2.6). Among plots lacking surficial rock, 3 7 % in uncut forest had scores > 0, indicating a greater likelihood of grouse presence than absence, while only 2 0 % in ITS had scores > 0.  32  -4  -2  0  2  4  Discriminant function score Fig. 2.6. Cumulative percentile plots of discriminant function scores for 0.1-ha plots in individual-tree selection (ITS) and uncut control treatments. Discriminant function scores >0 indicate increased likelihood of grouse presence.  Discussion Using habitat choices as an index of habitat quality Habitat use surveys, such as the plots and edge transects used here, equate habitat use choices of individuals with the quality of the habitat. This assumes that such choices are adaptive, maximizing the individual's fitness compared to the alternative choices available. The assumption is most likely to be true when the range of habitat types available is similar to the range available to the species in nature, presumably the range of conditions to which the species is adapted. When an animal is faced with novel habitat types, habitat choice shaped by evolution could produce maladaptive results. The habitat models in the current study rely on comparing use or lack of use of areas by grouse across a range of conditions found in natural older forest, and should largely be free of the problems of interpretation when animals face novel habitat types. In contrast, although the harvest treatments may mimic some aspects of natural high-elevation forests, they are novel in many ways, including the spatial and temporal abruptness of the habitat change due to harvesting. Apparent choices by grouse  33  of which harvest treatments to use are therefore at greater risk of misrepresenting the true quality of the treatments.  Treatment results should be used cautiously prior to testing with  more intensive studies that can directly measure fitness consequences of winter use of different treatments, such as overwinter survival and subsequent reproductive success.  Habitat use by spruce grouse Non-random use of habitat features by spruce grouse at the S C site was apparent at 2 scales, the general locations of high-use areas and the use of plots within high-use areas. Several habitat features were selected at both scales, including greater densities but lower basal areas of the 2 tree species, and greater occurrence of surficial rock. High-use areas were also characterized by lower shrub cover and lesser slopes than the habitat available overall. The relationship with shrubs is unlikely to be a direct one, because shrubs are generally completely covered in snow all winter at SC; nor is the relationship due to the negative correlation between tree density and shrub cover, because this covariance is accounted for in the multivariate discriminant function analysis. The negative relationship with shrub cover at the larger scale is likely an indirect reflection of grouse choosing particular stand types, which are characterized by a lack of shrub cover. Canopy cover and the density of relatively short trees were positively related to use of plots within high-use areas, although the 2 variables did not differ overall between G C P ' s and systematic plots. Preference for dense canopy is commonly reported for spruce grouse in winter (e. g., Allan 1985, Boag and Schroeder 1992). A preference for short trees has been reported as a correlate of selection for younger post-fire serai stages at a larger spatial scale in pine forests (Schroeder and Boag 1991), but this differs from the selection reported here for relatively short trees (shorter than expected for their diameters) within old-growth forest. Several of the habitat features characterising sites used by spruce grouse suggest a selection for areas with poor conditions for tree growth, including small, relatively short trees, and surficial rock. This observation is supported by the strong preference grouse show for  knolls and areas near open wetlands, where shallow soils on rock outcrops or water tables near the surface can limit tree growth. Toxic secondary compounds that restrict herbivore feeding on conifer needles are particularly important to spruce grouse in winter (Bryant and Kuropat 1980, Mueller 1993). However, trees in poor growing sites tend to produce greater concentrations of these secondary compounds, especially if they are limited by nitrogen availability (Mattson 1980, Herms and Mattson 1992). Structural characteristics of trees in poor growing sites, including lower, denser canopies, are compatible with thermal strategies or predator avoidance (c.f., hazel grouse, Swenson and Olsson 1991; and blue grouse, Pekins et al. 1991), and may explain the preference of spruce grouse for these sites.  Edge effects Use of forest by spruce grouse in winter showed a strong, but very short, negative response to edges of harvested openings, with decreased occurrence within 10 m of an opening, despite no trend in predicted habitat quality with distance from edge. A similar short negative edge effect was apparent adjacent to the natural openings of wetlands. Predicted habitat quality increased up to the wetland edge; observed occurrence of grouse followed the predicted increase until within 20 m of the edge, and then declined. The greater occurrence of grouse 20-35 m from wetlands is thus attributable to increasingly preferred habitat, while the decrease in grouse at shorter distances to edges is an inherent negative effect of the edge, not attributable to changes in measured components of habitat quality. Coupling a predictive habitat model with sampling at difference distances from natural edges allowed edge effects due to habitat change near edges to be separated from direct effects of edge, and demonstrated that the same form of direct edge effect occurs adjacent to natural and harvested openings. Two mechanisms could plausibly explain the short negative edge effect, avoidance of predators and avoidance of microclimatic extremes. Avian predators are the dominant cause of mortality for overwintering grouse (Ellison 1974), but the main raptor present at Sicamous 35  Creek in the winter is the Northern Goshawk (Accipitergentilis), which is believed to be adapted more for hunting in forests than in openings. Thus, predators should not directly cause grouse to avoid forest near openings, but there may still be a negative edge effect simply because grouse perceive a greater risk of predation near openings. More likely, frequent severe weather in winter, including the accumulation of blowing snow, produces inhospitable conditions in the forest at the edges of openings. Although some microclimatic edge effects are detectable >240 m into forests, windspeed decreases to less than half the speed in openings within 30 m of entering the forest (Chen et al. 1995, Novak et al. 1997). Field observations in winter at Sicamous Creek show a noticeable increase in snow loading on conifer branches near edges, but only immediately adjacent to openings. This extra snow loading, which can completely and persistently cover the foliage, would eliminate foraging opportunities for grouse. The area of the forest immediately adjacent to an opening would therefore have both reduced foraging opportunities and greater thermoregulatory costs due to higher winds, both effects that penetrate only short distances into the uncut stand.  Effects of alternative silvicultural systems Differences in the winter occurrence of spruce grouse between treatments were assessed in this study using only preferred habitat types that could be identified independently of the treatment (knolls and areas adjacent to wetlands), because this allowed an acceptable degree of power to detect treatment effects with the available sampling effort. Based on confidence intervals of the binomial distribution (Fig. 2.2 of Krebs 1989), a 3 3 % decline in occurrence in a treatment should be detected 9 5 % of the time using 31 plots in preferred habitat (where occurrence of grouse in controls was 60%). In contrast, random or systematic plots (where occurrence of grouse in controls is only 10%) would have required 400 plots to detect the same percent decline 95 % of the time. Restricting surveys to preferred habitat types also reduces the component of sampling error due to variation in habitat quality. Furthermore, by only sampling preferred habitats, the treatment results were not confounded  by potential differences in abundances of preferred habitat types between treatments, which could be a problem due to chance alone with only 3 replicates. A predictive model of habitat use thus improved the efficiency of the basic assessment of treatment effects, and helped overcome the problem of limited replication that is inherent in large-scale studies. The trade-off for the increased power of using plots in preferred habitats is the additional assumption that preferred habitats do not change in the different treatments. This assumption was not tested directly, but seems reasonable for spruce grouse at the Sicamous Creek site. In the 0.1-ha patch cut array, 1-ha patch-cut array and 10-ha clearcut units, grouse sign was never observed in the openings, and the knolls and areas near wetlands should remain the preferred habitat among the remaining uncut leave strips. In the ITS units, no undisturbed dense patches remain that might be preferred to the partiallyharvested knolls or areas near wetlands. Surveying only preferred habitats may not detect small reductions in density, if the remaining individuals concentrate their activities more in the preferred habitats. On the other hand, random surveys would also risk not detecting reductions, unless large numbers of surveys could be conducted. Occurrence of spruce grouse in preferred habitats in the patch cut and clearcut treatments dropped in proportion to the percent of forest removed (33%) or slightly more (Fig. 2.5). A greater decrease was expected in the 0.1-ha patch-cut array units based on the observed negative edge effect, because 6 5 % of the uncut forest in this treatment is within 10 m of a cutblock edge. The unexpected lack of greater decline in 0.1-ha patch-cut array units may indicate that the preferred habitat types surveyed in the treatments are used even if they are immediately adjacent to small openings. The difference between the different harvest systems with openings may also be due to chance with limited numbers of replicates, and should be tested at other sites. The percent reduction in occurrence of grouse in the uniform ITS treatment exceeded the percent of timber volume removed (68% reduction in occurrence versus 3 3 % volume removal). Unlike patch cut arrays, which retain intact leave strips with habitat features 37  unaffected at the 0.01-ha scale (plot size), ITS affects all of the stand at a fine scale, reducing tree densities and canopy cover throughout. These changes reduced the predicted quality of most 0.01-ha areas in ITS compared to uncut forest (Fig. 2.6). If a fixed volume of timber is to be removed from an area of previously uncut forest, use of a patch cut or clearcut system thus would have less immediate impact on occurrence of spruce grouse in winter than a uniform ITS system. However, these results address neither long-term occurrence of grouse throughout the harvest rotation, nor larger-scale influences on grouse presence during winter, including breeding success in the area and ability to disperse successfully.  Implications for maintaining spruce grouse winter habitat in managed high-elevation forests Studies demonstrating that spruce grouse use more open forest conditions in summer imply that partial cuts or small patch cuts could maintain or improve the breeding habitat of spruce grouse (Hedberg 1980, Boag and Schroeder 1992). Some spruce grouse move from breeding to wintering habitat, but such movements are short (median distances of 0.8 km for females, 0.4 km for males; Schroeder 1985), suggesting that suitable winter habitat must also be maintained near suitable breeding habitat. Results of this study suggest some strategies for maintaining winter habitat for spruce grouse in managed high-elevation forests: 1. Elevated knolls, even those only 2 m higher than surrounding topography, should be candidate sites for reserves in harvested openings. Sites with rock at or near the surface should be particularly favoured as reserves. In general, poorer growing sites with denser, but smaller and particularly shorter trees would be good reserve patches for wintering grouse. Choice of such sites as reserves is compatible with some forestry objectives, because these are difficult growing sites and difficult sites to regenerate; however, windthrow problems may be greater on exposed sites with shallow soils (Ruel 1995). Incorporating buffers of greater than 10 m width around reserves on knolls would alleviate the negative edge effect for grouse, and might reduce risk of windthrow.  38  2. Areas near wetlands should also be considered as reserves. Current regulations and standard practices guiding riparian management generally provide only buffers of limited width around wetlands (typically 10 m in the Sicamous Creek area). These areas immediately adjacent to wetland openings may be good habitat for spruce grouse, but are unlikely to be used as they are within 10 m of edges in two directions. Patches of at least 40 m width are recommended adjacent to wetlands for spruce grouse winter habitat, because these allow approximately one-half the area to be > 10 m from an edge. For spruce grouse, a 40 m riparian buffer strip around part of a wetland would be preferable to a 10 m strip around the entire wetland. 3. The short extent of the negative edge effect suggests that loss of forest interior conditions is unlikely to be a concern for spruce grouse winter habitat, unless abundant edges are created throughout the forest. However, arrays of small patch cuts that created abundant edge did not seem to have a large negative effect on grouse. Large-scale fragmentation with very large clearcuts may also threaten spruce grouse by preventing successful dispersal, but effects at this scale were not addressed in this study. 4. Uniform ITS systems should not be applied to extensive areas where spruce grouse winter habitat is a management concern, unless suitable reserves are incorporated. The partly conflicting results obtained for the 0.1-ha patch cut arrays (i. e., negative edge effects, but no apparent increased impact of the edge-rich arrays of 0.1-ha patch cuts) suggest caution is also warranted about extensive applications of small patch-cut systems. Systems using moderate-sized patch-cuts or clearcuts are more likely to provide suitable winter habitat for spruce grouse in the associated leave strips, without special reserves being required. The longer-term effects of these systems depends on the unknown suitability of the regenerating stands when the leave strips are removed in subsequent harvest entries. Variable-retention systems could also be appropriate for spruce grouse, as these systems have the flexibility to leave some patches of trees that are not  39  uniformly thinned out, and can easily incorporate reserves on knolls and adjacent to wetlands.  40  Chapter 3. Developing animal-habitat models: partitioning variance due to habitat, spatial trend and measurement error Chapter Summary Existing techniques to partition the environmental, spatial, shared and undetermined components of variation in an ecological data set are elaborated as a tool for developing animal-habitat models. Elaborations include: 1) further partitioning the environmental component into variation attributable to differences among habitat types, relationships with habitat elements and variation shared by these two ways of describing habitat; and, 2) estimating measurement error as a contribution to the undetermined component of variation. The variance partitioning can help to reveal when important habitat elements may have been omitted from a model, when observed relationships with habitat elements may be confounded by other variables differing between habitat types or showing a spatial pattern, and when unexplained variation does or does not warrant further effort at finding habitat relationships. The application and interpretation of the method is illustrated with data on small mammals caught in pitfall traps at 2 study areas, one a designed experiment, the other a retrospective survey. Unexplained variation in the abundance index was high for most study species, and equal to expected measurement error in half of the cases. Relationships with habitat elements were potentially confounded by habitat type differences and by spatial trends, particularly in the retrospective study, suggesting caution in their interpretation and further sampling designed to separate these factors. Unexplained variation, beyond that expected from measurement error, was found for some of the study groups, leading to or suggesting further habitat measurements and exploration of more complex modelling techniques. The elaborated variance partitioning method is presented as a preliminary step in identifying potentially causal, predictive relationships from correlations between animals and habitat variables. Rigorous testing of the habitat models is still required.  Introduction Models that reliably relate the population performance of species to measurable habitat characteristics are a cornerstone of informed land management (Verner et al. 1986, Morrison et al. 1992, Starfield and Bleloch 1992).  They are fundamental to the quantitative natural  history knowledge base, that remains our best tool for guiding many specific management decisions (Weiner 1995). Studies designed to develop habitat models by relating a measure of  41  population performance, typically abundance, to habitat measurements are therefore a common element of applied forest wildlife research. Researchers developing habitat models from field data cannot expect to relate all of the variation in species abundances or other population indices to habitat features. First, many ecological factors other than habitat features cause variability. Animal abundance in a habitat type is affected by: intraspecific social interactions (Fretwell 1972, Van Home 1983), interspecific interactions (e. g., Cody 1981, Rosenzweig 1981, 1985), stochastic events such as severe weather or disturbances (Ehrlich et al. 1972), larger-scale effects (Wiens et al. 1987, Hansen et al. 1993) and internal population processes producing spatial pattern (Legendre and Fortin 1989). The relative importance of habitat and non-habitat factors depends on the scale of the study (e. g., patch use by a foraging individual versus the location of a species' range), and the range of habitat conditions sampled, (e. g., subtle variation across a limited range to large differences across a wide range of conditions). A second source of unexplained variation in animal-habitat relationships is that empirical studies of habitat relationships are necessarily imperfect. Habitat is usually quantified in one of 2 ways, as a number of discrete "types" (e. g., upland or riparian; uncut, partially cut, or clearcut forest), or as a collection of quantified "elements" (e. g., number of logs, shrub cover, litter depth) that are combined using multivariate methods. Logistical and perceptual constraints mean that some distinct habitat types are not sampled separately, or important elements are not measured. At the same time, we may make distinctions between types, or measure elements, that are not relevant to the species being studied. Furthermore, spatial structure can lead to spurious apparent habitat relationships and excessive confidence in actual relationships (Clifford et al. 1989, Legendre and Fortin 1989, Thomson et al. 1996). Correlated conditions in neighbouring sample sites and overall trends across the study area are likely to occur even in designed experimental study areas, if only by chance due to limited replication, and are inevitable in studies that rely on natural variation of habitat elements or types (Legendre and Fortin 1989). Moreover, sampling or measurement error is always  42  present in empirical studies, particularly in the abundances or other population indices of the study species, and it can be a principal source of variability. Researchers analyzing typical field studies designed to develop habitat models are thus faced with the problem that only a portion of the variation they observed in their species is due to variation in habitat features.  There are dual risks when the explainable portion is  unknown: 1) "underfitting", or failing to explain some of the explainable variation by not measuring important habitat elements, not identifying distinct habitat types, or failing to identify important relationships during statistical analyses; and, 2) "overfitting" the model, by misidentifying relationships due to spatial pattern or the chance variation of measurement error as meaningful habitat relationships. Underfitting is a concern because even the most reliable habitat models rarely make precise predictions of species' responses to habitat change, and weakening models by missing important relationships could render them useless. Overfitting is a concern with complex multivariate statistics (James and McCulloch 1990) or algorithms such as neural network (Smith 1993) or classification and regression tree (CART; Breiman et al. 1984) analyses, because such models can appear very strong when developed, but prove to be unreliable when used on independent data sets (Chatfield 1995). The poor record of habitat models when tested at new sites (e. g., Laymon and Barrett 1986, Rotenberry 1986, Van Home and Wiens 1991) suggests that these problems are common. In this Chapter, I present a statistical methodology that can help develop habitat models from field data, and identify when underfitting or overfitting are likely risks. The method is based on Whittaker's (1984) approach to identifying the variance components of a multiple regression. Borcard et al. (1992) elaborated this technique for multivariate data, and demonstrated its usefulness for interpreting and understanding ecological measurements that can be related to both environmental and spatial variables. I have adopted the analysis method of Whittaker (1984) and the interpretation framework of Borcard et al. (1992) specifically for studies that are developing models from field measurements of habitat variables and species abundance or other population indices. The method identifies the components of 43  observed variation due to relationships with measured habitat elements, habitat types, and spatial patterns, their shared variation, and the variation expected from measurement error. The analysis and interpretation of results are illustrated with data from 2 projects designed to develop habitat relationships for insectivores and other small mammals based on extensive pitfall sampling. Ultimately, the success of a habitat model is judged by its success in predicting the response of species to habitat variation when it is tested in other areas (Conroy 1993, Lindenmayer et al. 1994). The method presented here is a useful preliminary step towards developing habitat models that are more likely to survive such tests.  Partitioning environmental and spatial components of variation - theory and utility Whittaker (1984) demonstrated how the use of "regression elements", different variance components, can be used to understand the independent and shared contributions of 2 or more independent variables in multiple regressions. Borcard et al. (1992) and Borcard and Legendre (1994) used this approach, modified for multivariate data, to separate the component of variation in a spatially-arranged data set of species abundances that is due to relationships with measured environmental variables, and the component due to spatial trends in the data. As with Whittaker's (1984) regression elements, the 2 sets of explanatory variables of Borcard et al. (1992) - environmental and spatial -  are not exclusive, because  some of the spatial pattern of the study species may be due to spatial pattern of the measured environmental variables. Conversely, observed relationships of species with environmental variables may be due to their independent spatial covariance. Four variance components result: 1) "pure environmental" variation, the variance component due to relationships with environmental variables that are independent of spatial trends; 2) "pure spatial" variation, the spatial trend in abundances that is independent of any spatial trend in the measured environmental variables;  44  3) "environmental+spatial" variation, the variation that could be due to either environmental or spatial variables when these covary; and, 4) "undetermined" variation not explained by measured environmental or spatial components. In the regression symbols of Whittaker (1984), these terms are equivalent to G(1:2), G(2:1), G(12:) and G(:12), where "1" refers to the environmental set of explanatory variables, and "2" to the spatial set of variables. Whittaker (1984) interprets the variation shared by 2 explanatory variables (component 3) as: 1) the difference between the variation attributable to the first variable when the second is excluded and when the second is included, 2) a measure of the substitutability of the one variable for the other, or 3) a measure of the effective balance of the sampling design. Thus, the shared "environmental+spatial" component of variation of Borcard et al. (1992) can be interpreted as the extent to which variation explainable by environmental variables could also be explained by spatial variables, or the degree of confounding or non-independence of the 2 sets of explanatory variables. The advantages of applying this variance partitioning to spatially-arranged ecological data sets are to recognize the relative importance of measured environmental variables and spatial pattern, and particularly to avoid errors of misinterpretation when these sets of explanatory variables are partially confounded. The method and interpretation framework of Borcard et al. (1992) has been used extensively, particularly in studies of vegetation (Heikkinen and Birks 1996, Hoiland and Bendiksen 1996, Nordbakken 1996, Rydgren 1996, Wiser 1998) and aquatic species assemblages (Magnan et al. 1994, Belgrano et al. 1995, Bechara 1996, Monti et al. 1996, Pinel-Alloul et al. 1995, Robertson et al. 1997, Truu et al 1998). Many of these studies are primarily interested in discovering environmental controls on species assemblages, but benefit from also examining and "partialling out" spatial trends. In addition to inherent spatial patterns due to contagious biological processes, spatial trends can also act as a surrogate for largerscale ecological processes (Legendre and Fortin 1989). Controlling these potentially confounding effects can help elucidate causal relationships between environmental variables 45  and species, or at least reveal reasonable causal hypotheses (Legendre and Fortin 1989, Thomson et al. 1996). Spatially detrending environmental analyses also reduces the risk of spuriously strong relationships due to spatial autocorrelation (Clifford et al. 1989, Legendre and Fortin 1989, Thomson et al. 1996). Conversely, some studies specifically examine spatial patterns, or the lack of spatial patterns, after removing environmental covariates (Belgrano et al. 1995, Legendre et al. 1997, Wiser 1998). Modifications of the method of Borcard et al. (1992) include applying the same general idea to separate the "pure" components of particular explanatory variables from that shared with other covarying non-spatial measurements (e. g., toxicological and environmental variables in environmental impact studies (Cattaneo et al. 1995, Pinel-Alloul et al. 1996), pH and other chemical measurements in lake acidification studies (Lonergan and Rasmussen 1996), land use and natural variables (Roche et al. 1998), or introduced species and other environmental factors (Godinho and Ferreira 1998)). The main objectives are to allow unconfounded measurements of the importance of the variable(s) of interest, or to warn when these variables cannot be separated from other factors and are liable to misinterpretation. Other modifications have retained the spatial component, but separated the environmental component into 2 sets of variables (e. g., abiotic and biotic (Bechara 1996), management and environmental effects (Thrush et al. 1998), pollution and climate effects (Liu 1997)), or added temporal variability as a third source of variance (Anderson and Gribble 1998).  Elaborations for developing habitat models: Habitat "types" and habitat "elements" The approach of separating the pure and covarying components of variation due to 2 partially independent sets of explanatory variables can be applied to help understand the 2 different, but related, ways in which "habitat" is described in studies of habitat relationships. Most commonly, habitat is described as a discrete "type", such as forest type, plant association, serai stage, or forest-harvest type. Many studies have measured abundances, relative abundances or other population measures of species in different habitat types, and the 46  habitat-type approach is the basis of most studies that look at the effects of spatial arrangement of habitats (Forman and Godron 1986, Franklin and Forman 1987), and the roles of habitat in community ecology (e. g., Rosenzweig 1981, papers in Morris et al. 1989) or foraging ecology (Stephens and Krebs 1996). The second approach describes habitat as an assemblage of measured habitat elements, such as vegetation structural measures in autecological studies (e. g., McCoy and Bell 1992) or snags, coarse woody debris, canopy cover, etc. in forestry-wildlife studies (e. g., Thomas 1979). The habitat-element approach is often used to examine finer-scale habitat use, and is the basis of models that predict the effects of different forest management strategies within stands. The 2 approaches have different advantages and limitations. The habitat-type approach implicitly captures all the variables and interactions that make a particular habitat type more or less suitable for a species, while the habitat-element approach will only be successful to the extent that the relevant elements have been measured and their potentially complex interactions captured in the statistical analysis. However, a successful habitatelement model allows predictions of the effects of natural variation in habitat elements or of management actions that affect particular elements, whereas the habitat-type approach requires measuring each combination as a separate "type". Habitat-element models can also allow a better mechanistic understanding of habitat requirements than merely describing associations with habitat types. The differences between the 2 ways of describing habitat parallel differences between holistic ("types") and reductionist ("elements") approaches in general (Allen and Starr 1988). Using both together in habitat studies can be complementary. When habitat types and elements are considered together, their relationship is similar to that between environmental variables and spatial trends as examined by Borcard et al. (1992). There clearly can be a "habitat type + elements" component of variation, because the 2 descriptors of habitat covary. For example, a study comparing the habitat types "uncut", "partial cut" and "clear cut" forest, and measuring elements including "canopy cover" will have a component of variation in abundance of the study species that could be due to either the 47  habitat type or the strongly covarying element of canopy cover. However, we can also expect a component of variation in species abundance that is explained by habitat type independent of habitat elements ("pure habitat type"), when measured elements do not include all relevant variables that differ between types, or when relationships between elements are not captured by the analysis of the habitat element measurements. Conversely, variation attributable to habitat elements independent of habitat types ("pure habitat element") would arise when species respond to variation of elements within types (e. g., variable canopy cover within the "partial cut" type), and when we fail to classify distinct types as the animal distinguishes them. Studies to examine habitat relationships can therefore benefit from measuring both habitat types and elements, and estimating the "pure habitat type", "pure habitat element" and "habitat type + element" components of variation. For example, if a study designed to produce a habitat element model finds a large component of variation due to "pure habitat type", the researchers should consider including additional elements that differ between types, or using an analysis procedure that includes more complex relationships among measured variables. If the study found a large "habitat type + element" component, the researchers should be cautious in predicting the effects of varying single elements, because the observed relationships could easily be due to relationships with the many other unmeasured variables that differ between types. A study of differences between habitat types that finds a large component of "pure habitat element" variation should recognize the importance of variability with the types and the probability that distinct types have been combined. Because of the importance and utility of distinguishing the 2 ways of describing habitat, my first elaboration of the technique of Borcard et al. (1992) was to divide their "environment" into "pure habitat type", "pure habitat element" and "habitat type+element" components. These 3 components together constitute the "combined habitat" component, equivalent to the "environment" component of Borcard et al. (1992). The combined habitat model and the spatial variables are subsequently partitioned into "pure combined habitat", "combined habitat  48  + spatial" and "pure spatial" components in exactly the same way that the "environment" component is treated by Borcard et al. (1992).  Elaborations for developing habitat models: Undetermined component and measurement error Many recent papers that apply the variance partitioning method of Borcard et al. (1992) have found the "undetermined" component of variation to be dominant, often exceeding 5 0 % of the observed variation. The undetermined component is generally attributed to unmeasured ecological factors operating at larger scales than the environmental measurements (Ohmann and Spies 1998), or at smaller scales than detected by the spatial trend model (Pinel-Alloul et al. 1995, He et al. 1996, Legendre et al. 1997). However, measurement error, the difference between the "true" value at a sample point and the actual value recorded from the sample, is always a component of variation in ecological field studies. Its presence can be particularly important in habitat models, which are often based on counts of species that are not abundant at each sample point (Link et al. 1994). My second elaboration of the technique of Borcard et al. (1992) as a tool for developing habitat models was therefore to compare the remaining "undetermined" component of variation with "expected measurement error". The expected measurement error component of variation in abundances can be estimated either by subsampling in time or space and assuming independence of the subsamples as estimates of the sample, or by assuming that the observed values for each sample come from a particular distribution. In the case of abundance data from counts where individuals can be assumed to act independently, the Poisson distribution may be an appropriate distribution for the expected measurement error. A comparison of expected measurement error and the undetermined component of variation can inform development or interpretation of the habitat model. If the undetermined component is much greater than the expected measurement error, there is a large potentially explainable component of variation, which should encourage further examination of habitat variables or spatial patterns not included in the model. If the undetermined component is 49  considerably smaller than the expected measurement error, there is a strong possibility that the model is overfit, at least partially modelling noise in the data, and unlikely to be reliable when tested elsewhere.  Methods Partitioning habitat-element, habitat-type and spatial variance components The analysis method is based on Whittaker (1984), because habitat models typically have a univariate dependent variable (the abundance or some other population parameter of the species). Terminology and ecological interpretations follow Borcard et al. (1992). The "pure habitat element", "pure habitat type" and "habitat element + type" variance components are first "partialled out" in a 3-step procedure. Regression and residual sums-ofsquares (SS) are recorded at each step. Step 1. Regression is used to fit the abundance index to the habitat-element variables. In the examples below, supervised step-wise multiple linear regression was used, including in the final analysis only variables with partial regression coefficients significant at P<0.15. Supervised step-wise regression allows the user to include pairs of variables that together contribute significantly to the final model, even if either variable alone does not. Linear regressions are most likely to be appropriate when only a limited part of the range of a habitat variable are examined (Jongman et al. 1987), as is usually the case in development of habitat models. Although more complex modelling techniques could be used, the overall variance partitioning procedure is only valid when similar degrees of freedom are used at each analysis step, because sums-of-squares are used as the variance measure without adjusting for the number of variables used (Borcard et al 1992). The results of the analysis can be used to indicate when more complex modelling procedures should be tried.  50  Step 2. Regression is used to fit the abundance index to the habitat types. This requires first coding the types with 1/0 "dummy" variables, n habitat types can be coded with n-1 dummy variables. In the examples below, simple multiple regression was used, without step-wise reduction of dummy variables, because there were relatively few habitat types compared to the number of habitat elements. If many types had been recognized, dummy variables making little contribution could be eliminated, effectively combining some habitat types. Step 3. Regression is used to fit the abundance index to both the habitat elements selected in step 1 and the dummy variables for habitat type from step 2. Following the method of Whittaker (1984), but the general terminology of Borcard et al. (1992), the regression and residual sums-of-squares from these 3 steps allow the calculation of the following variance components: 1) The "pure habitat element" component is the residual sum of squares from step 2 minus the residual sum of squares from step 3. Variation explained purely by habitat elements is the variation not explained by types alone that is explained by both elements and types together. 2) The "pure habitat type" component is similarly the residual sum of squares from step 1 minus the residual sum of squares from step 3. 3) The "habitat element + type" component is given by the regression sum of squares from step 1 minus the "pure habitat element" component. This is the component of variation explained by habitat elements that is also explained by habitat types. An equivalent calculation is therefore the sums of squares from step 2 minus the "pure habitat type" component. The "combined habitat" component is the component of variation due to habitat described in both ways (type and element), and is given by the regression sums-of-squares in step 3. It is equivalent to the "environmental" component of Borcard et al. (1992). The next phase of the analysis partitions out the "pure combined habitat" component, the "pure spatial" component and the "combined habitat + spatial" component:  51  Step 4. The spatial trend of the abundance index values is described using a supervised stepwise regression with the 9 terms completely describing a cubic trend surface (i. e., x, x , 2  x . y, y . y , xy, x y, xy ), following Borcard et al. (1992). Step-wise regression is also 3  2  3  2  2  used to reduce the number of parameters fitted at this step to only those with partial regression coefficients significant at P<0.15. Step 5. Regression is used to fit the abundance index values to the spatial trend surface variables from step 4, the habitat element variables from step 1 and the dummy variables for habitat type. The "pure spatial" variance component is calculated as the residual sums-of-squares from step 4 minus the residual sums-of-squares from step 5. The "combined habitat + spatial" component is the regression sums-of-squares from step 5 minus the "pure spatial" component. The "undetermined" component of variation is the total sums-of-squares of the abundances minus the "pure combined habitat", "pure spatial" and "combined habitat + spatial" sums-ofsquares. In the examples below, all of the variance components are expressed as a percentage of the total sums-of-squares.  Estimating expected measurement error The method of estimating the expected measurement error depends on the sampling design. In many studies, habitat measurements describe a larger area than was actually sampled. For example, an oceanographic study may measure physical variables that apply over several hectares, but only collect a plankton sample at one point; a vegetation study may describe the environment in 0.1-ha plots, but only record plant composition in small sub-plots. Part of the variation between sampling points then arises from measurement error due to the uniqueness of the smaller subsample. In these studies, independent subsamples should be taken at least at some sample points, and used directly in a nested analysis of variance to  52  estimate the percentage of overall variance due to measurement error (see Link et al. 1994 for discussion and example with repeated breeding bird surveys). In the small mammal pitfall examples below, the area sampled by the pitfall traps is similar to the plot size. However, using counts of discrete individuals introduces another potentially important source of measurement error, because samples can only contain integer numbers of individuals. An abundance index summarized the several years of pitfall abundances for each study group, using a log-transformed residual value of the count data after each year's mean abundance was subtracted (see Chapter 5 and Appendix 5.1). The expected measurement error of this index was calculated using Monte Carlo simulations, in which the number of captures at each sample site in each year was simulated from the Poisson distribution based on that year's mean capture rate. The simulated number of captures for each year at a given sample site were combined into a single abundance index in the same way the data themselves were treated. The sum of squares of these simulated abundance indices was then calculated across all sample sites. The simulation was repeated 100 times for each study group, with the mean sum of squares used as the estimate of the expected measure error. This estimate of measurement error indicates how much variance would be expected if all sample sites actually had the same abundances of the small mammal, but the number of animals differed by chance alone following a Poisson distribution. Analytical formulas based on the Poisson distribution, rather than Monte Carlo simulations, would be appropriate for similar count data when simpler transformations are used for the abundance index.  Case studies - study areas To illustrate the application of the elaborated variance partitioning framework, and its utility in interpreting field data used to develop animal-habitat models, I present results from pitfall-trapping studies of insectivores and other small mammals from 2 study areas in southern British Columbia, Sicamous Creek (SC) and East Barrier Lake (EBL). The S C site is described 53  in Chapter 1. The 5 harvest treatments at S C are used in this paper as a source of variation in habitat elements, and a source of 4 distinct smaller-scale habitat types: uncut forest (in a leave strip or contiguous control), partial cut, clearcut (regardless of the size of the opening), and edge (within 5 m on either side of a clearcut-uncut edge). E B L is a retrospective study site located 75 km northeast of Kamloops B.C. (51°14' N 119° 44'W) in high elevation E S S F forest and lower-elevation Interior cedar-hemlock forest (ICH, Lloyd et al. 1990). Each forest type contains 3 study units (stands or cutblocks) in uncut mature or old-growth forest, 3 units in partially-cut stands, and 3 units in 15 to 25 year old clearcuts. In ICH forest, an additional 3 study units are in more recent clearcuts. Each of the 7 combinations of forest type and harvest type was considered a habitat type. The wider range of forest types and variety of operational site preparation techniques at E B L produce a wider range of many habitat element variables than at SC. Because of the aggregated distribution of forest types and cutblocks with the different harvesting systems, study units of the 7 treatments are clearly not well-interspersed in this retrospective study design (Fig. 3.1).  Fig. 3.1. East Barriere Lake (EBL) study area. Darkest grey = recent clearcuts, dark grey = old ICH clearcuts, middle grey = partial cuts, light grey or white = uncut. X = sampled unit. Other harvested areas not shown. 54  Small mammal and habitat element data sets Each sampling site at both study areas consisted of a 4-m radius circle of 5 small pitfall traps and a habitat plot of 5.65-m radius centred on the trap circle. Shrews and small rodents were collected in the pitfall traps for 4 weeks at 2 seasons, shortly after snow melt ("spring") and in August, for 2 - 5 years depending on site and season. All animals were drowned in the liquid-filled pitfall traps. Small mammals were identified to species based on dentition, sexed by dissection, and classified as reproductively immature or mature based on development of reproductive organs. The study areas and sampling seasons were analyzed separately. Within species, the 2 sexes and 2 maturity classes were tested for different patterns of abundance in the different habitat types, or different linear relationships with habitat elements. Sexes or maturity classes showing no significant differences were combined for further analysis. An abundance index for each resulting study group was calculated at each sampling site as the average (of the several years of sampling) residual log-transformed abundance after the overall yearly mean for that group was subtracted. Details of the sampling methods and designs, tests of differences between sexes and maturity classes, and the abundance index are provided in Chapter 5 and Appendix 5.1. Ten habitat element variables were derived from measurements made at each sampling site: canopy cover; shrub cover; herb-layer cover; forest floor litter cover and depth; forest floor moss cover and depth; number of live trees > 7.5 cm in diameter; number of all stems > 7.5 cm diameter (including dead trees and stumps); number of smaller live trees (< 7.5 cm diameter, but > 30 cm tall); and volume of logs > 7.5 cm diameter. Variables were logtransformed if this improved normality. Other variables were measured but excluded, because they covaried strongly with included variables, or contained a high percentage of 0-values (>50%). Details of habitat element measurements are also provided in Chapter 5.  55  Results and interpretations Sorex cinereus ("masked" or "common" shrew), S. monticolus ("montane" or "dusky" shrew) and southern red-backed voles (Clethrionomys gapperi) were collected frequently enough at both sites and seasons for analysis; S. vagrans and S. hoyi were also moderately common at E B L (Table 3.1). The majority of shrews and almost all red-backed voles trapped were immatures. Males were substantially more common than females among immature shrews, and much more common among trapped adult shrews. Sex ratios of red-backed voles were more even.  At SC, none of the species showed significant sex or maturity class effects  in habitat type response (P>0.05 for all habitat and sex or maturity class interaction terms), nor significant differences in relationships with habitat elements (P>0.05, multivariate analyses of covariance). Maturity classes, but not sexes, showed different habitat type responses at E B L for S. cinereus, S. monticolus and S. vagrans (type*maturity factor significant at p<0.05 in one or both seasons).  Maturity classes of S. cinereus and S. monticolus also showed different  multiple linear regression relationships with habitat element measurements (p<0.05 in multivariate analysis of covariance in August). Red-backed voles and S. hoyi at E B L did not show significant sex differences in response to habitat types or habitat elements. Mature specimens of the latter 2 species were too rare to test for different responses of the maturity classes. Therefore, for analysis, maturity classes and sexes were combined for all species at S C , and for S. hoyi and red-backed voles at EBL. Immatures and matures were analysed separately for the other 3 species at EBL. The step-wise regressions of habitat elements and spatial co-ordinates both retained 1 to 6 variables at S C , and 1 to 5 variables at EBL, compared to 4 habitat types recognized at S C and 7 at EBL. The degrees of freedom used in the different steps are thus similar (Borcard et al. 1992). The actual habitat relationships for the different study groups are presented in Chapters 4 and 5, with validation results; this paper focus on interpreting the variance components.  56  Table 3.1. Total captures by species, sex and maturity class. Immature Female  Male  Mature  Site  Season  Species  EBL  Spring  S. S. S. S. C.  cinereus monticolus vagrans hoyi gapperi  67 80 26 9 10  91 116 46 14 8  Female 20 12 6 2 2  Male 146 68 28 4 0  August  S. S. S. S. C.  cinereus monticolus vagrans hoyi gappeh  317 161 69 14 99  433 208 88 53 88  59 21 10 1 1  233 51 30 3 5  Spring  S. cinereus S. monticolus C. gappeh  110 125 22  102 150 19  34 23 0  143 87 0  August  S. cinereus S. monticolus C. gappeh  249 201 104  252 245 83  27 11 0  81 53 0  The variance components of the various study groups are presented graphically in Fig. 3.2a-d. Only a small percentage of the total variance in the study groups' abundances at S C was explained by habitat or spatial trends, while moderate percentages were explained at EBL. The difference likely reflects the greater range of conditions created by the harvesting at EBL, particularly the variability caused by different site preparation techniques, and the wider range of forest types sampled in the E B L treatments. The recent treatments at S C may also not yet have had their full effect on small mammals.  Undetermined component compared to expected measurement error In half the example cases, the large undetermined component is equal to, or very similar to, the expected measurement error simulated with the Poisson distribution. Further work to improve the habitat model, such as measuring additional elements in the field or using more complex analysis techniques than step-wise regression, is probably not justified in these  57  CO LO TJ  >! II  a) .2 o o .E * g 3  i f< 8ce  - © O O)  i«  s; XJ  3  E 5 f *  8  --3^©  E  5 co  •I C o n U l * ! . O •= * .  5 E « •= oo S = s  0) © > 00  co  3 D) 3  © OI  ^  < _l  CO LU -Q8  "5 o oo  o CD  O "1-  9 0 U B U B A }Q  O CN  juaaidd  Q  —  1  3  £  o>ja c c S 33UBUBA  j o juaojadl  C T * 0 re -Q C g C  O | E P | ir— o c co J5 co w o 3 * ! o + « g. a) = £ - * i « E 3 o "5 » co o <• z, © c o w CO £  c -s  ©  ©  . E © c c  I  LU  i  s- = 2 S " 0>TJ JQ 0) fPC C CO £ n  •  J3  O ' B ^ C C3  S1  * °.  • o r © _ co — •© 8 £ r5  w  »  C C  ro  =  O)  <« £ > s  Q-  1 m i l l  CO  Q- 5 E ®  CO W o . o CD * "  o 00  o  co  33U6UBA  o  O  CM  jo j u a o i a j  aoueuBA j o lueojad  t E o  «  c  n S © iB  o O  « O « Q. • o •C > SS O © ==  >3 M S * «  TJ  2  cN-|i  re  cases. In fact, further analysis of the results is likely to result in spurious relationships, as apparent relationships are fit to purely random variation. For S. cinereus and S. monticolus at S C in both seasons, and for mature S. cinereus, S. monticolus and S. vagrans and immature S. monticolus at E B L in spring, the undetermined variance component is substantially larger than expected from Poisson measurement error alone. This potentially explainable variation in abundance suggests examining 4 possibilities: 1) . Additional habitat elements potentially important to these particular groups could be measured in the field. Habitat elements measured in this study were partially constrained by the applied context; variables needed to be potentially amenable to management and tied to variables used by the many other studies at the S C site. Studies purely of the natural history of the species could examine a wider range of habitat elements. The presence of a substantial "pure spatial" component for the insectivores at S C suggests looking for additional measurable elements that show broad spatial trends across the study area. 2) . Habitat "types" could be further divided. Work at another site indicates that some insectivores distinguish between leave strips and contiguous uncut forest (Huggard and Klenner 1998), which were combined in the "uncut" type in this preliminary analysis. The insectivores at S C may also distinguish between different sizes of openings. 3) . More complex modelling could be used to search for other relationships with measured habitat elements. Non-linear relationships between animal abundance and habitat variables, thresholds and substitutions between variables are all expected from ecological theory and natural history understanding (Jongman et al. 1987, Thomson et al. 1996), but are not captured in linear step-wise regression models. Searching a data set for complex relationships at the outset, however, is much more likely to produce spurious relationships, if only by chance because so many different possible relationships can be examined (Chatfield 1995). Before beginning complex analyses, researchers should be certain that simpler models, such as linear additive relationships, do not account for all the explainable variation 59  in the abundance data. Knowing how much of the variation is expected from measurement error may be useful in providing a stopping rule for further data analysis. 4). Many non-habitat factors affecting abundance could be examined. For example, distance to the clearcut-forest edge affects spring abundances of insectivores at another site (Huggard and Klenner 1998), and should be examined at the S C site. The many possible effects of interspecific interactions are likely to remain an unexamined "default explanation" for any remaining unexplained variation in applied animal-habitat studies, because of the extensive experimental manipulations required to measure such interactions. In 2 cases (red-backed vole in spring at EBL, and red-backed vole males in spring at SC), the total variation observed is no greater than expected from measurement error alone (i. e., expected measurement error > 100% of total variance). The observed sampling distribution of these groups therefore does not differ from random, strongly suggesting that any habitat models produced in these cases are likely to be unreliable. The model for S. hoyi at E B L in spring is also suspect, because it fits considerably more of the total variation than it should (i. e., expected measurement error > undetermined component). In all 3 cases, the study group was rarely caught at that season, with zero or one of the group caught at most sample points over several years.  Habitat types and habitat elements Of the small percentage of variation explained by habitat at S C , a "pure habitat type" component was relatively important for the red-backed voles (both sexes and both seasons), but only explained a small percentage of the total variance (Fig. 3.2c, d). The "habitat type+element" component was dominant for red-backed vole females in August, and also contributed substantially to the variance explained for S. cinereus in spring.  "Pure habitat  element" components were an important part of the variance explained by habitat for 5 of the 8 study groups at SC, suggesting that habitat elements that do not directly differ between habitat types were most important for these small mammals.  In particular, the treatments that created 60  the habitat types directly affected trees, while the variables included in the step-wise models for these small mammals were mainly moss, duff, and shrub cover. The dominant "habitat type+element" component for red-backed vole females in August suggests caution in interpreting or using the habitat-element model for this group, because the relationships may be confounded with unmeasured factors that differ among types. Thus, independent manipulations of elements may not affect this group in the way expected from the habitatelement model. The substantial "pure habitat type" component for the red-backed voles suggests that important habitat elements that differ between types were not measured, or that complex relationships among measured elements were not captured in the habitat element models for this species. At EBL, where a greater percentage of total variance was explained by habitat, the 3 components of habitat variation showed a wider range of relative importance. In many cases, "pure habitat type" was an important or dominant component, especially in spring (Fig. 3.2a). More pronounced differences in spring between habitat types, not related to measured habitat elements, may be due to differing phenologies of snowmelt and plant development in the different types, not directly to the habitat features themselves. The "habitat type+element" component at E B L often accounted for much of the variation that was explained by habitat, while the "pure habitat element" component was substantial in only a few cases (e. g., S.  monticolus immatures and S. vagrans matures in August, S. hoyi in spring; Fig. 3.2b). The greater range of variation in the retrospective treatments at E B L may have led to apparently stronger habitat-element models, but because most of the explained variation is shared with habitat-type differences, the habitat-element models may be no more predictive than the apparently weaker models from SC. It is particularly important to test these habitat element models in areas where the variation in relevant elements is not confounded with habitat types.  61  Spatial components "Pure spatial" components were a substantial part of the total variation for the 2 shrew species at S C and immature S. vagrans at EBL. Several other groups showed small "pure spatial" components. Such spatial trends independent of measured habitat variables are unlikely to be due to inherent contagious population processes, because the scale of the study areas were very large relative to shrew home ranges and movements. Contagious processes could produce numerous peaks and troughs of abundance, but not large-scale trends. The pure spatial component more likely represented either unmeasured habitat variables that showed a spatial pattern or the effects of larger-scale events, such as timing of snowmelt or other climatic factors. Most of the spatial trend in abundances at E B L was included in the "combined habitat+spatial" component. Given the large size of the E B L study area and the non-random arrangement of habitat types in the retrospective study, this component was likely driven by the habitat relationships (i. e., the spatial trends were seen only because the species were responding to habitat types that were spatially arranged). However, in the cases where much of the habitat model was also included in the "combined habitat+spatial" component (e. g., E B L August, S. vagrans immatures, S. hoyi, and to a lesser extent mature S. cinereus and red-backed voles), observed habitat relationships need to be interpreted cautiously in case they were spurious results of coincidental patterns of the small mammal abundances and the habitat features.  Discussion One immediate benefit of applying the elaborated variance partitioning technique of Borcard et al. (1992) to the insectivore data has been a better comprehension of the relevance of the small percentage of explained variance. The recognition that the large unexplained component of variation is, in many cases, just that expected from measurement error has curtailed a long search for more complex relationships in the data. This additional data exploration would likely have been fruitless in these cases, and misleading if it led to spurious 62  relationships. Although not making the habitat models more informative, explicitly estimating the measurement error variance component may have prevented the models from becoming misinformative. The analysis indicated where the data may support more complex analytical procedures, for study groups in which the current undetermined component is larger than the expected measurement error. The performance of C A R T analyses (Breiman et al 1984) and neural network techniques (Smith 1993) was evaluated for these groups (Chapter 4). In cases where most of the explained variation was due to relationships with habitat elements, and the undetermined component was equal to that expected from measurement error, improvements of the habitat element models appear unlikely with the current sampling designs. The emphasis will now be on testing the generality of these models at other sites. Identifying the substantial contribution of the "habitat type+element" component in several cases has also suggested caution in interpreting observed relationships with habitat elements prior to independent validation. While the necessity to validate models is widely recognized, they are nonetheless often published without validation (e. g., 9 7 % of models in a review of the aquatic sciences; Bourget and Fortin 1995). In applied contexts, management recommendations are often made prior to model validation. These preliminary interpretations of untested models are most likely to be in error if a high proportion of the model's explanatory power is shared with another set of variables. This is the case for several of the habitatelement models from EBL, where relatively high r values may otherwise have encouraged 2  management interpretations prior to testing. Applying the variance partitioning technique to the insectivore data sets has also helped direct the next steps in the development of the habitat models. For example, the substantial pure spatial component of variation for the shrew species at S C in August led to an examination of unmeasured variables that might show a similar spatial pattern. Maps of ecological site series, a combination of site moisture and soil productivity, at S C (Lloyd and Inselberg 1997) showed a similar trend and are promising candidate variables. Using the spatial trend to identify potential unmeasured habitat variables has an obvious limitation - the 63  better a variable corresponds to the spatial trend in abundance, the more likely it is to have a functional relationship with abundances, but the more difficult it is to separate that effect from the spatial trend itself (and the other unmeasured variables with the same spatial trend). Thus, determining the relationship of the shrews to site series at S C will have to rely on the local spatial variation of site series within the overall spatial trend to tease apart the effects of site series and the overall spatial trend. Such a test will be weakened by partialling out the shared spatial trend, and direct sampling of site series at other sites may be required. As another example of the variance partitioning analysis informing study development, the substantial "habitat type + element" component for several groups emphasized the importance of disentangling habitat element and habitat type relationships. This separation could be accomplished by directing sampling within types to produce wide variation in elements identified as important, or by manipulative experiments. At S C , treatments from an existing site preparation experiment that uses a split-plot design within each main treatment unit (Vyse 1997) are thus being sampled for small mammals. Although each of these treatments manipulates several habitat variables simultaneously, the habitat elements are at least changed in a way that is different from the variation produced by the main treatments, thus helping to better separate variation in habitat elements from habitat type differences. The elaborated variance partitioning analysis thus provided context for the large unexplained variance component in the small mammal data, suggested caution in preliminary interpretations of the habitat-element models, and directed further steps in model development. In a more general sense, the variance partitioning technique elaborated here is a step towards improving a basic dilemma in developing habitat models: the models are necessarily based on correlational data, but are intended to indicate causal relationships. Correlational data are necessary because manipulative experiments may be possible on appropriate scales for one or 2 habitat elements, but are infeasible for all combinations of many individual elements. Additionally, manipulating single elements generally has unintended effects on other habitat variables. For example, manipulations of coarse woody  64  debris levels on large plots at the S C site (Craig et al. 1997) also reduced forb cover in the short term and altered forest floor structure, probably for a longer time, due to the physical damage of moving large pieces of wood. Similarly, a controlled removal of shrub cover at the E B L site reduced forb cover in the short term through mechanical damage, but increased it in the longer-term, presumably due to reduced competition with shrub species. Manipulations of single habitat variables may therefore be misleading, if their partially correlated effects on many other variables are not recognized. Large-scale operational experiments, such as those at SC, modify many habitat variables; for habitat model development, they are more effectively a source of variability for correlational analysis than true controlled experiments. Retrospective studies of existing "treatments" and use of existing natural variation to develop habitat models are even more clearly correlational. In many vegetation and aquatic studies, the primary objective is to describe particular complex species assemblages (Bourget and Fortin 1995). Habitat modelling, however, is intended more often to find predictive relationships, generally for an applied purpose, such as predicting species' responses when habitat variables are manipulated. Habitat models must therefore rely on data that is correlational, at least to some extent, but must identify reliable causal relationships to be useful. The problem is not unique to habitat modelling, as many topics in field ecology face the same constraints (Rodriguez and Magnan 1995, Thomson et al. 1996). The variance partitioning technique is useful in identifying causal hypotheses from correlational data (Borcard et al. 1992, Bourget and Fortin 1995). In particular, the technique partially reduces the concern that the correlation observed between 2 variables is due to a common, unmeasured causal variable, rather than a direct relationship, by identifying the pure and shared (potentially non-causal) components of the habitat model. Causal interpretations are clearly limited by the variables included in the model, either directly or implicitly through synthetic variables. For habitat-element models, using habitat types and spatial trends as 2 synthetic variables can include more unrecognized potential co-causal variables. Rigorous testing of causal hypotheses identified from 65  correlational data requires manipulative experiments (e. g., Wootton 1994, Anderson and Gribble 1998). However, given the difficulties of controlled single-factor experiments with habitat elements and the impossibility of full-factorial experiments, the causal nature of relationships embodied in most habitat models is likely to be best demonstrated indirectly, by the predictive success of the models in independent tests and applications.  66  Chapter 4. Comparison of alternative modelling techniques for animal-habitat models  Chapter Summary This study compared the performance of linear.additive models, classification and regression trees (CART) and neural networks (NN) for developing animal-habitat models from field data. Models were developed for 12 data sets derived from several years of pitfall sampling of small mammals, and for 2 data sets on the occurrence of spruce grouse in sign-survey plots. The data sets were typical of ecological field data, with moderate sample sizes (n = 63 to 415), substantial uncertainty in measurements, and spatial autocorrelation. Model performance was evaluated primarily as the ability of a model developed with data from one site to predict abundances or occurrences in samples from another site, and, secondarily, as the ability of the model to suggest relationships warranting further analysis or study. Linear additive and NN models showed similar predictive ability across the 12 small mammal data sets (median r = 0.152 and 0.147, respectively), and the 2 spruce grouse data sets (median k-hat = 0.25 and 0.19, respectively). C A R T models had lower predictive success. At the point where overfitting began, as indicated by maximum cross-validation fit during NN training, many NN models closely approximated the linear additive model. There was no relationship between how well a model fit the original data set and how well it predicted observations at another site. The importance of testing model performance with independent data is thus emphasized, especially in comparisons of simple versus complex models. Linear additive models are easy to communicate and interpret, but were of limited value in identifying complex relationships. C A R T models are also easily interpreted and have the heuristic benefit of indicating important contingent relationships. In contrast, NN models are difficult to communicate and understanding the relationships implicit in NN models requires additional analysis.  However, univariate and bivariate plots of NN model behaviour can be a  powerful heuristic tool for exploring non-linear, contingent relationships between animals and habitat features. NN modelling, and C A R T analysis to a lesser extent, were therefore useful tools for developing habitat models with these field data sets, because they revealed potentially important, complex relationships to be studied to improve future models.  67  Introduction Models relating animal occurrence or abundance to measurable habitat elements are widely used to guide resource management decisions or to predict the effects of particular management actions (Verneret al. 1986, Starfield and Bleloch 1992). Recent habitat models typically rely on multivariate statistical methods, such as multiple regression or discriminant function analysis, to predict abundance or occurrence using linear additive combinations of the habitat variables. Linear additive models are popular because they are readily produced with commercial software, the underlying statistics are well-developed, and researchers and model users can interpret the additive equations easily. Although spurious relationships can be produced when many habitat variables are used, the contribution of individual variables and the overall significance of the model can be evaluated statistically to assess this risk (James and McCulloch 1990). However, a major disadvantage of these multivariate methods for developing habitat models is that the underlying assumption of linear additive relationships does not necessarily correspond well with expectations from ecological theory or natural history experience. A linear relationship between the abundance of a species and the abundance of a particular habitat feature is only expected over a limited range of variation of the habitat feature (Jongman et al. 1987, Borcard et al. 1992). Across a wider gradient in the habitat feature, animal abundance may show an asymptotic or unimodal distribution (Jongman et al. 1987, Borcard et al. 1992). Transforming habitat variables prior to a linear analysis may allow some of these non-linear relationships to be modelled, but choice of a transformation requires prior knowledge of the form of the relationship. Contingency effects, the dependence of the relationship with one habitat variable on the value of another or many other variables, can be expected from the ecological principles of limiting factors and substitutibility of resources. With resource substitution, a relationship with one habitat variable may only be seen when other, substitutable variables are at low abundance. For example, shrubs or large logs may both provide cover for a small mammal; the abundance of the species will only be affected by the 68  abundance of shrubs when large logs are uncommon, and vice versa. Limiting factors could lead to the opposite relationship, in which the relationship with one limiting habitat variable is only apparent when other features are abundant enough not to be limiting (Blackman 1905, Thomson et al. 1996). In the small mammal example, if shrubs were actually providing food, the abundance of the species may only respond to the abundance of shrubs if there were enough large logs providing cover. The detailed knowledge of a species' ecology required to predict a priori the form of non-linear, contingent habitat relationships is lacking for most species. Discovering these complex relationships from multivariate empirical data requires more flexible techniques than linear additive models. Two alternative approaches to analyzing multivariate data offer promise for developing habitat models: classification and regression trees (CART) and artificial neural networks (NN). C A R T analysis (Breiman et al. 1984) produces bifurcating "trees" based on continuous or categorical independent variables (habitat measurements) that separate the samples into groups that are most homogeneous with respect to the dependent variable (abundance or occurrence of the species). The group of samples are split at each node in the "tree" based on the value of an independent variable. The variable and cut-off value at each node are chosen to produce 2 subsets of samples that are most homogeneous in the dependent variables (i.e., the splits minimize the resulting within-groups variance). The branching structure of C A R T models emphasizes contingent relationships, because lower-level branching decisions are contingent on higher-level branching decisions based on other independent variables. The dichotomous branches, however, only represent threshold-type responses, although some indication of more complex relationships is possible because the same independent variable can be used at several branching nodes within a single C A R T model. Recent ecological applications of C A R T models include identifying forest pathology risk factors (Byler et al. 1990, Gottschalk et al. 1998), describing bird species richness patterns (O'Connor et al. 1996) and evaluating the effects of human disturbances on nesting bald eagles (Grubb and King 1991, Grubb etal. 1992). 69  Artificial neural networks integrate input variables (habitat measurements) to produce predicted output (animal abundance) using weighted connections in networks patterned after the connections between biological neurons (Rumelhart et al. 1986, Smith 1993, Murray 1995). In the simplest network structure, the values of the input variables in a sample all have a weighted effect on the value of a number of implicit variables, called "nodes", in a hidden layer of the network. Each hidden node then has a weighted effect on the output value. The combined input at each node is transformed with a fixed non-linear function, such as the logistic equation, to produce its output. A neural network is trained with a set of training samples by iteratively comparing the output predicted value with the known observed values from the samples, and adjusting the independent weighting factors so that predicted and observed values of the output variable converge. Neural networks can capture complex nonlinear relationships, because each independent variable affects each hidden node with independent weightings and non-linear transformations are used at each node (Smith 1993, Tu 1996). Contingent relationships are also represented, because all independent variables have weighted effects on each hidden node. The potential of artificial neural networks to capture complex multivariate relationships has led to their recent use in a variety of ecological applications: relating fish occurrence or abundance to stream characteristics (Baran et al. 1996, Lek et al. 1996, Mastrorillo et al. 1997), modelling fish species richness globally (Guegan et al. 1998), predicting algal dynamics (Yabunaka et al. 1997, Whitehead et al. 1997, Recknagel 1997) and ecosystem variables (Brey et al. 1996, Paruelo and Tomasel 1997), classifying vegetation from satellite imagery (Moody et al. 1996, Foody et al. 1997) and automating taxonomic identification (Edwards and Morse 1995, Culverhouse et al. 1996).  The primary purpose of most empirical habitat models is to predict the effect of changing habitat variables on the study species, often for an applied purpose (Conroy 1993). Because of their greater flexibility to capture complex ecological relationships, neural network and C A R T analyses should theoretically produce better predictive habitat models. Practically, however, their predictive ability may be limited by the small sample sizes and substantial 70  component of measurement error in most ecological field studies. Use of complex analyses on such data can lead to "overfitting", the modelling of idiosyncrasies or "noise" in the data set. Resulting models fit the data well, but have little predictive ability (i. e., they are precise, but not general; Chatfield 1995). Overfitting is a particular concern with neural networks, because the weights for each of the many connections are estimated, using the iterative back-propagation technique, from the data. The degrees of freedom used in estimating the many parameters in even moderately complicated neural networks may exceed the sample size of typical ecological studies. Such models will fit the data perfectly after enough training iterations, but have dubious predictive ability (Smith 1993). C A R T models, while presenting fewer parameters in the final classification tree, can use many degrees of freedom in recursively arriving at the tree. For example, searching for a single branching node with 10 independent variables in a noisy data set can use up to 15 degrees of freedom (Ye 1998). The problem of using many degrees of freedom with relatively few samples is made worse in many ecological field studies by spatial autocorrelation of both the dependent and independent variables, which reduces the effective sample size (Clifford et al. 1989, Thomson et al. 1996). These concerns about applying complex modelling procedures to typical, moderatesized ecological data sets, made effectively smaller by spatial autocorrelation, suggest a cautious interpretation of studies recommending neural network methods over linear models on the basis of a better fit to the data (e. g., Baran et al. 1996, Lek et al. 1996, Mastrorillo et al. 1997, Guegan et al. 1998). More complex models will produce a better fit to the data simply because they have more free parameters. Some previous tests of modelling methods have also used cross-validation, which excludes some of the samples from the model fitting and then tests the model with the excluded data. Cross-validation may provide a better indicator of a model's predictive ability, but should still be interpreted cautiously, because it indicates only the precision of a model's predictions within the study area for which the model is being developed (Hjorth 1994). Because at least some component of site-specificity is expected in ecological systems (e. g., in habitat relationships; Rotenberry 1986, Maurer 1986, Fielding and 71  Haworth 1994), cross-validation results will overestimate true external predictive ability (Breiman 1992, Chatfield 1995). The limitations of cross-validation are greatly exacerbated by spatial autocorrelation within the study site. If spatial autocorrelation is strong, the samples excluded from model fitting are effectively not excluded at all; the model is also fit to them by virtue of highly correlated neighbouring points being included in the model fitting. Thus, while alternatives to additive linear models have great potential for empirical habitat modelling, their ability to improve the predictive ability of the models still requires rigorous testing for typical ecological data. In particular, the predictive ability of models generated by different methods needs to be tested on independent data (Chatfield 1995). A second purpose of ecological models is heuristic, to improve our understanding of the system so that future research and analysis will produce models that are more predictive. Learning from and adapting an imperfect model, within reason, is likely a more efficient way of discovering predictive relationships than immediately rejecting the model (Loehle 1987), especially in ecological systems where initial models are rarely reliable. The heuristic value of a model depends, in part, on how the model is structured, with simpler models generally conveying information more readily. Particularly complex models may thus capture more features of an ecological system, but be less informative (Hilborn and Mangel 1997). If models generated by several methods all perform equally when tested on independent data, the ones that most clearly demonstrate the important relationships are of the greatest value for future model improvements (e. g., Alsberg et al. 1997). In this paper, I generate habitat models for 2 groups of forest-dwelling species, using linear additive models, C A R T analyses and artificial neural networks. The size and quality of the data sets, and the potential for spatial autocorrelation of sampling points, are typical of many studies designed to generate animal-habitat relationships for applied use by land managers. The predictive ability of the models for both groups are tested using data collected at other sites. I also examine the heuristic value of the models by assessing how readily they  72  suggest relationships that can be used to guide studies and analyses to develop more successful predictive models in the future.  Methods Two groups of data sets are analyzed, one on the abundance of 3 species of small mammals based on pitfall trapping, the other on the winter occurrence of spruce grouse based on plot surveys of grouse sign. Both studies are part of a larger project at the Sicamous Creek Silvicultural Systems study area (see Chapter 1). All studies at the Sicamous Creek site are intended to provide information for forest management throughout a range of high-elevation E S S F forests of southern B.C., and thus the generality of results from the Sicamous Creek site needs to be tested in other E S S F forests. For the small mammals, a comparable pitfalltrapping study in high-elevation forest at East Barriere Lake, 90 km northwest of Sicamous Creek, was used. For the spruce grouse, surveys at 5 other high-elevation sites 10 - 90 km from Sicamous Creek provided the test data. Models from Sicamous Creek were tested using the other sites, and vice versa.  Data sets - 1. Small mammal abundance in pitfall traps Small mammals at Sicamous Creek were collected in small pitfall traps (Huggard and Klenner 1997). A circle of 5 traps, 8 m in diameter, was used as the sampling unit. A total of 111 trap circles at Sicamous Creek sampled clear cuts, small patch cuts, cutblock edges, partial cuts, and uncut forest. Traps were set for 2 consecutive 2-week periods at 2 times of year: immediately following snowmelt in late June ("spring") and in August to early September ("August"). Three years of post-harvest data from August and 2 years from spring sessions are available. Yearly values were combined into an abundance index for each species at each season, calculated for each trap circle as the log-transformed residual catch-per-unit-effort after the overall yearly mean for that season had been subtracted. Details of the sampling design and the rationale for this abundance index are provided in Chapter 5 (see Chapter 5, 73  Appendix 5.1 for how abundance index was calculated). Circular habitat plots of 5.65-m radius (0.01 ha) were conducted at each trap circle to measure non-floristic structural habitat variables. Variables were transformed using log(x+1) if this improved the normality of the distribution. These transformations were intended to reduce the effect of the few samples that had particularly high values of the variable. When 2 variables covaried strongly (r > 0.80), only one was used in the analysis. The 10 habitat variables used were: canopy cover, density of live trees, density of all tree stems including snags and stumps, shrub cover, herb-layer cover, moss cover and depth, duff or litter cover and depth, and volume of coarse woody debris. These variables are explained in detail in Chapter 5. A second study of small mammals collected in pitfall traps was conducted at East Barriere Lake (EBL) from 1991 to 1996. The E B L study used a retrospective study design, with a total of 63 pitfall trap circles sampling clearcuts, partial cuts and uncut forest in both E S S F forest and Interior cedar-hemlock (ICH) forest. Abundance indices were calculated for spring and August seasons as at Sicamous Creek, and the same habitat variables were measured in 5.65-m radius plots at each trap circle (although transformations for normality sometimes differed). Three species of small mammals occurred frequently enough at both sites for analysis, Sorex cinereus ("masked" or "common" shrew), S. monticolus ("montane" or "dusky" shrew) and southern red-backed voles (Clethrionomys gapperi).  Preliminary analyses indicated that  male and female red-backed voles at Sicamous Creek and immature and mature shrews at E B L responded somewhat differently to the overall treatments. However, sexes or maturity classes were not analysed separately, because the preliminary analyses did not indicate any substantial differences in the responses of the sexes or maturity classes to the habitat elements. The problem of large sampling error due to relatively few captures is also reduced by not subdividing the species. Analyses were conducted separately for the spring and August seasons.  74  Data sets - 2. Occurrence of spruce grouse Occurrence in winter of spruce grouse was assessed by searching 5.65-m radius plots (0.01 ha) for grouse droppings at snow melt (Huggard 1997). Sets of 13 plots, centred on areas where grouse had been detected in earlier surveys during the display season ("grousecentred plots"), were conducted from 1994 to 1996. Habitat features were measured in each plot and transformed using log(x+1) if this improved the normality of the distribution. The 9 variables used were: slope, canopy cover, density and basal area of live subalpine fir (Abies lasiocarpa) trees (m /ha), density and basal area of live Engelmann spruce (Picea 2  engelmannii) trees (m /ha), shrub cover, density of live trees that were shorter than expected 2  from the height-diameter relationship and the presence or absence of surficial rock. These variables are explained fully in Chapter 2. Initial analyses of the spruce grouse data showed a much greater occurrence of spruce grouse on knolls, which are a rare topography type, and no winter use of plots in harvested or natural openings (Chapter 2); the analysis here examines only non-knoll plots outside of openings (415 of 503 plots at Sicamous Creek). Plots on knolls were not used because these preferred habitats are readily identified, without the need for any further habitat modelling. If plots on knolls had been included, they would have strongly influenced the comparison of habitat features in plots used by grouse versus those not used. The resulting models would thus have been largely describing just the difference in habitat features between knolls and non-knolls. Instead, the analysis is addressing the question, What habitat features distinguish plots used by grouse from those not used by grouse when they are not on knolls? In 1997, identical grouse-centred plots were conducted at 5 other sites in E S S F forest 10 - 90 km from the Sicamous Creek site. A total of 242 plots were assessed in 19 sets of 13 plots (a few of the plots were not conducted because they were in standing water, on roads or over cliffs). Of these 242 plots at validation sites, 173 plots were not on knolls or in openings and were used in these analyses.  75  Analyses - 1. Model fitting Linear additive models, classification and regression trees (CART) and neural network (NN) models were developed for each of the 12 small mammal data sets (3 species x 2 seasons x 2 sites), and the 2 spruce grouse data sets (Sicamous Creek and validation sites). Supervised step-wise regressions were used as the linear additive model to relate the abundance indices of the small mammal species to the 10 habitat variables. Only variables having a partial regression coefficient significant at P<0.15 were included in the final model. Supervision of the step-wise procedure allows the researcher to examine pairs of variables, which might be significant together, but not individually. Discriminant function analysis was used with the data on occurrence of grouse, to distinguish plots used in winter by grouse from unused plots based on the 9 habitat variables. Linear additive models were calculated using Systat 7.0. C A R T analysis will produce a classification tree with each sample on a separate terminal node, unless a stopping rule is used to limit the bifurcations. Two stopping rules were used for the C A R T analysis of the grouse and small mammal data: 1) terminal groups contained a minimum of 10 samples for the dichotomous occurrence data, or 5 samples for the continuous small mammal abundance data; 2) each branching node had to reduce overall error by a minimum proportion. Five C A R T trees were produced for each data set, with different minimum proportional reduction in error (minimum PRE): 0.1, 0.05, 0.02, 0.01, 0.0. A higher minimum P R E produces simpler trees with fewer branches. The minimum P R E of 0.0 means that branching is constrained only by the minimum terminal group size. The fit of C A R T models is measured by the overall proportional reduction in error (overall PRE). When least square deviations are used as the measure of variation, overall P R E has a similar interpretation to the coefficient of determination in regressions. C A R T models were derived using Systat 7.0. Neural network models approach their maximum fit asymptotically, although not completely monotonically, over many iterations. A neural network with enough input variables 76  and hidden nodes will eventually fit the data perfectly, with the rate of approach to the maximum a function of the data complexity, number of hidden nodes, and learning parameters used in the back-propagation algorithm (Smith 1993). Stopping model fitting at a predetermined number of iterations is therefore arbitrary. Additionally, at some point, the neural network is fitting the peculiarities of sampling error in the data set, rather than general patterns. The recommended solution to the problem of overfitting is to train the network on a random subsample of the data and to use the remaining sample for cross-validation (Smith 1993). Although the fit of the model to the training data increases continually, the fit to the cross-validation samples reaches a maximum then declines as overfitting starts. The peak of the cross-validation fit therefore provides a stopping rule for the model fitting. For the small mammal and grouse models, two-thirds of the samples were chosen randomly as the training data, with the remaining one-third used for cross-validation. Training continued for a minimum of 2000 iterations, or for 200 iterations after a peak in the cross-validation fit if the peak occurred after 1800 iterations. Initial runs compared the peak cross-validation coefficient of determination (r ) for 2  networks with 2, 4 and 6 hidden nodes, using 3 different randomly chosen two-thirds subsets of the samples in each data set for training. Networks with more hidden nodes were not examined, because with 9 or 10 input variables, these more complex networks would have contained more free parameters than available samples. The initial runs showed that differences in the peak cross-validation coefficient of determination for networks with 2, 4 or 6 nodes were minor compared to the differences due to the different, randomly-selected subsets of samples used for training (Fig. 4.1). Models with 2 nodes occasionally had slightly lower peak cross-validation values, and thus 4-node networks were used subsequently. Because of the apparently pronounced effect of the particular subset of samples selected for training, 10 neural network models were produced for each data set, using a different randomly selected two-thirds of the samples for training each time. In all cases, the model parameters at the  77  iteration with the peak cross-validation coefficient of determination was retained as the best model.  0.4  ^ c o  0.3  •  2 0.2 rs > J)  g  0.1  •  •  0.0 L  ,  .  1  •  2  4 6  • .  Nodes: 2 4 6 Subset:  •  •  2  4 6 2  3  Fig. 4.1. Example of the peak cross-validation fit of neural networks for one small mammal data set, using networks with 2, 4 or 6 hidden nodes with 3 different, randomly-chosen subsets of the data used for training. Analyses - 2. Model testing As outlined in the Introduction, the fit of models with different degrees of freedom cannot be used to compare their performance, and cross-validation is also a dubious measure of performance, particularly in the presence of spatial autocorrelation. Testing of models in this paper therefore relies on comparing the predictions of models generated at one site with the independent observations at the other site or sites. For the small mammals, comparisons between sites were made within the same season (e. g., predictions of the spring E B L models were tested against observations from spring at Sicamous Creek). The degree of correspondence between a model's predictions and the actual observations at the test site was summarized with Pearson's correlation coefficient for the continuous small mammal abundance indices. Plots of predicted versus observed values were also examined for obvious non-linear relationships, or dependence of residuals on the predicted value.  78  For the spruce grouse presence/absence data, discriminant function and C A R T models produce a probability of occurrence at each sample point. The NN models used here produced a quantitative prediction that tends to be between 0 and 1, but cannot strictly be interpreted as a probability because it is not constrained to this range. In the tests, the models were considered to predict that grouse would be present if the probability or NN value was greater than the observed occurrence of grouse in the data set used to fit the model, (e.g., a model based on Sicamous Creek data, being tested with the data from the validation sites, would use the observed occurrence at Sicamous Creek as the probability cut-off value). The ability of the model to correctly predict presence or absence was indexed with the k-hat statistic of Lillesand and Kiefer (1994, p. 616). The statistic compares the predictive ability of the model to "chance" guesses, ranging from 0 when predictive ability is no better than chance, to 1 when predictions are always correct. Negative values are also possible, when predictions are worse than chance.  Results and Discussion Fit of models Step-wise regression models for the 12 small mammal data sets included 1 to 6 of the 10 habitat variables, with coefficients of determination (r ) between 0.03 and 0.47 (Table 4.1). 2  All models except that for S. cinereus at Sicamous Creek in August were statistically significant (P < 0.05, not compensating for spatial autocorrelation or degrees of freedom used in the stepwise variable selection procedure). For 3 of the small mammal data sets, C A R T models at the highest minimum P R E value could not produce branches. All other C A R T models produced branches, fitting between 0.105 and 0.747 of the variance in the abundance indices (Table 4.1). The number of nodes included in the C A R T models increased substantially with each decrease in minimum P R E levels. Overall P R E also increased with decreasing minimum P R E levels, except for a few  79  data sets that showed small decreases in overall P R E between minimum P R E levels of 0.02 and 0, although trees at the latter level included more branches. NN models showed substantial variation in training and cross-validation coefficients of determination at the cross-validation peak, depending on which randomly chosen two-thirds of the data set were used for training. Medians and ranges of 10 runs are thus presented for each data set (Table 4.1). Median training coefficients of determination ranged from 0.06 to 0.72, while median cross-validation coefficients of determination ranged from 0.00 to 0.46. The model iteration at which the cross-validation peak occurred ranged from 16 (the minimum possible) to 5673. The fit of C A R T models with the higher minimum P R E limits was higher than, but correlated to, values from step-wise models (Fig. 4.2a). The fits of C A R T models with no minimum P R E limits were much higher than those of step-wise models, and only weakly related (Fig. 4.2a). Median cross-validation coefficients of determination for neural network models were generally close to the values for step-wise regression models for the various data sets (Fig. 4.2b), while training coefficients of determination were higher and more variable. Many of the neural network models showed a rapid increase in training and cross-validation fit, followed by a prolonged slow increase (Fig. 4.3), at which time the cross-validation fit was typically similar to that of the step-wise regression model. With further iterations, training fit increased more rapidly, while cross-validation fit declined, presumably as the network began to fit non-linear relationships particular to the training data. For the spruce grouse data sets, the median training coefficient of determination for the NN models was comparable to the linear additive discriminant function, while the crossvalidation value was lower (Table 4.2). Overall P R E in C A R T models with 9 or more nodes at Sicamous Creek and 3 or more nodes at grouse validation sites exceeded coefficients of determination of the discriminant function. 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Peaks in the first 15 iterations, indicated by hatched area near Y-axis, were ignored. Predictive ability of models Statistically significant correlations between model predictions and observed values occurred in the cross-site tests for at least one modelling technique for all small mammal study groups except S.  monticolus in spring (models from both sites) and S. cinereus in August from  E B L (Table 4.3). However, correlation coefficients for all cross-site tests were generally low. Thus, the models can generally predict trends in the abundance indices at many points 83  00  o CN CN CN O O c CO CO O LA: d^ d  a) CN a O  TJ  c re c o  o co CN d  re o  "55 re  S>" oj > TJ .ti  c  TJ <U TJ Q.  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Across the 12 small mammal study groups, median and mean predictive correlations were highest for step-wise regression, slightly lower for neural network models and lowest for C A R T models (Table 4.3). For the spruce grouse, the k-hat summary statistic was highest for the discriminant function models with both data sets (Table 4.4).  The k-hat values for C A R T models, and the  median k-hat for NN models were similar with the validation site data. For the Sicamous Creek data, moderately complex C A R T models were better predictors than the median NN model. The 10 NN models at each site, based on different random two-thirds of the data, showed a wide range of predictive abilities, indexed by k-hat, including models that were better than any other method, and models that were considerably worse. Unfortunately, there appears to be no way of knowing which NN run will produce the best predictive model, other than testing with the independent data. C A R T and NN models tended to produce low predicted occurrences, resulting in many predicted absences. Thus, classification success of these models was usually higher when grouse were absent than when they were present. A lower probability cutoff might improve the overall performance of these models, but this cut-off would have to be determined by some other independent means.  Relationship between model fit and predictive ability None of the modelling techniques showed a relationship between the fit of a model and its predictive ability, across the 12 small mammal study groups (Fig. 4.4).  C A R T models for  most groups showed little relationship between predictive ability and model fit for trees of different complexity (Fig.  4.5a). There was also no apparent relationships between prediction  ability and either training or cross-validation coefficients of determination across the 10 different neural network runs within each study group (Fig.  4.5b). The same pattern held for  the spruce grouse models, with no relationship between fit and predictive ability between modelling techniques, or among the individual NN runs. With the small mammal data, NN  86  0.6  0.6  0.6  £ 0.4 c o  0.4  0.4  0.2  0.2  • •  1 2. o.o 0  2  -0.2  0.0  0.0  0.2  0.4  0.6  0.8  •  •  -0.2 0.0  Fit (r )  0.2  0.4  a J"  0.0  D  •  0.6  -0.2 0.0  0.8  0.2  Fit (overall PRE)  2  0.4  0.6  0.8  Fit (r ) 2  Fig. 4.4. Relationships between the fit of a model to the original small mammal data set and its ability to predict with the independent test data for: a) stepwise regression; b) CART (solid symbols = minimum PRE of 0.05; open symbols = minimum PRE of 0); and, c) NN models (solid symbols = cross-validation coefficient of determination used to indicate fit; open symbol = training coefficient of determination used). a. 0.8 0.6 c 0.4 0 ••a  o  3  0-2 0.0 -0.2  0.2  0.4 Fit (overall PRE)  0.6  0.8  0.0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  Fit (cross-validation f)  Fig. 4.5. Relationship between the fit of a model to the original small mammal data set and its ability to predict with independent data, for: a) CART models with different numbers of branches, determined by different minimum PRE values (lines join models of different complexity within the same small mammal data set); and, b) NN models (lines join the 10 different runs within the same small mammal data set, ordered by fit to the original data). Only 6 data sets are shown in b), for clarity.  models run to a minimum of 2000 iterations, well beyond the cross-validation peak in most cases, produced very good fit to the data (median training coefficient of determination = 0.668). These models were clearly overfitting, as they had very poor predictive ability in the cross-site tests (median correlation coefficient = 0.043). There was also no correlation between predictive ability and fit for these overfit NN models (r = -0.018). Some previous tests of neural network models with ecological data may have been misleading because they examined the models' abilities to fit data sets, rather than their  87  predictive ability. In this examination, there was no relationship between how well a model fit the data and how well it predicted when tested with independent data (with the obvious exception of a few C A R T models that did not fit the data at all, and thus had no predictive ability). In particular, the better fit of complex C A R T models or NN models run for many iterations did not result in better predictive ability. These results suggest that a researcher developing habitat models with these types of data sets cannot know the predictive ability of a model from its fit to the original data; independent tests of the model are required. Recognizing the difference between the fit of a model to its original data and its predictive ability with independent data is especially important in comparisons of simple modelling techniques with those that fit many parameters or examine many possible relationships before producing a final model. Many variations available for the basic modelling techniques used here were not examined in this study, including transforming variables to represent specific nonlinear relationships in additive models, other variable selection methods (Ibrahim and Chen 1997), Bayesian C A R T analyses (Denison et al. 1998), and more complex NN structures (Smith 1993, Murray 1995). All of these methods involve fitting increased numbers of parameters to the original data, and would undoubtedly have resulted in better fitting models. However, it is doubtful that the better fit of even more complex models would have translated into better predictive ability with these data sets.  Heuristics - interpretability of the models Models for red-backed voles at Sicamous Creek in August and for spruce grouse at Sicamous Creek were used to explore the heuristic value of the linear additive, C A R T and NN models. The habitat models for both species had relatively high predictive success, supporting belief in the generality of relationships contained in the models, at least within the forest type examined in this study. The C A R T models with minimum P R E of 0.01 were used for the examination, because these had the highest, or almost the highest predictive ability for both 88  species. From the 10 NN model runs per case, one was examined that had near-median predictive ability and cross-validation fit. Interpretation of regression or discriminant function coefficients is familiar to most ecologists (James and McCulloch 1990). For red-backed voles, step-wise regression coefficients and their significance (Table 4.5) suggest that the voles respond positively to 4 variables, negatively to 1 variable, and not at all to the 5 variables not included in the step-wise model. For spruce grouse, standardized coefficients from the discriminant function suggest a positive relationship of occurrence with the density of subalpine fir trees, but a negative relationship with their basal area, similar but weaker relationships with the density and basal area of spruce, and positive relationships with canopy cover, short trees and the presence of rock (Table 4.6). Although interpretation of individual coefficients can be misleading in multivariate statistics (James and McCulloch 1990), identifying dominant variables in exploratory analyses can suggest particular variables to examine, through specific manipulations in future studies. Understanding of non-linear or contingent relationships is not possible with linear additive models, unless specifically transformed variables or interaction terms are included a priori in the model.  Table 4.5. Step-wise regression for abundance index of red-backed voles at Sicamous Creek in August (n = 111, r*= 0.273, p<0.0001). Variable Constant log(Canopy cover + 1)  Coefficient -1.18  Standardized coefficient * P 0 <0.001 0  (2)  0.24  0.35  -0.03  -0.26  log(Shrub cover + 1)  0.27  0.22  0.04  Moss cover  0.002  0.15  0.08  log(CWD volume + 1)  0.29  0.16  0.05  Live tree density  0.02 0.009  The standardized coefficient is the regression coefficient of the variable divided by the standard deviation of the variable. P-value for test of the partial regression coefficient being different from 0. 1  2  89  Table 4.6. Discriminant function analysis for occurrence of spruce grouse. Variable  Coefficient  Standardized coefficient^  Constant  -1.72  Slope  -0.13  -0.05  Canopy  1.63  0.54  Subalpine fir density  2.41  0.65  -2.33  -1.000  1.27  0.38  -0.52  -0.32  Relatively short trees  1.08  0.32  Rocks (presence = 1)  0.60  0.23  Subalpine fir basal area Engelmann spruce density Engelmann spruce basal area  0  The standardized coefficient is the discriminant function coefficient of the variable divided by the standard deviation of the variable. 1  The tree diagrams produced by C A R T analyses identify important contingent relationships, as the relationships on each branch below a higher-level node are independently derived. Substitutions between habitat variables are particularly easy to identify. For example, the first split in the red-backed vole tree is into samples with greater than or less than 37.5% shrub cover, with the former generally having higher predicted abundance indices (Fig. 4.6). The first branch of the group with low shrub cover then separates samples with greater than or equal to 9 0 % moss cover from the others. The high moss cover samples have higher predicted abundance indices, suggesting that moss cover can substitute for shrub cover. No relationship with moss cover is seen on the branch with high shrub cover. Possible complementarity of habitat variables can also be inferred from C A R T trees. For example, the first node of the high-shrub-cover branch of the red-backed vole C A R T tree separates sites with higher and lower volumes of coarse woody debris (CWD), with the former having higher  90  > 155mVha—1 1.44 x > 12%—CWp volume < 155m /ha-H 5.20 x 3  > 80m /ha — C a n p p y cover 3  I  1.51 x  < 12%> 37.5%—CWD volume  0.53 x  I' 7  < 80m /ha—Live trees 3  Sj20% — > 6% ] <7-  1.10 x  Duff cover < 20%-  2.52 x  - C a n p p y cover < 6%  0.70 x  S h r u b cover >90%-  1.86 x  < 37.5%—Moss cover >20%< 90%  1.07 x  C a n o p y cover > 3cm -  1.01 x  > 1 7 % — D u f f depth < 3cm—  0.54 x  < 2 0 % — S h r u b cover < 17%-  0.50 x  Fig. 4.6. CART model for red-backed voles in August at Sicamous Creek (minimum PRE = 0.01). Terminal branches show predicted abundance compared to the mean of all sample sites. predicted abundance indices. C W D is not a factor on the low-shrub-cover branch of the tree, suggesting possible complementarity of shrub cover and C W D (i. e., higher amounts of both are required to produce high vole abundances). Separate shrub cover and C W D manipulations have been conducted at the small mammal study sites, based on previous identification of these as important habitat variables. The contingent relationship between the two in the C A R T analysis suggests that factorial manipulations of shrub cover and C W D would have been more informative, or that the one variable should at least be measured where the other has been manipulated. Contingent relationships are thus easily identified in C A R T models, but the dichotomous branching means that the form of habitat relationships can only be inferred weakly. Non-linear relationships are only hinted at when the same variable appears more than once in a tree. In the upper branch of the red-backed vole tree, for example, C W D volumes greater than 80 m /ha generally lead to higher predicted abundance indices, but volumes 3  91  greater than 155 m /ha have much lower predicted indices, suggesting that intermediate 3  volumes are optimal. Extracting the form of a relationship with a particular variable that recurs in a tree is difficult, however, because in most cases recurrences of the variable are on different branches or are separated by other nodes (as in the example given). Such partiallycontingent non-linear relationships may truly represent the ecological system, but they are nonetheless difficult to understand and to use for developing further critical hypotheses to test. C A R T models help simplify the multivariate description of habitat by excluding some variables, but they do not always facilitate identification of the most important variable or variables. In the spruce grouse C A R T model, for example, the first split into samples with more or less relatively short trees does not produce 2 groups of terminal nodes with high and low probabilities of occurrence (Fig. 4.7). The next node on each branch, separating samples with more or less live spruce trees, does so more consistently (i. e., more spruce trees lead to a greater predicted occurrence of grouse on both main branches). This pattern differs from the hierarchical pattern found in more familiar cluster diagrams or phylogenetic  >23% >2"  p=0.764  - C a n o p y cover < 23%-  >3-  p=0.458  - L i v e spruce >40.3m /ha— 2  <2-  < 40.3m /ha-  Relatively short trees  p=0.442  2  >3 < 3-  p=0.182  Bas'al area fir  p=0.552  Live spruce p=0.333 >2.5m /haI Basal area s p r u c e 2  >5°-  < 2.5m /ha2  p=0.000  > 13%—Slope  | <3-  is-  p=0.438  - C a n o p y cover [  >6.7m /ha2  p=0.031  < 1 3 % — B a s a l area fir <l 6 . 7 m / h a H p=0.333 2  Fig. 4.7. CART model for occurrence of spruce grouse at Sicamous Creek (minimum PRE = 0.01). Terminal branches show predicted probability of occurrence.  92  trees, potentially confusing interpretation. A final heuristic limitation of C A R T models is that the cut-off value used for a dichotomous split of a continuous variable, while producing the optimal reduction in variance, is necessarily arbitrary. Our expectation of continuous gradients in many ecological responses is affronted by exact cut-offs, such as a much higher predicted abundance of red-backed voles with 150 m /ha of C W D than with 160 m /ha. Acceptance of 3  3  C A R T models for applied purposes may be hindered by scepticism about seemingly arbitrary cut-off values. Although linear additive models can be communicated as equations or statistical tables and C A R T models can be communicated as trees with their associated statistics, there is no comparable way of communicating neural network models. A description of model structure, the equations of non-linear transformations used at nodes, final weights of all connections and constants used to scale input fully captures the model, but does not in any way allow understanding of the relationships it embodies. The combination of multiple connections of all input variables and non-linear transformations at nodes permits the high flexibility of NN models, but prevents their reduction to simpler equations. NN models are in effect "black boxes", an obvious heuristic limitation. The standard approach to learning from NN models is to vary each input variable independently while all the others are held constant, generally at their mean or mid-range value (e. g., Figs. 4.8 and 4.9). This approach shows the form of the embodied relationship, including any non-linearities, and can suggest which variables have the greatest effect on the output value. Non-linear responses were apparent in most NN models examined in this study, but were rarely pronounced. This corresponds to the observation that the NN model fit at peak cross-validation (the models used here) was often similar to that of linear additive models. For red-backed voles, canopy cover showed a pronounced non-linear response, with greatly increased red-backed vole abundances predicted at the highest levels of canopy cover. This form suggests that the logarithmic transformation of canopy cover, used to normalize the variable for regression analysis, may have actually obscured a more linear relationship of vole 93  Shrub cover  c 4.0 ro a>  E  cu 2.0 o c n TJ C 3 1.0 SI  Moss depth Canopy Duff cover  ra  TJ  CD  o TJ  C W D volume  0.5  Moss cover  CD  0.3 Min  1  8  9  Max  Decile Fig. 4.8. Univariate plot of the behaviour of the NN model for red-backed voles in August at Sicamous Creek. Each variable is independently ranged from its minimum to maximum value while all others are held at their mid-range values (4 variables omitted for clarity). Y-axis value is predicted abundance compared to mean of all trap sites.  x  CD  "2 CD O  <D 3 O  8  1.2 Density live fir Canopy cover Short trees ^=$Slope Shrub cover  1.0 0.8 0.6 0.4  TJ a> 0.2 o TJ CD  Basal area spruce  0.0  -0.2  _i  Min 1  2  3  4  5  6  Basal area fir  i  7  8  9 Max  Decile Fig. 4.9. Univariate plot of the behaviour of the NN model for spruce grouse at Sicamous Creek. Each variable is independently ranged from its minimum to maximum value while all others are held at their mid-range values (2 variables omitted for clarity). abundance with (untransformed) canopy cover. Shrub cover, forb cover and moss depth also showed increasingly strong positive relationships at higher values of the habitat variables, while the density of live trees and duff cover had their strongest positive relationships (i. e., steepest slopes in Fig. 4.8) at mid-range values. The relationships between predicted occurrence of spruce grouse and individual habitat variables were generally more linear. The directions and relative magnitudes of the slopes correspond closely to the standardized  94  coefficients of the discriminant function (Table 4.6), demonstrating that the NN model at the cross-validation peak closely approximated the linear additive model. These univariate explorations can show the potentially complex forms of relationships in NN models, but conceal the other advantage of the technique, its ability to capture contingent relationships or interactions among variables. A s an additional aid to interpreting NN models, I also plotted bivariate diagrams, in which 2 variables were independently covaried across their ranges of values. In the spruce grouse example, the 2 variables with the strongest relationship with predicted occurrence of grouse also show interacting, non-linear effects when plotted together in bivariate plots (Fig. 4.10). The form of the relationship with basal area of subalpine fir changes with changes in the number of subalpine fir trees, while the number of trees has its strongest effect on predicted occurrence at mid-range values of basal area.  Basal area fir (m /ha) 2  Fig. 4.10. Bivariate plot of NN model predictions for spruce grouse at Sicamous Creek as basal area of subalpine fir trees (X-axis) and density of subalpine fir trees (individual lines) are varied from their minimum to maximum values.  In the red-backed vole example, C W D is predicted to have only a weak effect on redbacked vole abundance at low levels of shrub cover (Fig. 4.11a), with predicted abundances generally always low. The NN model predicts that abundances overall, and the effect of C W D levels on abundances, both increase dramatically at higher levels of shrub cover, with maximum predicted abundances at the highest shrub covers and mid-range values of CWD.  95  The relationship of C W D volume and predicted red-backed vole abundance is both non-linear and contingent on the level of shrub cover. Three-way interactions can be examined by plotting a series of bivariate diagrams at different levels of a third variable. For the red-backed voles, the bivariate C W D and shrub cover diagrams plotted at 3 levels of canopy cover show a clear 3-way interaction in predicted RBV abundance (Fig. 4.11a-c), with the form of the predicted C W D relationship at both high and low shrub cover changing in different ways as canopy increases. These 3-way interactions are interesting and potentially very informative about the species' biology, although the logistics of a manipulative experiment to test the predictions would be formidable. An obvious limitation to the bivariate plots is that the number of possible pair-wise combinations of variables (45 with 10 habitat variables) precludes examining all combinations.  a.  20  b.  30  50  100  200  CWD volume (m /ha) 3  300  20  c.  30  50  100  200  300  20  30  50  CWD volume (m /ha)  100  200  300  CWD volume (m /ha)  3  3  Fig. 4.11. Bivariate plots of NN model predictions for red-backed voles in August at Sicamous Creek as coarse woody debris (CWD; X-axis) and shrub cover (individual lines) are varied from their minimum to maximum values, at: a) mid-range canopy cover; b) 8 decile canopy cover; and, c) maximum canopy cover. Y-axis value is predicted abundance compared to mean of all trap sites. th  Researchers will tend to examine only pairs of variables that are already known to, or are likely to, have interesting interactions, reducing the chance of unexpected interactions being revealed by NN models. This limitation increases with 3-way plots (120 combinations of 10 habitat variables). The ability of C A R T models to identify prominent contingent relationships could be used to suggest interactions to explore in NN models. For example, the 3-way  96  interaction explored in Fig. 4.11a-c was suggested by the upper branch of the C A R T tree for red-backed voles (Fig. 4.6). An important concern with heuristic explorations of NN models, as well as C A R T models, is that while the validity of the model overall may be substantiated by good predictive success, there is no reason to believe that all of the complex relationships embodied in these models are correct. James and McCulloch (1990) express similar concerns about interpretation of causation of individual variables in multivariate models. Thus, particular relationships found while exploring complex models must be treated as hypotheses to be tested prior to use, even if the overall model performs well.  Summary and Recommendations The non-linear and contingent relationships that NN and C A R T techniques can represent do exist in ecological systems. However, the practical question in evaluating the utility of these techniques for habitat modelling is whether they can reliably identify these complex relationships from typical data sets. The studies examined here are like many field studies designed to produce empirical habitat models, in that they have moderate sample sizes, a moderate to very large component of measurement error in the dependent variable, and logistically cannot cover all possible combinations of the full ranges of the habitat variables, especially when these covary. Tests of the predictive ability of models generated by C A R T and NN suggested that they do not perform any better than simple linear additive models with these types of data sets. Alternative modelling techniques are thus not likely to provide a panacea to the difficulties of developing predictive habitat models with field data. Neural networks, which tended to have the same predictive power as linear additive models in these tests, require considerably more analytical effort. Cross-validation is required to identify the inevitable onset of overfitting, and with spatial autocorrelation, a substantial fraction of the data set needs to be used for this purpose. This process reduces the sample size available for training, and introduces sampling variability into the resulting model, requiring 97  multiple runs on different random subsets of the data. NN models are also difficult to communicate, and additional analysis is required for even a partial understanding of their behaviour. Tu (1996) similarly concluded that logistic regression and NN models in clinical medicine had similar predictive ability, with NN models offering more flexibility, but great communication challenges. C A R T models, on the other hand, are easily implemented with existing software, and fairly readily interpreted and understood, but in these tests they had lower predictive abilities than linear additive models. Despite their shortcomings, NN and C A R T methods can both be useful tools in habitat modelling. As generators of predictive models, NN are likely to excel when data sets are substantially larger and have less measurement error than those used here. Reducing measurement error in the small mammal studies would require much more intensive sampling. Studies that sampled across a very wide range of habitat conditions may also benefit more from the ability of NN analyses to find the non-linear relationships expected under these circumstances. With data sets comparable to the ones used here, the primary benefits of NN modelling will probably be heuristic, rather than the direct production of more predictive models. The potential of NN to identify non-linear relationships, and, using bivariate diagrams, contingent interactions of variables, could be critical in improving habitat models. These complex relationships, expected in ecological systems but not captured by standard linear models, could be a prime reason for the predictive failure of many linear habitat models. C A R T models can complement explorations of NN models by identifying dominant contingent relationships, particularly those not expected by the researcher. These heuristic benefits alone, with their potential for guiding further studies to better habitat models in the future, are worth the additional effort of using these analysis techniques in habitat modelling. However, the better fit of these more complex models should not be taken as an indication of better predictive abilities, unless this has been demonstrated with tests from independent sites. Even in models  98  that do have independent predictive power, particular relationships identified in heuristic explorations should be considered hypotheses until these too have been tested independently.  99  Chapter 5. Harvesting effects and habitat models for shrews in a high-elevation forest Chapter Summary Effects of harvesting high-elevation forest on the shrews  Sorex cinereus and S.  monticolus and on southern red-backed voles (Clethrionomys gappen) were measured at a large-scale, replicated experimental site at Sicamous Creek, B.C. Treatments included 10-ha clearcuts with surrounding 20-ha leave strips, arrays of 1-ha or 0.1-ha patch cuts with leave strips, individual-tree selection partial cuts, and uncut controls. Finer-scale "harvest types" (clearcut, edge, uncut leave strips and contiguous uncut forest) were also compared. Abundance indices were derived from 3 years of post-harvest pitfall sampling in spring and August. Treatment and harvest type results are presented as likelihood functions, facilitating evaluation of various effect sizes and, through Bayes' theorem, combination of the Sicamous Creek results with prior probabilities derived from the literature. Abundance of S.  cinereus  declined 3 9 % after harvest in clearcuts but increased slightly in partial cuts, while S.  monticolus increased marginally in both harvest types. Immature red-backed voles declined 5 7 % (females) or 2 6 % (males) in clearcuts, with numbers decreasing with time since harvest. Abundances in edge sites were similar to uncut forest for S.  cinereus, were similar to clearcuts  for red-backed voles, and were greater than either adjacent type for S. arrays of 0.1-ha patch cuts had more positive effects on S.  monticolus. Overall,  cinereus and red-backed voles than  expected from the responses to the individual harvest types, probably reflecting better incidental protection of shrubs in the small openings due to harvesting logistics. Habitat models relating species' abundances to 10 habitat elements measured at each trap site were developed in a previous comparison of step-wise regression, C A R T and neural network modelling techniques and are presented with interpretation here. Predictive abilities of models for the shrews were poor when tested with data from an independent site. Models for red-backed voles had better predictive abilities. Models for both shrew species in spring included weak positive associations with cover provided by shrubs, herb layers, or deeper forest floor litter. A few non-linear relationships or interactions of habitat variables were suggested for future examination. Models for shrews in August showed few, if any, relationships with habitat variables. Models for red-backed voles showed positive and interacting relationships with canopy, shrub cover, and coarse woody debris. The treatment effects and habitat models suggest that harvesting itself is of less concern for management of these species in the short term than direct or indirect effects of forestry operations on groundlevel habitat features.  100  Introduction Maintaining shrews in managed temperate forests is desirable because shrews are a component of biological diversity and play important roles in forest ecosystems. Shrews are prey for avian and mammalian predators, and may be particularly important to these animals when their primary prey species are at cyclic or irregular low densities (Korpimaki and Norrdahl 1989). A s active year-round insectivores, shrews consume many forest pest insects, (e. g., larch sawfly, Buckner 1966; pine sawfly, Hanski 1987), and may help limit damage caused by these insects. Shrews also consume seeds of coniferous trees, potentially limiting natural regeneration when population densities are high (Tevis 1956). Because of these ecological roles, forest management would ideally maintain shrew species in all areas at abundances that are neither extremely reduced nor extremely elevated from natural levels. Our ability to forecast effects of forest management on shrews is limited by a lack of directly applicable information. Most intensive studies of shrews have focussed on population dynamics (Getz 1989, Sheftel 1989, Henttonen et al. 1989, Dokuchaev 1989) or community composition (Dickman 1988, Kirkland 1991, Fox and Kirkland 1992) in unmanaged or nonforest environments, or on comparisons of different ages or types of unmanaged forests (Brown 1967, Gilbert and Allwine 1991, West 1991). Few studies have directly measured effects of harvesting on shrews, and those that have done so report wide variation in the response. For example, 8 studies reviewed by Kirkland (1990) reported responses of shrew  v abundance to recent clearcutting of coniferous forests ranging from an increase of 3 4 5 % to a decrease of 5 3 % in clearcuts compared to uncut forest. It is unclear whether the variability in response is predictably related to forest type, or is due to the high inherent variability of small mammal populations (e. g., Sheftel 1989, Getz 1989, Marcstrom et al. 1990) combined with limitations in the designs of some of the studies (e. g., lack of replication, or single-year sampling).  Effects of harvest systems other than clearcuts have received even less attention,  with similar variability in response (e. g., Martell 1983, Monthey and Soutiere 1985, Von Trebra etal. 1998). 101  In addition to sampling error expected with highly variable populations and betweensite differences typical of natural systems, variable responses of shrews to harvest systems are also expected because of the considerable differences in habitat conditions possible within one harvest system. Harvest systems are usually defined by their effect on trees and canopy cover, but a given system can have widely varying effects on forest features more directly relevant to small mammals, such as forest floor structure, herb-layer and shrub cover, and coarse woody debris (Carey and Johnson 1995). Models relating abundance of shrews to particular microhabitat features that are affected by forestry operations are therefore an important complement to direct comparisons of treatments (Carey and Johnson 1995). Many studies have attempted to generate habitat models for shrews by relating abundances at trap sites to habitat variables (e. g., Terry 1981, Gunther et al. 1983, Adler 1985, Yahner 1986, Taylor et al. 1988, Raphael 1988, Gore 1988, Vickery et al. 1989, Morrison and Anthony 1989, Belketal. 1990, Corn and Bury 1991, Gilbert and Allwine 1991, West 1991, Ford etal. 1997). The main generality that can be derived from these studies is that shrews show clear responses to few, if any, measured habitat variables. The lack of significant habitat relationships may reflect a true indifference of shrews to habitat variables (at least those typically measured by field researchers). Alternatively, or additionally, weak habitat models may reflect difficulties in model development for small mammal data, which can have large measurement error in the independent variable (e. g., Chapter 3), and embody complex, nonlinear relationships not well represented by linear additive models (Chapter 4). Relationships that have been found with habitat variables in particular studies generally indicate positive responses of shrews to coarse woody debris (CWD) (Terry 1981, Gore 1988, Carey and Johnson 1995), ground-level plant cover (Terry 1981, Yahner 1986, Gore 1988, Morrison and Anthony 1989, Gilbert and Allwine 1991, Corn and Bury 1991, Carey and Johnson 1995) and forest floor litter (Terry 1981, Gore 1988). Relationships found in particular data sets have rarely been tested with independent data, or re-examined in other studies, in part because the same habitat variables are rarely measured in more than one study (Bunnell 102  and Huggard 1999). Thus, although there is evidence that shrews respond to habitat features affected by forest harvesting and silvicultural activities, quantitative models tested for generality are not available to predict the effects of specific management options. This study was designed to measure directly the effects of different forest harvesting practices on shrews in a high-elevation forest, and to develop relationships between shrews and specific micro-habitat elements. Additional information is presented on immature redbacked voles, which were sampled by the same traps. Previous analyses of the small mammal data partitioned observed variation in species' abundances into components due to relationships with habitat elements and types, spatial trends, undetermined sources and measurement error (Chapter 3), and compared the utility of linear additive, classification and regression tree (CART; Breiman et al. 1984) and neural network modelling techniques (Rumelhart et al. 1986) for developing habitat-element models (Chapter 4). This chapter summarizes the ecological information on harvest effects and habitat relationships of shrews and immature red-backed voles from the study, combines this with information from other studies in the literature, and outlines implications for the management of high-elevation forests.  Methods  Study area The Sicamous Creek (SC) site is described in Chapter 1. In addition to the overall treatments, the harvesting at S C is a source of variation in habitat elements, and a source of 5 distinct smaller-scale "harvest types": .  contiguous uncut forest (in control treatments),  .  uncut leave strip (in the 0.1-ha patch cut arrays (PCA), 1-ha P C A and 10-ha clearcut (CC) treatments),  .  clearcut (in a 0.1-ha, 1-ha or 10-ha opening),  .  edge (within 5 m of a clearcut-uncut edge), and  .  partially-cut forest (in the individual tree selection (ITS) treatment). 103  The edge distance of 5m was used because the trap circle itself covered approximately this distance. A second study, at East Barriere Lake (EBL), was used to test habitat models from SC. E B L is a retrospective study site located 75 km northeast of Kamloops B.C. (51°14' N 119° 44'W) composed of high elevation E S S F forest and lower-elevation Interior cedar-hemlock forest (ICH, Lloyd et al. 1990). Three study units (stands or cutblocks) were chosen in each forest type in uncut mature or old-growth forest, 3 units in partially-cut stands, and 3 units in 15-25 year old clearcuts. In ICH forest, an additional 3 study units were used in more recent clearcuts (3-6 years old). The recent ICH clearcuts were at a similar, herb-dominated successional stage to the older, but slower-growing E S S F clearcuts. Sampling units at E B L were chosen opportunistically from suitable road-accessible sites.  Sampling small mammals Shrews and small rodents were collected using small pitfall traps, originally deployed at the sites to sample ground-dwelling invertebrates. Traps were 400-ml plastic cups with a 9.5 cm opening diameter, set flush with the ground surface and protected from rain and debris by a cover board held 15 cm above the ground on stakes. Traps were set by adding 100 ml of propylene glycol, a non-toxic, non-volatile liquid. Five pitfall traps were arranged in a circle 8 m in diameter. An animal caught in one trap was clearly no longer available to be caught in an adjacent trap within a circle. Because of this non-independence of individual traps, the trap circle is considered to be the basic sample unit. Trap circles were arranged in sets of 3 circles in a row, with 50-75 m separating adjacent circles. This separation is greater than the typical home range diameter of shrews (Hawes 1977). One set of 3 trap circles was initially used in each study unit at SC, with a second set of 3 added later. Twenty-one additional trap circles at S C were used to sample across the edges of the patch cuts and clearcuts, and to improve representation of the different harvest types (openings, edges and uncut leave strips) in the  104  non-uniform treatments. One set of 3 circles was used throughout the study in each study unit at E B L Traps at both sites were set for 28 days from early August to early September, from 1992 to 1994 (pre-harvest) and 1995 to 1997 (post-harvest) at S C  and from 1992 to 1996 at  EBL. Traps were also set for 28 days shortly after snow melt ("spring"), which occurred from late June at S C and May through early June at EBL. Spring trapping was conducted from 1996 to 1997 at S C and from 1994 to 1997 at EBL. In the 1994 spring session at EBL, only the middle circle of each set of 3 circles was trapped. All circles were sampled in all other trapping sessions.  Specimens were collected after 2 weeks and at the end of the session.  All mammals collected were identified to species based on skull characteristics. Animals were weighed and sexed, and reproductive state (immature or mature) was determined based on development of testes in males or evidence of pregnancy or lactation in females.  Habitat measurements Habitat characteristics were recorded in circular plots of 5.65 m-radius (0.01 ha) centred on each trap circle. Percent cover was estimated for: tree canopy, woody-stemmed shrubs >15 cm tall, herbs (including forbs, grasses and woody stemmed plants <15 cm tall), duff and moss. Typical duff and moss depths were recorded. Duff included unconsolidated fine organic debris, primarily conifer needles, fine branches, leaves of deciduous shrubs, and dead herb and grasses. The number of live trees with diameter at breast height (DBH) > 7.5 cm, and total number of all stems (including dead trees and stumps) with DBH or stump diameter >_7.5 cm were recorded. The 35.5-m perimeter of the circular plot was used as an intercept transect to estimate coarse woody debris volumes (following van Wagner 1968) for all pieces of wood with diameter >_7.5 cm at the point of interception. Other habitat variables were measured in the plots, but are not used in the analysis because of high covariance with included variables. Habitat variables were examined graphically and  log(x+1)-transformed 105  prior to analysis if this improved normality. The logarithmic transformation was more effective at normalizing the positively-skewed percent cover variables than an arcsine square-root transformation. Habitat plots at S C were conducted in August 1995 (first year post-treatment) and August 1997 (third year post-treatment). The main successional changes observed in openings were an increase in herb-layer cover and a decrease in moss cover. Because these changes were small, and shrews did not show obvious successional trends through the 3 postharvest years, 1995 and 1997 habitat measurements were averaged to provide a single mean post-harvest value for each trap circle.  Catch index, and combining age and maturity classes Analyses were conducted separately for the spring and August sessions at the 2 sites because different population processes might be occurring at the different times (e. g., possible dispersal of immatures in August), shrub and herb-layer cover are lower in spring prior to leaf-out, and monthly changes in small mammal distributions have been reported elsewhere (Belk et al. 1988). Number of captures of each study group for each circle and year was converted to catch per 1000 trap-nights (CPUE) to compensate for the occasional trap destroyed in the field, and transformed by log(x+1) (Carey and Johnson 1995). This transformation increased the normality of the catch data, and allowed the abundance index to represent relative, multiplicative differences among trap sites, independent of abundance, rather than absolute differences (e. g., traps that had captures 2 times the mean value would have the same abundance index, regardless of the absolute abundance of the species). Depending on season and site, 2 to 5 years of abundance data were available. Because the primary interest was the relationship between small mammals and harvest treatment or habitat attributes at the trap circles, rather than in the yearly variability in abundance, the years were combined for each circle. A residual catch index was calculated for each year after subtracting the mean catch index for that year. These residuals were then 106  averaged for the 2 to 5 years of sampling to obtain the "average residual catch index" for each trap circle (Appendix 5.1).  The log-transformation of the catch index allows these values to be  interpreted as the average factor by which the catch at a particular circle departed from the yearly mean. For example, a trap circle with average residual catch index of 0.2 for a particular species caught 1 0 ° or 1.6 times the average number of the species at that season. 2  (This back-transformation is somewhat approximate due the effect of adding 1 prior to the logarithmic transformation). Using the residuals of the log-transformed values after the yearly mean is subtracted has the advantage of weighting each year equally, rather than allowing differences between traps to be dominated by the years in which the species was most abundant overall. Differences between treatments may be less pronounced in years of greater abundance (e. g., as predicted by the Ideal Free Distribution; Fretwell and Lucas 1970, Rosenzweig and Abramsky 1985). Preliminary analyses were used within each of the species to determine whether the 2 sexes and 2 maturity classes responded differently to the habitat types or to the habitat elements. For each species, the abundance index was calculated for mature and immature individuals of the 2 sexes. Different responses to treatment (or harvest type) by sex or maturity class were indicated by significant interaction terms between treatment (or harvest type) and sex, maturity class or the sex-maturity class interaction, in a complete 3-factor A N O V A . Multivariate analysis of covariance (Zar 1984) was used to test whether sex, maturity class or their interaction term showed significantly different relationships with the 10 habitat variables. Sexes or maturity classes of a species that showed different responses to treatments, harvest types or habitat variables were subsequently analyzed separately, to avoid obscuring significant relationships with inter-class differences. Sexes or maturity classes that did not show significantly different responses were pooled to reduce the variability expected from relatively low numbers of captures in each class.  107  Treatment and harvest type comparisons The basic question in these comparisons was "What is the effect of a particular harvest type or treatment on abundance of the small mammals?" Statistical tests of "null" hypotheses, such as no difference between controls and a treatment, were not of interest, because there was no reason to think that the effect of any treatment would be exactly 0, rather than some arbitrarily small or large positive or negative value (McBride et al. 1993), and no general theory to be refuted if the magnitude of the effect was significantly different from 0. Therefore, instead of testing "null" hypotheses and subsequent power analyses for various arbitrary alternative hypotheses, the data were simply summarized directly, using likelihood functions (Edwards 1972). In continuous distributions, likelihood functions give the relative likelihood of one value compared to another. Alternate values, which could include a value representing "no difference", are typically compared to the most likely value (e. g., "value x is half as likely as the most likely value y", or "a difference of x is 10 times as likely as no difference"). This corresponds to the way most people interpret information, and would like to interpret 9 5 % confidence intervals (Berger and Barry 1988), facilitating use of study results (Ellison 1996). Likelihood functions can also be used, through Bayes' theorem, to add the evidence of new data to prior probabilities generated by subjective beliefs, results of other studies, or additional data sets. All comparisons used an effect size expressed as the ratio of the species' abundance in a particular treatment or harvest type to the abundance in contiguous uncut forest in the control treatment. An effect size of 0.5 therefore meant half the abundance in the comparison treatment or harvest type compared to uncut control; an effect size of 3 indicated triple the abundance compared to the control. Calculations were conducted using the differences between the logarithmic abundance index values, and then back-transformed to ratios to ease interpretation of the results. This back-transformed ratio neglects the effect of the constant (1) added to the C P U E . The effect size is therefore a conservative estimate, with the ratio somewhat closer to 1 (no difference from uncut), mainly when abundances are low. 108  A simple model based on the normal distribution was used for the likelihood function of the difference between the log-transformed C P U E values, because this is the expected distribution with the randomized design at SC. The likelihood (L) of a hypothesized mean (u.) of a normal distribution, when the mean (x) and standard deviation (s) are estimated from n data points, is given by Edwards (1972) as: L = exp{(-n/2).ln[1+(x-|a.) /s ]}. When differences 2  2  between 2 treatments are used, the mean difference is the difference between the means; the variance of the difference is the sum of the variances of each treatment. Means of the 3 elevational blocks used in the randomized block design at S C were first subtracted from the values for each study unit to analyse treatment effects without any effects of elevation.  Prior probabilities from the literature Prior probability distributions for effect sizes for  Sorex cinereus and S. monticolus could  be derived for some of the comparisons from previous published studies. Studies were used if they: 1) compared uncut coniferous-dominated forest to one of the other treatments or harvest types studied at S C ; 2) presented abundance indices for S.  monticolus, S. cinereus or S.  trowbhdgii (see below), or for shrews in general with some indication that one of these species was dominant in the sample; and, 3) had replication of at least one of the treatments and provided some indication of sampling error. Where several shrew studies have occurred in the Pacific Northwest, S.  trowbhdgii replaces S. cinereus, and was considered an "ecological  substitute" for the latter species. When data for individual replicates were presented in a publication, they were transformed with log(x+1) and analyzed in exactly the same way as the S C data, including taking the residuals after the yearly mean if data for more than one year were presented. When only treatment means and standard deviations were presented, or statistics from which these could be derived, "original data values" were simulated from the normal distribution with these parameters, then transformed and analyzed as above. The simulations were repeated until the mean and standard deviation of the difference (harvested treatment minus uncut) of 109  log-transformed simulated values stabilized (fluctuations less than +/-1%). The simulations therefore provided estimates of the mean effect size and its standard deviation, which were precise to within 1%. Variance reported in studies of S. probability distribution for S.  trowbridgii, used to form a prior  cinereus, was doubled as a subjective estimate of additional  uncertainty due to inter-specific differences. Two of the studies used (Sullivan and Sullivan 1982, Gunther et al. 1983) had replicated cutblocks, but only a single uncut unit. In these cases, the unknown variance for uncut forests was taken to be the same as that reported for the cutblock units. Likelihood distributions were produced based on the mean effect size and variance for each study. A combined likelihood function was obtained as the product of all likelihood functions available for a particular comparison and species. This combined likelihood function was converted to a probability distribution by scaling the area under the curve to 1. In a Bayesian context, this conversion process is equivalent to using a non-informative, or "neutral" prior, which is reasonable when no subjective beliefs of effect sizes existed prior to consulting the literature (Kass and Raftery 1995). The probability distribution derived in this way from the literature was used as a prior probability distribution, multiplied by the appropriate likelihood function from the S C data to form a posterior probability distribution of the effect size.  Relationships between small mammals and habitat elements Habitat models for the shrews and immature red-backed voles at S C and E B L were previously developed using step-wise linear regression, classification and regression trees (CART) and neural network (NN) techniques (Chapter 4). Seasons were analyzed separately, but sexes and maturity classes were combined to allow comparison between sites, and because there was no evidence of maturity or sex effects in habitat relationships (see Results). Models based on S C data were tested against E B L results. Unlike measurements of treatment or harvest type effects, the habitat models used each trap circle as an independent sample. In this case, spatial autocorrelation in animal abundances and habitat measurements between 110  nearby traps can artificially inflate the strength of apparent habitat relationships (Clifford et al. 1989). To compensate, an effective sample size that accounted for spatial non-independent was calculated for each model (following Clifford et al. 1989) and used in statistical tests of the models. Techniques to interpret neural network models are outlined in Chapter 4. Univariate plots of small abundance versus each habitat variable were used here, followed by bivariate plots to explore interactions of habitat variables that had strong linear or curvilinear effects in the bivariate plots. Variance partitioning (Chapter 3) showed that the source of a substantial component of the variation in abundance of shrews at S C remained undetermined after accounting for variation due to the habitat models and expected measurement error. Some of this variation showed a spatial trend, suggesting that an important habitat variable with a spatial trend at the S C site had not been measured. Ecological site series, a classification based on site productivity and moisture, showed a spatial trend similar to the trend in abundance of shrews (Lloyd and Inselberg 1997). The additional contribution of site series to explaining observed variation in abundance of shrews was thus evaluated with analysis of variance, using residual abundance of shrews indices after the appropriate harvest type means and expected values from the habitat-element model had been subtracted.  Results Summary of small mammal collection A total of 2,311 small mammals were collected with 78,834 trap-nights of effort in the 3 years of post-treatment sampling, an average of 29.3 mammals per 1000 trap-nights (Table 5.1).  Sorex cinereus and S. monticolus were numerically dominant in both spring and August  sessions, forming 43.2% and 38.7% of the total sample. Red-backed voles formed 4.7% of the sample in spring and 13.0% in August. S. long-tailed voles  vagrans, heather voles (Phenacomys intermedius),  (Microtus longicaudus) and northern bog lemmings (Synaptomys borealis)  each comprised less than 4 % of the sample, and were not abundant enough for further 111  Table 5.1. Total captures by species, sex and maturity class. Site SC  Season Spring  August  Immature Species Female Male Sorex cinereus 110 102 S. monticolus 125 150 Red-backed vole 22 19 S. vagrans 8 9 Heather vole 10 11 Long-tailed vole 5 1 Bog-lemming 1 0 S. cinereus S. monticolus Red-backed vole S. vagrans Heather vole Long-tailed vole Bog-lemming  249 201 104 13 30 13 3  252 245 83 15 33 12 3  Mature Female Male 34 143 23 87 0 0 2 8 0 0 0 0 0 0 27 11 0 7 0 0 1  Total 389 385 41 27 21 6 1  81 53 0 5 0 0 0  609 510 187 40 63 25 7  analysis. Among the shrews, immature animals dominated the samples, especially in August. Sex ratios of immatures were even in S. cinereus, while males were slightly more common among immature S. monticolus. Four times as many mature male shrews were collected as mature females. All rodents collected except one were immature, with approximately equal sex ratios. Catch per unit effort of the 2 common shrew species was fairly constant during August in the 3 post-treatment years (S. cinereus range, 12.5 - 17.5; S. monticolus, 10.7 - 16.1 per 1000 trap-nights) compared to the 3 pre-treatment years (S. cinereus range, 12.3 - 39.8; S. monticolus, 2.7 - 19.8 per 1000 trap-nights). There was no evidence of different trends in abundance in harvested and uncut sites in the 3 years following treatment. Catch per unit effort of red-backed voles did show an obvious decreasing trend in clearcut sites following harvesting (1995, 5.2; 1996, 2.7; 1997, 0.6 per 1000 trap-nights), while uncut controls did not decline (1995, 8.5; 1996, 5.3; 1997, 8.5 per 1000 trap-nights). Multivariate analysis of covariance showed no differences in the multiple regression relationship with habitat elements between sexes of the 3 common species or maturity classes of the shrews, in either season (P>0.09 for all effects). Sexes and maturity classes were 112  therefore pooled and habitat-element models developed for each species as a whole. A N O V A tests of treatment and harvest type effects showed no differences between maturity classes or sexes of the 2 shrew species at either season (P>0.25 for all effects). For red-backed voles, the sexes showed significantly different responses to harvest types in August (P=0.03). Harvest type and treatment comparisons were therefore conducted separately for male and female red-backed voles, while maturity classes and sexes were pooled for the 2 shrew species.  Treatment and harvest type effects Likelihood functions of the difference of the log-abundance index between uncut, contiguous forest (controls) and other treatments or other harvest types were generated separately for each season for S. cinereus and S. monticolus. Likelihood functions were only generated for August for the 2 sexes of red-backed voles, due to low capture rates in spring. When curves for the shrews in spring and August were similar, they were combined into one distribution by multiplying the 2 seasonal distributions (Edwards 1972). A s a rule-of-thumb, the seasonal curves were combined if the value that was most likely on the spring curve was at least one-third as likely on the August curve as the most likely August value (see Fig. 5.1), and vice versa. Kass and Raftery (1995) suggest that a likelihood ratio of less than 3:1 presents no evidence of a difference. Combining the likelihoods when the distributions are similar produces a more informative (precise) curve, and simplifies presentation of results. Most spring and August distributions were very similar and were combined. Exceptions were S. monticolus in ITS, S. cinereus in 0.1-ha patch-cut and S. cinereus in 1-ha patch-cut arrays. Compared to contiguous uncut sites, clearcut sites showed substantial reductions in female red-backed voles and in S. cinereus, moderate reduction of male red-backed voles and a slight increase in S. monticolus (Fig. 5.2). Declines of female and male red-backed voles in edge traps were similar to those in clearcut traps, while S. cinereus showed very little decline in edge traps, and S. monticolus increased considerably (Fig. 5.2). Thus, abundances of red113  Fig. 5.1. Examples in which spring and August likelihood functions (for the abundance in 0.1-ha PCA treatments compared to uncut controls) a) were not combined, or b) were combined, based on the 1/3 likelihood rule. In a), the maximum likelihood value for spring (0.9) is much less than 1/3 as likely on the August curve than the most likely value for August (1.35); in b), the most likely value in spring is almost as likely on the August curve as the most likely August value. [NOTE: Likelihood curves are each scaled to an area of 1 (i. e., a probability density function), to allow comparison of the shapes of different curves, but likelihood values are only compared within a curve, not between different curves (Edwards 1972).] a.  5 r 4 -  de  mc  3.0  Clearcut  . L e a v e strip  2.5  Leave strip  Clearcut  2.0  3  >. abil  1.5 r 2 -  XI o CL  1 •  1.0 0.5  0 -  r  0.0 2.0  2.5  0.5  2.0  2.5  0.5  C 7 r  <Clearcut  6 • >,  Jo 5 • c 0) T> 4 >N 3 -  ro XI g 2 CL 1 •  0 0.5  1.0  1.5  Effect s i z e (harvest type/contiguous uncut)  1.0  1.5  2.0  Effect s i z e (harvest t y p e / c o n t i g u o u s  2.5 uncut)  Fig. 5.2. Likelihood functions (each scaled to an area of 1 - see Fig. 5.1) for the effects of 3 harvest types compared to contiguous uncut forest: a) S. cinereus; b) S. monticolus; c) redbacked vole females; and, d) red-backed vole males. Spring and August curves are combined. Points on each curve indicate maximum likelihood value and 1/10 likelihood limits. 114  backed voles in edge sites were like abundances in clearcut sites, abundances of S. cinereus were like those in uncut sites, and abundances of S. monticolus in edge sites were greater than in clearcuts or uncut sites. Abundances of the different groups in uncut leave strips differed little from abundances in contiguous uncut forest, with female red-backed voles showing a slight decline and S. monticolus showing a slight increase (Fig. 5.2). ITS sites (and thus the treatment overall) showed slight increases in S. cinereus and S. monticolus and decreases of female red-backed voles compared to uncut controls, but in all cases no difference from uncut was also highly likely (Fig. 5.3). Male red-backed voles declined more substantially in ITS (Fig. 5.3).  0.5  1.0  1.5  2.0  Effect size (treatment/control)  2.5  0.5  1.0  1.5  2.0  2.5  Effect size (treatment/control)  Fig. 5.3. Likelihood functions (each scaled to an area of 1 - see Fig. 5.1) for the effects of overall treatments compared to uncut control treatments: a) S. cinereus; b) S. monticolus; c) red-backed vole females; and, d) red-backed vole males. Spring and August curves are combined, except where shown separately. ITS = individual-tree selection partial cut, PCA = patch-cut array. Points on each curve indicate maximum likelihood value and 1/10 likelihood limits.  115  Likelihood distributions for 1-ha patch cut array and 10-ha C C treatments overall were very similar within each study group and were combined, while distributions for the 0.1-ha patch-cut treatment were substantially different. Abundance of S. cinereus in the treatments with larger openings declined moderately compared to uncut controls, while abundances in 0.1-ha patch-cut treatments increased (Fig. 5.3a). S. monticolus increased substantially in the 1-ha patch-cut and 10-ha clearcut treatments, but not in the 0.1-ha patch-cut arrays (Fig. 5.3b). Female red-backed voles declined more in treatments with larger openings than in the 0.1-ha patch cut arrays, although variability was high in the latter treatment (Fig. 5.3c). Male redbacked voles showed no difference between uncut controls and 0.1-ha patch-cut treatments, and a slight decline in 1-ha patch-cut and 10-ha clearcut treatments (Fig. 5.3d). Quantitative prior probabilities could be derived from studies in the literature for 3 of the comparisons for shrews - S. cinereus in clearcuts, S. monticolus in clearcuts and S. cinereus in partial cuts. Six studies reported relative abundances of S. cinereus (or S. trowbhdgii) in clearcuts compared to uncut forest (Terry 1981, Sullivan and Sullivan 1982, Guntheret al. 1983, Martell 1983, Monthey and Soutiere 1985, Corn et al. 1988). Several other studies could not be used because they lacked any replication, did not report an estimate of sampling error, or caught very few (<10) shrews. Effect sizes for the 6 studies varied widely, from a reduction to 5 0 % of uncut levels through an increase to over 2 0 0 % of uncut levels. The combined literature distribution was dominated by the positive effect of clearcutting in Martell (1983), because of the good replication in this study (Fig. 5.4a). The posterior distribution produced from the combined literature probability distribution and the S C likelihood distribution somewhat reduced the negative effect of clearcutting expected from the S C data alone. Notably, the possibility of clearcuts having no effect or even a positive effect became greater when prior expectations from the literature were taken into account. Three studies of the effects of clearcutting on S. monticolus also reported a range of effects of clearcutting, from a reduction in population density to 3 7 % of densities in uncut forest through an increase to 2 1 5 % (Terry 1981, Gunther et al. 1983, Corn et al. 1988). Few 116  c re re o o *•*-" TJ CO  re a) to  sz re  OJ  75 o = Tg  .—. o £ }  10  to" c  r  II  -  S ?'"S . E l  3i  « ™ C re _  « TJ 3 +- * • to TJ 3 tU O) = C  2  -re3 2 o  «L II  - t u§ £  to  c re I, o TJ ^2  to o tu *3 CL  "•g  o) re  —. L_ oo  a.  w= cn TJ 2 O N . W  5 Sto« 2 to re CM  CN  O oi  CO 1 1 O CN  in  o  lined litera ture  CN  °  _  0 0  —  O )  re •_  TJ 3 = C OI|= c o re 3 > 2 o 0 CO II  re **  1  c TJ TJ XJ re tu 0 0 + J X. c TJ C 01 — a) re E 2 CD Q. — re re .Q co o = m W *m P £ W II  p  5  y f  £  53 £  in  £  LO o  re  m o  i s re *• re to o  .« tj (0 o  i\s  re j- o o >-  TJ S° ?  jc  tu  .  2J ^  1-  o 5  to XI Q. 3 E o— O o to E re o c  '  T  II  II  to  £  To  0 0  o>  to  ID  o  ~ tu 3 c o  lo-  5  s 1 co — to o  +S CD  E c re ^  « *  tu ,E C O TJ tU to  A}isuap AimqeqoJcj  A)|susp AiiiiqeqoJd  A)jsuap A)!|!qeqoJd  0J  c o re c OJ  tU £2 c C o  re 5  to <o Z  2 =  TJ  TJ E  = II tu  m c  o =  to c S . 2 o re CD T3 c -S! • 3 o « .2115 tl) r= c re — m  *= re re > (0 tu — •C 3 tu 2 to a)  •  o . •«  ' £I  o >. S . 2 re TJ t tU 3 o> iw ° 2 ~ 4-1 T- a ch re to iZ  s  replicates with high variability between them produced very flat likelihood distributions for 2 studies, with the third study therefore dominating the combined literature distribution (Fig. 5.4b). This prior probability distribution was itself very flat compared to the likelihood distribution from the more extensive S C data for S. monticolus. A s a result, the posterior probability distribution for clearcut effect size on monticolus at S C differed little from the distribution based only on the S C data themselves (Fig. 5.4b). Three studies reported the effects of various partial cutting systems on S. cinereus, with one moderately negative effect (Martell 1983), one moderately positive (Von Trebra et al. 1998), and one large increase in abundance (Monthey and Soutiere 1985). The latter was based on only 2 partial cut replicates with substantial variability, producing a wide likelihood distribution that had little effect on the combined prior probability distribution (Fig. 5.4c). The posterior distribution after combining S C data with the prior probabilities from the literature suggested a slightly greater positive effect on abundance of cinereus in partial cut treatments. More importantly, the similarity of the S C and literature distributions produced a posterior distribution that was more precise than either alone, indicating more strongly that neither substantial positive nor negative effects of partial cutting were likely for this species.  Habitat models The fit and predictive abilities of habitat models generated by step-wise regression, C A R T analysis and neural networks are discussed in Chapter 4 and summarized in Table 5.2. Models for shrews were generally weak (relatively poor fit to the original data and poor predictive ability when tested with the E B L data), particularly in August. In contrast, models for red-backed voles in August fit the original S C data better and had substantial predictive abilities with the E B L test data (Table 5.2). Models with very poor fit or no predictive ability are not discussed below.  118  Table 5.2. Fit and predictive ability of habitat models. Model Regression - all Regression - residual Regression - mature CART NN  1  Spring S. cinereus S. monticolus 0.188; 0.312 0.095; 0.124 0.129; <0 0.084; 0.023 0.120; 0.479 0.075; 0.259 0.117; 0.106  August S. cinereus S. monticolus 0.033; 0.443 0.013; 0.109 0.178; <0 0.168; 0.219 0.246; 0.240 -  RB vole 0.320; 0.468 0.208; 0.267 n/a 0.643; 0.546 0.256; 0.570  Note: Values in table are coefficient of determination (r ) for model fit to S C data (or proportional reduction in error for C A R T models); correlation coefficient (r) for model prediction versus observed at EBL. See Chapter 4 for details. "-" = model had negligible fit and predictive ability. 2  1  Regression model using residual values after harvest type means had been subtracted.  Habitat model details - Sorex cinereus The step-wise regression model for S. cinereus in spring included a positive relationship with the number of live trees and a negative relationship with the number of stems (including stumps and snags), a positive relationship with herb-layer cover and a statistically weak positive relationship with C W D (Table 5.3). The spring regression model based on residual abundances after harvest type means showed similar relationships, but was weaker and had no predictive ability at E B L (Table 5.3). The step-wise regression models for only mature S. cinereus in spring showed a similar positive relationship with the number of live trees but negative relationship with the overall number of stems, as well as weak positive relationships with duff depth and shrub cover (Table 5.3). The spring NN model showed dominant univariate relationships similar to the step-wise model, except that C W D was unimportant and some curvilinearity was suggested for the main relationships, with strongest effects at mid-range values (Fig. 5.5a). Most bivariate plots examined showed only additive relationships, except for some interaction between moss depth and live tree density (Fig. 5.5b), and between herb-layer cover and live tree density. Moss depth had a positive effect on predicted abundance of S. cinereus, but only at low densities of live trees, when predicted abundance is generally low (Fig. 5.5b). Herb-layer cover similarly had its largest effects at low tree densities. Herb-layer or moss cover may thus be a limited substitute for tree cover when the latter is at low levels. 119  O  CN  c o  co  CD  +—> CD  CN  o o  LO  o cn o o  co  o o  ^ —  o d o•  o CN o  LO CO CD  c CO CO C  CO CO TJCO o CM o CO  o X  d d d  CO  flj CD  1 *to 3  cu  l < or  CO  TO  O  CO  co o  CD O  > CO  o CO  S  LO  CO ^ c >^ o c: w ° CO 10 CD c  O o O d  2  CO CO — T  O d d  o>.2 CD CO i- co — CD  TO I- I  £ s  C  o 0  l_ 3  < o  CO  co O co P CO  CN CN  Sq  CD  CN LO  a-TO LO  p co b CD CD  CN  d^  o g , d v> £2C N LO s O o o CO  CO LO CO  TO c  co A  CO " 0  to <o a> £ o P d o  £ CD  •S  o c Q  CO T3  CO  o o  'co  ICO 0  cu •o o E c o '35  or o  CN  2! o> 2! cu  CO  O d  •<fr  00  CO CN  d  d  o  CN  CN CN CN  o  o o  1^  o o  O  CN CO  CO ^~  CN CN O  CN CO  CO  o o  CN CD CO  c:  TO  *- V c:  T—  ld  CD O  ° o| CD  a.  V  £ o-l  cu CO  Q. 0)  XI  re I-  •— m  CD O  CO  n  •  TO O  d  o'Oo  3  O  co  CO  'i  CD >  °;  o >  C 0 £ d CL Q w O i s a) co £ "<: a O O .> = O <H 3 O O _J _i < _J X Q oo> C  1  CO  o  TO "D . . CD O ~7  TO O TJ C  a.  Min  1  2  3  4  5  6  7  8  9  Max  Decile b.  Live trees (/0.01 ha) Fig. 5.5. Behaviour of neural network model for S. cinereus in spring: a) univariate plot of predicted abundance compared to mean for all sample sites as 6 variables are independently ranged from minimum to maximum values (4 variables not shown had curves the same as that for CWD volume); b) bivariate plot of predicted abundance as a function of live tree density at different values of moss depth (separate curves). In August, the very weak regression model for S. cinereus included only a slight positive relationship with canopy cover, which disappeared when residuals after harvest type were used (Table 5.3). The high predictive success of this simple model only reflected the stronger correlation between this species and canopy cover at the E B L site. The step-wise regression model for only mature S. cinereus in August was similar to the regression for mature animals in spring (Table 5.3), but failed to predict abundance of mature cinereus at  121  Table 5.4. Step-wise regression models for S. monticolus. Variable  All  Constant -0.539 (0.160) Herb% 0.006 (0.002) Duff% Log(Duff depth+1) 0.518(0.191)  Spring Residual  August Mature only  0  0.119(0.047) 0.108(0.045)  All  1  Mature only -0.254(0.084)  0.004 (0.001) 0.002 (0.001)  Note: Values are the coefficient for the variable (and its standard error). Partial regression significance of variables (excluding constant) indicated by font: P<0.01, 0.01<P<0.05, 0.05<P<0.15. No variables retained. 1  E B L in August. The other modelling techniques did not produce models with predictive ability for S. cinereus in August.  Habitat model details - Sorex monticolus The weak regression model for S. monticolus in spring suggested positive relationships of abundance with duff depth and herb-layer cover (Table 5.4). These relationships were also seen using residual values after harvest type (Table 5.4). The model for only mature S. monticolus in spring was very weak and not predictive at EBL. The NN model for S. monticolus in spring suggested a moderately strong negative response to the number of live trees, moderately positive responses to duff depth and number of stems, and strongly curvilinear relationships with herb-layer cover and duff cover (Fig. 5.6a). Most pairs of variables in bivariate plots showed additive relationships. However, an interaction was seen with number of live trees and herb-layer cover: more live trees always decreased the predicted abundance of S. monticolus except at the lowest levels of herb-layer cover, when few S. monticolus were always predicted (Fig. 5.6b). Moss cover and live trees showed a similar, but less pronounced, interaction (not shown). This species in spring therefore seems to prefer more open sites with at least some herb-layer and moss cover. C A R T was the only technique producing a model for S. monticolus in August that had any predictive ability. Low abundances were predicted with >85% duff cover. Higher abundances were predicted at lower duff covers, particularly if shrub cover was less than 40%. 122  a.  Herb-layer cover (%) Fig. 5.6. Behaviour of neural network models for S. monticolus: a) univariate plot of predicted abundance compared to mean for all sample sites in spring as each variable is ranged from its minimum to maximum value; b) bivariate plot of predicted abundance as a function of herb-layer cover across the range of live tree densities (separate curves). Variables not shown in univariate plot a) had nearly flat curves (i. e., no effect on predicted abundance). With the low predictive ability of all models for S. monticolus, these particular relationships are, at best, only possibilities to be examined in future studies.  Habitat model details - Red-backed voles The step-wise regression model for immature red-backed voles in August included a positive relationship with canopy cover accompanied by a negative relationship with the  123  density of live trees, implying highest predicted abundance in sites with a few large trees or trees with dense, broad canopies (Table 5.5). The regression also included positive relationships with C W D and shrub cover, and a weak positive relationship with moss cover.  Table 5.5. Step-wise regression models for red-backed voles. August Variable  AN  Constant  -1.176(0.250)  Log(Canopy%+1)  Live trees  Log(Shrub%+1) Moss% log(CWD vol+1)  0.235(0.089) -0.034(0.014) 0.271 (0.137) 0.002(0.001) 0.292(0.157)  Residual  0  0.144(0.071) -0.122 (0.045) 0.089(0.042) 0.069(0.041) 0.141 (0.065)  Note: Values are the coefficient for the variable (and its standard error). Partial regression significance of variables (excluding constant) indicated by font: P<0.01, 0.01<P<0.05, 0.05<P<0.15.  When residual abundances after harvest types were used, relationships were somewhat weaker, but remained the same in relative magnitude and statistical significance (Table 5.5). In the C A R T model, low abundances were predicted when shrub cover was <37.5%, except when moss cover was very high  (>90%; Chapter 4, Fig. 4.6). Lowest predicted  abundances occurred when shrub cover, moss cover and canopy cover were all low. The highest predicted abundances occurred at high shrub covers, moderately high C W D volumes, and moderate to high canopy cover. The NN model for red-backed voles showed the same positive response of predicted abundance to shrub cover, canopy cover and moss depth, particularly at the highest values of each (Chapter 4, Fig. 4.8). The NN model also suggested a complex relationship between abundances of red-backed voles and CWD, shrub cover and canopy cover (Chapter 4, Fig. 4.11a-c). Predicted red-backed vole numbers were always low at low to mid-range values of shrub cover and canopy cover, and always high at high shrub and canopy levels, unless C W D was very low. At intermediate levels of shrub and canopy cover, red-backed vole abundance were predicted to peak at moderate C W D volumes (Fig. 4.11b). Other habitat elements examined in bivariate plots did not appear to have complex interactions. 124  Site series Ecological site series explained a significant component of the variation in abundances remaining after harvest types and the step-wise regression habitat models only for S. cinereus in August (11.8% of residual variance, F=7.25, d.f.=2,108, P=0.001). Abundance of S. cinereus in August in the xeric to submesic site series (02 and 04) was 49.7% the abundance in the mesic to subhygric site series. For the other groups in August and both shrew species in spring, site series only explained 0.2% to 3.5% of residual variation (P>0.14 in all cases).  Discussion I. Field and analysis methods Pitfall captures as an index of habitat quality Most empirical research to measure the effects of forest harvesting or to develop habitat models relies on density of the study species as an index of habitat quality, despite well-recognized perils of doing so. With movements between habitat types, density may not indicate net productivity in a particular habitat (Pulliam and Danielson 1991), and may even be negatively correlated if social mechanisms force subordinate animals into poor quality habitats (Van Home 1983). This study partly avoided the concerns raised by Van Home (1983) by comparing abundances of immature and mature animals as a preliminary step. The lack of significant difference for the 2 classes in either treatment response or regression coefficients with habitat measurements suggests that the difference between maturity classes is relatively small compared to differences in the species' abundance overall between trap circles or treatments. Additionally, the short lifespan of shrews allows relatively little time for territorial displacement. In spring sessions, immatures are small, presumably recently born, and unlikely to have dispersed far from their natal site. In August, the decline in abundance of mature animals would reduce competition for territorial space in good habitats. October sampling at E B L (not possible at S C due to earlier snowfall) caught few mature animals, and winter 125  sampling at both sites caught only animals of the younger generation. Thus, density-based indices should always be viewed cautiously, but the social displacement that may lead to misleading densities is unlikely to operate strongly in shrews. Results reported here for redbacked voles are exclusively for juveniles and may not reflect habitat use by adults. The results for juvenile red-backed voles are meant to complement an intensive live-trapping study of adult voles at the Sicamous Creek site (W. Klenner, unpub. data). As an index of abundance, catches by pitfall traps present additional concerns. The number of animals caught at a particular time and place is a function both of the species' density and the amount of movement in the area. Dispersing animals may be particularly prone to pitfall traps, simply because they are moving more, and may be a poor indicator of actual habitat quality. This concern is lessened by the fact that all shrews are often active, because of their high metabolic demands and exploratory mode of foraging (Saarikko 1989, McNab 1991). The red-backed voles caught in pitfall traps are almost all very small, smaller than the smallest animals caught in live-traps (Klenner 1997), and presumably have not moved far from their natal area (Bondrup-Nielsen and Karlsson 1985). Animals living in poorer quality habitat may have to forage more and therefore have a higher capture rate that inflates densities in these habitats. This possible confounding effect cannot be ruled out with available information. Finally, pitfall traps remove animals from the population, which may affect local population densities directly, or indirectly by disrupting spacing behaviour. However, there are no long-term declines in abundance of any species in the multi-year pitfall data sets from S C and EBL. At E B L in 1994, only 1 of 3 trap circles in each set were set in the spring session and 2 of 3 were set in a 28-day session in July. When all traps were set later in the summer, there was no difference in abundance or maturity class composition of any species between previously trapped and untrapped circles (catch per 1000 trap-days (SE) S.  cinereus:  previously trapped 34.4 (4.7), untrapped 32.5 (3.8); S. monticolus: previously trapped 10.5 (2.3), untrapped 11.1 (2.8)).  126  Interpreting weak effects The general lack of large, obvious differences between treatments or harvest types for the shrews at S C presents challenges for traditional statistics. Overall there are no statistically significant treatment or harvest type effects for the 2 shrew species (randomized block A N O V A p-values for treatment or harvest type range from 0.20 - 0.71), although individual contrasts with uncut forest may be significant. However, such statistical tests do not distinguish between weak evidence for a strong effect versus strong evidence for a weak effect, or indicate the strength of evidence for the lack of a strong effect (Kass and Raftery 1995). Nonetheless, this is exactly the information needed by policy-makers, managers, or researchers interpreting data for applied uses (McBride et al. 1993, Ellison 1996). Likelihood functions present this information directly, and the user of the information can directly determine the likelihood of whatever effect size is deemed to be relevant. With the shrews in this study, positive and negative effects of treatments and harvest types were both detectable - no effect was highly unlikely in some cases - but the extreme increases or decreases in abundance that would be of particular management concern were also seen to be highly unlikely. The Bayesian combination of prior probabilities, based on values presented in the literature, with the data in the current study, is a promising approach to making knowledge grow for the many instances in ecological research in which parameter estimation is the objective. By explicitly deriving prior probabilities from other empirical results, the analysis avoids relying directly on subjective beliefs (a criticism of some Bayesian approaches; Edwards 1972). The model underlying the Bayesian approach could be improved if more relevant data were available. The analysis currently assumes that any study of the same species in coniferous forest is equally informative in forming a prior probability, while studies in other forest types were excluded. However, if we understood how relationships differed across geographical or ecological gradients, we would have an objective basis for weighting more heavily studies that are ecologically more relevant to our study system. A similar understanding of how related species respond could similarly be used to determine weightings 127  for studies of related species (compared to the arbitrary doubling of variance used here). Determining such "patterns of patterns" (Bunnell and Huggard 1999) is a valuable, but underemphasized and potentially daunting research objective. Despite this limitation to the Bayesian approach, it is still preferable to the more typical approach in the literature that presents the results of a study and narratively relates them to previous studies. Such narrative summaries tend to emphasize similarities in studies that produced similar results, and dissimilarities in conflicting studies. This implicit a posteriori weighting of other studies can give a false impression of the generality of results. Explicit, a priori, quantitative synthesis of relevant studies should be emphasized where possible. Unfortunately, a comparable likelihood and Bayesian approach to summarizing the multivariate habitat relationships was not possible in this study, because of the difficulty of presenting the joint likelihoods of many variables in an understandable way, and several difficulties in synthesizing multiple regression parameters from previous studies, including: 1) the same variables are rarely measured by more than one study (e. g., 18 studies of shrews measured a total of 178 habitat variables; only 40 (22.5%) were measured by more than one study; D. Huggard, unpub. summary updated from Bunnell and Huggard (1999)); 2) shared variables are often measured on substantially different scales (Van Home and Wiens 1991); 3) regression coefficients are sensitive to the range of independent variables sampled and to their covariance structure, which are rarely reported; and, 4) estimates of error of coefficients are rarely reported (especially for the effective coefficient of 0 for variables excluded in step-wise procedures). Semi-quantitative, subjective synthesis of previous regression models into prior probabilities may be possible, but was not attempted here because my own prior beliefs would not have been independent of the S C data. The inability to quantitatively synthesize shrew habitat models is particularly unfortunate because there have been numerous studies, most of which report weak relationships. Individual studies often have low precision because of the variability inherent in capture data, but in aggregate the studies might strongly indicate that relationships of shrews 128  to measured habitat elements are truly weak. Indirect evidence suggests that relationships are weak for shrews at S C . Fewer red-backed voles were caught than the 2 common shrew species, but habitat models for red-backed voles were stronger (better fit, predictive ability and clearer relationships with individual elements). This suggests that if strong habitat relationships did exist for the shrews, the sampling design would have been adequate to detect them.  II. Harvest effects and habitat relationships Treatment, harvest type and edge effects None of the overall treatments at Sicamous Creek had pronounced negative or positive effects on the 2 common shrew species. While S. cinereus declined substantially in clearcuts, abundances in both edges and leave strips were similar to contiguous uncut forest, so that the overall effect of removing one-third of the trees with 10-ha clearcuts or 1-ha patch cuts was minor. S. monticolus showed no effect of clearcuts and a positive response to leave strips and particularly edges, leading to an overall increase in the 10-ha C C and 1-ha patch-cut treatments. Given the harvest type results, overall responses of the 2 species to the 0.1-ha patch-cut treatments were surprising - S. cinereus should have declined slightly because of reduced abundance in openings, while S. monticolus should have increased because of the abundant edge created by the many small openings. However, S. cinereus actually increased substantially while S. monticolus showed no pronounced difference. Red-backed voles, particularly females, showed large reductions in abundance in clearcuts and edges, but declined less severely than expected in edge-rich 0.1-ha patch-cut treatments. The explanation for these discrepancies between harvest type effects and overall treatment effects may lie in the effects of the different treatments on ground cover, particularly shrubs, in the different sized openings. Random skidding (without defined skid trails) of harvested whole trees in the larger openings caused extensive damage to the existing shrubs, even with the buffering effect of the snow pack. In contrast, trees harvested in a 0.1-ha 129  opening could be placed by the feller-buncher in a small area, and skidding followed welldefined skid trails connecting the many small openings to a central landing. Much of the shrub cover was therefore undisturbed in the small openings. Post-harvest shrub cover around traps in 0.1-ha openings was 32.5% (SD 15.2%) versus 15.6% (SD 8.7%) in larger openings. The habitat models suggested that mature S. cinereus and red-backed voles respond positively to shrub cover, and they were unexpectedly abundant in the 0.1-ha openings.  Although  treatments were defined by their effects on the canopy, their different incidental effects on ground cover may be more relevant to small mammals. For red-backed voles, the area within 5m of an edge was effectively an extension of the clearcut; for S. cinereus it was an extension of the uncut forest; for S. monticolus it was a distinct habitat type preferred over both uncut forest and clearcut. At a lower elevation site in spring, capture rates of shrews were higher in clearcuts near south-facing edges, presumably as a response to earlier snow melt and plant growth (Huggard and Klenner 1998). At SC, various edge orientations were sampled, with no obvious differences in abundance between directions, although sample sizes were small for any particular orientation. Preliminary analysis of the trap circles at different distances from edges showed no clear trends in abundance of any species with distance away from the edge, although again variability was high because each distance was sampled by relatively few trap circles. However, the fact that leave strips differed little from contiguous uncut forest for any species suggests that these edge effects do not penetrate far into the forest. At a fine scale, partial cuts consist of skid trails with greater canopy removal and considerable ground-layer disturbance, interspersed with lesser canopy removal and little ground-cover disturbance. Individual species may perceive this treatment as "all edge", or as having no edge at all, depending on their scale of response. Response to the ITS treatment by the 3 small mammal species was similar to, but less extreme than, their response to edges red-backed voles declined slightly, S. cinereus showed little change, and S. monticolus  130  increased compared to contiguous uncut - suggesting that ITS acted for these small mammals as intermediate between uncut and edge sites. Overall, the abundance response of the species to the 4 harvested treatments does not strongly support recommending any one harvest system as being less disruptive to the small mammal community. The 0.1-ha patch-cut array system had somewhat less impact on redbacked voles, which were the most affected species, and increased S. cinereus, which otherwise decreased in treatments with larger openings. However, the more positive results for this treatment probably reflect the incidental differences in ground-level cover created by different skidding patterns. The longer-term responses to the different treatments clearly cannot be assessed at S C yet, but will depend critically on how the species respond to the regenerating stand, particularly expected declines in CWD, shrubs, forbs and moss as planted conifers grow (Carey and Johnson 1995).  Implications of habitat models Habitat models for the 2 shrew species differed in the relationships predicted with live trees (positive for S. cinereus, negative for S. monticolus), but consistently showed positive relationships with increasing ground-level cover from shrub, herb-layer, moss or duff layers. For all S. cinereus, herb-layer cover was the only variable that predicted substantial variation in abundance within a harvest type. A positive relationship with herb cover (Yahner 1986), . vegetation cover <0.5 m tall (Gore 1988), herbaceous biomass (and nitrogen content; Huntley and Inouye 1987) or a habitat gradient including herb and grass cover (Raphael 1988) represent the microhabitat relationship most consistently reported for S. cinereus, from studies across conifer forest types, in even-aged or old-growth deciduous forests, and in old fields. A threshold response was suggested for S. monticolus at S C , in which at least some cover by moss and herbs was required, but higher values were not necessarily beneficial. The few habitat relationships previously reported for S. monticolus include positive associations with cover of particular species (Mahonia sp. and Polystichum munitum; Terry 1981; Rubus and 131  Vaccinium; Gilbert and Alwine 1991), but it is uncertain whether this indicates a preference for ground-level cover in general, or a particular association with those plant species and their habitat types. The relationships of shrews with ground cover variables observed at S C were weak, suggesting that the range of ground conditions created by harvesting did not exceed the species' tolerances. Winter harvesting on a deep snowpack causes relatively little surface disturbance, except where skidded trees damage shrubs. Standard operational site preparation for this forest type was used in the summer after harvesting at S C , with spot mounding by small machinery used to create exposed mineral soil for planting. This treatment has relatively little additional effect on the forest floor. More intensive site preparation, such as broadcast burning or mechanical scarification, could be more detrimental to both species of shrews. This possibility is being tested at SC, with replicated subplots in each harvest treatment unit treated with 4 site preparation methods: no treatment, standard spot mounding, broadcast burn and complete removal of organic layer (Vyse 1997). The latter treatment in particular is predicted to have strongly negative effects on shrews, at least in the short term. In the longer term, even undisturbed moss cover in openings will decline, while duff depth and cover should decrease with the lack of litter input from canopy conifers. However, herb-layer cover will increase, and shrubs may recover from logging damage, possibly compensating for the reduction of other forest floor habitat elements. The reduced abundance of S.  cinereus in drier site series is consistent with previous  studies (Getz 1961, Wrigley et al. 1979). At SC, the reduction in drier sites is not due to differences in measured habitat variables, because site series differences were also apparent using residual values after habitat relationships had been removed. Drier sites may be less productive of herbaceous plants in summer, reducing the abundance of the arthropods fed upon by shrews, or inherent high rates of water loss in small-bodied shrews may be limiting in these sites (Getz 1961). Logging of high-elevation forests can exaggerate site moisture differences, as the water table rises when trees are removed from mesic or sub-hygric sites, 132  but drought can occur in exposed drier sites in mid-summer (Alexander 1986). Harvesting of drier high-elevation sites with larger openings may have negative effects on S.  cinereus in dry  years, but none of the 3 years of post-harvest sampling at S C included dry summers. The larger-bodied S.  monticolus did not differ across the range of site moistures sampled at SC.  Habitat relationships of red-backed voles were more clearly defined than those of shrews. In addition to canopy cover, shrub cover was a prominent positive correlate with abundances of red-backed voles. A positive association of red-backed voles with shrub cover has been reported from western conifer forests by Corn and Bury (1991), Gilbert and Allwine (1991), West (1991) and Carey and Johnson (1995) (in young managed forests only). In contrast, Taylor et al. (1988), Gore (1988) and Belk et al. (1988) reported positive associations with herb-layer cover, but only weak or no relationships with shrubs. At least moderate shrub cover was required for higher abundances of red-backed voles at S C , except possibly when moss cover was very high. Protection of shrub cover during logging and site preparation may help mitigate reductions of red-backed voles in harvested sites. Using defined skid trails or forwarders, rather than random skidding may minimize the area of shrub damage.  Shrub  species in the E S S F forest zone are slow growing and not resilient after disturbance; extensive site preparation such as broadcast burning or mechanical scarification should be avoided where maintenance of red-backed voles is an objective. Positive, but generally weak, relationships between C W D and red-backed vole abundances have been reported in several studies (e. g., Belk et al. 1988, Gilbert and Allwine 1991, Carey and Johnson 1995), but others found no relationship (Terry 1981, Gunther et al. 1983, Taylor et al. 1988). The more flexible C A R T and NN modelling techniques used with the S C red-backed vole data suggest that variable or weak results in regression models may be due to interactive or non-linear relationships of C W D and other habitat variables. C W D did not appear able to substitute for shrub cover, as predicted abundances of voles were always low when shrub cover was low. Given adequate shrub cover, at least a moderate volume of C W D would be required to maintain red-backed vole abundance. The emphasis for C W D 133  management should therefore be on avoiding very low levels, rather than maintaining particularly high levels. At SC, winter logging on a thick snowpack protected much of the existing CWD, and a proportion of decayed and broken stems left on the block maintained high abundances of C W D in the harvested areas (Huggard and Klenner 1997). This habitat element was therefore not what limited red-backed voles in openings, but C W D could become limiting with intensive site preparation. More importantly, local input of C W D would be required to restore red-backed voles if post-harvest C W D is eliminated. The potential reduction in vole abundance predicted at very high C W D levels should not be a management concern, as these C W D volumes (e. g., >150 m /ha) are unlikely in managed forests. However, the practice of 3  making spot piles of wood left after logging could produce local areas with both excessively high and excessively low volumes of C W D for voles.  Appendix 5.1. Calculation of the small mammal abundance index. The abundance index used to combine multiple years' data is described verbally in the main text, and outlined in mathematical notation here. The abundance index is calculated separately for each species group, season and study area. The 3 additional subscripts needed on every variable to indicate this have been omitted for clarity.  Let:  y = number of years sampled (at that study area for that season) nj = number of trap circles (the sample unit) sampled in the j year, j = 1... y x = actual number of animals caught at the i trap circle in the j year, i = 1... nj, j = 1...y tj = actual number of trap-days at the i trap circle in the j year, i = 1... nj, j = 1...y. [Note: Ideally and typically ty = 140 (= 5 traps * 28 days), but reality occasionally intrudes, in the form of cows, ground squirrels, floods, errant excavators, etc.] Cij = catch per 1000 trap-days at the i trap circle in the j year. th  th  th  y  ,h  ,h  th  , h  C =-^-1000 g  Ai = the abundance index for the i trap circle. th  134  A = 2[ fl(C, i)-H_!lL!—:] lo  +  y Note that equivalently, ^ A  i  2.  /  l o g  (C +1) s  X  V aeom.mean^a + 1V y  where geom.mearij means the geometric mean value for the j year. t h  135  C h a p t e r 6. G e n e r a l C o n c l u s i o n s a n d R e c o m m e n d a t i o n s  A s outlined in the introductory chapter, the work included in this dissertation focussed on developing habitat relationships for 2 groups of animals as part of a larger faunal research program. The faunal research program is itself part of the multidisciplinary silvicultural systems research project at Sicamous Creek. Large-scale experimental studies like the Sicamous Creek project are one valuable approach to providing the diverse kinds information forest managers now require for management decisions involving an increasingly complex array of resource values. In this chapter, I summarize general conclusions and recommendations derived from the work of the preceding chapters, and relate them to these larger contexts.  Methods for improving habitat models This dissertation concentrated on spruce grouse and 3 species of small mammals because they presented particular opportunities and challenges for developing habitat models. The opportunities came from the large available data sets and the expectations that the animals should have detectable relationships with the measured habitat elements or treatments. The main challenges were the imperfect study designs (no complex multidisciplinary project can ever be designed perfectly for all individual studies), the applied need for predictive models based on manageable habitat features, and the simple fact that habitat relationships were not readily apparent in the data. For some of the other species studied at Sicamous Creek, simple habitat relationships are apparent, or the limited available data may not warrant more complex analyses (e. g., pine marten, Huggard 1999; three-toed woodpeckers; grylloblattid insects, Huggard and Klenner  in prep.). However, the variance  partitioning, habitat modelling techniques and likelihood approaches explored in this dissertation will benefit several of the larger studies at Sicamous Creek for which analysis is not complete (e. g., mice and voles, broad invertebrate taxa and specific insect species).  136  The difficulties of determining habitat relationships are not endemic to Sicamous Creek. The poor performance of many habitat models (see introductions of chapters 3 and 4) is evidence of the widespread difficulties. In general, the low predictive ability of many habitat models is due to 2 factors: 1) Problems in developing empirical models from available data; and, 2) the fact that nature is variable in time and space. The methodological aspects of this dissertation deal with the first factor, and lead to some general recommendations for mitigating this part of the problem in future studies: 1. Spatial aspects of data sets should not be ignored, because they can produce misleading apparent relationships with environmental variables, or undue confidence in the strength of relationships. These concerns do not disappear with replicated, randomized experiments. Because realistic ecological experiments always have small or moderate sample sizes, some degree of spatial pattern is inevitable. As a minimum, the spatial autocorrelation of samples that are assumed to be independent should be measured, and effective sample sizes adjusted accordingly. Partitioning the spatial, environmental and shared components of ecological data sets is a further step to help understand the different types of patterns in a data set. This understanding can ultimately help prevent misinterpretation of environmental relationships and direct further steps in the research. 2. The 2 approaches to describing habitat for habitat models - as habitat types (harvest or treatment types here) or habitat elements - are complementary, with different advantages and disadvantages for habitat models. Using both approaches together, and understanding their pure and shared variance components can lead to better habitat models, and reduced chances of misinterpretation. The benefits of the variance partitioning technique would apply whenever 2 partially independent sets of explanatory variables are used, including habitat models that use nested spatial scales, or models that use both stand- and landscape-level variables. 3. Alternative modelling methods that can capture more of the non-linear and contingent effects expected in ecological systems, such as C A R T or neural networks, could have 137  obvious benefits for modelling animal-habitat relationships. However, caution is warranted. Even the fairly large data sets used in this dissertation did not overcome the high variability of ecological data enough to benefit fully from the more flexible modelling techniques. This limitation was most obvious from the calculations of the expected measurement error for the abundance of shrews. Despite extensive trapping effort and large numbers of captures compared to many other studies, most of the observed variance was just that expected from Poisson measurement error. Similar results are likely with any count-based animal surveys. This high component of measurement error increases the risk of "noise-modelling" with C A R T or neural networks, limiting their ability to produce better predictive models. The alternative modelling techniques are, however, worth pursuing for their potential heuristic benefits. Because field data are expensive to collect, it is worth fully exploring the available data, but we should not be blinded by the novelty or high fit of complicated modelling techniques. 4. Although the likelihood approach to presenting treatment differences is unfamiliar and requires additional interpretation because of that unfamiliarity, it has several advantages over the more typical approach of testing null hypotheses of no treatment effects. The results are presented in a form that answers the common-sense questions of applied users, so that users can directly evaluate the likelihood of effect sizes that are of importance to them. Likelihood functions allow results from multiple studies to be combined quantitatively, through Bayes' theorem. This is a critical benefit for forestrywildlife work, where there are often many similar studies, all of them inconclusive individually. Use of, and familiarity with, likelihood functions and Bayesian combination of results should be encouraged among applied researchers. Methods to improve development of habitat models from field data should help reduce the first factor causing the poor predictive ability of many models, problems in model development. They cannot affect the second factor, the variability of nature. This variability makes model validation essential, regardless of how much effort, skill or analytical technique went into the 138  original model development. The tests of different analysis techniques with the small mammal models showed that the fit of a model cannot be used to indicate its predictive abilities. With the spruce grouse, partially independent validation was possible within the Sicamous Creek site (for example, comparing edge effects adjacent to cutblocks to edge effects around wetlands, compensating for habitat differences). However, for both the small mammals and the grouse, work at independent validation sites was required to know whether the models had general applicability. Unfortunately, validation work is often neglected in ecology, and seems to be particularly difficult to get funded. This neglect contradicts our professed adherence to a hypothetico-deductive view of the scientific method. The search for relationships in empirical data, which is a primary focus of this dissertation and much other ecological work, represents only the first stage, hypothesis-generation. W e are more accustomed to thinking of hypotheses as being created by an act of imagination, or as being somehow "given" to us. However, searching for patterns in data is just as much an act of hypothesis generation, even if we often disguise this fact by presenting it in various ways as tests of statistical null hypotheses. Testing these generated hypotheses with data from independent validation sites is therefore an essential part of the hypothetico-deductive process. In a view of science less reliant on hypothesis-testing, validation is equally important as the way to determine how observed patterns change over space or ecological conditions (Bunnell and Huggard 1999).  Habitat relationships, treatment effects and edge effects The studies that I used for examining methods of improving habitat models were not conducted primarily for that purpose. They were intended foremost to provide information on how the studied species responded to changes in habitat elements that are affected by forestry activities, to alternative silvicultural systems treatments, and to the edges that are a prominent part of some alternative systems. These species were studied, along with a range of other taxa, as part of a larger strategy to represent "faunal diversity" (Huggard et al. 1999a). The  139  specifics of the habitat relationships, treatment effects and edge effects are presented in Chapter 2 for spruce grouse and Chapter 5 for the small mammals.  Here, I summarize some  general points that arise from these studies and other studies at Sicamous Creek. There was clearly a range in the strength of habitat-element models, from a moderately strong relationship for spruce grouse and red-backed voles through weak relationships for  Sorex cinereus and almost no relationship for S. monticolus. There is no compelling reason to think that some species actually have greater or lesser strengths of relationships with habitat features in general. Instead, the difference in the strength of the models presumably reflects the importance to the species of the particular habitat elements that we decide to measure. Detailed autecological studies could undoubtedly produce more predictive habitat models and a better understanding of habitat needs, particularly for the shrew species. However, those models would not necessarily better meet the applied objectives of this work, because we would have little idea how different management actions would affect the particular habitat variables included in such species-specific studies. Even for some of the variables that I did use in the models, such as moss and litter cover and depth, management effects are only roughly known. Good information on management effects is only available for trees and their direct products (deadwood, canopy cover). For management decisions to benefit directly from habitat models that use more detailed, species-specific habitat elements, additional research would be needed into how different practices affect the elements. Nonetheless, detailed autecological studies of a range of forest-dwelling species would ultimately benefit habitat management, by challenging the limited set of habitat elements that are almost always measured in wildlife-habitat studies (stemming largely from Thomas 1979). Our use of these elements may be so entrenched that they determine how we perceive forest habitat. Natural history studies of species without the restrictions of immediate application are needed to break these perceptual constraints. In addition to developing a wider set of canonical habitat elements, wildlife habitat studies would also benefit from considering habitat structure at a spatial scale intermediate 140  between individual elements and the overall stand. This represents the scale at which habitat elements (at least those related to trees) combine into local habitat structures. Some of this structure may be captured as the interaction of individual elements in the more complex analyses. However, lacking a convenient term for this scale, we tend to ignore it in our studies and planning. My evidence for the importance of habitat structure at this scale is based only on impressions during field work (naturalist's intuition, Weiner 1995) on the larger study animals at Sicamous Creek, spruce grouse, three-toed woodpecker and pine marten. The markedly lower abundance of grouse and marten in the individual tree selection treatments compared to the 0.1-ha patch cut arrays supports the importance of structures on the 0.010.1 ha scale. Habitat structures at this scale should be studied directly in animal-habitat studies. Operationally, variable group selection or variable retention harvesting systems would ensure more heterogeneity at this scale. Edge effects are a common element of many studies at Sicamous Creek, and a frequent concern in managed Western forests (Kremsater and Bunnell 1999). Edge responses of spruce grouse and the small mammal species were presented in Chapters 2 and 5, respectively. An observation common to several species at Sicamous Creek is that a positive or negative local response to edges did not equate to the same response to treatments with more edge. Grouse and red-backed voles, for example, showed negative responses to edges, but were more or equally abundant in patch cut treatments that created abundant edge. Marten showed the opposite effect, preferring edges locally, but avoiding harvest treatments in general. These contrary edge responses occurring at different scales suggest caution in extrapolating studies of local edge effects, which are relatively easy to design and implement, to the overall effects of different amounts of edge in the landscape. Many of the most basic results from Sicamous Creek - those on overall treatment effects -  cannot currently be tested, despite my emphasis on the need for validation at other  sites, because similar harvest units do not exist in E S S F forests. Large clearcuts are essentially the only operational treatment used in this forest type over the last 25 years. 141  (There are older partial cuts in E S S F , but they were selectively harvested, not uniformly partial cut). Despite the successful implementation of alternative systems at Sicamous Creek, larger clearcuts still dominate current operations and development plans. This homogeneity of operational systems is distressing in its own right, but is particularly harmful in thwarting the learning opportunities needed for adaptive management. Somewhat paradoxically, this situation weakens the Sicamous Creek study by preventing operational validation of treatment results, while at the same time making the study all the more important as one of our very few opportunities for learning about alternative operational systems. To resolve the paradox favourably, we need to implement similar alternative harvest systems in at least a few other E S S F sites.  Management  messages  Management implications for the individual study groups were presented in Chapters 2 and 5. This traditional approach to presenting applied research is probably not ideal for affecting management. One or two of the animals studied at Sicamous Creek may be of specific management interest at some time (pine marten, maybe woodpeckers or grouse). Most of them will undoubtedly never be. An onslaught of recommendations for managing individual species and other resource values can be as ineffective as no recommendations at all. Managers become frustrated by conflicting recommendations, and ignore most of what they hear. Integrated projects like the Sicamous Creek study are intended to avoid this problem by allowing a combined evaluation of the effects of feasible management options on numerous resource values. The approach is to allow managers to be informed about how the options they choose affect many resource values, rather than prescribing innumerable different "optimal" actions. The studies of individual species presented here are primarily intended to be applied as part of this collective, synthetic package. Given the wide range of best practices expected for the many resource values being studied, multi-disciplinary applied research seems destined to produce the often-heard  142  conclusion "Don't do the same thing everywhere." Why do the research at all, if the conclusion is so easily foreseen? First, while the message of heterogeneity may be obvious to researchers, current operational practices suggest it is not being heard by foresters. Tangible, on-the-ground proof that alternative harvesting systems are possible and valuable is one direct way to convey the message to practitioners. Second, policy constraints reinforce the homogeneity of operational practices. Demonstrating the need for different management for different resource values should encourage policy-makers to reconsider homogenizing rulebased systems. Third, when we advocate not doing the same thing everywhere, we are typically only thinking of stand-level harvest systems and broad landscape-level planning. Research into the actual organisms and other ecosystem components reminds us that heterogeneity must also be maintained for many other parts of the forest that are affected by other management activities. The importance of shrub cover, which is affected indirectly by harvesting and directly by site preparation, is an example derived from the small mammal study. The value of some wider buffers around high-elevation wetlands is another example of a neglected type of heterogeneity, suggested by the grouse study. Fourth, while different studies clearly emphasize the diversity of practices required, some patterns are observed commonly in a variety of studies. This can help determine the overall mixture of practices, and future options to evaluate. For example, several of the animals studied were disproportionately affected by the uniform partial cutting. Other studies, such as the windthrow research (Huggard et al. 1999), found similar patterns. While the uniform treatments undoubtedly benefit some values, patchier partial cutting or the small patch cut arrays should probably be emphasized among alternatives. 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