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Translocations of Mimulus cardinalis beyond the northern range limit show that dispersal limitation can… Bayly, Matthew 2015

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Translocations of Mimulus cardinalis beyond the northern range limit show that dispersal limitation can invalidate ecological niche models by  Matthew Bayly  B.Sc., The University of Victoria, 2011  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Botany)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  December 2015  © Matthew Bayly, 2015  ii  Abstract Correlative ecological niche models, built with species’ occurrence records, have become the most widespread methods to forecast range shifts with climate change, but these models assume species’ range limits are driven by their niche limits. If a species range limit is instead the result of dispersal limitation, then these correlative based models will be poorly calibrated and largely inaccurate. I used experimental field transplants within and beyond the northern range limit of the scarlet monkeyflower (Mimulus cardinalis) to test for dispersal limitation and to see if climatic-based ecological niche models were able to accurately predict site-level suitability. I also compared predictions from the niche models to a previous study that transplanted the species beyond its upper elevational range limit, which is known to be fitness limited rather than dispersal limited. Predictions from the niche model closely matched observed fitness from the field transplant experiment across the species’ elevational range limit, but not across the species’ northern latitudinal range limit. Consistently high fitness was maintained within and beyond the northern range limit and even in sites of low predicted suitability, suggesting the northern range limit is dispersal limited. I then constructed an alternative ecological niche model for M. cardinalis with stream habitat variables, rather than climatic variables and controlled for the influence of climatic mechanistically, with a simple thermal envelope. This alternative model demonstrated a large amount of suitable habitat beyond the northern range limit, further supporting that this range limit is largely dispersal limited rather than fitness limited. Dispersal limitation presents a serious systemic challenge for the correlative niche modeling framework and its associated applications. By combining niche models with field experiments, I was able to show both the strengths and weaknesses of these methods and use existing theory of dispersal limitation as a framework to assess the accuracy of these models.       iii   Preface The research presented in this thesis consists of unpublished work by the author M. Bayly, but is heavily integrated with and dependent on a series of closely related studies that have used the scarlet monkeyflower (Mimulus cardinalis) as a case study system to investigate the ecological and evolutionary dynamics of species’ geographical range limits. This body of literature has been primarily carried out by Dr. Amy L. Angert (University of British Columbia, Department of Botany) along with a network of collaborators. Some key example papers from this study system include Angert and Schemske (2005), Angert (2009), Paul et al (2009) and Angert et al (2011).  The climatically-based ecological niche model developed in Chapter 2 of this thesis (Section 2.2.3) is modified and repurposed, with permission, from an existing original manuscript currently under review, of which I am a co-author:  Angert, A., Bayly, M., Sheth, S., Paul, J. (2015) A test of range-limit hypotheses based on habitat suitability and occupancy of suitable habitat across the geographic range of the scarlet monkeyflower (Mimulus cardinalis). unpublished manuscript – submitted for review.  In Chapter 2 of this thesis, estimates of site-level fitness across the species’ elevational range limit were obtained from results previously published from a field transplant experiment by Angert and Schemske (2005). I used their estimates of growth and fecundity to make comparisons with predictions of site-level suitability estimates from the ecological niche models. The findings presented in Angert and Schemske (2005) serve as an integral baseline and inspiration for this study, as an opportunity to compare and contrast range-limiting mechanisms across both the species’ latitudinal and elevational geographic range limits. iv  Table of Contents  Abstract .......................................................................................................................................... ii Preface ........................................................................................................................................... iii Table of Contents ......................................................................................................................... iv List of Tables ................................................................................................................................ vi List of Figures .............................................................................................................................. vii List of Abbreviations ................................................................................................................. viii Acknowledgements ...................................................................................................................... ix Chapter 1: Introduction ............................................................................................................... 1 Chapter 2: Translocations of Mimulus cardinalis beyond its northern range limit show evidence for dispersal limitation and invalidate ecological niche models .................................. 7 2.1 Introduction ................................................................................................................. 7 2.2 Methods....................................................................................................................... 9 2.2.1 Study system ........................................................................................................... 9 2.2.2 Experimental transplant ........................................................................................ 10 2.2.3 Habitat suitability predictions from ecological niche models ............................... 13 2.2.4 Demographic models of population growth rates ................................................. 18 2.2.5 Did ecological niche models predict transplant performance? ............................. 23 2.2.6 Were plot-level microsite conditions similar across sites? ................................... 24 2.3 Results ....................................................................................................................... 24 2.3.1 Overview of main findings ................................................................................... 24 2.3.2 Suitability predictions from the ecological niche models ..................................... 25 2.3.3 Demographic models of population growth rates ................................................. 28 2.3.4 Did ecological niche models predict transplant performance? ............................. 29 2.3.5 Were plot-level microsite conditions similar across sites? ................................... 30 2.4 Discussion ................................................................................................................. 31 Chapter 3: Choice of predictor variables used in ecological niche models yields different conclusions of range-limiting mechanisms ............................................................................... 38 3.1 Introduction ............................................................................................................... 38 3.2 Methods..................................................................................................................... 41 3.2.1 Occurrence records cleaning and verification: ..................................................... 41 v  3.2.2 Stream habitat variables: ....................................................................................... 41 3.2.3 Incorporating a thermal envelope: ........................................................................ 42 3.2.4 Sampling pseudo-absence records: ....................................................................... 43 3.2.5 Ecological niche model methods: ......................................................................... 44 3.2.6 Evaluation of model performance:........................................................................ 45 3.3 Results ....................................................................................................................... 46 3.3.1 Model performance: .............................................................................................. 46 3.4 Discussion ................................................................................................................. 50 Chapter 4: Conclusion............................................................................................................... 56 References .....................................................................................................................................59 Appendices ....................................................................................................................................65  vi  List of Tables  Table 2.1 Parameters and vital rate regression functions used to parametrize the integral projection models. ......................................................................................................................... 21 Table 3.1 Accuracy and evaluation score for the ENMs developed with bioclimatic and stream habitat predictor variables. ............................................................................................................ 46 Appendix Table C.1: AUC scores for climatic-based ecological niche model of M. cardinalis. . 71 Appendix Table C.2: Site-level predictions from the climatic-based ecological niche models with short-term and long term climate data. ......................................................................................... 72  vii  List of Figures  Figure 1.1 Theoretical overview of the relationship between a species’ niche limits and its range limits. .............................................................................................................................................. 4 Figure 2.1 Map overview of transplant sites and occurrence records of wild populations. ......... 11 Figure 2.2 Spatial distribution of occurrence records used in the ecological niche model. ......... 15 Figure 2.3 Fitness across the northern and elevational range limits of M. cardinalis. ................. 25 Figure 2.4 Suitability from predictions from the ecological niche models. .................................. 26 Figure 2.5 Relationship between observed fitness from the field transplant experiments and predicted site-level suitability from the ecological niche models. ................................................ 27 Figure 2.6 Vital rate elasticities for the integral projection models for sites across the northern range limit of M. cardinalis. ......................................................................................................... 28 Figure 2.7 Principal component analysis of field transplant plots and plot-level microsite variables. ....................................................................................................................................... 31 Figure 3.1 Thermal envelope and distribution of occurrence records for the stream habitat ecological niche model. ................................................................................................................ 43 Figure 3.2 Predicted suitability projections from the stream habitat and bioclimatic ENMs. ...... 49 Figure 3.3 Spatial maps of the relative risk of extrapolation into novel environments, ExDet tool output. ........................................................................................................................................... 50  viii  List of Abbreviations AICc – Akaike Information Criterion, corrected for small sample size AUC – Area under the receiver operator characteristic curve  BRT – Boosted Regression Trees ENM – Ecological Niche Model  DEM – Digital Elevation Model GLM – Generalized Linear Model GAM – Generalized Additive Model IPM – Integral Projection Model MAP – Mean Annual Precipitation MAT – Mean Annual Temperature   MAX – MaxEnt (Maximum Entropy)  MRPP – Multivariate Response Permutation Procedure PCA – Principal Component Analysis RF – Random Forest TSS – True Skill Statistic Climatically-based ecological niche model (Chapter 2 of this thesis): MDTR – mean diurnal temperature range (Bio2) ISOT – Isothermality (Bio3) TSEA – Temperature Seasonality (Bio4) MTWQ – Mean temperature of the warmest quarter (Bio10) MTCQ – Mean temperature of the coldest quarter (Bio11) MAP – Annual Precipitation (Bio12) MPDM – Precipitation of the driest month (Bio14) PSEA – Precipitation Seasonality (Bio15) Stream habitat ecological niche model (Chapter 3 of this thesis):  ASD – Annual stream discharge (Bio12) PMD – Peak monthly discharge (Bio13) MMD – Minimum monthly discharge (Bio14) DSEA – Discharge Seasonality (Bio15) PQD – Peak quarterly discharge (Bio16) MQD – Minimum quarterly discharge (Bio17) DWQ – Discharge of warmest quarter (Bio18) DCQ – Discharge of coldest quarter (Bio19) ix  Acknowledgements I offer acknowledgements to my inspirational supervisor Dr. Amy Angert for providing the best possible research opportunity. Experience gained from the broad scope of field and modelling components associated with this project were invaluable. Additionally, all the help and support from my close-knit group of fellow lab members, Megan Bontrager, Barb Gass, Dr. Anna Hargreaves, Dr. Chis Kopp, Qin Li, Dr. Chris Muir, Racheal Wilson and Dr. Seema Sheth (arranged alphabetically). Special thanks to Barb Gass and Laura Super for their help assisting with field work. Help and guidance from Dr. Thomas Edwards (Utah State University) with easily adaptable R-scripts for the ecological niche models was also greatly appreciated. External funding through grants and awards were provided through the Oregon Native Plant Society, The Valdimir J. Krajina Scholarship and the Samantha Hicks Memorial Scholarship. Additional thanks to Adam Wilkinson for his help with permitting and logistics, as well as several anonymous Oregon landowners and Lane County Parks for their field support. Assistance with editing and feedback was also greatly appreciated from all participants associated with the UBC FLORUM discussion group, Alison Porter, Robin Elahi, Deirdre Logan, Cora Skaien and the UBC R-Study Group.   1  Chapter 1: Introduction How closely do species’ range limits coincide with their niche limits? As we travel across environmental gradients we routinely observe the turnover of species and their geographic distribution limits. In some systems the mechanisms driving range limits are clear and immediately observable, such as the change in alpine plant communities with elevation (Grinnell 1917; MacArthur 1972; Brown and Lomolino 1998). The fact that species show declining fitness across environmental gradients and then tipping points at which they are no longer able to persist is at the very foundation of niche theory (Hutchinson 1958; Levins 1968; Peterson et al 2003; Holt 2009). This has led ecologists generally to accept the notion that species’ distributions and limits are expressions of their physiological limits (or niche limits) in space (Sexton et al 2009; Holt et al 2009; Elith et al 2009). But for many species, mechanisms driving range limits are more complex than simple environmental constraints and can be influenced equally by historical biogeographic events, interactions with other species as well as subtle relationships between spatially structured populations and demography (Sexton et al 2009; Gaston 2009; Pigot and Tobias 2013).  Across any landscape, it is almost always possible to identify environmental gradients that seem to correspond with a species’ range limit, but it is difficult to determine whether these relationships truly have causal mechanisms or if they are just correlations (MacArthur 1972; Brown and Lomolino 1998; Kearney and Porter 2009; Dormann et al 2012). Studies translocating species to sites within and beyond their range limit, tracking the growth and survival of individuals, are the most direct tests of whether or not environments beyond a range limit truly result in lower fitness. Most of these field experiments find some decrease in fitness beyond a species’ range limit, but there are many cases where fitness beyond a range limit is equivalent to or even greater than at locations within the range (e.g. Marisco and Hellmann 2009; Samis and Eckert 2009). This occasional mismatch between fitness limits and range limits suggests simple correlative relationships with environmental variables are not always sufficient to explain species’ distribution limits (for review see: Langlet 1971, Sexton et al 2009, Hargreaves et al 2014). If conditions beyond a species’ range limit are suitable for growth, but individuals fail to colonize and occupy these areas, the range limit is considered to be dispersal limited. 2  Understanding the relationship between a species’ niche limits and range its limits is directly associated with how it will cope with climate change (Corlett and Westcott, 2013; Parmesan 2006). For any species, it’s unlikely that a perfect equilibrium is ever maintained in a dynamic environment, but the relative degree of mismatch between range limits and niche limits brings up several important questions: How will species’ distribution limits shift as they migrate northward and to higher elevations with future warming? Which species will be able to keep up with climate change? How have species’ distributions responded to past climate change? Answering these questions for species or areas of interest has fueled a major expansion and development of niche modeling techniques and tools that can be easily implemented and broadly transferable across taxa, regions and environments (Elith et al 2009; Guisan and Thuiller 2005; Pearson et al 2003).   Ideally, for any species of interest, accurate habitat suitability models and predictions of geographic range shifts with climate change would be guided by a strong understanding of relationships between population-level fitness and key environmental variables. Casual mechanisms between environmental variables and ecological process would be derived experimentally (Kearney and Porter 2009; Dormann et al 2012). Areas would then be delineated as suitable or unsuitable depending on whether the values of environmental covariates are expected to drive populations above or below replacement rates (Schurr et al 2012; Merow et al 2014). Unfortunately, conducting all necessary field and lab experiments to accurately build these relationships is either extremely difficult or impossible for most species. We instead must strive to make the best possible use of available, or feasibly obtainable, data. Records on the distribution and abundance of species are the most ubiquitous form of data. Occurrence records can be gathered easily from a wide variety of sources for most species of interest (e.g. www.gbif.org). These records can be then combined with values from various environmental datasets for modelling (e.g. landcover (Tuanmu and Jetz 2014), climate (Hijmans et al 2005) and topography). Correlative ecological niche models (ENMs) model habitat suitability based on relationships between occurrence records, the background environment and spatially derived environmental variables (Pearson and Dawson 2003; Guisan and Thuiller 2005; Elith and Leathwick 2009). Alternative names for this same framework include habitat suitability modeling, bioclimatic envelope modelling and perhaps most commonly (but usually less accurately) species distribution modelling. Modeling relationships between occurrence records 3  and environmental variables is currently the most widely used method for broad-scale niche modelling and generating spatial predictions of suitable habitat (Guisan et al 2013). Some of the main applications of ENMs include conservation and reserve planning for threatened species (Guisan et al 2013), forecasting habitat shifts with climate change, comparing niche breadth between related species (Broennimann et al 2012) and predicting areas likely to colonized by a recently introduced invasive species (e.g. Neubert and Parker 2004). The challenge between modeling a species’ niche limits from its distribution limits is illustrated in Figure 1.1. This general schematic has been described previously (Pulliman 2000; Holt 2009; Ehrlén and Morris 2015) and is adapted here. Two theoretical environmental variables (out of many) are shown to represent all possible environmental conditions across a landscape, which is contingent on the biogeography of the region. Through evolutionary history, a given species is able to tolerate some portion of this global environmental space. Tolerance in this sense is related to a species’ physiological limits, where population-level growth rates above replacement values are possible (fundamental niche limits) (Hutchinson 1958). A second environmental envelope could also be drawn on top of these same two variables to show the entire environmental space that is actually occupied by the species on the landscape (realized niche limits). Depending on the dispersal capabilities of a species, the realized niche may be smaller or larger than the fundamental niche (Pulliam 2000; Schurr et al 2012; Ehrlén and Morris 2015). The distribution limits (realized niche) may exceed its apparent fundamental niche limits though source-sink dynamics and episodic growth, with persistent life stages (e.g. seed banks, delayed extinction from large adults etc.). The distribution limits may fall short of the niche limit through dispersal limitation. With correlative ENMs, we are essentially attempting to model a species’ fundamental niche limits from its distribution (realized niche) limits, usually making the leap blindly between these two fundamentally different entities.  4   Figure 1.1 Theoretical overview of the relationship between a species’ niche limits and its range limits.  Beginning from the top left, two theoretical environmental variables are shown along with a species’ fundamental niche limits in relation to these two variables (in red). Depending on the interaction between a species’ dispersal ability, demographic processes and other biotic interactions the species may fall short of its niche limits due to dispersal limitation (fails to occupy the full range of environmental conditions up to its niche limits) or the species may temporarily occupy locations beyond its fundamental niche limits through source-sink dynamics. Individuals at these locations beyond the niche limit are either unable to complete their life cycle or persist only temporarily, experiencing negative population growth. When using correlative niche models, we are unable determine whether species’ range limits are equal to, less than or greater than their niche limits. NL = niche limits, RL = range limits.  Despite the widespread use of ENMs in ecology and conservation, very few studies have actually attempted to test and validate their predictions experimentally with field transplants (Ebeling et al 2008; McLane and Aitken, 2012; Swab et al 2014; Isaac-Renton et al 2014; Sheppard et al 2014). By validate here, I am referring to asking whether or not predictions are accurate with respect to their intended application: do predictions from ENMs match observed fitness from field trials? Making a general consensus from these few case studies has been challenging. Each of them have returned conflicting results, from either no relationship between ENMs and fitness (Swab et al 2014), to partial support (Sheppard et al 2014; Isaac-Renton et al 2014) and full support (Ebeling et al 2008; McLane and Aitken 2012). A more popular approach has been to correlate some metric of fitness observed from wild populations to predictions from ENMs (Elmendorf and Moore 2008; VanDerWal et al 2009; Monnet et al 2014; Thuiller et al 5  2014; Tredennick and Alder 2015). But with observations from wild populations, we are limited in our ability to tease apart correlation from causation with environmental predictor variables. Perhaps, rather than asking ‘are ENMs are validated by field trials?’ a more appropriate approach would be to ask where, when and under what conditions ENMs are expected to work. Our understanding of dispersal limitation can serve as an appropriate starting framework to test the validity of ENM predictions. Dispersal limitation becomes more prevalent at range limits where the relative steepness of the underlying environmental gradient is shallow (covering long distances) in comparison to a species’ dispersal distance (Kirkpatrick and Barton 1997). In other words, a species is more likely to be at an equilibrium with its niche limits when environmental gradients are steep and even propagules dispersing only short distances are able to reach all locations across the gradient. In terrestrial systems the most concrete example of steep and shallow environmental gradients are at species’ elevational and latitudinal range limits, respectivly (Sexton et al 2009; Halbritter et al 2013; Hargreaves et al 2014; Siefert et al 2015). For a given distance, temperatures and associated climate variables change much more rapidly across elevation in comparison to latitude (e.g. I.c. western North America, mean annual temperature decreases by about -1 oC for 100 m of elevation, in comparison to about ~ 200 km of latitude. Consequently, studies transplanting species within and beyond their range limits are more likely to find dispersal limitation across latitudinal range limits rather than elevational range limits (Sexton et al 2009; Hargreaves et al 2014). We therefore expect that on average, predications from ENMs are more reliable across elevational range limits in comparison to latitudinal range limits.   In Chapter 2 of this thesis, I test these predictions using Mimulus cardinalis (the scarlet monkeyflower) as a case study system. M. cardinalis (Phrymaceae) is a rhizomatous perennial herb that is an obligate to stream banks, seepages and other riparian areas. Its distribution extends across mountain ranges from the northern Baja Peninsula in Mexico up to the Klamath region in Southern Oregon (Hickman 1993). Previous studies with this species have focused on its elevational range limit in the Central Sierra Nevada Mountains (California, USA) describing the demography of wild populations (Angert 2006b; Angert 2009), their physiology (Angert 2006a) and fitness when transplanted beyond the range limit (Hiesey et al 1971; Angert and Schemske 2005). Experimental transplants clearly showed reduced fitness above the species’ elevational range limit as a result of cooler temperatures (Angert and Schemske 2005; Hiesey et 6  al 1971). In this study I use experimental field transplants across the species’ northern latitudinal range limit to determine if this range limit is fitness or if it is dispersal limited. High fitness maintained beyond the northern range limit from field transplants would suggest dispersal limitation. An ENM is then developed for M. cardinalis using climatic-based predictor variables. I then use data from the both field transplant studies across the species’ latitudinal and elevational range limits to test the validity of predictions from the ENM.    In Chapter 3 of this thesis, discrepancies between the field transplant study and the climatic-based ENM are partly explained through an alternative ENM for M. cardinalis, developed with stream habitat variables. This stream habitat ENM uses environmental variables associated with stream discharge and physical watershed characteristics. A mechanistically derived thermal envelope is used to mask predictions from the stream habitat model, so that these models account for known temperature-based physiological constraints, without relying on the potentially misleading relationships between distribution limits and climatic tolerance limits. Using predictions from the stream habitat ENM, I evaluate whether available habitat declines beyond the northern range limit. Predictions from both the stream habitat ENM and the climatic ENM are compared to assess areas of agreement and discrepancies. Both of the competing ENMs are evaluated based on their ability to make predictions beyond the range limit without extrapolating into novel environments and on their ability to correctly classify presence and absence records. Taken together, results from the stream habitat ENM, the climatic ENM and the field transplant studies provide a powerful framework for evaluating dispersal limitation as well as the strengths and uncertainties of correlative niche models.  7  Chapter 2: Translocations of Mimulus cardinalis beyond its northern range limit show evidence for dispersal limitation and invalidate ecological niche models 2.1 Introduction Geographic distributions are commonly thought to reflect species’ environmental niches in space (Brown and Lomolino 1998; Sexton et al 2009). Studies of the environmental drivers of distribution have a rich history as some of the most foundational works in ecology (Langlet 1971; Grinnell 1917; MacArthur 1972), and recently they have received a resurgence of interest to develop accurate forecasts of range shifts with climate change (Schurr et al 2012). Climate is generally considered to be the major driver of species’ range limits over large spatial scales, especially near polar and high elevation range limits (Sexton et al 2009; Gaston 2009). However, increasing attention has been given to cases where a species’ range limit falls short of its niche limit and suitable conditions exist beyond that limit. In this context, the failure of a species to occupy suitable habitat beyond its range limit is evidence for dispersal limitation. Some of the most notable examples of dispersal limitation include recolonization time lags following periods of deglaciation (e.g., Svenning and Skov 2004) and rapid range expansion of exotic species once introduced to a new continent (Davis 2009). Understanding dispersal limitation is critical for disentangling niche limits from range limits (a fundamental problem in ecology and biogeography) as well as for predicting range shifts with climate change (a pressing conservation issue).   Most efforts to forecast range shifts rely on the use of ecological niche models (ENMs). In general, these models correlate occurrence records with spatially explicit climatic or other environmental variables and build relationships through regression, machine learning or profile-based methods (For review see Pearson and Dawson 2003; Guisan & Thuiller 2005; Elith & Leathwick 2009). Dispersal limitation presents serious challenges for correlative ecological niche models (ENMs), which are built on the assumption of niche-driven range limits. These models rely heavily on a niche concept where locality records are assumed to have positive population growth rates (above replacement values). The locality records are also assumed to approximately cover the full breadth of the species’ niche and range of tolerable conditions for each environmental variable in the model (Pulliam 2000; Dormann et al 2012). These assumptions have made it difficult for ENMs to fit properly into more traditional niche concepts 8  (Pulliam 2000; Ehrlén and Morris 2015).  A majority of studies using ENMs consider dispersal limitation to be small or negligible, while some studies attribute suitable but vacant areas to be the result of dispersal limitation (e.g. MacKenzie 2006). What is most problematic is the potential for dispersal limitation, in and of itself, to affect the underlying parameterization of these models (Peterson 2003). If a species’ geographic distribution is at an equilibrium with the modeled climatic variables, then the predicted suitability from ENMs should mirror real world population performance. Alternatively, if a range limit is instead driven strongly by dispersal limitation or source-sink dynamics, then these correlative models will be invalid and over or underestimate the species’ niche limits.  Ideally, all ENMs would be parameterized with detailed demographic data on birth and death rates across different environmental gradients, instead of relying on occurrence records alone (Dahlgren and Ehrlén, 2011; Diez et al 2014; Merow et al 2014; Swab et al 2014). Demographic data would circumvent the potential disconnect between species’ distributions and their niche limits. But collecting these data even from a single wild population is challenging, requiring repeated field surveys and extensive individual-level sampling. As a result, most studies that collect demographic data do so at only a small number of sites (i.e. at the extremes of an environmental gradient). This makes it impossible to build response curves with environmental variables and then scale predictions up across landscapes (Tredennick and Alder 2014, Merow et al 2014). Combining predictions from conventional ENMs built with occurrence records and demographic field studies can be informative, balancing their strengths and tradeoffs.  Surprisingly, out of the now over ~ 2,500 publications (see Guisan et al 2013) that incorporate some form of ENMs, few studies have attempted to actually relate predicted suitability back to components of fitness. From these studies, only a very small handful of have actually attempted to experimentally test niche model predictions with field transplants. Experimental field transplants, within and beyond a species’ range limit are the most powerful tests to tease apart dispersal limitation from fitness limitation (Geber and Eckhart 2005; Sexton 2009). Isaac-Renton et al (2014) is perhaps the most comprehensive field validation of climatic-based ENMs to date, finding partial agreement between suitability predictions and growth of Douglas-fir (Pseudotsuga menziesii) from a large scale meta-analysis of field provenance trials. Sheppard et al (2014) found partial agreement between suitability predictions from ENMs and 9  individual-level growth rates for several invasive plant species in New Zealand. But two other studies found no relationship between predictions from ENMs and observed fitness from field transplants (Pattison and Mack 2008; Swab et al 2014). It is very difficult to come to a general consensus from these studies because they each used different ENM methods, compared different organisms from different life stages, and transplanted populations across vastly different environmental gradients. Critically, none of these studies evaluated how predictions compare across multiple range limits and only one of the studies examined lifetime fitness in a demographic framework (Swab et al 2014).  In this study I transplant populations of Mimulus cardinalis (the scarlet monkeyflower), to nine sites within and beyond its northern range limit to test for dispersal limitation. I transplant multiple life stages of M. cardinalis and generate estimates of population growth rates using integral projection models (Ellner and Rees 2006; Rees et al 2014). Results from this study are compared to findings from a previous study, which transplanted this species beyond its elevational range limit and found it to be fitness limited, with a steep underlying climatic gradient (Angert and Schemske 2005). Suitability predictions for all sites are then obtained from a climatically-based ENM. Observed fitness from both field transplant experiments, across the species’ latitudinal and elevational range limits, is then compared to their predicted suitability from the ENMs to test the validity of these correlative models. 2.2 Methods 2.2.1 Study system M. cardinalis is a rhizomatous, perennial herb that grows in small disjunct patches along streambanks and large seepages in Western North America (Hiesey et al 1971; Angert et al 2005; Nesom 2014). The species disperses downstream via small seeds and rhizome fragments, but lacks obvious mechanisms for long distance dispersal or across drainage basins (Levin 2000). Its full geographic distribution extends across mountainous areas from the northern Baja Peninsula in Mexico, through California and into southern Oregon. The focus of this study is on the species’ northern range limit at the conjunction of the Cascade and Klamath mountain ranges in south-central Oregon, USA.  10  2.2.2 Experimental transplant  Transplant field sites I selected five field sites within and four field sites beyond the species’ northern range limit of M. cardinalis (Figure 2.1; Appendix Table A.1). I defined the range limit from the northernmost reported population at 44.008 oN. Multiple herbarium specimens collected across several decades near this locality suggest this range limit does not fluctuate frequently. Annual demographic surveys of wild populations, initiated in 2010, also suggest site-level occupancy to be relatively stable in this region (A.L. Angert unpublished data). Field sites within and beyond the range limit covered a total latitudinal extent of 220 km and were each separated by ~ 20 – 50 km. (Figure 2.1; Appendix Table A.1). All field sites were standardized as closely as possible to each other in terms of stream hydrology (i.e. annual discharge) and underlying physical features, matching habitat conditions of large, wild populations in the region. 11    Figure 2.1 Map overview of transplant sites and occurrence records of wild populations.  Right: Overview of the geographic distribution of Mimulus cardinalis. Black dots represent all known locations of wild populations, across its entire distribution from occurrence records (described below). Left: Field transplant sites are marked by red (sites within the range limit) and blue (sites beyond the range limit) triangles. Underlying shading is elevation, with white representing mountainous areas.   Transplant size classes  The genetic source of individuals used for this study originated from two wild populations near the northern range limit. These populations were located in two drainage basins each separated by 40 km (Rock Creek and Coast Fork, Appendix Table A.1). I chose to use populations near the northern range margin for this study under the assumption that individuals from these populations would be most likely to disperse and contribute to future range expansion with climate change. Wild seeds were collected from fifteen individuals from each population in the fall of 2010 and two initial generations of controlled crosses were carried out under benign greenhouse conditions, to reduce potential maternal effects and ensure that all seeds were sourced from outcrossed parents. Seed families were randomly paired between individuals within 12  each population and mature flowers were manually outcrossed by hand pollination. The mature fruits and seeds from these plants then served as the source material for transplants used in this study.  To assay performance across the entire life cycle in a short-term field experiment, I prepared multiple size classes for transplanting. This was achieved by starting individual cohorts in the greenhouse at different times, each separated by several months. All individuals were grown under standard greenhouse conditions in a saturated peat mixture. Sizes (total stem length from all shoot) available for planting ranged from small seedlings (> 3 cm) to large adults (< 300 cm). To match the early spring phenology of wild populations, I grew plants indoors over the winter and simulated spring re-emergence by pruning all stems to 5 cm above ground and leaving plants outdoors in Oregon for two weeks prior to planting. Field plots and planting To sample average conditions across sites, I established 15 plots within each site for planting. Plots were positioned along the upper stream banks, just above the relative riparian elevation of most willows, to mimic wild populations in the region. All plots across all sites were standardized for similar features such as substrate conditions, canopy exposure and positioning relative to streams. Procedures for taking detailed microsite measurements and other plot-level characteristics (e.g. slope, soil moisture, inundation period, etc.) are described in Appendix B. I selected plots based on the general availability of suitable microsites within a site and haphazardly separated plots by a distance of 5 – 50 m within each site. Since wild populations naturally have a variety of size classes within a patch, each plot in this study also contained a representation of all size classes. I positioned transplants randomly within plots along a grid, with 0.50 m spacing maintained between plants to eliminate the potential for intraspecific competition. Plants were watered immediately after planting, but received no further provisioning. All planting took place in May of 2014. Transplant populations were then left for three months to adjust to field conditions, overcome initial transplant shock and establish root systems in the parental substrate material. Plant measurements used to parametrize the population models were made on August 30th – September 6th of 2014 (time t) and then July 29th – August 3rd of 2015 (time t+1). The census was earlier in 2015, to account for advanced phenology observed from both wild and transplant populations that year. 13  Data were also available from a very small-scale initial pilot study, carried out from the fall of 2013 to the fall of 2014, using the same methods outlined above. This pilot study only transplanted into six of the field sites with small seedlings (< 3 cm). Due to poor planting locations, a majority of the plots washed out with winter flooding and were therefore excluded from the analysis. Plant measurements  I measured growth as the total stem length of both non-flowering and reproductive stems. I also measured total basal stem diameter for plants, but used total cumulative stem length for all analysis since it was related more strongly with survivorship, growth and fecundity. I harvested all fruits prior to dehiscence in the fall each year to estimate fecundity for each individual. Fecundity was reported as the total fruit count × (average seed count / fruit). 2.2.3 Habitat suitability predictions from ecological niche models  Ecological niche models (ENMs) developed for this project were based on the relationships between presence and absence data and climatically-based predictor variables. Models were calibrated with occurrence records and pseudoabsence data and then tested with an independent testing dataset.  Training and testing datasets The ENMs developed for this study were unique in that they were calibrated from a training dataset of herbarium records and tested with a truly independent testing dataset, rather than splitting the same initial dataset for model calibration and testing. Presence-absence data for the testing dataset came from an independent survey (A.L. Angert unpublished data). This survey consisted of an extensive survey of wild populations of M. cardinalis, across its entire geographic distribution. The independent survey balanced sampling effort across both climatic space and geographic space across the distribution of M. cardinalis. The survey design initially targeted site-level abundance, but for the purpose of this ENM, the data is converted to binary presence/absence data of species occurrence at each site. From this field survey, 240 stream sites were surveyed from central Oregon to southern California. M. cardinalis was detected at 90 of the field sites (A.L. Angert unpublished data) (Figure 2.2).  14  Occurrence records verification and thinning Occurrence records for M. cardinalis, with latitude and longitude coordinates, were collected from the Global Biodiversity Information Facility (www.gbif.org), the Consortium of California Herbaria (ucjeps.berkeley.edu/consortium/) and the Oregon Flora Project (http://www.oregonflora.org/) in November of 2013. Specimens from the Northern Baja Peninsula in Mexico, Arizona and other records from New Mexico were excluded. These far southern and far eastern populations are distinct morphologically, climatically, geographically and are often mislabeled as a closely related sister species, M. verbenaceus (Nesom 2014; Sheth and Angert in press). This initial collection consisted of a list of 880 records. Data cleaning and record verification were required to remove duplicates (-91 records), poorly georeferenced locations (-33 records), vague discretions (e.g. “on Mount Baldy”) (-13 records), mismatches between locations and descriptions (-3 records) and cases where records fell in very close proximity to one another (<600 m, e.g. popular recreation pullouts, bridges and trailheads) (-318 records). 600 m was chosen as a distance for initial record thinning based on visual evaluation of Moran’s Correlograms (results not shown) with temperature variables used in the ENMs (described below); records falling within 600 m of each other had nearly identical climatic data. 432 records were available after the initial record cleaning and verification process (Figure 2.2).  Additional record thinning was required to reduce observer bias from the opportunistic herbarium dataset. OccurrenceThinner (Verbruggen 2012; Verbruggen et al 2013) was used to create subsamples of the initial dataset. OccurrenceThinner identifies areas of high record density across a landscape, based on a two-dimensional kernel surface of record densities and then generates subsamples from the original dataset that have reduced sampling bias. Of course, with this study, it’s not possible to truly tease apart high record density from sampling bias vs actual higher prevalence. A kernel density surface was generated with a fixed bandwidth distance of 80 km (equal to one standard deviation) using in CrimeStats (Levine 2010). ENMs were then run with 10 ‘pseudoreplicate’ datasets produced from OccurrenceThinner, each with reduced sampling bias (Figure 2.2). I refer to these subsamples as pseudoreplicates because are not true replicate datasets and therefore all model predictions are averaged over the pseudoreplicates.  15   Figure 2.2 Spatial distribution of occurrence records used in the ecological niche model.  Left: Map of all herbarium records that met the initial data validation criteria (described in Methods section). Center: Single sample (#1/10) of one of the thinned pseudo-replicate datasets with presence and pseudo-absence data used to calibrate the niche models. Right: Distribution of surveyed presence (pres) and absence (abs) records from the independent validation dataset used to test ENM predictions (from A.L. Angert unpublished).  Sampling pseudoabsence records It was necessary to generate pseudoabsence data for the training dataset, since this dataset consisted of only presence records. There are no ‘best’ methods to generate pseudoabsence data since any sampling approach will depend on the study system, nature of the background environment and the ecological question being addressed (discussed in Barbet-Massin et al 2012). Selection of pseudoabsence points was constrained based on several criteria from the presence-absence testing dataset. First, pseudoabsences could not exceed the upper elevation limits sampled by the presence-absence survey at any given latitude. This prevented psuedoabsences from being drawn from extremely high alpine areas. There was no lower elevational limit, since wild populations can occur at sea-level in coastal areas. Second, pseudoabsences were constrained with a maximum distance of 80 km and minimum distance of 600 m from any presence record. Finally, pseudoabsences were sampled in proportion to the relative abundance of true absences surveyed across US EPA Level III Ecoregions (U.S. Environmental Protection Agency, 2013). Due to the configuration of the landscape, sampling background records from a fixed distance to presence records would have resulted in a large portion of records falling in desert regions, which were purposely undersampled in the testing 16  data. From exploratory work, inclusion of records in desert regions resulted in inflated model evaluation scores, biased predictions and offered only limited utility for ecological explanation (e.g. showing that deserts are unsuitable for this non-desert species). Thus, adjusting the sampling of pseudoabsence records to reflect bioclimatic regions was more appropriate for this study, over a solely distanced-based approach. The ratio of pseudoabsence to presence data was set to 1:1 (Figure 2.2). Bioclimatic predictor variables Climatically-based environmental predictor variables were chosen for several reasons. First, they are prevalent in existing ENM literature and easily delineate a species’ presence from background data across broad spatial scales (Pearson and Dawson 2003). Incorporating climatic variables here also allows for conclusions from this study to be more transferable to other systems. Temperature has also been shown to be a strong determinate of site-level fitness from existing studies with M. cardinalis (Angert and Schemke 2005; Angert 2006a; Angert 2006b; Angert 2009; Angert et al 2011; Paul et al 2011; Sheth and Angert in press). Monthly climatic variables were obtained for all records from ClimateWNA (Wang et al 2012), using a 90 m digital elevation model (DEM) from the USGS HydroSHEDs (Lehner et al 2008).  ClimateWNA was chosen over other popular climatic data sources (e.g. WorldClim (Hijmans et al 2005) or PRISM Climate Group (2014)) due to its ability to downscale climate data with a customized DEM based on bilinear interpolation and adiabatic lapses (Wang et al 2012). For each record locality I created a collection-date-specific climate averages extending back thirty years prior to the date of collection, rather than using fixed-term climatic normals. Pseudoabsence were assigned dates randomly from the distribution of herbarium record collection dates. Nineteen Bioclimatic variables were then calculated from the monthly climate data using the ‘biovars’ function in the ‘dismo’ package (Hijmans et al 2014). These nineteen bioclimatic predictor variables were reduced down to only eight candidate variables after an initial variable selection process. For highly correlated variables (r ≥ 0.7), those thought to be more casual were retained over more distal variables, when possible. If this distinction was not immediately clear, variables with greater explanatory power in univariate general linear models were retained for sets of correlated predictors. The following eight variables were retained for use in the ENMs, PSEA (precipitation seasonality), MPDM (precipitation of the driest month), 17  MAP (annual precipitation), MTCQ (mean temperature of the coldest quarter), MTWQ (mean temperature of the warmest quarter), TSEA (temperature seasonality), ISOT (isothermality) and MDTR (mean diurnal temperature range). ISOT, MTWQ, MAP and MPDM were log-transformed prior to analysis.  Ecological niche model algorithms  Five unique statistical methods were used to develop the climatically-based ENMs: generalized linear models (GLM, McCullagh and Nelder 1989), generalized additive models (GAM, Hastie et al 2001) random forest models (RF, Breiman, 2001), boosted regression trees (BRT, Elith et al 2008) and maxent (MAX, Phillips et al 2006). These methods are commonly used in the existing ENM literature with binary presence-absence data and each have different strengths and weaknesses (Merow et al 2014; Elith and Graham 2009). By including parametric (GLM), semiparametric (GAM) and machine learning methods (BRT, RF, MAX), it is possible to understand the sensitivity of results to the underlying modeling methods. Model predictions are reported as the average predicted values across the ten separate pseudoreplicate datasets, subsampled with the OccurenceThinner program. An ensemble prediction across all five models was generated by taking the average predicted value across the five methods. All analyses were conducted in R, version 3.0.3, with code generously shared by Dr. Tom Edwards (USGS Utah Cooperate Fish and Wildlife Research Unit and Utah State University).  The GLMs were developed using both forward and backward stepwise variable selection from the initial set of the eight candidate predictor variables. Linear and quadratic terms for predictor variables were included in the GLM models. GAM models were run in the package ‘gam’ (Hastie, 2013). GAM models were also developed using a stepwise variable selection process from an initial scope list for each predictor. This scoping list for each variable included smoothing parameter values ranging from 2 – 5 (methods outlined in Wintle et al (2005)).  RF, BRT and MAX were run with the packages ‘randomForest’ (Liaw and Wiener, 2002), ‘gbm’ (Ridgeway et al 2013) and ‘dismo’ (Hijmans et al 2014) respectively. RF models were run with default setting (n trees = 500, number of variables randomly sampled as candidates at each split = square root of number of predictor, sampling conducted with replacement, minimum size of terminal nodes = 1, maximum number of terminal nodes unconstrained). Sensitivity tests of 18  RF models were conducted by changing n trees from 50 – 1500, changing the number of cross validation folds from 3 – 10 and changing the number of variables sampled at each slit from 2 – 5, but these changes only resulted in very marginal differences in predictions and AUC scores (results not shown). BRT models were developed by testing a range of learning rate and tree complexities, while selecting those that best balanced power (minimizing residual deviance) with parsimony (using the fewest trees). These final settings included a learning rate of 0.1, tree complexity of 3 and step size of 5. MAX models were run with default settings.  Response curves to individual predictor variables were generated using partial plots, where all variables except the target variable are held at their mean value, while predictions are made across the range of observed values for the target variable. Relative importance of predictor variables was determined by shuffling values for each predictor individually and assessing how the correlation coefficient changes between predictions from the shuffled datasets to the original dataset (Liaw and Wiener, 2002).   Model evaluation for all models was carried out based on AUC (Area under the receiver operating characteristic curve, see Lobo et al 2008) scores from internal validation and external validation. Internal validation consisted of resubstitution (leave one out) and five-fold cross validation. External validation was carried out with the independent testing dataset with surveyed presence and absence records (A.L. Angert unpublished data).  2.2.4 Demographic models of population growth rates Integral projection models  I compared the population-level growth rates of transplants across sites using integral projection models (IPMs). IPMs are similar to conventional size-structured matrix models in population ecology, only instead of breaking down the life cycle of an organism into a few discrete stages, IPMs describe how a continuously size-structured population could change over time (Easterling et al 2000, Rose et al 2005, Ellner and Rees, 2006). I chose to use IPMs rather than matrix models because the life cycle of M. cardinalis can be more easily modeled with a continuous size-based state variable predicting key vital rates such as growth, survivorship and fecundity. The use of continuous vital rate functions in IPMs also required far fewer estimated parameters from the already limited transplant dataset (Ramula et al 2009). The IPMs developed 19  for M. cardinalis growing in transplant sites describes the change in population size (n) over annual time steps. In IPMs, a population is described by a probability density function n(x, t) based on size x and time t. n(x, t)dx is the number of individuals in the size range (x, x + dx) at time t (Eqn 1). A kernel K(y, x) is constructed for each population (transplant site) and describes all possible size transitions from recruitment and growth, from individual at size x to individuals of size y at time t + 1 (Eqn 1).   𝑛(𝑦, 𝑡 + 1) = ∫ 𝐾(𝑦, 𝑥) 𝑛(𝑥, 𝑡)𝑑𝑥 The kernel is broken down into two components describing growth and survivorship P(y,x) and recruitment of new individuals into the population from reproductive individuals F(y,x) over discrete time steps (Eqn 2).   𝑛(𝑦, 𝑡 + 1) = ∫ [𝑃(𝑥, 𝑦) + 𝐹(𝑥, 𝑦)] 𝑛(𝑥, 𝑡)𝑑 The survival and growth, P kernel, predicts individuals surviving to the next time step based on their current size s(x) and then, conditional on survival, growing to a subsequent size y in t + 1 based on the current size x, g(x, y) (Eqn 3).   𝑃(𝑥, 𝑦) = 𝑠(𝑥)𝑔(𝑥, 𝑦) The fecundity and recruitment, F kernel, is broken down such that at time t, individuals have a size specific probability of becoming reproductive (individual starts flowering), Fl(y) (Eqn 4). Conditional on an individual becoming reproductive, plants then have a size-specific fecundity (fruit output) Fec(y) for that year (Eqn 4). In the subsequent year, t + 1, the number of new recruits entering the population will be a product of the number of fruits produced in the previous year, multiplied by the number of seeds per fruit and then multiplied further by the probability of a seed establishing as a new recruit. All of this is summarized by the PEf function. The new recruits that enter the population will have a size distribution of Se(y). The P and F kernels are combined to form the K kernel and describe all possible size transitions and growth for a population. All IPM analyses were run in R, version 3.0.3, using code modified from the supplementary tutorial provided in Rees et al (2014).  20   𝐹(𝑥, 𝑦) = 𝐹𝑙(𝑦)𝐹𝑒𝑐(𝑦)(𝑃𝐸𝑓)𝑆𝑒(𝑦) Statistical models of population vital rates Four size-specific vital rate functions were parameterized for each site: survival, growth, maturity (flowering) and fecundity. All vital rate functions and parameter estimates were developed with the global dataset, including a site-level effect as a fixed factor and the interaction between site and size, if relationships were significant. Global vital rate functions were necessary due to the limited number of observations at some sites for some vital rate functions. Separate IPMs were developed for each site with the estimated site-level parameter values from each of the vital rate functions. Data were available for two interannual transitions (2013 – 2014 and 2014 – 2015), but since the first year only consisted of only a small pilot study across six sites with small seedlings (< 3 cm) and a very small number of individuals surviving to the next year (n = 0-10 per site, excluding plots washed out from winter flooding), I only used data from the 2014 – 2015 transition. Total stem length was log-transformed for all individuals. This was necessary to meet normality assumptions of the underlying regression equations. Log(total stem length) was then used as the primary state variable in all vital rate functions.  Variable microsite conditions across plots within sites were highly influential for all vital rate estimates in the IPM. Mixed models were therefore required for each vital rate estimate to account for the non-independence of individuals in within plots. A plot-level random intercept was used in all vital rate equations. Following methods outlined in Zuur et al (2009), I tested the possibility of using plot nested within site and site alone as random intercepts, but these resulted in lower likelihood estimates for vital rate functions, so I chose a single plot-level random intercept. Alternative competing models for each vital rate function could then include effects of size, site or the interaction between size and site, as possible covariates (Table 2.1). All model selection was carried out by comparing alternative fixed effect structures using Akaike information criterion adjusted for small samples sizes (AICc) (Burnham and Anderson 2002). Growth of an individual i, of size x, in plot p and site s was modelled as:  𝑔𝑟𝑜𝑤𝑡ℎ (𝑦𝑡+1 ) =  𝛼 + 𝛽1(𝑥𝑡) + 𝛽2 (𝑠) + 𝛽3(𝑥𝑡, 𝑠) + 𝑅𝐸𝑝 + 𝜖𝑖 21  where β’s represent coefficients for initial size xt, site s and the possible interaction between s and xt (Eqn 5). The growth increment for an individual, included a global intercept β0 and was influenced by a random plot-level intercept REp. The error for the model ϵi, was modelled as Gaussian for the growth model. Growth models were developed using the lmer function from the lme4 package (Douglas et al 2014).  Survival, maturity and fecundity were modeled with the same basic model formula as growth (Eqn 5), only the underlying methods changed to accommodate the specific data structure (e.g. binary outcome of survivorship, count data of fruit) (Table 2.1). Survival of an individual was modeled using general linear mixed models, with the function glmer (Douglas et al 2014), using a Bernoulli sampling distribution and logit link function. Maturity (flowering), was modeled with similar methods to survival, based on the binary nature of the data: individuals can be either flowering 1 or not flowering 0. I initially attempted to model fecundity, counts of fruits, with a Poisson distribution, but encountered issues with over-dispersion. Instead, a type 1 negative binomial error distribution was used and models were developed from the glmmADMB package (Fournier et al 2012).  Out of all plot-level microsite variables measured (Appendix B), plot-level moisture was the most influential variable across all four vital rates (Step AICc, forward and backward variable selection). However, vital rate models that incorporated microsite conditions as a plot-level random factor outperformed models where microsite conditions were incorporated as continuous fixed factors, based on likelihood estimation. In a separate analysis IPMs were generated without random effects and instead included plot-level moisture as a fixed effect, but this did not change overall conclusions (results not shown). Table 2.1 Parameters and vital rate regression functions used to parametrize the integral projection models. Site level estimates were obtained from the survival, growth, reproductive and fecundity vital rate functions and combined with the recruitment estimates (fixed values across sites). For each model, β0 is the intercept, β1 is the effect of size, β2 is the site-level effect, β3 is interactive effect of site and size and REp is the plot-level random intercept.  Model Component Plot-level variation incorporated as a random intercept in mixed models R package (function) Distribution Survival,  n= 571  𝑆(𝑥) =  𝛽0 + 𝛽1(𝑥𝑡) + 𝛽2 (𝑠) + 𝑅𝐸𝑝 + 𝜖𝑖  lme4  (glmer) Family: Binomial, link: logit Growth,  n = 247  𝑔(𝑥, 𝑦) = 𝛽0 + 𝛽1(𝑥𝑡) + 𝛽2 (𝑠) + 𝛽3(𝑥𝑡 , 𝑠) + 𝑅𝐸𝑝 + 𝜖𝑖  lme4 (lmer) Family: Gaussian  22  Reproductive, n= 881  𝐹𝑙(𝑦) = 𝛽0 + 𝛽1(𝑦) + 𝛽2 (𝑠) + 𝑅𝐸𝑝 + 𝜖𝑖  lme4  (glmer) Family: Binomial, link: logit Fecundity (No. of fruit),  n= 288  𝐹𝑒𝑐(𝑦) = 𝛽0 + 𝛽1(y) + 𝛽2 (𝑠) + 𝛽3(𝑦, 𝑠) + 𝑅𝐸𝑝 + 𝜖𝑖  glmmADMB (glmmadmb) Family: Negative Binomial (1), link: log Seeds per fruit Fixed values across sites: 1152   Recruitment rate PEf Fixed values across sites: 0.08, for each fruit   Mean recruitment size Se(y) Fixed value across sites: log(1.8 cm)   Recruitment size  σ of Se(y) Fixed value across sites: log(1.89 cm)    Estimation of missing life stages This field study could not follow the fate of seeds PEf or recruitment size Se(y), due to permitting restrictions (seed addition not allowed; mature fruits to be collected before dehiscence). Estimating these values and other life history transitions from external studies was therefore necessary, to complete the life cycle for M. cardinalis and make the IPMs complete. Estimates of seeds per fruit, establishment rate of seeds and the mean size and size distribution of new recruits were obtained from an ongoing demographic survey of natural wild populations of M. cardinalis in Oregon (A.L. Angert, unpublished data). These values were averaged across three northern wild populations in the region and then held constant across IPMs developed for each transplant site in this study (Table 2.1). The mean size and size distribution of new recruits were taken directly from new individuals, from time t to time t+1, that entered plots in the demographic survey. Estimating the establishment probability of an individual seed is not feasible, due to the challenge of small tracking seeds (<1 mm) in a riparian environment. Instead, I estimated this process PEf indirectly by taking the ratio between the number of fruits produced at a site at time t to the number of new recruits that emerged in the site at time t + 1 (Table 2.1).  Finally, with all parameter estimates in hand, IPM kernels could be developed separately for each site. I discretized kernels into 100X100 matrices to calculate the asymptotic population growth rate, λ, for each site as the dominant eigenvalue of the matrix.   23  Confidence intervals for site level estimates Confidence intervals around parameter estimates and lambda values were calculated by bootstrapping the original dataset 5,000 times. For each bootstrap replicate, observations of individual transitions were draw at random, with replacement, from the original dataset. Due to the nested structure of the dataset, bootstrap datasets were balanced at the plot level. Separate IPMs were run for each bootstrapped dataset. Bootstrapping produced a probability distribution for each parameter. 95 % confidence intervals generated by taking the 2.5 % and 97.5 % percentiles from the distribution of values for each estimate (as in Jacquemyn et al 2010). Elasticity estimates Calculating vital rate elasticity values is important to gauge the relative influence of each vital rate on final lambda estimates. Elasticity values for each vital rate were calculated by perturbing each variable by 1% and then dividing the relative change in each vital rate by the relative change in lambda (de Kroon et al 2000, Jacquemyn et al 2010). Using this method, elasticity values could then be compared directly against the uncertainty around each estimate.  2.2.5 Did ecological niche models predict transplant performance?  I compared site-level demographic estimates (i.e. of each vital rate and lambda) to site-level suitability predictions from the ecological niche models. Suitability predictions for the transplant sites could be generated using site level climate data from either long-term normals (1981 – 2010) or a short-term climate data, only extending over the duration of the transplant experiments (2014 – 2015). I chose to compare site-level suitability predictions from both long-term (30 year) averages and short-term (1 year) climatic data to account for the potential effects of interannual variability. Similarly, to compare predictions from the previous transplant study across the species’ elevational range limit, in addition to long term averages, short-term climate data was averaged from 2001 – 2003, when the field component of the study by Angert and Schemske (2005) took place. Short-term climate averages from 2001 – 2003 were obtained directly from ClimateWNA (Wang et al 2012), but short term climate data from 2014 – 2015 had to be obtained by multiplying monthly temperature and precipitation data by month-specific weather anomalies from 1981 – 2010, for the year starting and ending in August (PRISM Climate Group, 2015).  24  2.2.6 Were plot-level microsite conditions similar across sites?  Since different microsite conditions across sites could potentially confound site-level differences in fitness, I tested plot-level similarity within and beyond the northern range limit and across sites using all variables in a Principal Component Analysis (PCA). A PCA was run for all plots across all sites with environmental values from the ten plot-level microsite variables (Appendix B) using the ‘vegan’ package (Oksanen et al 2015). A correlation matrix was used and all variables that were either positively or negatively skewed were first log-transformed to meet normality assumptions. Since the number of plots per site was unbalanced (n = 12 – 17), a multi-response permutation procedure (MRPP, see (McCune and Grace 2002)) was used to test for significant differences between plots within each sites, as well as to test for significant differences between plots located within or beyond the range limit. Plot-level estimates of each vital rate (obtained from the plot-level random intercepts from the mixed effects models) were also overlaid on the PCA plots to visualize areas in environmental microsite space of high and low growth, survivorship and fecundity (Appendix Figure B.3). This made it possible to visualize the fine-scale dependency of these vital rate processes on the underlying plot-level microsite conditions.  2.3 Results 2.3.1 Overview of main findings  Population growth rates of M. cardinalis transplanted beyond its northern range limit were highly variable across sites, but growth rates beyond the range limit were still as high (and occasionally higher) than at sites within the range limit (Figure 2.3). Ecological niche models (ENMs) showed a sharp decline in predicted suitability in regions beyond the northern range limit (Figure 2.4; Appendix Figure C.1). Suitability predictions matched observed fitness from the field transplant studies only across the species’ elevational range limit, but not across the species’ northern range limit (Figure 2.5). Estimates of population growth rates and underlying vital rates were highly variable across the northern range limit, from variable plot-level microsite conditions.  25   Figure 2.3 Fitness across the northern and elevational range limits of M. cardinalis.  Pink vertical bars mark the species’ natural range limits. Red and blue points denote sites within and beyond the range limit respectively. Left panel: Estimates of asymptotic population growth across the northern range limit for the eight field transplant sites. Right panel: Data from Angert and Schemske (2005), relative fitness (normalized average of growth and fecundity) across the species elevational range limit.  2.3.2 Suitability predictions from the ecological niche models Predictive performance of the ENMs, evaluated with AUC scores, showed a reasonably strong ability for these models to discriminate between presence and absence records (average AUC scores for internal resubstitution: 0.83, internal cross-validation: 0.75, external validation: 0.75, Appendix Table C.1). Across the each of the five modelling methods, temperatures of the warmest quarter (MTWQ) and coldest quarter (MTCQ) generally had the strongest influence on suitability predictions (Appendix Figure C.2). Across all environmental predictors, there were some similarities in the shapes of response curves (e.g. MTWQ, MAP) across each of the underlying modelling methods, but most of the modeled relationships between probability of occurrence and environmental variables were highly variable. The response curves also occasionally differed across the ten pseudoreplicate datasets (Appendix Figure C.2).  26   Figure 2.4 Suitability from predictions from the ecological niche models.  Continuous color gradient shows predictions from an ensemble average across all five of the separate niche modelling methods. The abrupt shift from yellow to orange marks a threshold value that maximizes sensitivity and specificity from the testing dataset. Black dots denote existing wild populations while triangles present transplant sites within and beyond the northern range limit.   Spatial predictions of suitability, mapped across the study region, showed overall agreement across each of the separate ENMs methods (Appendix Figure C.1; Appendix Figure C.4). Predicted suitability declined towards the northern range limit and remained low beyond the range limit (Figure 2.4; Appendix Figure C.1). Spatial prediction of residuals (predicted suitability values for presence records), showed some negative clustering towards the northern range limit (Appendix Figure C.4).  The rank order of predicted suitability for transplant sites across the northern range limit was not greatly affected by the underlying method (Appendix Table C.2; Appendix Figure C.3). Overall (apart from Hunter Creek), sites within the range limit had higher predicted suitability than sites beyond the range limit (t-test, p = 0.036). For transplant sites across the species’ elevational range limit, from Angert and Schemske (2005), suitability predictions declined sharply beyond the upper elevational range limit. Site-level suitability predictions did change, 27  depending on whether predictions were made with short term or long term climate data (Figure 2.5; Appendix Table C.2). But the overall rank order of suitability predictions for the transplant sites, across each of the field experiments, was relatively insensitive to whether short-term or long-term climate data were used.     Figure 2.5 Relationship between observed fitness from the field transplant experiments and predicted site-level suitability from the ecological niche models.  Top row shows suitability predictions for sites when site-level climate data consists of 30 year climate averages (1981 – 2010). Bottom row shows site-level suitability predictions generated with short-term climate averages, over the duration of the field study. Left and right columns show relationships for the northern range limit and elevational range limit, respectively. Horizontal error bars show the range of values across the five niche modelling methods (GLM, GAM, RF, BRT & MAX). Red and blue points represent sites within and beyond the range limit respectively. 28  2.3.3 Demographic models of population growth rates The parameterization of the IPMs for transplant sites gave reasonable estimates of asymptotic population growth rates for sites, without having to estimate any missing life history parameter directly from the IPMs. Final λ values ranged from 0.33 – 2.09 for the mixed models (Figure 2.3).  Final vital rate functions included initial size and site-level intercepts in all models (Table 2.1). Initial size of individuals x was positive across all vital rate functions and had the strongest influence out of all variables evaluated, when competing models were compared based on maximum likelihood. The interaction term between initial size and site-level effects were only included for growth and fecundity functions (Table 2.1). Elasticity analysis showed that contributions of vital rates to lambda estimates were not overwhelmingly influenced by any single vital rate (Figure 2.6; Appendix Figure E.1). Survivorship components were more influential than reproduction components (fecundity and probability of flowering). Recruitment-related estimates, obtained from the external demography survey of wild populations, were still relatively high (Figure 2.6).  Figure 2.6 Vital rate elasticities for the integral projection models for sites across the northern range limit of M. cardinalis.  The top panel shows elasticity values for IPMs developed using mixed-effect models to parametrize the underlying vital rate functions, where a plot-level intercept enters the model as a random effect (see Table 2.1). Error bars represent the range of elasticity values across all eight field transplant sites (Appendix Figure E.1). Acronyms are as 29  follows: S, G, R and F stand for Survivorship, Growth, Reproduction (prob. flowering) and Fecundity (no. fruit), respectively; Int and Slope are Intercept and Slope and Site-Int or Site-Slope indicate the site-level intercept or slope; SPF, seeds per fruit; Estb, seed establishment probability; m-Recr, mean size of recruits; sd-Recr, standard deviation of recruits.   Comparing vital rates and lambda estimates across the northern range limit of M. cardinalis suggested strong evidence for dispersal limitation. When vital rate estimates and λ values (Figure 2.3) were plotted against latitude, there was no immediate decrease in these fitness metrics in areas beyond the range limit. In fact, one site beyond the range limit (Thomas Creek) had the highest population growth rate, λ = 2.09 (Figure 2.3). Overall, population growth rates were highly variable across sites within and beyond the northern range limit. Estimates of relative survivorship, growth and fecundity were also highly variable, but sites beyond the range limit generally had lower survivorship estimates than sites within the range limit (Appendix Figure C.3).  2.3.4 Did ecological niche models predict transplant performance?  When suitability predictions from the ENMs were compared to transplant data across the species’ northern range limit and the species’ elevational range limit (Angert and Schemske 2005), a positive relationship was only found across the elevational range limit, but not across the northern range limit (Figure 2.5). Even when results were compared between all five ENMs and all four vital rate estimates, I still failed to find any positive relationship between suitability predictions and fitness (Figure 2.5; Appendix Figure C.3). In fact, there was actually a weak negative relationship between predicted suitability and population growth rates. Across the elevational range limit, predictions from the ENMs generally had a positive relationship with fitness estimates from the transplant study by Angert and Schemske (2005). Interestingly, the site with the highest fitness across the elevational transplant study only had the second highest predicted suitability from the ENMs (Figure 2.5).  I also tested how suitability predictions changed whether site-level climatic data consisted of yearly data (extending only the duration of the study period) or long-term averages (1981 – 2010). Overall relationships between predicted suitability and actual population growth rates remained relatively unchanged whether or not short-term or long-term climatic data were used (Figure 2.5).  30  2.3.5 Were plot-level microsite conditions similar across sites?  Principal Component Analysis (PCA) of all transplant plots, with the eleven underlying microsite variables, showed some weak clustering at the site level, but there was still a general overlap of microsite conditions across sites (Figure 2.7; Appendix Figure B.2; Appendix Figure B.3). This indicated that site-level differences were not entirely the result of differing microsite conditions. A reasonably high amount of the variability was explained across the first two axes (PCA1: 29.1%, PCA 2: 19.2 %), suggesting this was an appropriate space to visualize plot-level microsite variability. The MRPP analysis found significant group-level differences between plots within sites (p = 0.004, A-statistic = 0.066), but not between plots within and beyond the range limit (p = 0.385, A statistic = -0.0006). A post-hoc test revealed site-level differences were due to the different microsite conditions in Wiley Creek (turquoise diamonds in Figure 2.7) vs Calapooia (orange squares in Figure 2.7). When plot-level random intercept estimates from the mixed models were plotted on top of the PCA of microsite variables, there was some weak apparent clustering (areas of high fecundity and growth) (Appendix Figure B.3). Alternative vital rate functions were tested with the inclusions of any of the first three PCA axes (or any of the other microsite variables) as additional covariates, but these did not improve models, suggesting that the plot-level random intercept alone was sufficient to account for most plot-level variability in the integral projection models.   31   Figure 2.7 Principal component analysis of field transplant plots and plot-level microsite variables.  The left panel shows plots within sites, each marked by a unique symbol and color for each site. The right panel show plots within (red circles) and beyond (blue triangles) the northern range limit.    2.4 Discussion The transplant experiment across the northern range limit of Mimulus cardinalis demonstrated that this range limit is dispersal limited. Estimates of population growth rates were highly variable across sites, but there were no immediate decreases in population growth rates, or any of the underlying vital rates, beyond the northern range limit. Variability within sites was also high due to the influence of microsite conditions across plots, which are inherently difficult to control in a riparian environment. Findings of a dispersal-limited northern range limit and a fitness-limited elevational range limit (Angert and Schemske 2005) for M. cardinalis fit well with a prior expectations based on the underlying steepness of these two environmental gradients (Kirkpatrick and Barton 1997; Sexton et al 2009; Halbritter et al 2013; Hargreaves et al 2014). When the site-level suitability predictions from the ENMs were compared to the observed fitness from the field transplant experiments, results generally converged across the species’ elevational range limit, but showed no clear relationship across the species’ northern range limit. Transplant sites beyond the northern range limit were therefore climatically marginal in relation to the species’ distribution, but not in relation to the species’ fundamental niche limits.  32  Comparability of the northern range limit and the elevational range limit It is important to recognize that the elevational and latitudinal range limits compared in this study are far from being equivalent climatic proxies for each other. Transplant sites extended across a 200 km long transect across the northern range limit, but the difference between maximum and minimum mean annual temperatures (MAT) was only 1.2 oC. Along the previous elevation transect, transplant sites were separated by 2,595 m (of elevation), but the difference between minimum and maximum MATs was 13.1 oC. For sites across the latitudinal transect to have experienced the equivalent temperature range as those across the elevational transect, it would have been necessary to distribute sites from central California up to into northern British Columbia (M. Bayly, unpublished results). Surprisingly, predicted suitability values from the ENMs across the northern range limit still decreased by approximately the same range as they did for sites across the elevation transect, despite only a marginal environmental turnover with latitude. Thus, having this latitudinal and elevational comparison was informative to gauge the transferability of ENMs in space.  There were also underlying methodological differences between the latitudinal and elevational transplant studies, which may limit their comparability. The experimental gardens used for the transplant study across the species’ elevational range limit were established in cleared areas, not immediately adjacent to the streams and watered with artificial irrigation (Angert and Schemske 2005). The stream-side plots used in this study across the species’ northern range limit mimicked the full range of conditions experienced by wild populations, but introduced a high amount of environmental stochasticity within field transplant sites.  Strength of a demographic approach The demographic approach used to compare transplant sites across the northern range limit in this study is the most informative metric of fitness to test for dispersal limitation and to validate predictions from the ENMs. Estimates of population-level growth rates (lambda) are ultimately what ENMs aim to predict (Pulliam 2000; Guisan and Thuiller 2005). If only a single metric of fitness was measured across field sites (e.g. relative fruit number or survivorship), it would have been difficult to know its contribution to lambda or account for important demographic tradeoffs across vital rates (Parker 2000; Ehrlén 2003; Ramula 2009). In this study, 33  vital rates measured across sites were only weakly correlated to themselves and to lambda estimates. Therefore, if only one vital rate were measured, overall conclusions would be misleading. This was further supported by the elasticity analysis. Lambda values were not strongly dependent on any single underlying vital rate. Despite a large number of studies that have experimentally transplanted species beyond their range limit to test for dispersal limitation (reviewed in Hargreaves et al 2014; Sexton et al 2009), very few have actually assessed fitness with demographic models (e.g. Moore 2009; Latimer et al 2009). Absolute estimates of lambda are also themselves useful and ecologically meaningful. Estimates of lambda for transplant sites across the northern range limit from the mixed models ranged from 0.33 – 2.09, suggesting that there were ecologically important site-level differences (rather than values for all sites being either far greater than or lesser than 1.00).  Due to permitting restrictions at sites beyond the northern range limit, it was not possible to plant seeds or allow fruits from adult plants to dehisce. It was therefore necessary to hold demographic estimates for rates of seed establishment constant at all sites in the IPMs. These early life stages likely act as important demographic bottlenecks beyond the northern range limit (e.g. Giménez-Benavides et al 2010). In a demographic survey across wild population of M. cardinalis, Angert (2006b) found important differences in rates of seed establishment between populations at the species’ elevational range center verse range margin. Further field experiments are necessary to test how conditions beyond the northern range limit affect seed establishment and germination rates.  Was the ENM developed here fit for purpose? Local adaptation and the influence of non-stationary responses to environmental predictors across the species’ distribution could have been partly responsible for the mismatch between suitability predictions from the ENMs and observed population growth rates. Source material for the transplant experiment originated from two wild populations near the northern range limit and these populations might be better suited for conditions beyond the range limit, in comparison to populations near the range center. The ENMs developed here assume a globally uniform (rather than population specific) response to environmental variables across the species’ distribution. Incorporating varying population-level response curves to environmental covariates should result in more accurate predictions (Pearson and Dawson 2003; Angert et al 2011; Hothorn et al 2011; 34  Isaac-Renton et al 2014). Specifically, for M. cardinalis, Angert et al (2011) found important population-level response curves to temperature that would be masked by a global ENM. Through exploratory model development, I excluded records from the south and south-central portions of the species’ range, but surprisingly, predictions at the northern range limit remained relatively unchanged. Populations at the southern portion of the species’ distribution occupied warmer and drier conditions (not experienced near the northern range limit). Therefore, only the tails of response curves were affected by their inclusion or exclusion. Residual plots of predicted suitability values for occurrence records showed some negative clustering at the northern range limit, suggesting local adaptation (Appendix Figure C.4). However, comparative physiological work has shown that these northern population are capable of higher growth rates in warmer climates and could actually be maladapted to their local environments (Angert et al 2011; Paul et al 2011). From any short-term field transplant study, it is always difficult to understand the influence and importance of rare extreme events, which are only observable through long-term studies (e.g. 5 – 50 years). These are almost never accounted for in field studies, but may still be important environmental drivers of range limits (VanDerVeken 2007; Thompson et al 2013). It is not possible to fully circumvent the influence of rare extreme events without long term studies; however, other anecdotal evidence still supports dispersal limitation for M. cardinalis. Estimates of 30-year extreme minimum temperature were highly correlated with 30-years climate averages for occurrence records. This relationship didn’t change dramatically with latitude (R2 = 0.92 – 0.95). Also, the persistence and resilience of one wild population of M. cardinalis, introduced to a stream site 350 km north of its current range limit in the late 1800s, has neither spread to adjacent streams or died off (Don Knoke and Dr. David Giblin (Collections Manager of University of Washington Herbaria) personal communication, 2014). Lastly, climatically marginal populations near the species’ elevational range limit experience more severe low temperatures than populations at the species’ northern range limit. Thus, across the species’ distribution, populations at the northern range limit do not necessarily occupy low temperature extremes, which is also a signature of dispersal limitation (see Halbritter et al 2013; Siefert et al 2015). Since the ENMs developed here were modeling large regional-scale processes, they may not be immediately scalable to site-level predictions, without larger sample sizes or broad spatial 35  replication (Elith and Leathwick 2009; Swab et al 2014). Predictions from the ENMs may have failed to match observations from the field transplant study across the northern range limit due to the high uncertainty of population growth rate estimates within sites. In a related study, Swab et al (2014) also found that site-level predictions were swamped by the influence of variable microsite conditions, not captured in their climatic-based ENMs. In the transplant study across the species’ elevational range limit, Angert and Schemske (2005) planted into controlled gardens, rather than stream-side plots, allowing for microsite conditions to be more standardized. Other studies comparing the mismatch between species’ distributions and their environments, using the same general correlative framework of ENMs, but operating at much smaller scales (i.e. 1 – 10 m), usually (but not always; Diez et al 2014) find strong agreement between suitability predictions and metrics of fitness (Antoine and McCune 2004; Wright et al 2006; Moore and Elmendorf 2006). At these small scales, individual-level presence-absence data and demographic processes may be more closely linked. This may be in part due to access to more relevant, measureable, and time-sensitive environmental variables (e.g. soil nitrogen, moisture, etc.) and the ability to account for density dependence and other important biotic interactions (Soberon and Peterson 2005).  A key challenge for any ENM is developing models with the appropriate level of complexity. ENMs become overfit when response curves to environmental variables begin fitting superfluous relationships between presence-absence data (Merow et al 2014; Elith and Graham 2009). In this study, the use of the five different modeling methods acted as a partial sensitivity test of model complexity. The response curves to environmental predictors increased in their levels of complexity across the different methods (simplest: GLM, MAX, GAM, BRT, most complex: RF) (Appendix Figure C.2). Regardless of which modeling method was used, there were still no discernable patterns between predicted suitability and observed fitness across the northern range limit. There were however some interesting relationships between model complexity and observed fitness across the species’ elevational range limit. The most complex and potentially overfit models (BRT and RF), incorrectly predicted lower suitability at the lowest elevational field transplant site in the central valley, when actual fitness at this site was the highest. This mismatch was likely due to suitable climate at these lower elevations, but insufficient stream habitat, resulting in both the training and testing datasets returning absence 36  (and pseudoabsence) records in these areas and modelling these lower elevations as unsuitable. In this case the ENMs correctly predict the absence of the species, but for the wrong reason. In addition to dispersal limitation influencing the estimation of environmental response curves, it is also possible that the absence of other key environmental predictors negatively affected ENM predictions beyond the range limit. Plot-level microsite effects within transplant sites across the species’ northern range limit were highly influential, even after attempts to standardize for similar conditions across plots prior to planting. Williams and Levine (2004) transplanted M. cardinalis into stream sites and found higher fitness at confluences with tributaries, relative to sites along the main channel. Attempts were made to include stream habitat variables as candidate environmental predictor in the ENMs, but climatic variables alone resulted in a higher discrimination ability between the presence and absence records. I explore the use of stream habitat variables further in Chapter 3 of this thesis using an alternative ENM framework. Do ENMs predictions match field experiments? From an overview of existing case studies, evidence for any positive correlation between suitability predictions from ENMs and observed fitness from field transplant experiments is extremely weak. The two studies that found a positive relationship between predicted suitability and transplant performance were conducted across very broad spatial scales (i.e. continental) (Ebeling et al 2008; Isaac-Renton et al 2014). The large climatic differences between sites in these two studies made them more comparable to the transplant across the elevational range limit of M. cardinalis. But, other case studies that failed to find any clear relationship between predicted suitability and field experiments still covered a relatively large climatic gradient (MAT range ~ 3 oC) (Sheppard et al 2014; Swab et al 2014). Other studies have compared correlates of fitness from wild population to predicted suitability from ENMs, but results from these observational studies have also been mixed, with some finding strong positive associations (VanDerWal et al 2009; Monnet et al 2009) and others finding no relationships (Tredennick and Alder 2015). Generating conclusions from this limited set of case studies is exceedingly challenging since they all used distantly related species (both native and non-native) and different environments.  37  Conclusions The popularity and broad scale applications of ENMs have far outpaced attempts to validate their predictions experimentally. This case study demonstrates one of the fundamental challenges ENMs face with dispersal limitation and the mismatch between a species’ niche limits and its distribution limits. Many studies have advocated for the adoption of demographic distribution models, that incorporate birth and death rates, in addition to occurrence data (Schurr et al 2012; Dahlgren and Ehrlén 2011; Diez et al 2014; Merow et al 2014; Swab et al 2014). Demographic distribution models would compensate for the potential influence of dispersal limitation. But gathering sufficient data to parameterize these models can be a monumental undertaking (see Merow et al 2014a). The output of conventional ENMs, regardless of terminology used (e.g. ‘predicted suitability’, ‘probability of occurrence’ etc.), needs to be addressed with more scrutiny, since it still lacks clear connections back to population ecology (Thuiller et al 2014). Attempts to validate ENMs through demographic surveys of wild populations and experimental translocations have been highly context dependent. This has made it challenging to identify when and where ENM predictions are actually expected to be useful and good surrogates of fitness. By comparing predictions from ENMs to field experiments across a dispersal-limited northern range limit and a fitness-limited elevational range limit, it was possible to dissect how and why the accuracy of these models can be context dependent.  38  Chapter 3: Choice of predictor variables used in ecological niche models yields different conclusions of range-limiting mechanisms  3.1 Introduction For a species to be able to expand its range without evolving new environmental tolerances, there must be suitable habitat beyond the range limit and the species must have the ability to disperse to and establish these locations (MacArthur, 1972; Gaston 2009; Hampe 2011). A range limit is characterized as being dispersal limited if suitable habitat exists beyond the range limit, but the species fails to colonize and occupy these locations. A range limit is characterized as being fitness limited if no suitable habitat exists beyond the range limit and individuals that disperse to areas beyond the range are unable to complete their life cycle. However, these two processes are not necessarily mutually exclusive (Hampe 2011; Delattre et al 2013). For example, if available habitat decreases rapidly beyond a species’ range limit, but very small unoccupied and isolated patches still persist beyond the range limit, the species’ range limit would be largely fitness limited, but it would still also be described as being dispersal limited. Understanding the relative influence of dispersal and fitness limitation as range limiting mechanisms is critical for many conservation applications, such as accurately predicting potential geographic range shifts with climate change. Studies that transplant a species within and beyond its range limit to assess the change in relative fitness serve as the gold-standard experimental design to assess whether or not a range limit is dispersal limited (Sexton et al 2009; Hargreaves et al 2014). But these field experiments are usually only able to test (and usually non-randomly) a small number of sites.  At the regional scale, these sites are usually only just points on the landscape, rather than a representative sample of all available habitats within and beyond a species’ range limits. Therefore, although field transplant experiments are the most direct and accurate methods to test for dispersal limitation, they still generally lack the ability to quantify suitable habitat within and beyond a species’ range limit (Gusian and Thuiller 2005; Swab et al 2014; Merow et al 2014).  In Chapter 2 of this thesis, results from the translocation experiment demonstrated that the northern range limit of Mimulus cardinalis is dispersal limited. Fitness at field sites beyond the range limit was equivalent to and occasionally greater than at sites within range limit. These 39  results conflicted with predictions from the climatically-based correlative ecological niche models (ENMs). These ENMs, developed with climatic predictor variables, showed a sharp and dramatic decline in suitable habitat beyond the northern range limit and suggested that this range limit was strongly fitness limited. Although there were several potentially insufficient aspects of the field study that resulted in high uncertainties in lambda estimates (i.e. the short time scale and the strong influence of microsite variables), failure to find any relationships between climatically based estimates of site suitability and fitness invalidated predictions from these climatically-based ENMs.  If climatic variables used to develop the bioclimatic niche models are only indirectly or distally related to fitness beyond the northern range limit, are there still other environmental variables, or other niche dimensions, that might become more immediately limiting beyond the northern range limit? The northern range limit could be both fitness and dispersal limited if these other niche dimensions became more limiting than climatic constraints beyond the northern range limit. For the transplant study, field sites were not selected randomly, but were restricted to streams with physical habitat characteristics that matched conditions of wild populations. As an obligate riparian species, M. cardinalis is limited to streams and seepages and can have differential fitness within these environments (Levine 2000; Williams and Levine 2004). It is possible that with increasing distance beyond the northern range limit, cooler climates force the species to occupy lower elevations with latitude and eventually push populations into foothills and valley bottoms where stream flow regimes are unsuitable (i.e. shallower slopes, finer depositional material, longer periods of inundation as well as wider and deeper meandering channels). Thus, these lower elevations may have suitable climate, but insufficient quantities of suitable stream habitat across the landscape. Chardon et al (2014) demonstrated a similar phenomenon for northern populations of Pinus coulteri, which were ultimately climatically limited, but more immediately limited by other habitat features beyond their northern range limit. Ideally, all key influential environmental variables would be included in a single niche model, but this is not always possible. Some environmental variables may not be transferable across different spatial or temporal scales, such as to population and individual-level microsite variables (Diez and Pulliam 2007; Mackey and Lindenmayer 2001). The selection of different sets of candidate environmental variables and their apparent explanatory importance will depend on how the background environment is sampled (VanDerWal et al 2009). This is especially 40  concerning, since there is no a priori way of knowing the ‘best methods’ for sampling the background environment with ENMs, regardless of whether true absences or pseudoabsences are used. Also, because most ENMs methods are regression-based, it is necessary to select predictor variables that are not strongly correlated to avoid issues of multicollinearity. Suitability prediction from the ENMs within a species’ geographic distribution should be relatively unaffected by variable selection (if variables are highly correlated). However, when suitability predictions are made beyond a species’ range limits, the correlation structure between variables will often change in these novel environments and regions (Elith et al 2010; Mesgaran et al 2014). Failure to properly distinguish correlation from causation and to identify key environmental predictor variables can lead researchers to largely incorrect conclusions about range limiting mechanisms (Zhu et al 2012; Rödder et al 2009).   For this study, I develop an alternative set of ENMs for M. cardinalis with physical stream habitat variables to compare with the climatically-based niche models developed in Chapter 2 of this thesis. These stream habitat models are optimized to describe the physical structure of drainages, stream discharge and discharge seasonality. These stream habitat models do not rely on relationships between occurrence records and climatic variables. Instead, known physiological constraints of temperature on the fitness of M. cardinalis (see Angert 2006a; Angert et al 2006b; Angert et al 2011) are incorporated into these models using a simple thermal envelope (a mask layer). This makes the stream habitat models partial hybrid ENMs, with correlative variables (stream variables) and a mechanistic thermal envelope. If M. cardinalis is largely dispersal limited beyond its northern range limit, predictions from the stream habitat ENMs should show no large decline of available stream habitat beyond its range limit. Alternatively, if stream habitat decreases rapidly beyond the northern range limit, this would suggest that the range limit is also largely fitness limited, in addition to being dispersal limited. I compare agreement and discrepancies of suitability predictions from both the stream habitat and bioclimatic ENMs within and beyond the species’ northern range limit. I evaluate performance of models in terms of their discrimination ability (ability to correctly classify presence and absence records within the range – AUC scores) as well their ability to safely make predictions beyond the range limit without extrapolating into novel environments.   41  3.2 Methods 3.2.1 Occurrence records cleaning and verification: The same initial set of occurrence records used for the bioclimatic niche model (developed in Chapter 2 of this thesis), were also used here to develop the stream habitat ecological niche model for M. cardinalis. Additional record verification and thinning was required because small spatial errors of less than 1 km could easily lead to incorrectly extracting stream data from a major river versus a small tributary. Each record was manually verified against its description and location in relation to the stream network. If the spatial accuracy and precision was not immediately clear, the record was dropped from the dataset. Unlike the climatic data, stream variables from records in close proximity to one another were not strongly spatially autocorrelated (Moran’s I, Annual Stream Discharge = 0.05 (p = n.s); Temperature of warmest quarter = 0.24, (p < 0.001)), due to the dendritic nature of stream networks. I therefore did not thin or resample subsets of the data to reduce spatial clustering. Populations of M. cardinalis in the far southern portion of its geographic distribution (the Transverse Mountain Range, Southern California) tended to almost always occupy much smaller streams or seepages than records in the central and northern portion of its distribution. This was immediately apparent during the record verification process and anecdotally through field observations. To avoid the confounding effects of non-stationarity with stream habitat variables across the species’ latitudinal range, I excluded all records south of 35o N. All predictions and further applications of this model are therefore limited to the northern and central regions of the species’ distribution. After the data verification and record cleaning, 241 occurrence records remained for use in the stream habitat model (Figure 3.1).  3.2.2 Stream habitat variables: The USGS National Hydrography Database, NHDPlus V2 (Horizon Systems Coorporation 2013), was used as an underlying contiguous surface across the entire study area, so that all record data and spatial predictions could be made from the same hydrological framework. The NHDPlus stream network is highly detailed. Originally developed from a <30 m digital elevation model (DEM), it captures many small micro-tributaries. There were only three M. cardinalis records (1.2%) from the final dataset that, occupied some sort of extremely small spring, seepage 42  or microtributary and were not captured by this network. An initial set of candidate stream habitat variables to include in the model were related to stream discharge and physical morphology of the watersheds. All stream discharge variables were derived from mean monthly discharge estimates obtained from the NHD Plus V2 EROM extension (Horizon Systems Coorporation, 2013). Estimates of monthly stream discharge were converted to analogs of Hijman’s Bioclimatic Variables using the biovars function in the R-package dismo (Hijmans et al 2014) (ASD, Annual Stream Discharge; PMD, Peak Monthly Discharge; MMD, Minimum Monthly Discharge; DSEA, Discharge seasonality; PQD, Peak Quarterly Discharge; MQD, Minimum Quarterly Discharge; DWQ, Discharge of Warmest Quarter; DCQ, Discharge of Coldest Quarter). Other physical stream habitat variables included total area upstream of the drainage basin from a record, total length of all upstream stream reaches, stream slope at an individual reach and topographic roughness. All variables except for topographic roughness were obtained directly from the NHDPlus database. Topographic roughness was calculated as the standard deviation of a 90 m DEM (USGS HydroSHEDs, Lehner et al 2008), when the gridded surface was aggregated by a factor of twenty (90 m to 1.8 km).  3.2.3 Incorporating a thermal envelope:  It was necessary to limit suitability predictions to areas that are within the species’ physiological thermal limits. A temperature envelope was generated for M. cardinalis as a mask layer using the ecocrop function in the dismo package (Hijmans et al 2014). This function generates a very simple mechanistic niche model with a continuous output of suitability, based on known values of temperature-related optimal growth conditions. Values to parameterize this function were obtained directly from a previous study, which ran ecocrop with population-specific thermal performance curves for M. cardinalis (see: Angert et al 2011 for details). The ecocrop function was run with minimum and maximum temperature values across all populations sampled by Angert et al (2011) (the species’ envelope). The continuous temperature suitability output from ecocrop was then converted to a binary thermal envelope mask layer, based on the threshold value that set the sensitivity of occurrence records to 90%. This thermal threshold value was justified based on several criteria. First, this value agreed with results from field transplants experiments across the species’ northern range limits (Chapter 2 of this thesis) and elevational range limit (Angert and Schemske 2005). Second, as the thermal threshold limit was set to slightly more conservative values (made slightly warmer), it began to quickly exclude 43  many presence records (decreasing sensitivity). All portions of the stream habitat model are calibrated and projected within this thermal envelope (Figure 3.1 thermal envelope mask). Suitability predictions for all locations beyond the thermal mask layer are set to zero. 3.2.4 Sampling pseudo-absence records:  Without true absence records to use for the ecological niche models, it was necessary to generate pseudoabsence records to make suitability predictions based on binary presence/absence data. Random sampling of psuedoabsences was restricted to points along the stream network. Point sampling was further restricted to a minimum distance of 1.5 km from any presence record and a maximum distance of 15 km from any presence record. The minimum distance was necessary to prevent overlap on a stream with any presence records, while the maximum distance was chosen to avoid sampling pseudoabsence (background) data from distant areas, which may have been inaccessible to the species due to dispersal limitation. Sampling of pseudoabsences was then finally restricted to areas within the thermal envelope mask layer (Figure 3.1). Throughout preliminary exploration of the data, ratios of presence:pseudoabsence from 1:1 to 1:100 were tested. But any inferences from lower quantities of pseudoabsences tended to be highly variable and dependent on the random sampling (issue discussed in Barbet-Massin et al 2012), so I choose a ratio of 1:100 (presence:pseudoabsence) to more accurately sample the background environment.  Figure 3.1 Thermal envelope and distribution of occurrence records for the stream habitat ecological niche model.  44  Left: Thermal envelope (black = unsuitable) used to restrict predictions for the stream habitat ENMs based on the lower thermal limits of M. cardinalis. Center: Map of all herbarium presence records and pseudoabsence records used to calibrate and parametrize the stream habitat ENMs. Right: Distribution of surveyed presence and absence records from the independent validation dataset used to test ENM predictions (from A.L. Angert unpublished).  3.2.5 Ecological niche model methods: The initial set of eleven candidate stream discharge and physical habitat variables was reduced to five predictor variables after removing variables that were highly correlated (r ≤ |0.8|). Most stream habitat variables were highly correlated, more so than the climatic variables. Variable selection between correlated pairs was based on two criteria. First if a candidate variable was thought to be more causal rather than distal (e.g. total drainage area vs. total length of upstream reaches). Second, whether or not a given variable showed greater predictive power though univariate linear models. The final variable set included ASD (annual stream discharge), DSEA (stream discharge seasonality), slope of a stream reach, total drainage area and topographical roughness. ASD and total drainage area were log transformed to meet normality assumptions.  The same five statistical methods used for ecological niche model development with the bioclimatic variables (Chapter 2 of this thesis) were also used here. These included two regression methods: generalized linear models (GLM, McCullagh 1989) and generalized additive models (GAM, Hastie 2013) - as well as three machine-learning-based methods: random forest models (RF, Breiman, 2001), boosted regression trees (BRT, Ridgeway 2013) and maxent (MAX, Phillips et al 2006). Running these multiple alternative modelling approaches served as partial sensitivity tests. Predictions of suitability can be based on agreement across these alternative methods (Merow et al 2014; Elith and Graham 2009; Aguirre-Gutiérrez et al 2014). The same methods used in Chapter 2 of this thesis to parameterize these models with the bioclimatic variables were also used here.  Response curves for individual predictor variables were generated using partial plots, where all other variables except for the target variable are held at their mean value while predictions are made across the range of observed values for the target variable. Relative importance of predictor variables was determined by shuffling values for each predictor individually and then assessing how the correlation coefficient changes between predictions from the shuffled datasets to the original dataset (see Liaw and Wiener, 2002). 45  Mapped suitability predictions from each of the five ecological niche model methods were converted from a continuous output to a binary output (suitable-1 or unsuitable-0). The threshold that maximized sensitivity and specificity (see Lui et al 2013) was chosen as a threshold cutoff statistic for suitability predictions from the ENMs. The maximum sensitivity-specificity threshold was selected due to the unbalanced ratio of presence to pseudoabsence records in the stream habitat ENMs (1:100) and the different ratio used for the bioclimatic niche models (1:1). The maximum sensitivity-specificity threshold is less sensitive to record prevalence and different ratios between presence and pseudoabsence records (Lui et al 2013; Freeman and Moisen 2008). These binary (0/1) predictions from the five statistical methods (GLM, GAM, RF, BRT and MAX) were then summed for all locations. Similar to vote counting, a value of zero indicates that the location was below the suitability threshold for all models, a value of one indicates that at least one model predicted the area to be suitable and a value of five indicates a location was predicted to be suitable across all five models. The final output from both ecological niche models developed with stream habitat variables and bioclimatic variables were then overlaid to visualize spatial agreement and discrepancies in their predictions.  3.2.6 Evaluation of model performance:  Model performance was evaluated in two ways. First, the ability to correctly classify and discriminate between presence and absence records from the testing and training datasets was assessed using AUC (Area under the receiver operating characteristic curve) scores. Second, to assess the relative risk of extrapolation into novel environments when suitability projections were made beyond the northern range limit, I used the ExDet Tool Ver. 1.0 (Mesgaran et al 2014) to visualize novel environments across the landscape. The ExDet tool is similar to the more commonly used Multivariate Environmental Similarity Surface (MESS) proposed by Elith et al (2010), but is instead able to detect novel environments in multivariate space, based on Mahalanobis distance, in addition to novel environments for any single predictor variable. The ExDet tool was run for environmental variables used in bioclimatic niche models and the stream habitat niche models separately, to assess their transferability in space and relative risk of extrapolating into novel environments beyond the range limit.  I converted final predictions from the ENMs from a continuous scale to a binary output (0 = unsuitable or 1 = suitable) by using a threshold value that maximized sensitivity (rate of true 46  presences) plus specificity (rate of true absences). From the binary suitability maps, I also calculated TSS (True Skill Statistic) scores (see Allouche et al 2006), as a way to assess model accuracy from the binary suitability maps.  3.3 Results 3.3.1 Model performance:  The ecological niche model (ENM) developed for M. cardinalis with the stream habitat variables and the thermal envelope, achieved reasonably high AUC scores, in comparison to the bioclimatic model developed in Chapter 2 of this thesis (Table 3.1). AUC values from cross-validation ranged from 0.81 from the GAM, to 0.90 from the BRT model. However, very low AUC values were returned from the validation against the external testing dataset (0.54 – 0.63) (Table 3.1). These low AUC values were not related to complications with thermal envelope. From the independent testing dataset, there was only one presence record that fell outside of the thermal envelope and converting this value from 1 to 0 had negligible effects on model evaluation scores. Accuracy evaluation scores were similar whether assessed based on the continuous output, from the AUC scores (threshold independent) or the binary output (threshold dependent), based on the maximum sensitivity plus specificity threshold.  Table 3.1 Accuracy and evaluation score for the ENMs developed with bioclimatic and stream habitat predictor variables.  The top box shows accuracy values for the stream habitat ENMs (developed in Chapter 3 of this thesis) and the bottom box shows accuracy values for the bioclimatic ENMs (developed in Chapter 2 of this thesis). AUC (Area under the receiver operator characteristic curve) scores were calculated internally through resubstitution (leave one out) and a five-fold cross-validation and externally with an independent testing dataset (described in text). TSS (True Skill Statistic) scores are also provided from the threshold that maximized sensitivity plus specificity.  Stream habitat ENM Validation Method Metric GLM GAM RF BRT MAX Internal Resubstitution AUC 0.829 0.839 0.817 0.941 0.848 Internal Cross-validation AUC 0.822 0.815 NA 0.883 0.843 External Validation AUC 0.560 0.548 0.629 0.591 0.568 Accuracy From Maximum Sensitivity Specificity Threshold  Internal Resubstitution TSS 0.47 0.49 0.54 0.65 0.54 Internal Cross-validation TSS 0.46 0.46 NA 0.49 0.51 External Validation TSS 0.12 0.08 0.2 0.11 0.1               Bioclimatic ENM Validation Method   GLM GAM RF BRT MAX 47  Internal Resubstitution AUC 0.769 0.812 0.840 0.998 0.764 Internal Cross-validation AUC 0.732 0.674 NA 0.871 0.756 External Validation AUC 0.733 0.743 0.760 0.760 0.758 Accuracy From Maximum Sensitivity Specificity Threshold  Internal Resubstitution TSS 0.42 0.49 0.55 0.96 0.38 Internal Cross-validation TSS 0.37 0.30 NA 0.41 0.38 External Validation TSS 0.36 0.38 0.43 0.38 0.43        From the stream habitat predictor variables in the ENMs, areas of high suitability were generally associated with high topographical roughness, relatively high stream discharge levels, moderate slopes and smaller rather than larger watersheds (Appendix Figure D.1). Analysis of variable importance indicated that stream discharge followed by topographical roughness were the most influential variables driving predictions across all model types. The shapes of variable response curves were also similar across all five of the niche modelling methods used (GLM, GAM, RF, BRT and MAX).  Maps of predicted suitable stream habitat mostly delineated areas above the suitability threshold in mountainous regions across the entire study area (Figure 3.2). At the northern range limit, the density of stream habitat predicted as suitable for M. cardinalis was higher across the Coast and Cascade Range (beyond the northern range limit) than in the Klamath Mountain Range (within the range limit). The stream habitat model alone in general showed abundant suitable, but unoccupied, habitat beyond the northern range limit.  Predictions of suitable habitat for M. cardinalis from the stream habitat model and bioclimatic ecological niche model were highly divergent both within and beyond the northern range limit (Figure 3.2). Within the northern range limit, predictions of suitable habitat converged across both modelling approaches only in the Sierra and Klamath mountain ranges. At lower elevations, valley bottoms and foothills were generally characterized as being suitable from the bioclimatic model, but not from the stream habitat model. Areas predicted as suitable from the stream habitat model were highest at mid elevations, in areas of high topographic relief. Beyond the northern range limit, predictions of suitable habitat from both modelling approaches diverged greatly (Figure 3.2). Predictions of suitable habitat from the bioclimatic model stopped almost immediately at (or before) the northern range limit, whereas the stream habitat continued to delineate suitable habitat far beyond the northern range limit into northern Oregon and southern Washington.  48    49  Figure 3.2 Predicted suitability projections from the stream habitat and bioclimatic ENMs.  The stream habitat models are shown in the bottom, the climatic ENMs are shown in the middle panel and combined predictions from bother the stream habitat model and the bioclimatic model are shown in the top most panel. The color gradients across each of the models indicate agreement across each of the five niche modelling methods used (GLM, GAM, RF, BRT and MAX), where a value of zero indicates the location was below the threshold across all five methods and a value of five indicated full agreement across the niche modeling methods.   Use of the ExDet tool revealed overall that the relative degree of extrapolating into novel environments was low beyond the northern range limit for both the bioclimatic and stream habitat models (Figure 3.3). But the bioclimatic niche model was much more likely than the stream habitat model to encounter novel environments when projections were made outside of the species’ distribution, especially to the east and northeast. The bioclimatic niche model presented a much more serious risk of extrapolation into novel environments when novelty in environmental space was considered (Type II novelty, see Mesgaran et al 2014). Across the entire study area, major basins to the east of the species’ distribution presented a more serious relative risk of extrapolation in both univariate and multivariate environmental space (Figure 3.3).  50   Figure 3.3 Spatial maps of the relative risk of extrapolation into novel environments, ExDet tool output.  The panel to the far left shows the distribution of presence (white) and absence (dark grey) records from the testing dataset for reference. The top row shows the relative degree of extrapolation into novel univariate environmental space (Type 1 Novelty, see Mesgaran et al 2014). Hotter colors indicate environmental values are outside of the range of predictors from the dataset used to calibrate the models (MESS surface, Elith et al 2010). The bottom row indicates the relative degree of extrapolation into novel multivariate environmental space (Type 2 Novelty). The left column shows risk of extrapolation for the bioclimatic niche model and the right column shows the risk of extrapolation for the stream habitat model. Values are averaged across the US EPA Level III Ecoregions from a random sample of 50,000 points sampled across the entire study area.   3.4 Discussion  Predictions from the stream habitat and climatically-based ecological niche models diverged greatly beyond the range northern limit of M. cardinalis. Each of the models gave completely different and opposing predictions regarding the influence of dispersal limitation and fitness limitations as alternative mechanisms structuring the species’ northern range limit. From the stream habitat model, abundant suitable but unoccupied habitat beyond the range limit suggests it 51  is predominantly dispersal limited. The bioclimatic niche model, in contrast, suggests that the northern range limit is largely a result of fitness limitation, rather than dispersal limitation, with suitable habitat declining rapidly beyond the species’ range limit. The conflicting results between these two alternative niche models serves as a useful demonstration of the sensitivity of these general methods to the underlying steps and decisions required during their development.  From Chapter 2 of this thesis, I demonstrated that predictions from the bioclimatic niche model were inaccurate and did not match observed fitness from the field transplant experiment beyond the northern range limit of M. cardinalis. However, this field transplant experiment was not able to either support or refute predictions from the stream habitat ENMs, since all field sites were selected across a gradient of climatic suitability, but standardized for similar stream habitat features. Similarly, the transplant experiment across the species’ elevational range limit, by Angert and Schemske (2005), was also standardized for similar site-level habitat features. If the stream habitat ENMs provide an accurate representation of the species’ habitat requirements and niche limits, then the northern range limit would be described as being highly dispersal limited. I compare the stream habitat and bioclimatic niche models here based on their prediction accuracy, strengths, limitations and their ability to make predictions beyond the species’ northern range limit.  Model accuracy and performance  Based on AUC scores alone as a measure of accuracy, the bioclimatic ENMs outperformed the stream habitat ENMs. The stream habitat ENMs had slightly higher AUC scores from internal validation, but much lower values from external validation. From external validation, AUC scores dropped close to 0.50 for the stream habitat ENMs, which indicates that these models had almost zero predictive accuracy (no better than a random guess). In contrast, the bioclimatic ENMs had slightly lower AUC scores from internal validation, but AUC scores only dropped to ~ 0.75 when models predictions were applied to the testing dataset.  We were fortunate to have a completely independent testing dataset available for model validation and testing. Usually, most applications of ENMs only have one single dataset available and accuracy tests are only possible through either internal resubstituting or some form of cross-validation (Elith and Leathwick 2009; Elith et al 2010; Bahn and McGill 2013). However, even spatial cross-validation and related methods cannot fully match the power of 52  having an external testing dataset (Peterson et al 2007; Bahn and McGill 2013; Searcy and Shaffer 2014). The external testing dataset used here was collected with different survey methods, by different individuals and didn’t share the same internal biases as the training dataset of herbarium records. Without the external testing dataset, I would have concluded that the stream habitat ENMs were better in all respects, when in reality these models were not easily transferable across the datasets and therefore had inflated accuracy scores.  It is possible that the poor predictive performance of the stream habitat ENMs, when evaluated against the external testing dataset, could have been the result of potential biases in this survey. Surveyed absence records were more frequent in larger stream and rivers in the testing dataset, while in the training dataset pseudoabsences were largely drawn from much smaller stream and seepages (Appendix Table D.1). The field survey used as the testing dataset was targeted and stratified across climatic space, but was not necessarily balanced across the full range of available stream habitat types (A.L. Angert unpublished data). If the survey had sampled more small streams and tributaries, it’s possible that AUC scores would increase. The absence of M. cardinalis from many medium and large streams in the testing dataset may have also been in part due to complications with low prevalence across the landscape. If only a narrow range of stream habitats were sampled, out of the full range of conditions on the landscape, and occupancy of these suitable habitats is already intrinsically low, then low accuracy scores would not necessarily indicate poor model performance. Further studies on stream habitat available and the occupancy of these habitats would be useful to help untangle these challenges.  The stream habitat ENMs were also better able to make predictions beyond the species’ distribution without extrapolating into novel environments. Surprisingly, neither the stream habitat, nor the bioclimatic ENMs, presented a serious risk of extrapolation immediately beyond the northern range limit, but the bioclimatic niche model still presented a more serious risk of extrapolation overall. It is important to point out that since the bioclimatic ENMs had eight predictor variables, vs only five predictor variables for the stream habitat ENMs, the large discrepancy in the risk of extrapolation was expected to some extent. But I do not consider the variables individually, instead only assessing the final output from the two models. The high degree of extrapolation into novel environments, from the bioclimatic ENMs, compounds one of their existing criticisms of routinely overfitting relationships between occurrence data and predictor variables (Merow et al 2014b; Elith et al 2010; Fitzpatrick and Hargrove 2009). With a large number of uncorrelated environmental variables, any predictions made beyond the species’ 53  range limits are almost guaranteed to be projections into novel environments. This was apparent from the ExDet maps that showed an increasing degree of environmental novelty as we moved away from the Mediterranean climate of California and southern Oregon. This has, in part, been why many researchers have advocated for the use of mechanistic (or process) based models, over correlative ENMs, to make predictions beyond species’ range limits (Kearney and Porter 2009; Merow et al 2014a; Merow et al 2014b). To assess the transferability of an ENM in space, we must determine the degree to which we are extrapolating into novel environments when making suitability predictions beyond a species’ range limit, in addition to evaluating models solely based on their ability to discriminately correctly between presence absence records.  Ecological interpretability of the models Despite the high performance of the stream habitat ENMs, there were still several discrepancies between the variable response curves and known (or expected) relationships with these variables based on existing observations and field studies. This made it difficult to justify to what extent these predicted relationships have direct casual connections back to individual or population-level fitness. M. cardinalis had the highest predicted suitability (or probability of occurrence) in large streams and rivers, rather than smaller stream and tributaries. But existing field studies (supported by personal observation) have shown that the species actually has higher fitness in small streams and tributaries (Levine 2001; Williams and Levine 2004). These small streams, seepages and tributaries (with the exception of springs) do not occur randomly over the landscape, but are instead systematically associated with larger streams and rivers due to the dendritic nature of stream networks. By relying on opportunistic occurrence records from herbarium databases and public surveys, it’s possible that location reporting could have been biased towards larger streams, especially for older records (e.g. no way of knowing if individuals were growing near a tributary confluence or along the main stem of a river). A majority of the variability in fitness occurs within stream sites, where individuals and patches are subject to varying levels of moisture availability and canopy exposure at small scales (Levine 2001; Williams and Levine 2004; Chapter 2 of this thesis). These larger stream networks likely influence the availability of these suitable microsite conditions, but direct causal links are not clear. There is also no reason to believe that predicted suitability measured on a continuous scale rather than above a threshold level, from the stream habitat ENMs, should provide any additional utility. In contrast, climate variables, especially temperature, have more direct and measurable 54  physiological effects on individuals and ultimately population-level fitness for M. caridnalis (Angert 2006b; Angert et al 2011; Paul et al 2011). Although there was no relationship with predicted suitability and the field transplant experiment across the northern range limit, there was a continuous negative relationship with predicted suitability and elevation. Implications for other study systems  It would be ideal to fit all relevant predictor variables into a single model, but the predictive power of the alternative variable sets were dependent on the spatial scale and methods used to sample the background environment. These same issues have been discussed for other applications of ecological niche models, where relevant small-scale and large-scale predictor variables are available, but their importance is scale dependent (Wiens 2002; Graph et al 2005; Barbet-Massin et al 2012; Jackson and Fahrig 2015). In this case study, rather than combining predictions in a single spatially nested framework (e.g. Talluto et al 2015; Domish et al 2015), these two classes of models were competing with each other as alternative ENMs. These two alternative ENMs also demonstrated the challenge of spatial autocorrelation in correlative modelling, where the relationship between a species’ distribution and environmental variables can be inflated by location alone. New methods are emerging for scaling the probability of occurrence based on location across different scales and models, which if applied here, could help balance predictive accuracy and uncertainty between these competing ENMs (Talluto et al 2015; Bardos et al 2015). Comparing alternative ENMs, developed with different sets of predictor variables and alternative methods, is useful to gauge the sensitivity and validity of their predictions (Peterson and Nakazawa 2008; Zhu et al 2012; Rödder et al 2009). In this study I showed how maps of predicted suitability can be compared to identify highly divergent inferences about range limiting mechanisms. Controlling for climate in the stream habitat ENMs with only a simple thermal envelope may be insufficient to account for more complex relationships between fitness and other precipitation or seasonality-related variables, but still proved to be a useful comparison to gauge the magnitude of differences in predictions. For M. cardinalis and other study systems, failing to account for relevant species-specific environmental variables could lead to largely inaccurate estimations of niche limits and resulting projections of geographic range shifts with climate change.  55  Conclusions Spatial predictions of suitable habitat beyond the northern range limit of M. cardinalis were drastically different between the bioclimatic and stream habitat ENMs compared in this chapter. These models gave opposing predictions of either a fitness limited or dispersal limited range limit. In isolation, each of these ENMs has its own merit and justification, but when combined they offer a powerful comparison to gauge the uncertainty and sensitivity of their predictions to their underlying methods. The bioclimatic ENMs had higher predictive accuracy from external validation, but they failed to predict fitness from the field transplant experiments across the northern range limit. The stream habitat ENMs supported results from the field transplant experiment across the northern range limit and showed a lower degree of extrapolation into novel environments when predictions were made into these areas, but the stream habitat ENMs still largely failed to make accurate predictions to the independent testing dataset.  Too often, ENMs are developed with the most easily accessible and readily available environmental variables (i.e. climatic predictor variables), and then are applied broadly across taxa, rather than seeking out the most causal predictors that are reflective of a species’ natural history (Elith and Leathwick 2009; Franklin 2010). No group of predictor variables can be characterized as being fundamentally either more or less important. For this specific study system, at the northern range limit of M. cardinalis, stream habitat variables outperformed climatic predictor variables in terms of their ability to support results from the field transplant experiments. This should be seen as a more powerful test than predictive accuracy from presence-absence data. When results from the field transplant experiment in Chapter 2 of this thesis were combined with suitability predictions from the stream habitat ENMs, I was able show strong evidence that the northern range limit of M. cardinalis is largely dispersal limited.  56  Chapter 4: Conclusion Species’ geographic range limits and their niche limits are two fundamentally different entities, but for convenience they are often treated as being one in the same. The degree of mismatch between species’ niche limits and their range limits hinders our ability to infer one from the other (Gaston 2009; Holt 2009; Sexton et al 2009; Pigot and Tobias 2013; Ehrlén et al 2015). In particular, dispersal limitation should cause a range limit to fall short of a niche limit. Yet widely used ecological niche models (ENMs) have largely ignored dispersal limitation or assumed that its effects are only trivial. These assumptions can have serious downstream consequences regarding the accuracy of predictions from ENMs and their intended applications.  In this thesis I used experimental field transplants and ENMs to demonstrate how dispersal limitation and fitness limitation structure the northern range limit of M. cardinalis. I then evaluated how well suitability predictions from the bioclimatic ENMs matched observed fitness from the field experiments. Using data from a previous study by Angert and Schemske (2005), that transplanted the species within and beyond its upper elevational range limit, I was able to show how the accuracy of ENMs can be highly context dependent. At the upper elevational range limit, predicted suitability from the ENMs matched observed fitness from the field transplant, while beyond the northern range limit, the ENMs failed to predict the high fitness observed in the field transplant experiment. Agreement between suitability predictions from the ENMs and observed fitness from the field experiments fits well with existing expectations based on these range limits being either dispersal or fitness limited. Transplant sites beyond the northern range limit were climatically marginal in relation to the species’ distribution, but not in relation to the species’ fundamental niche limits.  The field transplant across the northern range limit of M. cardinalis demonstrated that this range limit was dispersal limited. Transplant sites were non-randomly chosen to encompass favorable stream conditions (which might be quite infrequent on the landscape). On its own, the transplant experiment was not able to rule out the possibility that the range limit might be both dispersal limited and fitness limited. Predictions from the physical stream habitat ENMs did not show an immediate drop-off in suitability beyond the northern range limit. This supported conclusions from the transplant study, suggesting that the northern range limit is largely dispersal limited. The stream habitat ENMs and the climatic-based ENMs developed in this thesis offered entirely different predictions of range limiting mechanisms. Their comparison was invaluable to demonstrate the sensitivity of ENM methods to baseline decisions, such as variable selection. 57  Although I was not able to experimentally validate predictions from the stream habitat ENMs, their predictions fit well with results from the field transplant experiment and were able to highlight the potential magnitude of dispersal limitation at the species’ northern range limit. Despite the prevalence of dispersal limitation being a prominent mechanism structuring species’ range limits (reviewed in Sexton et al 2009; Halbritter et al 2013; Hargreaves et al 2014; Siefert et al 2015), only four studies have actually attempted to validate predictions from ENMs experimentally with field transplants (Ebeling et al 2008; Sheppard et al 2014; Swab et al 2014; Isaac-Renton et al 2014). The highly mixed results from these field experiments would seem to suggest that accuracy (or ability) of correlative ENMs to actually predict niche limits is both species’ specific and highly idiosyncratic. In this thesis, I demonstrated with M. cardinalis how the accuracy of these models can fit well with existing theory and predictions of dispersal limitation across elevational versus latitudinal range limits.  Experimental field transplants across all life stages that use a demographic approach to estimate lifetime fitness and finite population growth rates should serve as the gold-standard experimental design to assess suitability predictions from ENMs and alternative mechanisms structuring species’ range limits (Angert and Schemske 2005; VanDerVeken et al 2007; Sexton et al 2009; Hargreaves et al 2014; Swab et al 2014). By delineating suitable vs. unsuitable sites on the landscape, ENMs are ultimately trying to predict tipping points at which population and regional growth rates are expected to fall below one (Peterson et al 2003; Guisan and Thuiller 2005; Holt 2009; Elith and Leathwick 2009). If this study had compared only a single metric of fitness, such as fecundity or survivorship, it would have been possible to come to potentially misleading conclusions, since vital rates were largely uncorrelated and occasionally demonstrated potential life history tradeoffs.  It is challenging to say for certain what the long term trajectories are for the populations transplanted within and beyond the northern range limit of M. cardinalis, since the field experiment was not able to account for inter-annual variability. Additionally, it is still not always clear how (or if) population growth rates estimated from small-scale field sites can scale up to regional-level growth rates driving the dynamics or stability of range limits (Merow et al 2014a; Ramula 2014; Swab et al 2014; Ehrlén et al 2015; Tredennick and Alder 2015). This disconnect between the spatial and temporal scales at which ENMs operate and the spatial and temporal scales represented in field studies make it exceedingly difficult to design logistically feasible experiments to validate predictions from ENMs (but see Isaac-Renton et al 2014; Thuiller et al 58  2014). It is therefore useful and informative to attempt to combine and integrate predictions from field studies and broad scale spatial models.  We need to help fit ENMs back into conventional niche theory before broadly applying their predictions at the scale we have been (see Guisan et al 2013). More broad scale tests are needed with demographic data collected either across the distribution of a single species, or perhaps across several species, to develop a better framework to gauge the accuracy of ENMs. The collection of demographic data is invaluable to achieve this goal and should be combined with predictions from ENMs developed for key species of interest (Tredennick and Alder 2015; Ehrlén et al 2015). In the absence of this information, ENMs that forecast range shifts with climate change (see Parmesan 2006; Corlett and Westcott, 2013), the potential spread of invasive species (see Neubert and Parker 2006; Rödder et al 2009) or plans for assisted migration (see Isaac-Renton 2014) could be largely inaccurate. The coarse association between species’ niche limits and their range limits, along with the availability of large scale geospatial environmental datasets have fueled the popularity and widespread use of ENMs, but attempts to experimentally validate their predictions have been exceedingly sparse. Through this study, I demonstrated how field experiments analyzed with a demographic framework can gauge the accuracy of predictions from ENMs. I found that dispersal limitation caused bioclimatic ENMs to underestimate the species’ niche limits. 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Short term climate data from 2014 – 2015 (Northern Range Limit) and 2001 – 2003 (Elevational range limit) is reported below in (brackets).  Transplant sites across the northern range limit      Site Name Within or beyond Latitude (oN) Longitude (oW) Elevation (m) MTWQ (oC) MTCQ (oC) MAP (mm)  Looking Glass Creek Within 43.144088 -123.475052 176 19.02 (22.7) 5.83 (8.95) 989 (782) Rock Creek Within 43.37876 -122.952072 326 18.7 (22.3) 4.78 (7.81) 1584 (1248) Coast Fork Willamette Within 43.6517 -123.087967 260 18.05 (21.7) 4.98 (8.13) 1317 (1026) Mosby Creek Within 43.721298 -122.976311 243 17.83 (21.4) 4.97 (8.13) 1267 (982) Calapooia Creek Beyond 44.359642 -122.842903 146 18.22 (21.8) 5.15 (8.3) 1272 (994) Wiley Creek Beyond 44.412022 -122.675446 176 17.98 (21.6) 4.9 (8.06) 1334 (1036) Thomas Beyond 44.711785 -122.61087 229 17.67 (21.2) 4.43 (7.6) 1690 (1310) Hunter Beyond 44.922787 -123.327316 101 18.3 (21.9) 5.15 (8.3) 1229 (917)         Angert and Schemske 2005: Transplant sites across the elevational range limit    Site Name Within or beyond Latitude (oN) Longitude (oW) Elevation (m) MTWQ (oC) MTCQ (oC) MAP (mm)  Jamestown Within 37.91738 -120.42128 420 24.23 (24.7) 8.52 (8.85) 702 (647) Mather Within 37.88558 -119.855377 1398 20.07 (21.1) 4.2 (4.8) 915 (863) White Wolf Beyond 37.87188 -119.65078 2417 14.98 (16.1) 0.25 (0.90) 1305 (1282) Timberline Beyond 37.96158 -119.280884 3008 11.33 (12.4) -4.27 (-3.7) 991 (905)   66  Appendix B  Plot-level environmental microsite variable measurements Plot-level environmental microsite variables were collected at each plot in the field transplant experiment (Table A.1; Figure 2.1). These variables capture variable moisture, sun exposure and physical features of the plots in the riparian environment:  Aspect (exposure): Aspect 0 – 360o, converted to ‘southness’ (180 – aspect) so that values ranged from 0 (highlight) to 180 (lowlight). Values log-transformed.   Canopy cover: Light exposure (%) measured with a field spherical convex densitometer.  Mean grain size: Mean grain size of plot substrate (silt, sand, gravel ect). Initial measurements taken as percent cover of each substrate type and then converted to a continuous scale from Phi values, following methods in Leeder (1981). Values log-transformed.  Gain size standard deviation: Standard deviation (evenness) of grain size distribution.   Moisture score: Qualitative moisture score from 0 (very dry) to 5 (fully saturated). Values based on whether substrate was damp on surface (+1), damp under the first 2 cm of soil (+1), damp under 5 cm of soil (+1), damp under 10 cm of soil (+1) and damp at the 20 cm (+1).   Soil water content: Water content measured as percent from field weight of 200 g composite soil sample, minus dry weight after 48 hrs in a desiccation chamber.   Vertical distance to water: Negative distance (m), vertical distance to the water’s edge from the closest stream reach. D – A, in Figure B.1.  Horizontal distance to water: Horizontal distance from water’s edge to closest reach of stream. C – B, in Figure B.1.  Bank seasonality: In Figure B.1, cross sectional area of water’s edge to bankfull point (C*D)/2.  Bank Slope: Slope of bank (o) underlying plot. In Figure B.1, ((D/C) + (A/B))/2.  Wetted area to bank area: Ratio of cross sectional area up the bank and away from the plot, to cross sectional area down and towards the stream from the plot. In Figure B.1, (A*B/2):((C-B)*(D-A)/2).  Appendix Figure B.1: Diagram of plot-level microsite measurements.  This sample diagram shows a typical plot (diagonal frame in the center) with the stream to the right and the upper bank to the left. Distance to stream = C – B. Vertical distance to water = D – A. 67   Appendix Figure B.2: Plot-level microsite measured for field sites across the northern range limit of M. cardinalis.  The eight field sites are grouped along the x-axis from south to north. Sites within and beyond the range limit are colored red and blue, respectively. A single measurement was taken for each plot and boxplots show the distribution 68  measurements for plots within each site (n = 12 – 17). A linear model was run for each microsite variables to test for any differences between sites (r^2 and p-values are shown above each panel).    69    Appendix Figure B.3: Principal component analysis for field transplant plots and microsite variables with vital rates for M. cardinalis.  First two axes of the PCA show the distribution of transplant plots in environmental space. Plot-level estimates for each of the four vital rates are shown separately in each panel. Color shading corresponds to the plot-level random intercept estimates from the mixed models. Blue denotes areas of high survivorship, growth, maturity or fecundity, while grey and orange correspond to low plot-level estimates.    70   Appendix C  Supplementary material for the climatic-based ecological niche model  This appendix was included to provide supplementary material for the climatic-based ecological niche models (ENMs) developed in Chapter 2 of this thesis. Content includes model evaluation scores for each of the separate niche modelling methods (Appendix Table C.1), site-level suitability predictions across the niche modelling methods with long-term and short term predictions (Appendix Table C.2), maps of predicted suitability for the five niche modelling methods (Appendix Figure C.1), variable response plots for the ENMs (Appendix Figure C.2) and relationships between each of the four vital rates from the field transplant experimental and predicted suitability estimates from the ENMs (Appendix Figure C.3).    71  Appendix Table C.1: AUC scores for climatic-based ecological niche model of M. cardinalis.  AUC (Area Under the Receiver Operating Characteristic Curve, see Lobo et al 2008) scores are shown across the five niche modelling methods (GLM – General Linear Model; GAM – Generalized Additive Model; RF – Random Forest; BRT – Boosted Regression Tree; MAX – MaxEnt and EN – Ensemble average). Internal validation scores were calculated from the same initial dataset used to calibrate the models, either through resubstitution (leave one out) or a five-fold cross-validation (not possible for RF). External validation AUC scores were calculated from the independent testing dataset of surveyed presence/absence records (described in text, A.L. Angert unpublished data).  Validation Method GLM GAM RF BRT MAX EN Internal Resubstitution 0.769 0.812 0.84 0.998 0.764 0.837 Internal Cross-validation 0.732 0.674 NA 0.871 0.756 0.758 External Validation 0.733 0.743 0.76 0.76 0.758 0.751    72  Appendix Table C.2: Site-level predictions from the climatic-based ecological niche models with short-term and long term climate data.  Transplant sites across the latitudinal and elevational range limits ordered from increasing elevation or latitude.   30-year climate normals (1981 - 2010)  Latitude GLM GAM RF BRT MAX EN Look 43.144 0.524 0.568 0.524 0.515 0.469 0.52 Rock 43.379 0.405 0.412 0.837 0.752 0.409 0.563 Coast 43.652 0.327 0.335 0.577 0.513 0.374 0.425 Mosby 43.721 0.323 0.327 0.419 0.301 0.354 0.345 Calapooia 44.36 0.365 0.334 0.261 0.191 0.36 0.302 Wiley 44.412 0.344 0.325 0.412 0.512 0.348 0.388 Thomas 44.712 0.223 0.186 0.135 0.172 0.282 0.200 Hunter 44.923 0.427 0.437 0.464 0.407 0.421 0.431 Short-term climate data (2014 - 2015)  Latitude GLM GAM RF BRT MAX EN Look 43.144 0.894 0.886 0.725 0.391 0.534 0.686 Rock 43.379 0.867 0.871 0.666 0.819 0.517 0.748 Coast 43.652 0.844 0.855 0.513 0.737 0.483 0.686 Mosby 43.721 0.843 0.851 0.487 0.695 0.467 0.669 Calapooia 44.36 0.826 0.839 0.481 0.678 0.471 0.659 Wiley 44.412 0.833 0.84 0.466 0.694 0.464 0.659 Thomas 44.712 0.757 0.718 0.267 0.217 0.419 0.476 Hunter 44.923 0.876 0.88 0.656 0.632 0.521 0.713 30-year climate normals (1981 - 2010)  Elevation GLM GAM RF BRT MAX EN Jamestown 420 0.775 0.71 0.494 0.326 0.55 0.571 Mather 1398 0.652 0.664 0.728 0.523 0.489 0.611 Timberline 3008 0.00E+00 0.015 0.08 0.034 0.079 0.042 White Wolf 2417 0.094 0.161 0.179 0.071 0.232 0.147 Short-term climate data (2001 - 2003)  Elevation GLM GAM RF BRT MAX EN Jamestown 420 0.93 0.842 0.544 0.478 0.639 0.687 Mather 1398 0.933 0.892 0.769 0.96 0.6 0.831 Timberline 3008 0.003 0.088 0.281 0.334 0.111 0.163 White Wolf 2417 0.771 0.63 0.302 0.478 0.364 0.509    73  Appendix Figure C.1 Maps of continuous suitability predictions from climatic-based ecological niche models across the five modelling methods.  This figure is an extension of Figure 2.4 (Ensemble prediction), showing predictions for each of the GLM, GAM, RF, BRT and MAX models separately. Left column is a close up of transplant sites, right column shows predictions across the entire species range. The sharp jump from yellow to orange along the color gradient, marks the maximum sensitivity/specificity threshold.    74  Appendix Figure C.1 (continued)    75  Appendix Figure C.2: Variable response plots for the climatic-based ecological niche models.  Eight climatic variables are plotted for the five unique niche modelling methods. Response curved were generated using partial plots and variable importance estimates were estimated by shuffling values for each variable and comparing predictions to the original dataset (see: Liaw and Wiener 2002). Multiple red lines correspond to each separate pseudoreplicate dataset. Presence and absence data are shown for a single dataset with presence points (red circles) and pseudoabsence points (crosses).    76   77  Appendix Figure C.2 Continued 78  Appendix Figure C.2 Continued  79  Appendix Figure C.2 Continued  80  Appendix Figure C.2 Continued   81  Appendix Figure C.3: Relationship between site-level vital rate estimates and predicted suitability from the ecological niche models. The following twenty panels show the relationships between survivorship, growth, maturity and fecundity with suitability predictions from the climatic based GLM, GAM, RF, BRT and MAX models across the species northern range limit. Significant positive or negative relationships are marked with a dashed line.     82   83  Appendix Figure C.4: Residual predictions of presence (occurrence) points from the ecological niche models. Predicted suitability values are shown for all presence records used to calibrate the ENMs. Clustering of blue or red points indicated negative or positive spatial autocorrelation for occurrence records of M. cardinalis.    84  Appendix D  Supplementary material for the stream habitat ecological niche models Appendix Figure D.1: Variable response plots for the five environmental predictor variables used to develop the stream habitat ecological niche models.  Similar to Appendix Figure C.2, variable response plots were generated using partial plots (described in text). A flat line indicates that the variable was excluded from the given model. Variable importance values were calculated by shuffling values and comparing the correlation coefficient to the original dataset (see Liaw and Wiener 2002).        85  Appendix Figure D.1 Continued (2/5)    86  Appendix Figure D.1 Continued (3/5)    87  Appendix Figure D.1 Continued (4/5)    88  Appendix Figure D.1 Continued (5/5)    89   Appendix Table D.1: Range of stream habitat predictor variables across the training and testing datasets. Mean values are shown for all five predictor variables with standard deviation in brackets. The training dataset consisted of herbarium and opportunistic occurrence records of M. cardinalis used to calibrate the stream habitat ENMs, along with pseudoabsence records. Mean values and standard deviations are also shown for presence and absence records from the testing and training datasets (described in text).  Predictor variable DSEA Slope TerrRough ASD Drn Area Training dataset Presence n= 243 83 (24.1) 0.05 (0.06) 85.2 (43.7) 6.17 (2.3) 0.56 (0.14) Absence n= 24,300 57.3 (40.6) 0.06 (0.07) 52.1 (43.7) 3.2 (2.6) 0.55 (0.33) External testing dataset Presence n= 66 86.9 (16.4) 0.06 (0.06) 85.5 (39) 5.45 (1.76) 0.57 (0.14) Absence n= 114 82.7 (24.7) 0.05 (0.06) 63.8 (35) 5.65 (2.0) 0.54 (0.14) DSEA: Discharge Seasonality Slope (o) TerrRough: Topographic roughness ASD: log (annual stream discharge, cf/s) Drn Area: log (drainage area, sq Km)   90  Appendix E  Site-level elasticity estimates from the integral projection models  Appendix Figure E.1 Vital rate elasticities for individual sites across the northern range limit of M. cardinalis.   This figure is an extension of Figure 2.6, showing elasticity estimates for sites individually from the integral projection models. Acronyms are as follows: S, G, R and F stand for Survivorship, Growth, Reproduction and Fecundity, respectively; Int and Slope are Intercept and Slope and Site-Int or Site-Slope indicate the site-level intercept or slope; SPF, seeds per fruit; Estb, seed establishment probability; m-Recr, mean size of recruits; sd-Recr, standard deviation of recruits.       

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