SAMPLING METHODS A N D POPULATION PREDICTION IN Lambdina fiscellaria lugubrosa (LEPIDOPTERA: GEOMETRIDAE ) IN BRITISH COLUMBIA BY Qiwei Liang B.Sc. (For.) Nanjing University of Forestry, 1982 M.Sc (For.) School of Graduate Studies, Chinese Academy of Forestry, 1985 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES INDIVIDUAL INTERDISCIPLINARY STUDIES GRADUATE PROGRAM We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January 1997 Â© Qiwei Liang, 1997 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of J^dvi/io/u^/^ /u+*^)^r,lj>6*!*ux*(j GrrzuePatfa SfU^i'k^Ty^^^\ The University of British Columbia Vancouver, Canada Date CTat*^ . 2.9 , / v /?97 / , DE-6 (2/88) ii Abstract Outbreaks of Lambdina fiscellaria lugubrosa in British Columbia have always been preceded by a rapid population growth. Sampling methods and population prediction models are needed to provide forest managers with the capability of monitoring and predicting populations of the insect. I sampled eggs, larvae, pupae and adults of Lambdina fiscellaria lugubrosa at various locations in the province of British Columbia from 1992 to 1994. Population estimates of eggs and larvae, directly obtained from habitat units, were fitted to theoretical spatial distribution and mean - variance models. Sampling plans, based on fixed sample size, sequential sampling, and binomial sampling methods, were developed. Pupae were sampled with burlap traps of different designs. Because more pupae were trapped in two or three layers of burlap than in a single layer, traps with at least two layers are recommended for future use. The strong linear relationship of pupal density between burlap traps and open tree bark units validated the use of burlap traps as a sampling tool. Spatial continuity of larval and adult densities was found along forest roads, although the range and magnitude of the spatial dependence varied significantly between years and among sites. Also, larval and adult densities along the road were closely related to those within the stands. The results showed a great potential of roadside sampling for the management of this insect. Regression models showed strong quantitative relationships of population estimates between successive life stages, which can be used to predict population density. Defoliation I l l prediction was conducted with discriminant analysis, in which defoliation classes were related to insect population estimates and tree DBH. Like many other studies in insect sampling, the insect samples were non-random in this study. Randomization tests were used to validate results from conventional statistical analyses and to examine the general necessity of using randomization tests in insect sampling. The results suggested that non-random insect samples do not seriously hamper the use of conventional statistical analyses. The implications of this study to the management of western hemlock looper and other forest insects were discussed. iv Table of Contents Page Abstract . ii Table of Contents iv List of Tables vii List of Figures xii Acknowledgment xvi Chapter 1 Overview 1 1.1 Introduction 1 1.2 Biology of the western hemlock looper 2 1.3 Objectives 4 1.4 Study areas 8 1.5 Statistical computing software packages 9 Chapter 2 Literature review . 11 2.1 Population expression 12 2.2 Sampling universe and sampling unit 17 2.3 Sampling design 19 2.4 Spatial distribution 24 2.5 Sample size 29 2.6 Binomial sampling 34 2.7 Spatial statistics 36 2.8 Population prediction 37 2.9 Summary 39 Chapter 3 Egg sampling of Lambdina fiscellaria lugubrosa 42 3.1 Introduction 42 3.2 Materials and methods 44 3.2.1 Sample collection 44 3.2.2 Sample processing 45 3.2.3 Statistical analyses 45 3.3 Results 48 3.4 Discussion and conclusions 60 Chapter 4 Larval sampling of Lambdina fiscellaria lugubrosa 62 4.1 Introduction 62 4.2 Materials and methods 64 4.2.1 Sample collection and processing 64 4.2.2 Statistical analyses 65 4.3 Results 66 4.4 Discussion and conclusions 78 Chapter 5 Pupal sampling of Lambdina fiscellaria lugubrosa 82 5.1 Introduction 82 5.2 Materials and methods 83 5.2.1 Burlap trap designing 83 5.2.2 Trap placement and collection 86 5.2.3 Statistical analyses 87 5.3 Results 89 5.4 Discussion and conclusions 103 vi Chapter 6. Forest roadside sampling for larvae and adults of Lambdina fiscellaria lugubrosa 107 6.1 Introduction 107 6.2 Methods 109 6.2.1 Study areas 109 6.2.2 Sampling methods 110 6.2.3 Statistical analyses I l l 6.3 Results 113 6.4 Discussion and conclusions 122 Chapter 7. Population density and defoliation prediction in Lambdina fiscellaria lugubrosa 125 7.1 Introduction 125 7.2 Methods 127 7.3 Results 130 7.4 Discussion and conclusions 143 Chapter 8 General discussion 147 8.1 Population expression, spatial dispersion and sampling plans . . . . 147 8.2 Sampling and randomization tests 150 8.3 The development of a population monitoring and prediction system for western hemlock looper in British Columbia 152 8.4 Further work in population monitoring and prediction 157 Reference cited 161 vii List of Tables Page 3.1 Analysis of variance of egg counts of Lambdina fiscellaria lugubrosa in the upper, middle and lower strata of crowns of Tsuga heterophylla at six locations in the interior of British Columbia, 1992 50 3 2 Optimum sample size (numbers of 40 g lichen sample) for egg sampling of Lambdina fiscellaria lugubrosa in the interior of British Columbia, at various mean densities and precision levels 54 â€¢3.3 Termination points for sequential sampling of eggs of Lambdina fiscellaria lugubrosa in the interior of British Columbia, based on the Green and the Kuno methods 55 3.4 Characteristics of sample trees (Tsuga heterophylla) used for egg of Lambdina fiscellaria lugubrosa from the upper, middle and lower strata of crowns at six locations in the interior of British Columbia, 1992 . . . . 56 3.5 Analysis of covariance of egg counts of Lambdina fiscellaria lugubrosa in the lower stratum of crowns of Tsuga heterophylla at six locations in the interior of British Columbia, 1992 58 3.6 Statistical significance of analysis of variance and t-test between conventional approach and randomization testing for Lambdina fiscellaria lugubrosa 59 V l l l 4.1 Sampling statistics of larval density of Lambdina fiscellaria lugubrosa in the interior of British Columbia, 1993-1994, with density expressed on three kinds of sampling units 67 4.2 The Taylor power law models and the Iwao patchiness regression models for early and late larvae of Lambdina fiscellaria lugubrosa in British Columbia 69 4.3 Optimum sample sizes for sampling larvae of Lambdina fiscellaria lugubrosa in the interior of British Columbia 70 4.4 Termination points for sequential sampling of early and late larvae of Lambdina fiscellaria lugubrosa in the interior of British Columbia 73 4.5 Parameter values for estimating the variance of log (m) in binomial sampling plans for larvae of Lambdina fiscellaria lugubrosa in the interior of British Columbia 76 5.1 Sampling statistics of pupal density of Lambdina fiscellaria lugubrosa by plot, trap type and zone in the interior of British Columbia, 1993-1994 90 5.2 Analysis of variance of the effect of location and trap type (A and B) on catches of pupae of Lambdina fiscellaria lugubrosa in burlap traps in the interior of British Columbia, 1993 . . 9 2 5.3 Analysis of variance of the effect of burlap zone within types A and B traps on catches of pupae of Lambdina fiscellaria lugubrosa in British Columbia, 1993 92 ix 5.4 Pearson correlation coefficients of pupal counts of Lambdina fiscellaria lugubrosa among burlap zones within type A trap 94 5.5 Pearson correlation coefficients of pupal counts of Lambdina fiscellaria lugubrosa among burlap zones within type B trap 94 5.6 Pupal catches of Lambdina fiscellaria lugubrosa in Type C traps in the interior of British Columbia, 1993 96 5.7 Pupal catches of Lambdina fiscellaria lugubrosa in type D traps at different locations in the interior of British Columbia, 1994 97 5.8 Pupal catches of Lambdina fiscellaria lugubrosa in type D traps on different tree species in the interior of British Columbia, 1994 98 5.9 Analysis of covariance of the effect of stand variables on catches of pupae of Lambdina fiscellaria lugubrosa in burlap traps of type D in a grid plot (60 m x 200 m) in the Sugar Lake area, British Columbia, 1994 99 5.10 Regression models for relationships of pupal density of Lambdina fiscellaria lugubrosa between burlap traps and tree bark units (30 cm x40 cm) in the interior of British Columbia 1994 102 5.11 Statistical significance of analysis of variance between conventional approach and randomization testing for Lambdina fiscellaria lugubrosa 104 6.1 Sampling statistics for catches of male adults of Lambdina fiscellaria lugubrosa in pheromone traps in Capilano, Seymour and Coquitlam Watersheds, British Columbia, 1993-1994 114 X 6.2 Summary of results for spatial autocorrelation analysis of male adults of Lambdina fiscellaria lugubrosa, caught in pheromone traps along the main road in Seymour Watershed, Vancouver, British Columbia, 1993-1994 115 6.3 Summary of results for spatial autocorrelation analysis of male adults of Lambdina fiscellaria lugubrosa, caught in pheromone traps along the main roads in the Capilano Watershed and the Coquitlam Watershed, Vancouver, British Columbia, 1994 118 6.4 Summary of results for spatial autocorrelation analysis of larvae and male adults of Lambdina fiscellaria lugubrosa, along the Sugar Lake Forest Road, Kamloops Forest Region, British Columbia, 1994. Larvae were sampled with a pole pruner from the lower crown of Tsuga heterophylla and adults with pheromone traps 120 7.1 Regression models of population densities of Lambdina fiscellaria lugubrosa among different life stages in the interior of British Columbia, 1993 131 7.2 Regression models of population densities of Lambdina fiscellaria lubrosa among different life stages in the interior of British Columbia, 1994 . 132 7.3 Regression models of plot mean densities of Lambdina fiscellaria lugubrosa among different life stages in the interior of British Columbia, based on pooled data of 1993 and 1994 134 xi 7.4 Quantitative relationships between egg density of Lambdina fiscellaria lugubrosa and defoliation in the interior of British Columbia, based on the pooled data of 1993, 1994 and 1995 135 7.5 Quantitative relationships between larval density of Lambdina fiscellaria lugubrosa and defoliation in the interior of British Columbia, 1993 139 7.6 Quantitative relationships between larval density of Lambdina fiscellaria lugubrosa and defoliation in the interior of British Columbia, based on pooled data of 1993 and 1994 . 140 xii List of Figures Page 1.1 Sampling locations for Lambdina fiscellaria lugubrosa in British Columbia, 1992-1994, with cities indicated by solid circles and sampling locations by empty triangles. HC = Hungry Creek; MB = McBride; WC = Walker Creek; ML = Mud Lake Road; WR = West Raft Road; RD = Revelstoke Dam; TR = Tangier River Road; JC = Jumping Creek and SU = Sugar Lake 10 3.1 Egg counts of Lambdina fiscellaria lugubrosa in the upper, middle and lower strata of crowns at six locations in the interior of British Columbia, 1992 49 3.2 Mean - mean crowding relationship for eggs of Lambdina fiscellaria lugubrosa in the interior of British Columbia. Egg density is expressed as numbers of eggs per 40 g lichen sample 52 3.3 Mean - variance relationship for eggs of Lambdina fiscellaria lugubrosa in the interior of British Columbia. Egg density is expressed as numbers of eggs per 40 g lichen sample 52 4.1 Mean - mean crowding and mean - variance relationships for early larvae (A, B) and late larvae (C, D) of Lambdina fiscellaria lugubrosa in the interior of British Columbia 71 4.2 Relationships between the proportion of branch-tip samples with no larvae and mean larval density for early and late larvae of Lambdina fiscellaria lugubrosa in the interior of British Columbia, m is the mean larval density and p is the proportion of branch samples with no larvae 77 The design of burlap trap types A and B for pupae of Lambdina fiscellaria lugubrosa 84 The design of burlap trap types C and D for pupae of Lambdina fiscellaria lugubrosa 85 Relationship of pupal density between burlap traps (x) and open tree bark units for Lambdina fiscellaria lugubrosa in the interior of British Columbia, Canada. The two variables were transformed into In (x +1) and In (y +1), respectively, 100 Actual and predicted values of population density of pupae of Lambdina fiscellaria lugubrosa based on regression model In (y +1) = 0.62 In (x +1), where y is density in open tree bark units and x is density in burlap traps. Pupal density is expressed as numbers of pupae per 100 cm 2 burlap surface area. . . 101 Spatial correlograms of male adults of Lambdina fiscellaria lugubrosa, caught in pheromone traps, along the main forest road at: A) Seymour Watershed in 1993, distance class intervals are 2.71 km; B) Seymour Watershed in 1994, distance class intervals are 3km; C) Capilano Watershed in 1994, distance class intervals are 3 km, and, D) Coquitlam Watershed in British Columbia, 1994 distance class intervals are 3 km 116 xiv 6.2 Spatial correlograms of late larvae (A) and adults (B) of Lambdina fiscellaria lugubrosa along the Sugar Lake Forest Road, Kamloops Forest Region, British Columbia, 1994. Distance class intervals are 3 km 121 7.1 Relationship of population densities between early and late larvae of Lambdina fiscellaria lugubrosa, based on pooled data of 1993 and 1994. Larval density is expressed as numbers of larvae per 100 g dry needles 136 7.2 Relationship of population densities between early larvae and pupae of Lambdina fiscellaria lugubrosa, based on pooled data of 1993 and 1994. Larval density is expressed as numbers of larvae per 100 g dry needles and pupal density as numbers of pupae per 100 cm 2 burlap surface area 137 7.3 Relationship of population densities between late larvae and pupae of Lambdina fiscellaria lugubrosa, based on pooled data of 1993 and 1994. Larval density is expressed as numbers of larvae per 100 g dry needles and pupal density as numbers of pupae per 100 cm 2 burlap surface area 138 7.4 Actual and predicted density of late larvae of Lambdina fiscellaria lugubrosa, based on regression model In (y+l)=0.97 In (x+1), where y is late larval density and x is early larval density. Larval density is expressed as numbers of larvae per 100 g dry needles. . . 141 Actual and predicted density of pupae of Lambdina fiscellaria lugubrosa, based on regression model In (y+l)=0.36 In (x+1), where y is pupal density and x is early larval density. Larval density is expressed as numbers of larvae per 100 g dry needles while pupal density is expressed as numbers of pupae per 100 cm 2 burlap surface area xvi Ackno wle dgments Drs. Bradfield and Otvos, my co-supervisors, have made this project a great learning experience for me during the past five years. Without Dr. Otvos's experience with hemlock looper ecology and Dr. Bradfield's background in statistical ecology, this project would not have been possible. Their patience and willingness to help have been extraordinary. I would also like to thank the other members of my committee: Drs. Jack Maze, Michael Feller and Les Lavkulich who gave their assistance in various stages of the project. Bob Betts and Nicholas Conder (Pacific Forestry Center ) helped with several field trips under very bad weather conditions, including falling trees for egg sampling. Students Kevin Buxton, Dion Manastyrski and Nicole Wallace from the University of Victoria also assisted with some field work. I was very fortunate to meet John Howell (Greater Vancouver Regional District) who assisted me with the pheromone traps placement and collection in the three watersheds. Drs. Jerry Carlson (Phero. Tech. Ltd.), Lorraine Maclauchlan (Kamloops Forest Region, B. C. Ministry of Forests) and Art Stock (Nelson Forest Region, B. C. Ministry of Forests) have provided their support for this project. The Pacific Forestry Center has provided me with facilities for the project. Financial support for this project was provided by the Science Council of British Columbia (G. R. E. A. T. Scholarship), the Canada-British Columbia Partnership Agreement on Forest Resource Development (FRDA II, 1991-1996) and the B. C. Ministry of Forests. X V I 1 I thank my wife, Donrnei, for accompanying me to Canada, and especially for the sacrifices she has made to support our family. Without her patience, this project would have been much more difficult for me. My sincere thanks also go to my family members in China for their constant encouragement. Finally, I dedicate this thesis to my 6 year old son, Wei. 1 Chapter 1 Overview 1.1 Introduction The western hemlock looper (WHL), Lambdina fiscellaria lugubrosa (Hulst) (Lepido-ptera: Geometridae) is a destructive defoliator with a distribution mainly west of the Rocky Mountains, including British Columbia(Harris et al. 1982), Oregon and Washington (Caro-lin et al. 1964). The species also occurs in Alaska (Torgersen and Baker 1969, Torgersen 1971) and Idaho (Dewey et al. 1972, Meyer and Livingstone 1973). Although the preferred host of this insect is western hemlock, Tsuga heterophylla (Raf.) Sarg., many other coniferous species are also attacked, especially during severe outbreaks. These less preferred hosts include western red cedar, Thuja plicata Dorm; Douglas-fir, Pseudotsuga menziesii (Mirb.) Franco; spruces, Picea spp.; true fir, Abies spp.; western white pine, Pinus monticola Dough; and western larch, Larix occidentalis Nutt. (Hopping 1934, Kinghorn 1954). Western hemlock looper infestations generally occur in mature stands. The older larvae are wasteful feeders, usually eating only a proportion of a needle before moving to another. Large numbers of needles are thus damaged and turn reddish-brown as they die, resulting in growth reduction, top-kill, and eventually, tree mortality. During outbreaks, considerable tree mortality may occur over large areas (Hopping 1934, Kinghorn 1954). Outbreaks have been recorded both on the coast and in the interior of British Columbia (Harris et al. 1982, Turnquist 1991), but they have been more common in the interior over the past two decades. Since 1911, seven outbreaks have been recorded in the 2 interior (Turnquist 1991, Wood and Van Sickle 1992). During the period of 1990-1994, the interior experienced the most severe western hemlock looper outbreak in its recorded history and the infestation covered an estimated area of 186,000 ha in 1992 (Wood and Van Sickle 1992). In the Nelson Forest Region alone, this insect was estimated to have killed 5.5 million m 3 of timber during the outbreak, which was equivalent to about the entire annual allowable cut of the Region at that time (Art Stock, pers. comm.). Outbreaks are characterized by a rapid population increase. By the time an outbreak is detected, usually from aerial surveys, it is too late to initiate control measures to prevent extensive tree mortality. Therefore, advances in population monitoring and population prediction are urgently needed to allow sufficient time for planning, organizing and conducting control operations to minimize damage. 1.2 Biology of the western hemlock looper Western hemlock looper belongs to the family Geometridae (McGuffin 1987). The different life stages are described as follows. Eggs. The eggs are smooth, oval in shape, with a saucer-like depression at one end. They are bluish green at oviposition, but the fertile eggs turn copper-brown later. The egg is the overwintering stage. In British Columbia, eggs are laid between September and October (Erickson 1984), singly (Shore 1989) or in small groups of two to 10 eggs (Hopping 1934), on substrates such as moss and lichen, in bark crevices on the trunk and branches of trees (Shore 1989), and on the foliage of trees (Hopping 1934). The preferred oviposition 3 substrate is mosses on the coast, but lichens in the interior (Alectoria spp.) (Thomson 1958, Shore 1989), which usually hang from the branches of mature trees. During an outbreak, eggs can also be found on forest floor litter (Koot 1994). Larvae. In Canada, almost all larvae of the family of Geometridae have two pairs of prolegs, one on the sixth abdominal segment and the second on the last abdominal segment (McGuffin 1987). Lacking prolegs on the middle abdominal segments, the larvae crawl in a looping manner and thus are given their common name (Coulson and Witter, 1984). The larvae of western hemlock looper have five instars and vary in body length from 5 mm to 25 mm depending on the instars. The first instar larva, which hatches from eggs from late May to the early or mid-June, has a black head and the body is marked with grey and light grey. From this stage on, there is considerable variability in body color. In the second instar, horizontal fine lines appear on the dorsal side of the body. The body colour becomes darker in the third instar and black dots appear at the base of each seta. The fourth and fifth instars are similar in colour and pattern. The young larvae feed lightly on the elongating new shoots, but as they mature, they become heavy feeders on the foliage (Furniss and Carolin 1977). Larvae of all instars, can drop on silken threads to the lower branches of host trees or on to the forest floor in search of food (Furniss and Carolin 1977). Pupae. The pupae are 11-16 mm long and the colour varies with age. The colour is light green initially and changes to yellowish-brown later with light brown spots to dark brown when the spots almost disappear before adult emergence. Pupation occurs from mid-August to early September and usually last about two weeks. Pupae are found in protected places such as bark crevices, moss, lichen and debris on the forest floor (Furniss and Carolin 1977, Erickson 1984, Koot 1994). My own observations over 3 years suggest 4 that pupation occurs more frequently in bark crevices than in other places. Adults. The adults are fawn in colour, with a wing expanse of about 35 mm. The forewings are marked with two darker wavy lines with a dark spot in between. The hind wings have only one darker brown wavy line. Unlike the Douglas-fir tussock moth, Orgyia pseudotsugata (M.), another important forest defoliator in British Columbia, hemlock looper females can fly. The adults generally eclose in the evening and mate from late August to mid-October (Erickson 1984, Hopping 1934). A n individual female adult can lay up to 140 eggs (McGuffin 1987). Four intersex individuals (adults with male antennae on their heads and eggs in their abdomens) were found during this study and wil l be reported on separately. 1.3 Objectives Sampling meuiods and population prediction models provide the information base for decision making in integrated pest management (IPM) (Coulson and Witter 1984, Waters etal. 1985, Speight and Wainhouse 1989). Previous studies of sampling methods for western hemlock looper (Thomson 1958, Shore 1989, 1990) provided the initial steps toward the development of a more extensive sampling protocol that would include all life stages of the insect. Methods for egg and pupal sampling have been explored, but little attention has been given to the appropriate expression of populations. For example, although burlap trap size varied considerably with D B H of sample trees, pupae were expressed as numbers per trap (Shore 1989). On the other hand, no sampling study has been reported for larvae, the critical life stage causing tree damage through defoliation. 5 The first objective of this thesis was to develop sampling methods for the different life stages of western hemlock looper, with emphasis on population expression, sampling units and sampling plans. Population expression constitutes the foundation for any ecological study in entomology (Morris 1955, Southwood 1978). Since the precision of absolute population estimates reported for forest insect defoliators is low (Volney 1979, Batzer et al. 1995), basic population estimates became the choice for western hemlock looper eggs and larvae in this thesis. The concept of relative population estimate (Morris 1955, Southwood, 1978) appears to be useful for western hemlock looper pupal sampling, but it does not distinguish between measured and unmeasured sampling units. Because burlap traps for western hemlock looper pupae vary considerably with the size of sample trees and trap size should be taken into account in population expression, the concept of relative population estimates was expanded in this thesis. The fact that many forest insects use a variety of substrates during their various life stages has made the choice of sampling units an integral subject in forest insect sampling (Thomson 1958, Carolin et al 1964, Fowler and Simmons 1988, Regniere et al. 1989, Shepherd and Gray 1990 b). In western hemlock looper, different sampling units were previously examined for eggs (Thomson 1958, Carolin et al. 1964), but not for larvae. In addition, only a preliminary examination was made on pupal sampling prior to this thesis (Shore 1989). Before sampling forest insects, it is necessary to know about the numbers of samples required at different insect densities and for different precision levels. Sampling plans for insects have been developed based on three approaches: the fixed sample size method (Karandinos 1976, Ho 1993), the sequential sampling method (Stark 1952, Fowler and Lynch 1982) and the binomial sampling method (Gerrard and Chiang 1970, Binns and Nyrop 6 1992). In forest defoliators, examples include the Douglas-fir tussock moth (Mason 1970, 1987, Shepherd et al. 1984), the spruce budworm, Choristoneura fumiferana (Clem.) (Morris 1954, Dobesberger and Lim 1983), the spruce budmoth, Zeiraphera canadensis (M. & F.) (Regniere et al. 1988) and the gypsy moth, Lymantria dispar (L.) (Thorpe and Ridgway 1992). However, no sampling plan has been developed for the western hemlock looper. The roadside sampling method (Seber 1982), in which sampling is conducted along a road, has the advantage that large areas can be quickly surveyed. The method is particularly useful for forest areas where accessibility to trees within stands may be a problem. I conducted roadside sampling of larvae and adults along a number of forest roads and applied spatial autocorrelation analysis to examine the spatial continuity of insect counts along the roads. The information will be used to provide guidelines for the selection of sample trees or the placement of pheromone traps along the roads. Since some aspects of adult sampling had been the objectives of another study (Evenden et al . 1995), I conducted adult sampling only to explore the spatial continuity of trap captures along forest roads. Prediction of insect population trends and defoliation have been a major objective in forest insect management (Coulson and Witter 1984, Waters et al. 1985, Speight and Wainhouse 1989). With population estimates of the western hemlock looper obtained from successive life stages, it became possible to address this concern. Thus, the second objective of this thesis was to predict population density and defoliation. Different approaches have been proposed for insect population prediction, including life table studies (Varley et al. 1973), computer simulation (Hines 1979), regression analysis (Fowler et al. 1987, Sanders 1988) and time series analysis (Royama 1981, Mason 1996), but regression 7 analysis has the best practical value for insect management. Regression models for population prediction of western hemlock looper were presented in Chapter 7. Also, defoliation prediction models using discriminant analysis were developed. Random sampling of forest insects has always presented a challenge, especially for those occurring in natural forests. Without random samples, the assumption of random-ness underlying many statistical tests can not be met (Zar 1984). Randomization testing is a method which permits statistical inferences to be made on non-random samples (Manly 1991, Edgington 1986). A significant result from a randomization test implies that there is a pattern in the data that is not likely to have occurred purely by chance. In some cases, the significance level of a test statistic in a conventional statistical analysis may be very similar to that from randomization testing, which has been the argument for using conventional statistical analysis on non-random samples. However, there are other cases when the two approaches disagree. Manly (1991) provided an example based on artificial data, but no field data from ecological studies have been used. As a major interdisciplinary component of this thesis, I compared the significance of test statistics between conventional statistical analysis and randomization testing, using field data from western hemlock looper sampling. An agreement between conventional statistical analyses and randomization tests will validate the use of non-random insect data for conventional statistical analyses. This dissertation has been organized according to the following format. A literature review is presented in Chapter 2. Sampling methods for separate life stages are described in Chapters 3 - 6 , which also include results of comparison between randomization and conventional statistical tests. Chapter 7 presents a synthesis of the information by 8 exarnining the quantitative relationships of population estimates among the life stages. In Chapter 8, a general discussion highlights the main points of the dissertation. 1.4 Study areas The study was mainly conducted at different locations within the Interior Cedar-Hemlock Zone (ICH) of British Columbia (Krajina 1965, Meidinger and Pojar 1991) from 1992 to 1994. The ICH zone has an interior, continental climate dominated by easterly moving air masses that produce cool wet winters and warm dry summers (Meidinger and Pojar 1991). The ICH zone is also one of the wettest areas in the interior of B. C , with a mean annual precipitation of 500-1200 mm. As the most productive forest zone in the interior of B. C , the ICH zone is dominated by mature climax forests in which western hemlock and western red cedar are the main species and subalpine fir, Abies lasiocarpa, white spruce, Picea glauca, Engelmann spruce, Picea engelmannii, and their hybrid the associated components. A total of nine locations were selected in three forest regions for study: Hungry Creek (HC), Walker Creek(WC) and McBride (MB) in the Prince George Forest Region; Tangier River (TR), Revelstoke Dam (RD) and Jumping Creek (JC) in the Nelson Forest Region; Mud Lake(ML), West Raft River (WR), Sugar Lake ( SU) in the Kamloops Forest Region (Figure 1.1). These locations were selected based on forest type and the detectability of W H L populations. Besides the fixed size plots in these nine locations, three grid plots (60m X 200m) were established at HC, WC and SU separately to examine the spatial pattern of pupal catches and the influence of stand variables. Roadside adult sampling was conducted in 9 the Capilano, Seymour and Coquitlam watersheds in the greater Vancouver area, coastal British Columbia, where WHL infestation was a concern due to previous outbreaks. In the interior, roadside sampling was conducted along the main forest roads in Sugar Lake area. Further details about the sampling areas can be found in Chapters 3, 4, 5, 6 and 7. 1.5 Computer software packages Several statistical computing software packages were used in this thesis: SAS (SAS 1988) for conventional statistical analyses, R-package (Legendre and Vaudor 1991) for spatial autocorrelation analysis and RT (Manly 1994) for randomization testing. In addition, computing programs developed by Ludwig and Reynolds (1988) were used for analysis of spatial dispersion patterns of the western hemlock looper. 10 Figure 1.1. Sampling locations for Lambdina fiscellaria lugubrosa in British Columbia, 1992-1994, with cities indicated by solid circles and sampling locations be empty triangles. HC=Hungry Creek; MB=McBride; WC=Walker Creek; ML=Mud Lake Road; WR=West Raft River Road; RD=Revelstoke Dam; TR=Tangier River Road; JC=Jumping Creek and SU=Sugar Lake. 11 Chapter 2 Literature review The application of statistical methods for insect sampling dates back to at least the early 1940s when Yates and Finney (1942) determined the relative efficiency of different sampling units for wireworms. In the following year, Prebble (1943) reported a study in which sampling methods were developed for European spruce sawfly, Gilpinia hercyniae (Hartig). In the late 1940s, statistical methods were used for sampling aphids (Anscomb 1948,1949, Broadbent 1948) and grasshoppers (Davies and Wadley 1949). Morris (1955) was one of the entomologists to address insect sampling in detail. Although his focus was mainly on forest defoliators, especially on the spruce budworm, he has also discussed many issues which are generally applicable to insect sampling. His own experience with sampling the spruce budworm and several other defoliators added an unusual depth to his discussion. Today, the article is still considered a 'classic ' in insect sampling (Binns and Nyrop 1992). Southwood (1978) provided a more comprehensive coverage of insect sampling, including choice of sampling units, categories of population expression, spatial dispersion and the development of sampling schemes. With an encyclopedic writing style, he has incorporated some of Morris' thoughts, such as the classification of population estimates and the selection of sampling units, into his book. Two major review articles on insect sampling were published recently (Kuno 1991, Binns and Nyrop 1992). Kuno (1991) focused on variance-mean models and presence-absence sampling. Binns and Nyrop (1992), on the other hand, addressed insect sampling 12 within the framework of integrated pest management (IPM) decision making. Some of the general concerns repeatedly encountered by entomologists in sampling insects are: 1) How to express insect populations? 2) How to define the sampling universe? 3) How to choose a particular sampling unit? 4) How to design a sampling layout in the field? 5) How many sampling units are necessary to achieve a pre-deterinined precision level? Although general sampling theory is available (Morris 1955, Southwood 1978, Coch-ran 1977, Scheaffer et al. 1979, Kuno 1991, Binns and Nyrop 1992), the answers to the above questions are, to a large extent, related to the biology of the target insect in question. Because a large number of studies on insect sampling have been published, I will concentrate my review on forest defoliators, the group of insects to which the western hemlock looper belongs. 2.1 Population expression Insect populations can be expressed in direct or indirect terms, with the former referring to a direct counting of insects while the latter to the counting or measurement of insect-related material such as frass (Morris 1955). For direct population expressions, four 13 categories were given by Morris (1955) and Southwood (1978): (1) Absolute population estimate: number of insects per unit of forest area (e.g. per ha). (2) Basic population estimate: number of insects with regard to the size of a habitat unit (e.g. per 100 cm 2 of branch foliage surface area or per 100 grams of fresh branch weight). (3) Population intensity: number of insects per habitat unit (e.g. bud, leaf, shoot or branch) regardless of the size of the unit. (4) Relative population: number of insects per artificial unit (e.g. burlap traps or sticky traps). Obviously, (4) is only loosely defined if the size of an artificial unit is not taken into account. Taking burlap traps as an example, 10 pupae caught in a burlap band that is 20 cm long would not be equal to the same numbers found in a burlap band mat is 40 cm long. Therefore, (4) should be classified into two categories, one which considers the size of the artificial unit and one which does not: (4a) Relative population estimates: number of insects per artificial unit where the size of the unit is taken into account (e.g. number of pupae per 100 cm 2 burlap surface area). (4b) Relative population intensity: number of insects per artificial unit regardless of the size of the unit (e.g. number of insects per burlap trap). Biologically and statistically, (1) and (2) are more sound than (3), while (4a) is better 14 than (4b). With a lot of variability existing in sampling unit size, (1), (2) and (4a) usually provide more appropriate data for quantitative studies, such as spatial dispersion and optimum sample size. The use of (3) and (4b), in many cases, lies in the fact that they are relatively inexpensive and more feasible to use than the other methods. Surprisingly, there has not been much discussion of the relative merits of absolute population and basic population estimates in the literature. In some cases, only absolute population estimates are mentioned (Coulson and Witter 1984). Given the importance of population expression in insect management, a greater consideration of these two issues is warranted. The fact that forest insects feed on trees or tree materials indicates that trees or tree materials should be used as the primary units for population expression and stands as the secondary units. Basic population estimates not only indicate insect abundance on the primary units, but also provide the basis for absolute population estimates. Forest insect defoliators use a variety of habitat substrates during their life cycles. For example, the western hemlock looper uses lichen for egg laying, foliage for larval feeding, and bark crevices for pupation. With absolute population estimates, insect abundance can be expressed on a common basisâ€”area, which makes the comparison of insect density between different life stages possible. Absolute population estimates are usually used to calculate insect survivorship between life stages. However, in order to convert basic population estimates to absolute population estimates, the total number of habitat units in a stand or plot has to be estimated, which often involves the development of specific statistical models. For example, to describe an absolute population estimate of the mountain pine beetle, Dendroctonus ponderosae Hopkins, in a stand, the total bark surface 15 area of pine trees in a stand has to be estimated. Because the total bark area in a stand is relatively easy to estimate, absolute population estimates have been used for several bark beetles (Coulson and Witter 1984, Waters et al. 1985). The estimation of total foliage or shoots in a stand is more difficult than estimating bark surface areas. In an attempt to obtain absolute population estimates of the lesser maple spanworm, Itame pustulari (Gn.), the total number of shoots in a stand was estimated by a regression model using the diameter of the tree crown as a regressor (Volney 1979). As 36% of the variation remained unexplainable by the regression model, the author concluded that 'simulation techniques wil l be more rewarding in the short term'. Obviously, the low precision in shoot estimates wil l result in a much lower precision in insect estimates. Another example in which absolute population estimates have been used for forest defoliators is a detailed study of the forest tent caterpillar, Malacosoma disstria (Hbn.) in aspen stands in which tree D B H was used as an estimator of population density of eggs, small and large larvae and cocoons (Batzer et al. 1995). To obtain the number of tent caterpillar per ha, the distribution of DBH and the number of trees per ha had to be estimated. Although several models were developed, the precision of the estimates remained generally low. The error margin of the population estimates ranged from 0.21 to 0.41 for eggs, from 0.30 to 0.82 for small larvae, from 0.28 to 0.53 for large larvae, and from 0.19 to 0.56 for cocoons. For a study conducted in 16 stands over a period of 5 years, the results were not very rewarding. 16 Absolute population estimates have been used for gypsy moth, Lymantria dispar (L.), in which gypsy moth populations were expressed as number of egg masses per ha (Carter and Ravlin 1995, Kolodny-Hirsch 1986). However, the host trees for gypsy moth are smaller than those for many other defoliating insects. Furthermore, egg masses of gypsy moth are more conspicuous. In fact, the overall use of absolute population estimates in the studies of forest defoliators is not common. By contrast, basic population estimates and population intensity have been used for a large number of forest defoliators including the western spruce budworm, Choristoneura occidentalis (F.), (Campbell et al. 1984, Carolin and Coulter 1972, Foltz and Torgersen 1985, Schmid 1984, Srivastava et al. 1984, Torgersen et al. 1993,1994), the spruce budworm (Morris 1954, Waters 1955, Miller 1958, Dobesberger and Lim 1983, Regniere and Sanders 1983, Regniere et al. 1989), the Douglas-fir tussock moth (Mason 1970,1987, Shepherd 1985), the oak worm, Anisota senatoria (J.), (Coffelt and Schultz 1994), the jack pine budworm, Choristoneura pinus (F.), (Kulman and Hodson 1962, Nealis and Lysyk 1988, Fowler and Simmons, 1985), the western blackheaded budworm, Acleris gloverana (W.), (Shepherd and Gray 1990 a, b), the Douglas-fir cone moth, Barbara colfaxiana (K.) (Sweeney and Miller 1989), the spruce budmoth, Zeiraphera canadensis (M. & F.), (Turgeon 1986, Turgeon and Regniere 1987) and a number of other caterpillars (Zandt 1994). One drawback with basic population estimates is that they do not permit a comparison of survivorship rates between insect life stages. But they can be used for other purposes such as statistical prediction of insect density (based on correlation of density among different stages) and defoliation. Moreover, in the review article of Morris (1955 p. 228), the following statement is made: ' If there is no serious disturbance to the stand, 17 basic population figures, without conversion, may be reasonably good indicators of absolute population changes over a limited period of years '. 2.2 Sampling universe and sampling unit Many statistics textbooks use the words 'universe' or 'population' to refer to the entire number of individuals from which a sample is to be drawn (Cochran 1977, Scheaffer et al. 1979, Schreuder et al. 1993). While sampling theory says the universe should be clearly specified, it still exists as a theoretical concept. Often, a universe is so large that it can only be imaged (e.g. all the western hemlock loopers in a given forest type or in a given watershed). In forest insect sampling, the term 'universe' has conventionally been used to represent the habitat in which the insects occur. For example, Morris (1955) suggested that any stand with a homogeneous condition is to be considered as a sampling universe. Within a stand, either fixed area or variable area plots may be used for obtaining population estimates. The former have been used for gypsy moth (Carter and Ravlin 1995, Kolodny-Hirsch 1986, Wallner et al. 1989), western spruce budworm (Srivastava et al. 1984) and pear thrips (Teulon and Cameron 1995) and the latter for a wider range of insect species including eastern hemlock looper (Dobesberger 1989), spruce budworm (Dobesberger and Lim 1983), Douglas-fir russcok moth (Mason 1970, 1987, Shepherd 1985), western spruce budworm (Torgensen et al. 1993, 1994), and peach twig borer (Weakley et al. 1990). Cochran (1977) addressed the general principles of selecting a sampling unit, whereas Morris (1955) provided more specific criteria for choosing sampling units in entomological 18 studies. In choosing a sampling unit, the kind and size of the unit are two major concerns to be dealt with. For insect sampling, these are normally determined in the context of the biology of the target insect, with the optimum sampling unit or the optimum unit size being the one that gives the smallest variance for a given cost or the smallest cost for a prescribed variance (Cochran 1977). In practice, the optimum unit size may be more difficult to determine than the optimum unit kind (Yates 1971, Yates and Finney 1942). Nevertheless, the unit size should not be too small or too large, because insects may not be present in a very small unit, and a very large unit wi l l result in unnecessary effort in sample collecting and processing. Habitats for forest defoliators vary with species and, even within an insect species, they vary with the life stages. The various oviposirion sites of forest defoliators provide many choices for sampling units for eggs, which was demonstrated in western hemlock looper (Carolin et al. 1964, Thomson 1958), eastern hemlock looper (Dobesberger 1989), blackheaded budworm (Shepherd and Gray 1990 a, b) and gypsy moth (Carter and Ravlin 1995). A branch tip has been widely used as a sampling unit for larvae of spruce budworm (Regniere and Sanders 1983, Dobesberger and Lim 1983), the western spruce budworm (Schmid 1984, Srivastava et al. 1984, Campbell et al. 1984, Foltz and Torgersen 1985, Torgersen et al. 1993, 1994), the jack pine budworm (Fowler and Simmons 1988, Nealis and Lysyk 1988), the Douglas-fir tussock moth (Mason 1987) and the oakworm (Coffelt and Schultz 1994). Because branch tips can be measured by fresh weight, dry weight and foliage surface area, comparisons have been made to examine the efficiency of these different units of measurement for population expression (Fowler and Simmons 1988, Regniere et al. 1989, Shepherd and Gray 1990 a, b). Burlap bands have been used as sampling units for gypsy 19 moth larvae (Lance and Barbosa 1979, Wallner 1983, Liebhold et al. 1986) and western hemlock looper pupae (Shore 1989). For adults of many forest defoliating insects, pheromone traps have become the standard trapping protocol (Coulson and Witter 1984). 2.3 Sampling design Random samples are normally required to make statistical inferences because statistical tables are generally based on the theoretical distributions for all equally probable samples. In the absence of random samples, the use of F or t distribution tables is valid only to the extent that the significance given by a table approximates that given by the randomization test procedure. By definition, simple random sampling is the way in which each individual has the same chance of being selected (Cochran 1977, Scheaffer et al. 1979, Schreuder et al. 1993). Random samples can be drawn by using tables of random numbers (Cochran 1977, Scheaffer et al. 1979, Schreuder et al. 1993). However, this creates some problems in forest defoliator sampling, because all the trees or sampling units in a stand have to be listed. Even with a list, random sampling may result in an inefficient crisscross of the stand to maintain a sequence. Milne (1959) once proposed sampling the central tree of a stand as an equivalent to random sampling. Despite his statement that the resulting statistics are 'at least as good ' as those from random sampling, this method has not been widely accepted. Legg and Yearcan (1985) introduced a random coordinate method for random sampling of insect populations in which the x-y coordinates of all sampling units are to be recorded. To the best of my knowledge, this method has not been used for forest insects. 20 Based on my review of a large number of sampling studies of forest defoliators (Morris 1954, Waters 1955, Miller 1958, Kulman and Hodson 1962, Mason 1970, 1987, Carolin and Coulter 1972, Dobesberger and Lim 1983, Regniere and Sanders 1983, Schmid 1984, Torgersen and Beckwith 1984, Campbell, et al. 1984, Srivastava et al. 1984, Foltz and Torgersen 1985, Fowler and Simmons 1985, Kolodny-Hirsch 1986, Nealis and Lysyk 1988, Shepherd and Gray 1990 a, b, Torgersen et al. 1993, 1994, Coffelt and Schultz 1994, Volney and McCullough 1994, Zandt 1994, Carter and Ravlin 1995, Teulon and Cameron 1995), random sampling has not been used. In fact, some studies claiming to have used random sampling did not follow the procedure of random sampling (Cochran 1977, Scheaffer et al. 1979, Schreuder et al. 1993). Often, the concept of randomness is not used statistically, but as an equivalent to the situation where no particular sampling rules are followed. In practice, it may be necessary that ' representative ' samples ratlier than random samples be taken (Hurlbert 1984, Binns and Nyrop 1992). Systematic sampling is another sampling method in which the first sample is taken randomly and the rest are taken at every k th interval thereafter (Cochran 1977). As compared with random sampling, systematic sampling is easier to conduct and hence is less subject to interviewer errors than simple random sampling (Cochran 1977, Scheaffer et al. 1979, Schreuder et al. 1993). Systematic sampling has been used in sampling spruce budworm (Fowler and Simmons 1985). However, it should be pointed out that systematic sampling may be as difficult as random sampling in the field. For example, the k th tree may be a snag or may not be suitable for sampling with a pole pruner. By avoiding these trees, the underlying assumption of systematic sampling may no longer be met. This explains why haphazard sampling has been more popular than either random or systematic 21 designs in forest insect sampling. Since insect samples, especially forest insect samples, are often not really random at all, a sampling study is unlikely to give a definitive result. Evidence of an effect has to be demonstrated consistently at different times and locations before it is convincing, which has been the traditional approach for many years. A relatively new approach is to use randomization testing which permits valid statistical inference on non-random samples (Edgington 1986, Manly 1991). The method was first addressed by Fisher (1935), but was not used much until the advent of faster computers (Edgington 1986, Manly 1991). In randomization testing, a statistic s is chosen to measure the effect or pattern in a data set. The value, So, of s for the observed data is then compared with the distribution of s that is obtained by randomly rearranging the data many times. Ii the null hypothesis is true, so should appear as a typical value from the randomization distribution of s. Manly (1991) considered randomization testing as a special case within a broader category of Monte Carlo tests and also compared randomization testing with bootstrap methods. Bootstrapping differs from randomization testing in the same way that sampling with replacement differs from sampling without replacement. Taking analysis of variance as an example, randomization testing involves allocating all observed values of a response variable to different treatments in random order, whereas bootstrapping chooses the observed values from a treatment randomly, with replacement, and assigns them to the same treatment. Randomization testing has two main advantages for general applications. First, unlike many statistical methods which assume normal distribution, randomization testing does not require any assumptions about the underlying distribution of the data. Second, 22 even with a relatively small set of non-random samples, randomization tests can at least tell us whether a certain pattern in the data could have arisen by chance. Randomization tests have been used in several fields including psychology (Edgington 1986) and biology (Manly 1986, 1991). In biology, randomization tests have been used for testing dietary differences of animals (Patterson 1986), species occurrence patterns on archipelagos (Ryti and Gilpin 1987), vegetation distribution patterns (Dale and Maclsaac 1989, Dale and Powell 1994), niche overlap of animals (Linton et al. 1989), independence of animal locations (Solow 1989) and insect geographical distribution (Manly 1991). No application of randomization testing was found in studies of forest insects prior to this thesis. In some cases, the significance level of a test statistic from a conventional statistical analysis is very similar to that from a randomization test, which has been the argument for using conventional statistical analysis on non-random samples (Manly 1991). However, there are other cases when the two approaches disagree. An example can be found in Manly (1991, p. 103) in which a regression analysis was conducted on an artificial data set. A conventional t-test gave a significance level of p = 0.0054 and p = 0.0067 for the two independent variables Xi and X2, respectively. With randomization testing, by contrast, the significance levels were p = 0.1024 and p = 0.3858, respectively 1 . Edgington (1986, p 94) discussed other cases in psychology where randomization tests consistently give different significance results than a t-test. But no real data from insect sampling studies have been used to make a similar comparison. Given the popularity of non-random sampling in 1 entomology, especially in forest entomology, a comparison based on field data is needed. 1 A r e v i s e d procedure w i l l appear i n the second e d i t i o n of the book by Manly to be published i n 1997 and t h i s may change the r e s u l t s presented i n the t h e s i s . Readers should r e f e r to the new book when i t i s a v a i l a b l e . 23 The conventional statistical analyses which have been tested with randomization tests include analysis of variance, t-test, simple regression analysis and multiple regression analysis (Edgington 1986, Manly 1991). The randomization tests are as follows: Analysis of variance. The null hypothesis of the randomization testing is that there is no significant treatment effects. The randomization testing involves randomly allocating the samples to the treatment combinations. If MSo from the conventional A N O V A is not significantly larger than those from randomization distribution, the null hypothesis is accepted. By contrast, if MSo is significantly larger than the randomized MS values, the null hypothesis is rejected. In summarizing the results from the randomization testing, the percentage of MS values that are greater than or equal to MSo is calculated and used as the significance level of MSo. T-test. A t-test can be used to test the difference between two sample means. Manly (1991) indicated that the mean difference is equivalent to the t value. Because the mean difference value is simpler to calculate than the t-value, it is often used as the test statistics in randomization testing. Randomization testing for the mean difference of two sample groups involves allocating the samples randomly to each group and determine the difference between the two means. If the mean difference from a conventional t-test (Do) is not significantly larger than those D values from the randomization allocation plus Do, the null hypothesis is accepted. Otherwise, the hypothesis is rejected. The percentage of D values which is larger than Do is the significance level of the randomization testing. Regression analysis. The null hypothesis for a simple regression analysis is that the regression coefficient bo is not significantly different from zero. In randomization 24 testing, the regression coefficient bo is compared with the randomization distribution of b which is approximated by bo and 4999 values obtained by randomly pairing the observed independent and dependent variable values. If bo is not significantly larger than those from the randomization distribution, the null hypothesis is accepted. The percentage of randomized b values which are greater than or equal to bo is considered as the significance level of bo. For a multiple regression with p independent variables, the null hypothesis is that the regression coefficients h (I = 0 to p) are not significantly different from zero. Randomization testing compares each of the observed regression coefficients, ho, with the randomization distribution of h , which is approximated by bio and 4999 values obtained by randomly pairing the observed independent and dependent variable values. If bio is significantly larger than those from the randomization distribution, the null hypothesis is rejected. The percentage of randomized b; values which are greater than or equal to boi is considered as the significance level of h . 2.4 Spatial dispersion The dispersion of populations describes the pattern of distribution of animals in space (Southwood 1978). In the literature, dispersion has also been termed as spatial dispersion due to its spatial nature (Trumble et al. 1995). By contrast, the term dispersal is generally used to describe the movement of insects (Southwood 1978). The concept of dispersion is ecologically significant, affecting not only the sampling program, but also the method of analyzing the data (Taylor 1961, 1965, 1970, Iwao 1968, Southwood 1978, Kuno 25 1991, Binns and Nyrop 1992). Population simulation models in the context of insect management also require information about the spatial dispersion of an insect. The investigation of spatial dispersion has been the topic of a large number of ecological studies in entomology (Taylor 1961, Morisita 1962, Lloyd 1967, Iwao 1968, Patil and Stiteler 1974, Myers 1978, Southwood 1978, Perry and Hewitt 1991, Perry and Woiwod 1992). The findings from these studies will be described below. The conventional methods for mvestigating the spatial dispersion of insects can be classified into two categories: frequency distribution and indices of dispersion. Frequency distribution. This is the traditional method in statistical text books (Zar 1984, Walpole 1982). First, a hypothesis is stated that the numbers of individuals per sampling unit are from a particular theoretical frequency distribution. Next, the observed frequencies and the expected frequencies from the particular distribution are calculated and a goodness of fit test statistics are used to test whether the observed differs from the expected significantly. Among theoretical frequency distribution models, one of the simplest one is the Poisson distribution: p(x) = (juxe^)/x\ (2.1) where e is the base of the natural logarithms, x! is the factorial of x and \JL is the mean. With u as the only parameter, the model permits the classification of the observed insect data into one of three categories: uniform, random and contagious distribution (Ludwig and Reynolds 1988). Most of the observed insect distribution data has been found to be contagious, with 26 the variance larger than the mean (Southwood 1978, Kuno 1991). For the contagious distribution, the negative binomial is the most widely used model: p(x) = f-kV k+ juj \k+ pj (2.2) where x and u are the number of insects in the sampling unit and mean density, respectively, and k is a parameter related to the degree of contagion. This model has been found to describe many insect populations well (Kuno 1991). Besides the Poisson and negative binomial distributions, others such as Neyman's type A and the Weibull distribution can also be found in entomology (Pielou 1977, Southwood 1978). The frequency distribution method has been used in the examination of spatial dispersion for the carpenter bee larvae, Xylocopa spp. (Ludwig and Reynolds 1988) and the two-spotted spider mite, Tetranychus urticae, (So 1991). This method requires more calculation than the method of indices of dispersion. Indices of dispersion. The methods of calculating indices of dispersion can be further classified into two categories: simple functions of dispersion and mean-variance relationships (Kuno 1991). The simple functions include variance/mean ratio and other functions developed by Morisita (1962), Green (1966), Lloyd (1967) and Perry and Hewitt ( 1991). Myers (1978) compared these indices by simulation and concluded that the Green and the Morisita coefficients (standardized) are good measures of dispersion. Hurlbert (1990), based on his study on mountain unicorns, found that mean/variance ratio is invalid as a measure of departure from randomness and a measure of dispersion. 27 Because many of the above simple functions include mean and variance, the mean-variance relationships obtained from a series of samples may provide us with more comprehensive information useful for population estimation and management. The mean-variance relationships described by Iwao (1968) and Taylor (1961) have thus been the major approaches for insect spatial dispersion (Southwood 1978, Kuno 1991). Based on evidence from 24 data sets, Taylor (1961) showed that many animal species were distributed non-normally and that the relationship between the mean (x) and the variance (s2) can be described as: s1 = ax" (2.3) The logarithmic form of the relationship is: \og(s2) = b log x + log a (2.4) where slope b is a species-specific measure of aggregation with a value of <1 for a uniform distribution, =1 for a random distribution, and >1 for an aggregated distribution. Lloyd (1967) proposed the concept of mean crowding as follows: M* =x \x J = s2-x (2.5) Using Lloyd's concept, Iwao developed a relationship for mean density and mean crowding (Iwao 1968, Iwao and Kuno 1968) as: 28 M* = a + f3 x (2.6) where M* is the mean crowding, x is its mean, and values of a and P are characteristics of the insect's distribution (Iwao and Kuno 1968). a is the index of basic contagion indicating the number of other individuals with which an individual occurs in the sample unit. P is called the 'density-contagiousness coefficient' which indicates the distribution of individuals with reference to density, p takes values of <1, =1, and >1 for uniform, random and aggregated distributions, respectively. Kuno (1991) compared the Taylor power law model and the Iwao patchiness model in terms of descriptive ability, simplicity and theoretical rationality, concluding that the former, although having better descriptive ability than the latter, does not differ much from the latter in mathematical simplicity. Regarding theoretical rationality, each model has its merits, with the Taylor model being more suitable for description over a wide range of means, and the Iwao model being more effective for specific ranges of means. The two models were also discussed briefly by Binns and Nyrop (1992). Routledge and Swartz (1991) reexamined the Taylor power law model and raised some concerns about it, in particular, its validity for mean=0. In the following year, Perry and Woiwod (1992) replied to these concerns and defended the Taylor model. Most recently, Tokeshi (1995) compared the mathematical bases between the Taylor model and the Iwao model and indicated that the former tends to fit a data set better than the latter. Insects, unlike plants, move. The data collected by insect ecologists are therefore less precise than those collected by plant ecologists. Accordingly, the analysis of spatial pattern has developed largely independently in plant and insect ecology. In plant ecology, the 29 spatial coordinates of plant individuals are usually recorded. By contrast, the spatial coordinates of insects are rarely recorded. In entomology, the mean-variance relationships (Taylor 1961, Iwao 1968) have been the standard approach for spatial dispersion patterns. Perry and Hewitt (1991) stated that 'studies employing variance-mean relationships can prove valid, albeit limited information about animal distribution even if the spatial locations of sample units are unrecorded '. 2.5 Sample size The cost involved in sampling a forest insect is often substantial, which makes the collection of an excessively large sample unwise. The total number of samples required depends on the desired degree of precision (small variance) and accuracy (lack of bias) (Fowler and Witter 1982, Binns and Nyrop 1992). However, entomologists are mainly concerned with precision because of the bias inherent in insect sampling: 1) bias in probability sampling, 2) bias due to use of an estimator invalid for the situation and 3) bias caused by non-sampling error (Fowler and Witter 1982). Precision has been widely described with the mean-variance relationship proposed by Taylor (1961) and Iwao (1968). In determining the total number of samples necessary to yield a particular precision level, two approaches have been used: the fixed sample size method, and the sequential sampling method (Binns and Nyrop 1992). In the former, the number of samples is determined prior to the actual sampling, whereas in the latter, it is not. Fixed sample size method. Two articles provided detailed discussion.of the fixed sample size method in entomology (Karandinos 1976, Ruesink 1980). Precision of a 30 population estimate can be defined in terms of standard error (SE) of the mean or error margin (SEM). Both can be set to a fixed value or as a fraction of the mean. SEM is calculated by: SEM=ta,,2(-j=) (2.7) where n is sample size, s is the standard deviation of the sample, t is the value of the t distribution with probability level a' and n-1 degree of freedom. When SEM is expressed as a fraction, d, of the sample mean: SEM = dxx (2.8) the sample size can then be calculated by : ta'72 i n = (â€”fs2 (2.9) ax where xis the sample mean. Replacing the s2 with axb (power law model), equation (2.9) becomes: n = ft v ' 0 7 2 V d ax"'2 (2.10) Iwao and Kuno (1968) developed a mean-variance relationship based on Iwao's 31 patchiness regression model (Iwao 1968): s2 =(a + l)x + (/3 -\)x2 (2.11) Substituting s2 in equation (2.9) with (2.11), the following is obtained: n = la'l2 \ d a + l + P -1 (2.12) V x Sampling studies in which fixed sample size was used can be found in Mason (1970) for Douglas-fir tussock moth, Croft et al. (1976) for apple mites, Dobesberger and Lim (1983) for spruce budworm, Nealis and Lysyk (1988) for jack pine budworm, Lysyk and Axtell (1986) for house flies, Hutchison et al. (1988) for pea aphids and Ho (1993) for mulberry mites. For the Douglas-fir tussock moth, the number of sample trees required to provide various levels of precision for estimating larval population was determined. Sequential sampling. Fixed sample size methods generally require a large number of samples (Fowler and Lynch 1987). In addition, mean density is not known in advance. The use of a sequential sampling method solves some of these problems. Based on Fowler and Lynch (1987), sequential sampling plans require, on average, only 40 to 60 percent as many observations as an equally reliable fixed-sample procedure. The book written by Wald (1947) on sequential analysis laid the foundation for sequential sampling. Sequential sampling was introduced into forest entomology in 1950's (Stark 1952, Morris 1954, Waters 1955). Since then, the method has been used for a large number of forest insect species, including the larch sawfly, Pristiphora erichsonii (H), (Ives and Prentice 1958), the forest tent caterpillar, Malacosoma disstria (H.) (Shepherd 32 and Brown 1971), the spruce budworm (Cole 1960), the lodgepole pine borers, (Monochamus spp.) (Safranyik and Raske 1970), the swaine jack pine sawfly, Neodiprion swainei (M.), (Tostowaryk and McLeod 1975), the Douglas-fir tussock moth (Shepherd et al. 1984), the spruce budmoth, Zeiraphra canadensis (Turgeon and Regniere 1987, Regniere et al. 1988), the eastern hemlock looper (Dobesberger 1989), and several cone and seed insects (Kozak 1964). Three types of sequential sampling plans have been developed. The first type of sampling plan is Wald's sequential probability ratio test (SPRT) plan, which tests a hypo-thesis, Ho: 9=0o against another hypothesis Hi: 0=0i. For insects, 0 is the insect density variable, and 0o and Â©i are two threshold densities for decision making. To design an SPRT procedure, besides the desirable levels of probability for making type I and type II errors, a and p, the two threshold densities need to be provided. In addition, the spatial distribu-tion pattern of the insect has to be known. The second type of sequential sampling plan was described by Iwao (1975) which tests the null hypothesis Ho: u= Uc against all other alternative hypotheses Hi: u<Uc or u>Uo Iwao's plan depends on his patchiness regression model (Iwao, 1968), in which the acceptance and rejection boundaries are the upper (Tu) and lower (Ti) limits of the 100 (1-a) percent confidence interval for the total number (Tn) of insects in n observations when Ho is true. By taking samples from a population and recording the cumulative number of insects in n observations (Tn), the following rules are used: 1) if T n>T u, stop sampling and conclude u>Uc; 2) if T n <Ti, stop sampling and conclude u<Uc ; and 3) if Ti<Tn<Tu, then continue sampling until a final decision can be reached. This plan has no restriction on the distribution pattern of the insect as long as Iwao's patchiness regression relationship holds. 33 The third type of sequential sampling plan was proposed by Kuno (1969) and modified by Green (1970). Instead of classifying the mean density of an insect population into two or three classes, sampling is terminated when a defined level of precision (p) is achieved. In Kuno's plan, sampling is stopped when: where T n is the cumulative number of insects counted after sampling n sampling units, a and P are coefficients from the Iwao patchiness regression model, d=precision (SE/mean), and n is the number of sampling units. Green (1970) modified the Kuno plan based on the Taylor power law model (1961). Sampling is stopped when: a + fi (2.13) d2-(p-\)ln (anl-b)],{2-h) d2 (2.14) or: s l/(A-2) n , ( A - l ) / ( A -2 ) (2.15) where a and b are parameters from the Taylor power law model. The Kuno method has been used for the study of the western blackheaded budworm (Shepherd and Gray 1990 b) and the Green method has been used for the pea weevil, 34 Bruchus pisorum (L.), (Smith and Hepworth 1992), the western corn rootworm, Diabrotica virgifera (L.), (McAuslane et al. 1987), the citricola scale, Coccus pseudomagnoliarum (Trumble et al. 1995 ) and the orange-striped oakworm, Anisota senatoria (J.) (Coffelt and Schultz 1994). 2.6 Binomial sampling Sampling can also be made easier and less time consuming by substituting binomial counts for complete counts, which is termed binomial sampling (Binns and Nyrop 1992), presence and absence sampling (Kuno 1991), or frequency sampling (Mason 1987). A binomial sampling plan is based on a model that expresses the relationship between the mean density and the proportion of sampling units containing more than h individuals. There have been two main models used in entomological studies, one based on empirical relationships (Gerrard and Chiang 1970, Kuno and Sugino 1958, Nachman 1984) and the other based on a theoretical distribution (Anscombe 1948, Pielou 1977). Kuno (1991) provided a discussion on these models. A n empirical model for estimating mean density of insects from the frequency of occurrence of t individuals was developed by Gerrard and Chiang (1970) as: x = atM - log( l -p ) ] (P + 5 1 Â° g t ) (2.16) where x stands for the mean, t for a specific threshold density, p for the proportion of samples containing t insects, a, B, X and 5 are parameters to be estimated. The logarithmic form of the above model can be written as: 35 log x = loga + B log[- log(l - p)] + X log t + 5(log t) log[- log(l - p)] (2.17) The above relationship can be confined to a specific threshold density. In the case of t=l, model (2.15) can be simplified to a model describing the relationship between the mean and the proportion of sample containing no insect (Nachman, 1984): logx = a + /? log(- logp 0 ) (2.18) where po is the proportion of samples containing no insect. The predicted natural logarithm of the mean insect density (log x) can be calculated using the estimated parameters a and p and an observed value of po. There are three error sources connected with the predicted mean in Model (2.18), error in the estimates a and /?, biological error and sampling error. Five models have been proposed to account for the variance associated with the predicted mean, including the Gerrard & Chiang model (1970), the Nachman model (1984), the Kuno model (1986), the Binns & Bostanian model (1990) and the model developed by Schaalje et al. (1991). The last model is believed to be the only one which account for all error sources: V = W2 0 - Po)] / [Â«Po On P0 )2 ] + MSE{\ I N + [log(- log p0) - pf I SSP} + MSE - exp{a + (b - 2)[d + ft log(-logp0)]} / n (2.19) where d and /? are the regression estimates of a and P in Model (2.18 ), n is the 36 number of samples taken from a populations used to fit Model (2.18 ), N is the number of populations used to fit the regression model, MSE is the residual mean squared error from Model (2.18), SSP is the sum of squared deviations of the log (-log po) values from p and a and b are parameters from the Taylor power law model. The past two decades have seen an increased use of binomial sampling methods in entomology (Kuno 1991, Binns and Nyrop 1992). On forest trees, the method has been used for Douglas-fir tussock moth (Mason 1987), gypsy moth (Thorpe and Ridgway 1992, Carter and Ravlin 1995), leafminer (Jones 1991) and spruce budworm (Lysyk and Sanders 1987). 2.7 Spatial statistics Insect sampling has traditionally been conducted without considering the spatial coordinates of the sampling units in the field. In recent years, with new interest in spatial statistics, entomologists have started paying some attention to the spatial information in insect counts (Schotzko and O'Keeffe 1989, 1990, Gage et al. 1990, Liebhold and Elkinton 1989, Liebhold et al. 1991, Perry and Hewitt 1991, Midgarden et al. 1993). Although there are a variety of tools in spatial statistics, entomological applications have mainly used spatial autocorrelation analysis and variogram analysis. Unlike the traditional methods that infer spatial patterns from frequency distri-butions or mean-variance relationships, spatial autocorrelation analysis and variogram analysis provide a direct measure of spatial patterns. Perry and Hewitt (1991) indicated 37 that most of the traditional methods can still provide valid information about insect distributions even if the spatial locations of the sampling units are not recorded. However, spatial autocorrelation analysis and variogram analysis do provide us with alternatives. Spatial autocorrelation analysis has been used to examine the spatial distribution of gypsy moth defoliation (Liebhold and Elkinton. 1989), and counts of the western corn rootworm (Midgarden et al. 1993). On the other hand, variogram analysis has been applied in studies of the pink bollworm, Pectinophora gossypiella (S.) (Borth and Huber 1987), gypsy moth egg masses (Liehold et al. 1991), western corn rootworm adults (Midgarden et al. 1993), and the legume bug, Lygus hesperus, (Schotzko and O'Keeffe 1989, 1990). 2.8 Population prediction Planning is a critical step toward the successful management of any forest insects, especially for western hemlock looper, a species capable of increasing its populations rapidly within a short time. However, to make a good plan, the future trends of the insect population have to be predicted. Population dynamics has thus become a hot topic in insect ecology and pest management (Coulson and Witter 1984, Waters et al. 1985, Berryman 1992, Mason 1996). Population dynamics of several of the most significant forest insect pests in North America have been studied extensively: the Douglas-fir tussock moth (Shepherd et al. 1985, Mason 1987, 1996,), the gypsy moth (Campbell 1973, Liebhold and Elkinton 1986, Liebhold et al. 1991), the spruce budworm (Morris 1963, Royama 1992, Sanders 1988) and the Dendroctonns bark beetles (Hines 1979, Waters et al. 1985). The statistical methodologies used for population dynamics studies include life 38 tables, population simulations, time series analyses and regression analyses. In the life table approach, an insect population is normally observed in the field and detailed statistics about mortality are recorded continuously over a number of generations or years (CoulsOn and Witter 1984). Varley et al (1973) conducted a life table study for the winter moth, Operophtera brumata, in which winter disappearance was identified as the key factor. However, there are problems with the life table approaches such as the high demand of time and labor, the difficulty of identifying some mortality factors and the destruction of insect habitats due to frequent sampling or observations. In population simulations, a population process is considered as a function of a large number of insect and environmental variables (Waters et al. 1985). The simulation system for the southern pine bark beetle, Dendroctonus frontalis (Zim.) (Hines 1979) was comprised of a large number of sub-models, with each model describing the survivalships of a particular life stage as the function of some insect and environmental factors. While the development of such models represent a great effort, their application value is generally low. One major reason is that many of the simulation models are differential equation which treated insect population processes as deterministic rather than stochastic (Waters et al. 1985). In recent years, fewer publications have used the life table and simulation approaches for forest insects. New approaches which considered insect population process as stochastic rather than deterministic have been used, including time series analyses (Royama 1977, 1981, 1992, Liang and L i 1992, Berryman 1992, Volney and McCullough 1994, Mason 1996) and correlation or regression analyses (Fowler et al. 1987, Sanders 1988, Evenden et al. 1995). Unlike the life table and the simulation approaches, these approaches examine insect 39 population change based on the numeric characteristics of population estimates. The drawback with time series analysis is that it requires data collected over a large number of generations. But this requirement does not apply with regression analyses. Based on short term data, regression models have been developed for gypsy moth (Gage et al. 1990), jack pine budworm (Fowler et al. 1987), spruce budworm (Fowler et al. 1987), Douglas-fir tussock moth (Shepherd et al. 1985) and western hemlock looper (Evenden et al. 1995). 2.9 Summary The purpose of sampling, in brief, is to obtain information about a universe from a small proportion of that universe. The advantages of sampling are to cut cost, reduce manpower requirements, gather vital information more quickly and increase the accuracy of the information because more skillful investigators can be hired and less information has to be dealt with (Cochran 1977, Scheaffer et al. 1979, Schreuder et al. 1993). The develop-ment of insect sampling methods has reflected these principals. In particular, insect sampling has been developed to assess insect population faster and at less cost. The development of sampling methods in forest entomology has gone through several periods. Methods from sampling theory were introduced to estimate insect population parameters in the 1940s (Prebble 1943). In the 1950s and 1960s, sequential sampling was applied to determine optimum sample size for a number of insects (Stark 1952, Ives and Prentice 1958, Morris 1959, Waters 1955, Cole 1960, Kozak 1964, Mason 1969). From the 1970s, mean-variance relationships, described by Taylor (1961) and Iwao (1968), were introduced to examine the spatial aggregation and sample size (Mason 1970, Dobesberger 40 and Lim 1983, Kolodny-Hirsch 1986 ). At the same time, binomial sampling methods were used for developing sampling plans (Mason 1987, Lysyk and Sanders 1987, Jones 1991, Thorpe and Ridgway 1992, Carter and Ravlin 1995). Beginning in the 1980s, with the concept of integrated pest management and an increasing demand for quantitative data, binomial sampling methods and sequential sampling methods have become more popular (Lysyk and Sanders 1987, Jones 1991, Thorpe and Ridgway 1992, Cater and Ravlin 1995). Greater computer power also rendered Monte Carlo simulation to be used to examine the errors encountered in using sequential sampling plans (Fowler 1983), and to the further development of sequential sampling plans (Lynch et al. 1990). During the late 1980s and early 1990s, spatial statistics have been used to investigate the spatial patterns of insects (Borth and Huber 1987, Schotzko and O'Keeffe 1989, 1990, Gage et al. 1990, Liebhold et al. 1991, Liang et al. 1997). In statistics, the precision of an estimator refers to the magnitude of the departure of sample estimates from their mean, whereas the accuracy of an estimator is the degree of the deviation of the sample estimator from the real population parameters (Cochran 1977). Although the accuracy of estimation is important, it is almost unknown in insect sampling because of bias sources from an invalid estimator, probability sampling and non-sampling error (Fowler and Witter 1982). Fowler and Witter (1982) gave a detail description of these bias sources, and in particular, a summary table of some non-sampling errors associated with insect density estimates which includes an incomplete coverage of the target insect population, observation error due to human mistake or inaccurate instruments, and sampling with unknown probability. Apparently, many of the bias sources are difficult to avoid. Therefore, Fowler and Witter (1982) stated 'entomologists should emphasize the 41 precision of their estimates. Accuracy can only be referred to when estimates are unbiased or the bias sources are known. This is hardly ever possible in real-world situation'. In entomological literature, emphasis has always been given to precision rather than accuracy. For example, precision, not accuracy, has been the concern in the determination of optimum sample size (Mason 1970, Karandinos 1976, Ruesink 1980, Lysyk and Axtell 1986, Hutchison et al. 1988, Ho 1993). In comparing die efficiency of different sampling units (Fowler and Simmons 1988, Regniere et al. 1989, Shepherd and Gray 1990 b), precision was also used as the criterion. The fact that sampling studies are being increasingly published in entomological journals reflects the importance of insect sampling. With more statistically sound data, our confidence in making insect management decisions will be greatly increased. We may not be able to avoid biases in insect sampling, but we should try to reduce them. 42 Chapter 3 Egg sampling of Lambdina fiscellaria lugubrosa 3.1 Introduction Western hemlock looper overwinters in the egg stage, lasting from October through May in British Columbia (Koot 1994). Such a long period of time has made eggs the preferred stage for sampling (Thomson 1958, Shore 1990). On the coast of British Columbia and Washington, hemlock looper adults mainly oviposit on moss, trunks and limbs of trees (Hopping 1934, Thomson 1958, Carolin et at. 1964). In the interior, however, the preferred oviposition site is on lichens (Alectoria spp.), hanging from branches of mature trees (Thomson 1958, Shore 1990). Egg sampling in the interior of British Columbia involves the collection of lichen samples from trees. Although the amount of lichen varies from tree to tree, it is possible to obtain the same amount of lichen from different trees, giving an equal size of sampling units (Liang et al. 1996). In insect sampling, sample size has long been a concern (Binns and Nyrop 1992), but not much attention has been paid to sampling unit size. Because an equal size of sampling units is statistically more sound than an unequal size (Cochran 1977, Southwood 1978), it should always be the first choice. In the case of the western hemlock looper, a previous study (Shore 1990) used lichen samples of different sizes and egg density was standardized to numbers per 100 g. An equal size of sampling units would have been used if egg density had been expressed on the same amount of lichens. Many of the western hemlock trees in a mature stand can be up to 30 m in height, making insect sampling from the upper and middle strata of crowns difficult. The vertical 43 distribution of eggs within crowns needs to be examined because a homogeneous vertical distribution would justify sampling eggs solely from the lower stratum of crowns. The conclusion of a homogeneous distribution suggested by a previous study ( Shore 1990) was based on a relatively small sample size (26 trees from 4 locations) and an unequal size of sampling units. Given the importance of egg stage in western hemlock looper sampling, a confirmation of the conclusion with a larger number of sample trees and with an equal size of lichen samples was needed. An integrated western hemlock looper management system would require information about sampling statistics for eggs, the spatial dispersion pattern of eggs, the effect of tree variables (height, diameter at breast height, crown length, crown width and presence of heartrot) on egg density to develop sampling plans and population prediction models. As described in Chapter 2, sampling plans can be developed with the fixed sample size and the sequential sampling methods. Also, as egg counting of the western hemlock looper is a slow, tedious and time-consuming procedure, binomial sampling may be a solution. Another solution is to reduce the size of the lichen samples. The objectives of this study were to: (1) examine the vertical distribution of eggs within tree crown with an equal size of sampling units, (2) determine optimum sample size and develop sampling plans for the egg stage, (3) investigate the effect of tree variables (height, diameter at breast height, crown length, crown width and presence of heartrot) on egg density, and (4) examine the effect of halving sampling unit size on estimates of sample mean and variance. In addition, randomization tests were used to validate the statistical significance levels from conventional statistical analyses. 44 3.2 Materials and Methods 3.2.1 Sample collection. Egg sampling was conducted at 13 locations (four at Sugar Lake area ) within the Interior Cedar-hemlock Zone (Krajina 1965, Meidinger and Pojar 1991) of British Columbia in 1992, 1993 and 1994. At each location, a sample plot (300 m X 100 m) was established in a mature hemlock stand to define the sampling area and dominant or co-dominant trees were used as sample trees. Because both random sampling and systematic sampling were not practical in mature hemlock stands, the sample trees were selected subjectively. To avoid bias, sample trees were distributed throughout a plot and trees that were severely defoliated or at plot edges were avoided. In 1992, eggs were sampled from 65 trees (10 trees at each of five locations and 15 trees at one other location) to compare the vertical variation in egg density within the crown. Sample trees were measured for diameter at breast height (DBH), height, crown length, crown width and the presence of heartrot to examine their effects on egg density. DBH and crown width were measured before trees were felled and tree height, crown length, and the presence or absence of heartrot, a disease caused by the Indian paint fungus, Echinodontium tinctorium (Etheridge and Hunt 1978), were measured or recorded on the fallen trees. The crown of each cut tree was divided into three equal strata (lower, middle and upper) and a sample of lichen was taken from each stratum. The amount of lichen collected from each crown stratum was to approximately fill a polyethylene bag measuring 20 cm x 10 cm x 46 cm. The sampling in 1993 and 1994 was conducted without felling trees and measuring the tree parameters. In total, 79 trees were sampled (15 trees at each of five locations and four trees at one other location) in 1993 and 30 trees were sampled (six trees at each of five 45 locations) in 1994. Lichen samples were taken with pole pruner from the lower crown level only. As looper populations collapsed and result in sparse population density at some locations, the sample locations for 1993 and 1994 were not the same as in 1992 . 3.2.2. Sample Processing. Debris (dead branchlets) was removed by hand from the lichen before the lichen samples were air-dried and weighed. Forty grams of air-dried lichen were randomly selected as a sample. The eggs were separated from the lichen using the bleach method (Otvos and Bryant 1972). A lichen sample was placed into a 2 L pyrex beaker and submerged in 5% household bleach solution. The beaker was agitated on a mechanical shaker at the lowest setting for 20 min. The contents were then poured through two nested strainers, a large-meshed (1000 micron) top strainer to remove the debris but allow the eggs to pass through, and a fine- meshed (250 micron) bottom strainer to retain the eggs. Finally, the eggs were rinsed out of the solvent with tap water into a plastic jar and poured onto a 12.5 cm diameter filter paper. The filter paper was placed on the top of a vacuum pump to speed up the filtration process. The eggs on the filter paper were sorted and counted under a 10-x dissection microscope according to the following four categories: healthy (brown), infertile (green), parasitized (black), and old (opaque with a hole at one end) (Otvos and Bryant 1972). For the purposes of this study, only current year eggs (healthy + infertile + parasitized) were analyzed. 3.2.3 Statistical analyses. For 1992 data only, a two-way analysis of variance (ANOVA) with interaction (Dunn and Clark 1987) was used to compare the number of hemlock looper eggs among locations and crown strata, with a natural logarithmic transformation used for the egg counts to adjust for potential violation of the assumptions underlying A N O V A (Steel and Torrie 1980). In addition, the lower crown egg counts were regressed against the pooled egg counts of the middle and upper crown strata. In this 46 regression analysis and those hereinafter, a residual analysis (Dunn and Clark 1987), in which residuals were plotted against the corresponding fitted values, was used to diagnose the possible violation of the assumptions in regression analysis such as outliers, correlated error term and heteroscedasticity. To examine the effect of halving the 40 g lichen samples on sample mean and variance estimates, the mean and variance of egg counts between a set of 40 g lichen samples (n =29) collected in 1994 and their 20 g subsamples were compared with the method of paired comparisons (Dunn and Clark 1987). The egg counts of the western hemlock looper for three years were fitted to (1) the Poisson distribution, (2) the Taylor power law (Taylor 1961), (3) the Iwao patchiness regression (Iwao and Kuno 1968), and (4) the negative binomial distribution. A procedure described by Ludwig and Reynolds (1988) fitted the egg count data of the hemlock looper to Poisson distribution, in which the expected frequencies of egg counts from a Poisson distribution were calculated and compared with the observed frequencies. The difference was then tested by chi-square statistics. The null hypothesis that the frequency distribution of egg density follows Poisson distribution was rejected if the chi-square statistics was greater than the tabular chi-square statistics. In applying the Taylor power law model, the natural logarithmic form (Model 2.4) was used in which x is the mean plot density of eggs, s2 is the variances, and b is a species-specific measure of aggregation with a value of < 1 for an uniform distribution, = 1 for a random distribution, and > 1 for an aggregated distribution. The Iwao model (Model 2.6) was also used to describe the relationship between the mean and the mean crowding. When a and p are both > 0, a clumped distribution is suggested. The negative binomial distribution was fitted by the iterative procedure described by Ludwig and Reynolds (1988), in which an initial estimate of k was obtained from sample 47 data and the final estimate from an iterative procedure. With the final k, the expected frequencies of egg counts from the negative binomial distribution were calculated and compared with the observed frequencies. Then, a chi-square test was used in a similar way as in fitting the Poisson distribution to determine whether the null hypothesis should be rejected. In determining the optimum sample size, both the fixed sample size and the sequential sampling approaches were used. The former involved the use of Model (2.12) and the latter Model (2.13 ) and Model (2.15), respectively. In Models (2.13) and (2.15), n is the number of lichen samples, Tn is the cumulative number of eggs and d is chosen as 0.1, 0.2, 0.4, 0.6 and 0.8. The parameters a and p in Model (2.13) were obtained from Model (2.6) while a and b in Model (2.15) were from Model (2.4). Statistics for tree height, DBH, crown width and crown length measured in 1992 are listed in Table 3.1. The influences of heartrot, tree height, DBH, crown width and crown length on variability of egg density were examined with multiple covariance analysis, in which the tree variables were used as covariates and location and heartrot as class variables (Huitema 1980, Dunn and Clark 1987). Model (2.17) was used for estimating mean egg density from the frequency of occurrence of > t eggs, in which x stands for the mean egg density, t for the threshold density, which was taken as 1, 10, 30, 50, 70, 90 , 110, 130, 150 and 170 based on the data, and p for the proportion of lichen samples containing at least t eggs. Due to limited numbers of samples containing no eggs, Model (2.18) was not examined. For data from 1994 only, a t-test was used to test the mean density difference between the 40 g lichen samples and their 20 g subsamples. Randomization testing was used to compare with the A N O V A results on vertical distribution of eggs. The randomization testing involved randomly allocating the lichen 48 samples to the treatment combinations of crown, location and crown x location interaction and followed the rules as described in Chapter 2. The numbers of randomization in the test were 4999, as suggested by Manly (1991) for a test at the 0.05 level. 3.3 Results Vertical distribution of eggs within tree crown. Egg density varied significantly from location to location (p< 0.01), but the effect of crown and crown X location interaction was not significant (Figure 3.1, Table 3.1). Although a homogeneous vertical distribution of eggs was found, egg density in the lower crown stratum accounted for 47% of the variation in pooled egg density of middle and upper crown strata. The relationship between egg density in the lower crown stratum (X) and egg density of the pooled middle and upper crown strata (Y) was described as: Y = 57.59 + 1.36 X (r2 = 0.47, p < 0.01) (3.1) Both the'intercept and slope in the model were significant (p < 0.01). Spatial distribution pattern. In the chi-square test, the null hypothesis that egg distribution follows the Poisson distribution was rejected (p < 0.01), but the null hypothesis that egg distribution follows the negative binomial distribution was not rejected (p > 0.05). The k value for the negative binomial distribution, based on the iterative procedure, was 1.21. Both the Taylor power law and the Iwao patchiness regression model fitted the data well. The Taylor power law described the relationship between plot mean of eggs and the variance as: 49 (S9 |diues uai|oi| 6 ofr Jad) sB6g jo - O N Table 3.1. Analysis of variance of egg counts of Lambdina fiscellaria lugubrosa in the upper, middle and lower strata of crowns of Tsuga heterophylla at six locations in the interior of British Columbia, 1992. Source DF SS MS F Pr > F Location 5 32.48 6.50 26.19 0.0001 Crown 2 0.79 0.39 1.58 0.2083 Location x crown 10 1.37 0.14 0.55 0.8523 Error term 187 45.28 0.24 51 In s2 = 0.42+ 1.53 In (x) (3.2) (r 2 = 83, p<0.01) The slope was significant at the 0.05 level, but the intercept was not. Because b=l.53, which is larger than 1, an aggregated distribution is suggested. The Iwao method (Iwao 1968) gave the following model for the relationship between plot mean and the mean crowding: Both the slope and the intercept of the model were significant at the 0.05 level. With the values of a and P both being >0, the model suggested a clumped distribution of eggs on the tree crown. The mean-mean crowding relationship was not affected by an increasing egg density (Figure 3.2), but the mean-variance correlation decreased with an increasing egg density (Figure 3.3). As indicated, the mean-variance relationship is most appropriate for low to moderate (< 60 eggs per 40 g lichen sample) egg densities. Sample size. The optimum sample size of lichen samples (40g) for estimating egg densities, under the fixed sample size method, are given in Table 3.2. The number of samples required for d values of 0.1, 0.2, 0.4, 0.6 and 0.8 decreases as mean population density increase. A n d value of about 0.2 is generally considered appropriate in insect sampling (Southwood, 1978). Based on Table 3.2, the number of lichen samples required for a mean density of 50 eggs per sampling unit is 9. Since one lichen sample is taken per M * = 11.2 + 1.06x (3.3) (r2 = 0.96, p < 0.01) 0 40 80 120 160 200 240 M e a n e g g d e n s i t y Figure 3.2. Mean - mean crowding relationship for eggs of Lambdina fiscellaria lugubrosa in the interior of British Columbia. Egg density is expressed as numbers of eggs per 40 g lichen sample. Figure 3.3. Mean - variance relationship for eggs of Lambdina fiscellaria lugubrosa in the interior of British Columbia. Egg density is expressed as numbers of eggs per 40 g lichen sample. 53 tree, the number of sample trees required is also 9. How many samples are required will depend on how much lower than the 0.2 error margin needs to be. Sequential sampling plan. The sequential sampling plan based on the Kuno method terminates sampling at a higher number of eggs than the Green method (Table 3.3). For a sample size of 16 trees and a precision level of 0.2, the cumulative number of eggs required to stop the sampling is 101 based on the Green method, whereas the Kuno method would required 377. A sample size of 16 trees is required by the fixed sample size method for a mean density of 25 eggs and a precision level of 0.2 (Table 3.2). In the sequential sampling method, however, 16 trees are required for a mean density of 7 eggs ( 101/16) based on the Green method and 21 eggs (337/16) based on the Kuno method (Table 3.3). Since sample size tends to decrease with increasing density within the assigned density range, less than 16 trees are required by the sequential sampling method for a mean density of 25 eggs. Obviously, the number of sample trees needed by the sequential sampling method are less than that of the fixed sample size method. Binomial sampling. The relationship between mean egg density and the frequency of lichen samples containing at least t eggs (t = 1, 10, 30, 50, 70, 90, 110, 130 , 150 and 170) was obtained as: In (mean) = 1.13 +1.21 In [ -In (1-p)] + 0.78 In t - 0.19 (In t) In [ -In (1-p )] ( r 2 = 0.80, P<0.01) (3.4) Table 3.2. Optimum sample size (numbers of 40 g lichen samples) for egg sampling of Lambdina fiscellaria lugubrosa in the interior of British Columbia, at various mean densities and precision levels. d(95% error margin / mean) Mean 0.1 0.2 0.4 0.6 0.8 1 1316 329 82 36 21 25 63 16 4 2 1 50 37 9 2 1 1 75 28 7 2 1 1 100 24 6 1 1 1 125 21 5 1 1 1 150 19 5 1 1 1 The mean is expressed as average numbers of eggs per 40 g lichen sample Table 3.3. Termination points for sequential sampling of eggs of Lambdina fiscellaria lugubrosa in the interior of British Columbia, based on the Green and the Kuno methods. Cumulative number of eggs (at the precision level of 0.2) Tree (n) the Green method the Kuno method 11 154 353 16 101 337 21 74 329 26 58 324 31 48 321 36 41 318 41 35 317 46 31 315 51 27 314 56 25 313 61 22 313 66 20 312 71 19 312 76 17 311 81 16 311 86 15 310 91 14 310 96 13 310 Per 40 g lichen sample per tree. 56 Table 3.4. Characteristics of sample trees (Tsuga heterophylla) used for eggs of Lambdina fiscellaria lugubrosa from the upper, middle and lower strata of crowns at six locations in the interior of British Columbia, 1992. Location Variable Mean SD Min. Max. WR (n =15) TR (n = 10) ML (n = 10) RD (n = 10) HC (n = 10) MB (n =10) Height (m) 28.4 4.8 19.0 34.5 DBH (cm) 48.5 11.0 66.0 27.0 Crown width (m) 7.8 1.4 5.3 10.5 Crown length (m) 20.1 5.6 9.7 27.0 Height (m) 28.6 5.2 21.6 40.0 DBH (cm) 53.8 13.4 36.7 84.3 Crown width (m) 8.7 1.3 6.9 11.0 Crown length (m) 19.7 2.7 15.5 23.0 Height (m) 25.7 5.4 19.0 36.0 DBH (cm) 45.7 12.2 29.0 73.0 Crown width (m) 8.6 1.7 5.3 10.8 Crown length (m) 20.3 4.4 15.5 30.5 Height (m) 23.9 4.2 15.0 28.0 DBH (cm) 50.0 7.2 39.6 59.2 Crown width (m) 9.0 1.7 6.2 11.2 Crown length (m) 18.1 3.9 10.5 23.8 Height (m) 28.9 2.6 25.0 34.0 DBH (cm) 65.9 7.7 55.0 78.5 Crown width (m) 8.2 1.1 6.5 9.6 Crown length (m) 19.7 2.6 16.0 23.5 Height (m) 22.7 1.6 19.6 25.0 DBH (cm) 38.5 8.1 31.8 56.5 Crown width (m) 6.4 0.7 5.0 7.3 Crown length (m) 13.7 1.5 11.5 16.0 57 Both the intercept and the three regression coefficients in the model were significant at 0.05 level. The model accounted for 80% of the variation in the proportions of samples with t eggs-Relationships between egg counts and tree characteristics. Summary statistics of the tree variables is given in Table 3.5. Although sample trees varied significantly in height, DBH, crown length, crown width and presence of heartrot, none of these variables had a significant influence on egg density (p > 0.05) (Table 3.5). Effect of halving the 40 g lichen sample on sample mean and variance. The 40 g lichen samples and their 20 g subsamples had a mean egg counts of 0.85 and 0.82 (eggs per gram) and a standard deviation of 0.41 and 0.43, respectively. Based on a t-test, the difference of the two means was not significant at the 0.05 level. However, a F-test indicated that the difference of the two variances was significant at the 0.05 level. As the 20 g subsamples had a greater variance than the 40 g samples, more 20 g samples would be required to estimate the mean. Randomization tests. In the randomization testing for the vertical distribution of eggs within tree crown, 0.02% of the randomized MS values for location were greater than or equal to MSo = 5.91,which rejected the null hypothesis at the p = 0.0002 level. For crown stratum, as 47.01 % of the MS values from randomization were larger or equal to MSo = 0.29, the null hypothesis was not rejected and the significance level for crown stratum was p =0.47. For location X crown interaction, 98% of the randomized MS values was larger than or equal to MSo = 0.54, which failed to reject the hypothesis at a significance level of p = 0.98. Randomization testing reached the same conclusion as the conventional analysis of variance, although the significance level differed slightly (Table 3. 6). Table 3.5. Analysis of covariance of egg counts of Lambdina fiscellaria lugubrosa in the lower stratum of crowns of Tsuga heterophylla at six locations in the interior of British Columbia, 1992. Source DF SS MS F Pr > F Location 5. 65175.01 13035.00 5.35 0.0005 Heartrot 1 351.40 351.40 0.14 0.7057 Height 1 378.69 378.69 0.16 0.7057 DBH 1 23.48 23.48 0.01 0.9222 Crown width 1 2158.27 2158.27 0.89 0.3509 Crown length 1 4989.87 4989.87 2.05 0.1583 Error 54 131622.14 2437.45 01 > 01 U C CJ 1 c/5 â€¢ a .a S o T3 c OS (0 C o C > c o U O N O o o o IN O 00 O OS d o Â© o r H OS o CN o o s Â© o 00 d d d cn u â€¢43 â€¢B B cn <D 0) 0) lH lH >H <C cO CO 3 3 3 o-1 cr to cn to c c c rtJ tC 0) QJ <U 2 2 2 _0> > 01 TS O < > O z < â€¢S3 c < c o rt XI u ^ bo >J â€¢Â£ <+* 60 3.4 Discussion and conclusions The choice of sampling unit size is important in developing a sampling plan. The optimum unit size is the one that gives the smallest variance for a given cost or the smallest cost for a prescribed variance (Cochran 1977). In practice, the determination of optimum unit size may be difficult (Southwood 1978), but a uniform size should be used whenever possible. I used 40 g as the sampling unit size because it was the smallest amount common to all trees that were sampled. In other cases, the unit size can be modified depending on the amount of lichen available in the samples. However, the unit size should not be too small or too large, because eggs may not be present in a very small unit and a very large unit is less practical to collect and process. The result of no significant difference in mean egg counts between 40 g lichen samples and their 20 g subsamples indicated that a 20 g lichen sample can be used. But the 20 g subsamples also significantly increase the variance of sample estimates. Thus, the balance between a smaller sampling unit size and a greater variance is a practical issue to be considered in the field. In laboratory, Shepherd and Gray (1972) once suggested the use of removal sampling (Seber 1982) to reduce the effort in egg counting, but it is unlikely that an equal probability, the assumption under the removing sampling method, can be achieved when eggs are separated from lichen. This study confirmed, based on an equal size of sampling units (40 g) and a larger sample size of trees (n = 65), the finding of Shore (1990) (n = 26) that egg density of the western hemlock looper in the three strata of a crown is basically homogeneous. Therefore, hemlock looper eggs can be sampled from the lower stratum of the crown without felling the tree. A homogeneous distribution of egg masses and larval density among the upper, 61 middle and lower crown strata have also been found for western spruce budworm on Douglas - fir (Campbell et al. 1984). For spruce budworm larvae, Schmid (1984) also found no significant difference of density among the three crown strata. However, egg masses of Douglas-fir tussock moth were found to be concentrated on the upper stratum of the tree crown (Mason 1970). Many insects have an aggregated distribution pattern (Taylor 1961, Kuno 1991, Binns and Nyrop 1992). Although the egg masses of many insects are randomly distributed, the distribution of individual eggs is generally clumped (Southwood, 1978). The negative binomial distribution of the western hemlock looper eggs demonstrated that this insect has an aggregated distribution, which might be due to heterogeneity of environment or, more likely, the behavior of the moths. For many herbivorous insects, the selection of an oviposition site is a critical step in the life cycle because the newly hatched larvae are generally slow in searching for a host (Singer 1986). From an evolutionary point of view, insects should lay their eggs on a host plant where they can maximize the survival of the offspring. The non-significant correlation of western hemlock looper egg density to tree characteristics such as height, DBH, crown length, crown width and heartrot in the 1992 sampling suggested that these factors may not be important in determining host selection of hemlock looper for oviposition. The model based on frequency of lichen samples containing at least t eggs accounted for 80% of the variation in mean egg density, which indicated that a sampling plan based on the frequency of occurrence is effective. If the number of samples containing no eggs is large enough, a presence and absence sampling approach may be appropriate. A further study should be conducted to collect data from sparse egg densities and develop a model based on the presence and absence of hemlock looper eggs. 62 Chapter 4 Larval sampling of Lambdina fiscellaria lugubrosa 4.1 Introduction The success of western hemlock management is directly linked to the reduction of tree damage caused by larvae, the feedidng life stage. Larvae can cause defoliation, top-kill and eventually, tree mortality (Hopping 1934, Kinghorn 1954, Koot 1994). As larvae are usually the target stage for insect control and for assessing potential defoliation, larval population estimates provide the essential information to effectively manage the western hemlock looper. A three-tree beating method (Harris et al. 1972) has been used by Forest Insect and Disease Survey for larval sampling of western hemlock looper in British Columbia, in which larvae dislodged with a 3.66 m long pole from three trees fall onto a 2.10 x 2.75 m sheet placed beneath each tree. As no measurements are taken on the branch samples, the method only provides relative population estimates (Morris 1955 Southwood 1978). In the United States, Mason et al. (1989) suggested a beating method for Douglas-fir tussock moth, in which a 45 cm branch tip from the lower strata of a crown was beaten with a stick and the larvae were collected on a handheld l m 2 dropcloth. With the branch samples measured, the obtained insect density was almost a basic population estimate (Morris 1955, Southwood 1978). Unfortunately, sampling by beating a 45 cm branch tip can not be used for western hemlock looper as the majority of western hemlock trees are much taller than the Douglas-fir trees infested by Douglas-fir tussock moth. 63 A branch tip has been widely used as the sampling unit for some forest defoliators (Morris 1959, Southwood 1978). However, since branch tips vary in both size and weight, the expression of larval density as number of larvae per branch tip may be misleading (Fowler and Simmons 1988). Different sampling units on a branch tip have been examined for jack pine budworm (Fowler and Simmons 1988), spruce budworm (Regniere et al. 1989) and western blackheaded budworm (Shepherd and Gray 1990b), to determine the most desirable unit. It was indicated in many studies that the early larval stage of defoliators has different biological and ecological characteristics from the late larval stage (Morris 1959, Southwood 1978, Coulson and Witter 1984, Speight and Wainhouse 1989, Torgersen et al. 1993). Therefore, early and late larvae should be examined separately. No sampling study has been conducted and reported on the larval stage of western hemlock looper prior to this study. Because an IPM approach generally requires more precise information about an insect population (Waters et al. 1985), basic population estimate rather than population intensity should be the concern. To obtain basic population estimate with small variability for larvae of the western hemlock looper, different sampling units of a branch sample need to be compared. An IPM approach will also require information about the spatial distribution pattern of larvae and the development of sampling plans. Thus, the objectives of larval sampling in this thesis are to: (1) examine the efficiency of different sampling units on a branch-tip sample, (2) examine spatial dispersion and mean-variance relationships and, (3) develop sampling plans. 64 4.2 Materials and methods 4.2.1 Sample collection and processing. A branch tip, clipped approximately 45 cm in length, was used as the sampling unit for larvae, with density expressed as: (1) numbers of larvae per 100 cm 2 of foliage surface area, (2) numbers of larvae per 100 grams of fresh branch weight, and (3) numbers of larvae per 100 grams of dry needles. For (1), the foliated length of the branch tip and the maximum width were measured. As the shape of a branch tip is approximately triangular, the formula for calculating the area of a triangle was used to calculate its foliage surface area in which the foliated length was multiplied by the maximum width and divided by two. This approach was first reported by Fowler and Simmons (1988). Larval sampling was conducted twice a year both in 1993 and 1994, once at the early larval stage when the insect was in its 2nd instar and again at the late larval stage when the insect was in its 4th instar. In 1993, three plots (80m x 60m) were established at each of the six locations: WR, M L , RD, TR, H C and MB. In each plot, three branch tips were cut from the lower crown of each of five trees, using a pole pruner equipped with a basket to catch larvae which might drop from the branch tips. A total of 270 branch tips was collected for early and late larvae, respectively. In addition, late larvae were also sampled on small trees under the canopy by a beating stick which caused the larvae to fall onto a 40 cm x 70 cm cardboard collector. In 1994, locations WR, ML, MB and RD were excluded from sampling because of very low larval densities. Besides the H C and TR locations, three new locations were added: Walker Creek (WC) in the Prince George Region, Jumping Creek (JC) in the Nelson Forest Region and Sugar Lake (SU) in the Kamloops Forest Region. A total of 14 plots (100m 65 x 40m) with the long axis parallel to the forest road were set up in these locations, with four plots at each of the TR and SU locations and two plots at each of the HC, WC and JC locations. In each plot, three branch tips were sampled from each of six sample trees. The plot size for 1994 was somewhat different from that for 1993 because of variation in stand area. The cut branch tips were placed in paper bags and brought back to the a laboratory where the larvae were counted. After the counting, the branch tips were measured for fresh weight, length and maximum width, and placed in an oven for 48 h at 100 Â°C to obtain dry needle weight. 4.2.2 Statistical analyses. Because larval density was expressed on three different sampling units, coefficient of variation (CV), a criterion for determining the efficiency of sampling units (Fowler and Simmons 1988, Shepherd and Gray 1990 b), were used to compare the variability of density among the sampling units. Larval densities based on the optimum sampling unit (number per 100 g dry needles) were fitted to (1) the Poisson distri-bution, (2) the Taylor power law model, ( 3) the Iwao patchiness regression model, and (4) the negative binomial distribution. Model (2.12) was used to obtain the optimum sample size of branch tips under the fixed sample size method. In the model, n is the number of branch tips to be taken, a and p are parameter values from the Iwao patchiness regression model, and d is the precision levels with values of 0.1, 0.2, 0.4, 0.6 and 0.8. In developing sequential sampling plans, the cumulative number of larvae at which sampling can be stopped after sampling n branch samples was calculated based on Model (2.13) and Model (2.15). In both models, n is the number of branch-tip samples, T n is the cumulative number of larvae and d is the precision level. The parameters a and p in Model 66 (2.13) were from the Iwao patchiness regression model, while a and b in Model (2.15) were from the Taylor power law model on a natural logarithmic scale. The relationship between plot mean larval density and the proportion of branch samples containing at least t larvae was developed based on Model (2.17), on a natural logarithmic scale. With a large number of empty branch samples (no larvae), Model (2.18) was also used to describe the relationship between mean density and the proportion of samples with no larvae. Variance of predictions associated with Model (2.18) was estimated with Model (2.19). The Pearson correlation coefficient was used to relate larval counts on the cardboard collectors to larval densities estimated from branch-tip samples of larger trees. Randomization testing (Edgington 1986, Manly 1991) was used for comparison with results from conventional regression analyses for mean-variance, mean-crowding and mean-proportion relationships. The procedures of randomization testing for simple and multiple regression, as described in Chapter 2, were followed. 4.3 Results Sampling statistics and spatial dispersion. Early larval density was higher in year 1993 than in 1994 (Table 4.1). The maximum larval density was 75.6 ( no. / per 100 g) on the fresh branch weight unit, 258.7 (no. / per 100 g) on the dry needle weight unit and 86.5 (no. / per 100 cm2) on the foliage surface area unit. Based on the dry needle weight unit, mean plot density ranged from 0 to 39.4 in 1993, and from 1.7 to 33.0 in 1994. The maximum early larval density per plot occurred at location MB in 1993, while the lowest density occurred at location ML in 1993 (Table 4.1). 67 Table 4.1. Sampling statistics of larval density of Lambdina fiscellaria lugubrosa in the interior of British Columbia, 1993-1994, with density expressed on three kinds of sampling units. Year Instar Variable N Mean Min. Max. SD Var. CV 1993 Early Denb wet wt 268 6 41 0 75 56 10 92 119 15 170 22 Denn dry wt 268 23 90 0 258 67 37 43 1401 00 156 59 Denb area 268 7 86 0 86 49 13 40 179 55 170 56 Late Denb wet wt 225 1 48 0 15 61 2.38 5.64 160.53 Denn dry wt 225 4 71 0 44 27 7.23 52.21 153.41 Denb area 225 2 12 0 28 33 3.76 14.12 177.35 1994 Early Late Denb wet wt 261 1 41 0 17.89 2 64 6 98 186 99 Denn dry wt 261 5 58 0 60.00 9 78 95 58 175 05 Denb area 261 3 16 0 30.3 5 06 25 62 160 21 Denb wet wt 243 0 78 0 14.29 1 58 2 51 203 52 Denn dry wt 243 2 80 0 37.50 5 51 30 32 196 61 Denb area 243 0 51 0 7.62 1 03 1 07 203 84 N = number of branch -tip samples, Denb wet wt = numbers of larvae per 100 g of fresh branch-tip, Denn dry wt = numbers of larvae per 100 g of dry needles and Denb area = numbers of larvae per 100 cm2 of foliage surface area. 68 As expected, due to natural mortality, late larval density was generally lower than early larval density based on all the three sampling units. The maximum number of late larvae in a branch sample was 15.6 based on the fresh branch weight unit, 44.3 on the dry needle weight unit and 28.3 on the foliage surface unit (Table 4.1). Mean plot density of late larvae based on the dry needle weight unit ranged from 0.1 to 52.7 in 1993 and from 0.8 to 6.7 in 1994, with the highest density at the MB location and the lowest at the ML location, both in 1993. For both early and late larvae, the hypothesis that larvae follow Poisson distribution was rejected by chi-square test (p < 0.01), but the hypothesis of a negative binomial distribution was not rejected (p > 0.05). The k value for the negative binomial distribution, obtained from the iterative procedure, was k = 1.86 for early larvae and k = 1.54 for late larvae. Because the Taylor models gave b values larger than 1, an aggregated distribution was suggested for early and late larvae (Table 4.2). With both a and B values larger than 0, the Iwao model also suggested an aggregated distribution. However, because the Iwao models gave higher r-square values than the Taylor models, they fitted the data better. In the Taylor models, the smaller b value for early larvae indicated their lower degree of aggregation than late larvae. It was also shown that, in both early and late larvae, the mean-mean crowding relationship was not affected by an increasing larval density, but the mean-variance correlation decreased with an increasing larval density (Figure 4.1). Sample size. Based on the fixed sample size method, the optimum sample size of branch tips for estimating early larvae is given in Table 4.3. In general, the number of branch tips required decreases as larval density increases. Assuming an error margin of 0.2 and a mean density of 10 larvae per 100 g of dry needles, 16 branch tips would be the optimum sample size. Table 4.2. The Taylor power law models and the Iwao patchiness regression models for early and late larvae of Lambdina fiscellaria lugubrosa in British Columbia. Instar The Taylor model The Iwao model Early In (s2) = 0.86 + 1.44 In x m* = 2.01 + 1.28 X (r2=0.95, P<0.01) (r2=0.98, P < 0.01) Late In (s2) = 1.33 + 1.29 In x m* = 4.41 + 1.19 X (r2 = 0.86, p < 0.01) (r2 = 0.91, p < 0.01) In the models, both the intercepts and the slopes were significant (p < 0.05). Table 4.3. Optimum sample size1 for sampling Lambdina fiscellaria lugubrosa larvae in the interior of British Columbia. d (95% error margin / mean) Mean 0.1 0.2 0.4 0. 6 0.8 E 2 L 3 E L E L E L E L 1 353 598 88 150 22 37 19 33 6 9 5 94 136 24 34 6 9 9 17 2 2 10 62 78 16 20 4 5 3 4 1 1 15 52 59 13 15 3 4 2 2 1 1 20 46 49 12 12 3 3 1 2 1 1 25 43 43 11 11 3 3 1 2 1 1 1 numbers of branch tips 2 early instar larvae 3 late instar larvae 72 Table 4.3 gives the optimum sample size of branch tips for estimating late larvae. For a specific mean and d value, the number of samples required for late larvae were generally higher than for early larvae. Assuming an error margin of 0.2 and a mean density of 10 larvae per 100 g of dry needles are used, the optimum number of branch tips is 20 for late larvae, and 16 for early larvae. For a mean density of 15 larvae, 15 branch tips are required for late larvae, and 13 branch tips for early larvae. The Green and the Kuno methods gave similar sequential sampling plans for early larvae at the precision level of 0.2 (Table 4.4). For a sample size of 15 branch tips, early larval sampling can be stopped when the cumulative number of early larvae reach 173 (Green method) or 141 (Kuno method). The cumulative number of late larvae required to reach a specific precision level were also similar between the Green and the Kuno methods (Table 4.4). For a precision level of 0.2 and a sample size of 15 branch tips, late larval sampling can be stopped when the cumulative number of late larvae reach 200 (Green method ) or 198 (Kuno method). The difference between the two methods was larger in early larvae than in late larvae. In the fixed sample size method, a mean density of 20 early larvae requires a sample size of 12 branch tips to obtain a precision level of 0.2 (Table 4.3). In the sequential sampling method, however, 12 branches are needed for a mean density of 206/12 = 17 based on the Green method and 181/12 = 15 based on the Kuno method (Table 4.4). Thus, the sequential sampling method requires slightly fewer branch samples than the fixed sample size method for comparable densities. For late larvae, the number of branch tips required by the fixed sample size method, at a precision level of 0.2 and a mean larval density of 20, is 12 (Table 4.3). With sequential Table 4.4. Termination points in sequential sampling of early and late larvae of Lambdina fiscellaria lugubrosa in the interior of British Columbia. Cumulative number of larvae Branches (n) the Green method the Kuno method E 1 L 2 E L 12 206 220 181 224 15 173 200 141 198 18 150 186 123 184 21 133 175 113 175 24 120 165 106 169 27 109 158 102 164 30 100 151 98 161 33 93 145 96 158 36 87 140 93 156 39 82 136 92 154 42 77 132 90 153 45 73 128 89 151 48 69 125 88 150 51 66 122 87 149 54 63 119 87 148 57 61 116 86 148 60 58 114 86 147 63 56 112 85 146 Precision level = 0.2 1 early instar larvae 2 late instar larvae 74 sampling, 12 branch tips are the sample size to stop sampling at a mean density of 220/12 = 18 based on the Green method and 224/12 = 19 based on the Kuno method (Table 4.4). Therefore, the sequential sampling method required fewer branch tips than the fixed sample size method. Binomial sampling plan. The relationship between mean larval density (x) and the proportion of branch samples (Pt) containing at least t (t = 0, 1, 5, 10, 15, 20, 25, 30, 35, 40 and 45 larvae per 100 g dry needles) larvae was strong for both early and late larvae (Model 4.5 and 4.6, respectively). In (3c) = 1.21+1.12 In [-In (1-Pt)] +0.75 In t -0.18 (In t) In [-In (1-Pt)] (4.5) (r2 = 0.94, p < 0.01) In (3c) =1.46+1.03 In [-In (1-Pt)] +0.61 In t -0.13 (In t) In [-In (1-Pt)] (r2=0.86, p<0.01) (4.6) The intercept and the slope in both models were significantly different from zero (p <0.01). When t = 0, the relationship can be described as Model (4.7) for early larvae and Model (4.8) for late larvae: In (3c) =1.16 -1.08 In (-In P0) (4.7) (r* = 0.81, p < 0.05) In (3c) = 1.56-0.97In (-InP0) (4.8) (r2 = 0.73, p < 0.05) 75 The intercept and the slope in both models were significant at the 0.05 level. As the two models accounted for a substantially high proportion of the variation in mean densities, binomial sampling is applicable for larvae. A plot of predicted mean larval density against the proportion of branch-tip samples with no larvae is shown in Figure 4.2, while the relatively variability of the prediction is given in Table 4.5. Comparison of sampling units. The dry needle weight unit gave the highest early larval density, followed by the fresh branch weight and the foliage surface area units. In 1993, mean early larval density based on the dry needle weight unit had the smallest CV value. In 1994, however, density based on the foliage surface area unit had the smallest CV value, followed by the dry needle weight unit and the fresh branch weight unit (Table 4.1). The dry needle weight unit also gave the highest late larval density and smallest variability (lower CV values) in both 1993 and 1994. On the other hand, the fresh branch weight unit had somewhat lower variability than the branch surface unit. (Table 4.1). In general, the dry needle weight unit gave a higher density and a smaller variability than the other two units. Therefore, when the precision of data is a major concern, larval density should be expressed based on the dry needle weight unit. On the other hand, as the CV values for the dry needle weight unit are not much smaller than those for the other two units, cost factors should also be considered and may well be the decisive factor. Since a correlation relationship can be established between fresh branch weight and dry needle weight, density based on the fresh branch unit can be estimated from density based on the dry needle unit. If a high precision is not required, the fresh branch weight unit can simply be used. Table 4.5. Parameter values for estimating the variance of In (m) in binomial sampling plans for Lambdina fiscellaria lugubrosa larvae in the interior of British Columbia. Stage B N MSE p ssp a b Early instars 1.17 23 2.46 -0.02 10.28 0.86 1.44 Late instars 0.94 26 8.28 -0.70 22.92 1.33 1.29 P is the regression parameter in the Iwao patchiness model, N is the number of observations, MSE is the mean square of error from the Iwao model, ssp is the sum of squared deviations of the In (-In po) value from the average of p, a and b are parameters from the Taylor power law model. Early larvae 3.5 2.5 2 Â£ 1.5 1 0.5 0 -0.5 o o o o . . .a" -1.4 -0.6 -0.2 0.2 In [-In (p) ] 0.6 1.4 ~~o^ Regress ion 9 5 % confid. Late larvae -1 -0.5 In [-ln(p)] Regress ion 9 5 % confid. Figure 4.2. Relationship between the proportion of branch-tip samples with no larvae and mean larval density for early and late larvae of Lambdina fiscellaria lugubrosa in the interior of British Columbia, where m is the mean larval density and p is the proportion of branch samples with no larvae. 78 Larval counts on cardboard collectors. Larvae were found on the hand-held cardboard collectors at all locations in 1993. Mean larval counts at location MB were the highest (mean = 3.6, range = 0.9 to 4.9), followed by H C (mean = 2.0, range = 1.1 to 4.3), TR (mean = 0.3, range = 0 to 0.9), RD (mean = 0.3, range = 0 to 1.1), WR (mean = 0.2, range = 0 to 0.6), and ML (mean = 0.1, range = 0 to 0.3). There was a strong correlation of larval density between the cardboard collectors and branch-tip samples from overstory trees (r2 = 0.95, P < 0.05). Larval counts from understory trees, beaten by a stick and collected on a cardboard sheet, therefore, can also be used to indicate population trends in a stand, at least in a qualitative sense. Randomization testing. In randomization testing, the regression coefficients for mean-variance and mean crowding relationships of early larvae and late larvae were all significant at the p < 0.01 level, which was the same as the corresponding results in Table 4.2. For the relationship between mean larval density and the proportion of branch samples containing no larvae, randomization tests gave the same significance levels as those for Models 4.5, 4.6, 4.7 and 4.8. 4.4 Discussion and conclusions Different branch sizes and units for sampling forest insect defoliators have been compared in previous studies (Fowler and Simmons 1988, Regniere et al. 1988, Shepherd and Gray 1990 b). For example, three branch sizes (38 cm, 91 cm and whole branch) were used for jack pine budworm (Fowler and Simmons 1988), whereas a single branch size was used for spruce budworm (Regniere et al. 1988 ) and western blackheaded budworm (Shepherd and Gray 1990 b). In the jack pine budworm study, with three units for each of 79 the three branch sizes (air-dried weight, grid foliage surface area, and formula foliage surface area), grid foliage surface area for the whole branch was recommended as the best unit. On the other hand, the spruce budworm study which had three units on a 45 cm branch tip (fresh branch weight, foliage surface area and bud density), and the black headed budworm study, which dealt with three more units on a 46 cm branch tip (total twig length, branch volume and dry needle weight), both indicated that fresh branch weight was superior to foliage surface area. While this study suggested that dry needle weight be used for expressing larval density, one concern is that it may not apply for trees with severe defoliation as needles are stripped. In fact, trees with severe defoliation usually are avoided during sampling. Although fresh branch weight is easier and quicker to determine than dry needle weight, it is largely affected by weather conditions, especially precipitation (Wagner 1967, Shepherd and Gray 1990b). If there is not much variability in moisture content among branch samples, fresh weight of branch samples would be an acceptable and practical measurement unit. Mid-crown sampling is the suggested method for estimating density of a number of forest defoliators including Douglas-fir tussock moth (Mason 1970, 1987) and spruce budworm (Regniere et al. 1989) because mid-crown insect density is considered more representative of insect density for the entire tree. A homogeneous distribution of insect density among the upper, middle and lower crown levels has been found for western spruce budworm (Campbell et al. 1984 , Schmid 1984). Exarnining the vertical distribution of western hemlock looper larvae within tree crown is necessary, but it is difficult. The tree felling method used for eggs could not be used for larval sampling, because larvae would be dislodged from foliage when the tree is cut down. Due to resource constraints, other 80 approaches such as establishing a platform (Morris 1955) were not used. On the other hand, even if mid-crown sampling is required for western hemlock looper, it is impractical as many of the mature hemlock trees in B.C. are too tall to be reached by a pole pruner from the ground. The cardboard collector used by me, when used for a 45 cm branch tip, is similar to the method used by Mason et al. (1989), but its use is limited to small trees under the stand canopy. My study suggested that the use of a pole pruner to sample a 45 cm branch tip from the lower crown level is the desirable way to obtain basic population estimates in larval density of the western hemlock looper. On the other hand, the three-tree beating method may be modified by standardizing the number of branches to beat. Within a sample plot, the balance between the number of branches per tree versus the number of sample trees is always a concern (Morris 1955, Shepherd and Gray 1990 b). As the between-tree variation is usually larger than the within-tree variation, the approach has been to sample more trees and fewer branch samples per tree (Morris 1955, Shepherd and Gray 1990 b ). For defoliators, generally, two or three branch tips per tree is suggested (Mason 1970, Shepherd and Gray 1990 b). In mature western hemlock stands, tree crowns are not only isolated, but also overlapped, which means that a branch itself may be more important than the tree it belongs to. In this study, sampling plans for larvae were developed using three different approaches: fixed sample size method, sequential sampling and binomial sampling. Compared with the fixed sample size method, sequential sampling significantly reduced the number of branch-tip samples for basic population estimates. But it still requires a great deal of effort in insect sample processing and insect counting. By contrast, the binomial sampling plan, based on the close correlation between plot mean larval density and the 81 proportion of branch-tip samples with no larvae, can be use to estimate mean larval density without counting the exact number of larvae. Indeed, sampling with the binomial sampling plan saves insect managers a lot of effort. When using a binomial sampling model for prediction, the relative variance of the predicted mean density should be considered (Chapter 2). Although the latest model (Schaalje et al. 1991) is capable of considering all the bias error sources, the calculation is tedious. Hopefully, a simplified model can be developed in the future. Unlike the egg sampling study, the vertical distribution of larvae within tree crowns was not examined due to operational constraints. However, as the majority of hemlock trees can only be sampled for larvae from the lower crown stratum, the sampling plans developed in this study are useful. It is reasonable to expect a positive correlation of larval density between the lower crown stratum and the entire tree, although the strength of the correlation is presently unknown. With further study to quantify the correlation relationship, larval density on the lower crown stratum may then be used to more precisely represent larva density over the entire tree. 82 Chapter 5 Pupal sampling of Lambdina fiscellaria lugubrosa 5.1 Introduction The difficulties involved in collecting lichen samples for western hemlock looper eggs and branch-tip samples for larvae (Chapters 3 and 4) indicate a need for sampling pupae. Pupae are commonly found in protected locations such as bark crevices of trees (Hopping 1934, Shore 1989). Otvos (1974) reported that a strip of burlap (61 cm wide), wrapped several times around a tree, was an effective means of collecting large numbers of pupae of L. fiscellaria fiscellaria (Guenee), an eastern form of the western hemlock looper. The method was later used for the western hemlock looper (Shore, 1989). In these studies, because pupal density was expressed as counts per trap, the differences in the size of burlap traps were not considered. In mature hemlock stands, the forest type susceptible to western hemlock looper outbreaks, burlap trap size may vary considerably among trees. To make pupal counts from traps of different size comparable, pupal density has to be expressed relative to the surface area of the burlap trap. To use burlap traps as a sampling tool for the management of western hemlock looper, two other concerns need to be addressed. Firstly, responses of pupating larvae to different numbers of burlap layers should be examined, so that the optimum number of layers, which maximizes catches with acceptable variation and cost, can be selected. Pupae seem to prefer some kind of shelter for pupating which suggested that the addition of pockets to the trap may help to increase catches. Secondly, trap capture needs to be related to population density in open bark surface units to validate its use as an estimator. Density 83 in open bark surface units can be estimated by sampling from the open bark area of a tree with a burlap trap or nearby trees without traps. My approach here was to use the latter because it was more independent of trap sampling. In previous studies, burlap bands were wrapped around the whole tree trunk (Otvos 1974, Shore 1989). In mature hemlock stands, the circumference of a tree at breast height (1.3 m from the ground) can be as large as 7.53 m. Obviously, wrapping burlap traps entirely around the trunk of such large trees would require considerable time and burlap. Therefore, the use of partial wrapping can be considered. Western red cedar and Engelmann spruce are also infested by western hemlock looper, but no burlap traps have been tested on them prior to this study. The estimation of pupal density on these tree species is also needed for understanding hemlock looper-tree interactions at the stand level. Catches of pupae in a burlap trap may be affected by stand variables, such as tree DBH and crown conditions, which suggests that the effects of these variables need to be examined. Shore (1989) examined the effect of DBH on trap capture, but he did not consider other factors. 5.2 Materials and methods 5. 2.1 Burlap trap design. I designed and tested four types of traps (Figure 5.1 and 5.2). In trap type A, the entire bottom part of a burlap strip was folded-over 10cm and pockets were created by sewing the strip vertically at 20 cm intervals. In trap type B, the entire upper part of a burlap strip was fan-folded 10cm twice and pockets were created similar to tiiose in die type A trap. The design combined multiple burlap layers and pocket structures in one burlap band. Both type A and type B traps were wrapped once around the 84 Type B fully wrapped Figure 5.1. lugubrosa. The design of burlap trap types A and B for pupae of Lambdina fiscellaria 85 Tree b Type C partially wrapped Figure 5.2. The design of burlap trap types C and D for pupae of Lambdina fiscellaria lugubrosa. 86 bole of each tree at breast height (DBH ). Trap type C was made by cutting trap type A into a 40 cm X 40 cm piece and attaching it to part of a tree bole. In making trap type D, a commercially available burlap band (80 cm in width) was folded and wrapped once around the bole of each tree at 1.3 m above the ground level. 5.2.2 Trap placement and collection. In August 1993, prior to the start of pupation, all trees which had been used for larval sampling earlier in the same year were sampled for pupae with burlap traps. One trap of type A was placed on each of the five trees in a plot and type B traps were placed on another five trees nearby. A total of 30 traps (type A and B) were used at each location. When pupation was completed, the burlap traps were removed gently, and only pupae which were attached to the burlap were collected and counted. Those which pupated on the bark surface and in the bark crevices under the trap and those which fell to the ground were not collected because they were reported to be closely correlated to the numbers of pupae attached to the burlap traps (Shore 1989) and because a further examination of the variation was not the concern in this study. Owing to resource constraints, only WR, TR and H C locations were selected for testing type C traps with five trees at each location. In August 1994, the 14 plots which had been used for larval sampling earlier in the same year were used for sampling pupae with type D traps. In each plot, a type D trap was placed on each of six western hemlock trees to catch pupae. Besides western hemlock, I also placed type D traps on western red cedar and Engelmann spruce trees in two plots (A and D) in the Sugar Lake area where these species were relatively more abundant to compare trap capture among different tree species. 87 To examine the effect of stand variables on trap capture and the correlation of trap capture with pupal density in open bark areas on a fine scale, three grid plots (60m X 200m) were established at the HC, WC and SU locations. Within each plot, 30 subplots measuring 20 m x 20 m were set up and one trap was placed on a central tree of each subplot. All western hemlock trees were measured for DBH to determine the total basal area of western hemlock. Other stand variables including crown ratio, crown class and defoliation class were estimated based on the following criteria. Defoliation was classified as: 1 = 0 % defoliation; 2 = 1% to 25%; 3 = 26% to 50%; 4 = 51% to 75% and 5 = > 75%; Crown ratio was divided as : 1 = crown <20% of total tree height; 2 = 21% to 40%; 3 = 41% to 60%; 4 = 61% to 80%; 5 = 81%. Crown classes were: 1 = open crown (isolated), 2 = dominant (exposed sides), 3 = codominant (exposed top only), 4 = intermediate and 5 = suppressed. To relate trap capture to pupal density in open bark surface units, pupae were also recorded in an open bark surface unit (30 cm X 40 cm) of a nearby tree. 5.2.3 Statistical analyses. Three zones and four zones were defined for trap types A and B, respectively, with type A possessing the following zones: (a) inside pocket, (b) single layer outside pocket, and (c) double layer outside pocket (Figure 5.1). Besides zones a and b, trap B had two more zones: (c) triple layer outside pocket and (d) under pocket (Figure 5.2 ). Zones were not defined for trap types C and D as they did not have the pocket structure. Pupal density was expressed as counts per 100 square centimeters burlap surface area. A two-way A N O V A (Dunn and Clark 1987) examined the effects of location and trap type on pupal density. Due to differences in trap design, the variance of density among the zones was examined by a one-way A N O V A (Dunn and Clark 1987) on an individual trap type basis. The coefficient of variation was compared between trap types and among zones 88 within a trap type for efficiency. Correlation of catches between type A and B traps as well as among zones within each trap type was examined by the Pearson correlation analysis (Zar 1984). For the three grid plots, the effect of stand variables on trap capture of pupae was analyzed with analysis of covariance (ANCOVA) (Huitema 1980, Dunn and Clark 1987), in which pupal density was the response variable, basal area and DBH of trap trees the covariates and defoliation class, crown ratio, and crown class the class variables. The correlation relationship of pupal density between traps and open bark surface units was examined with regression analysis (Dunn and Clark 1987). Prior to ANOVA, A N C O V A and regression analysis, a In (x+1) transformation was used to adjust for potential violation of the assumptions underlying these analyses (Steel and Torrie 1980, Montgomery and Peck 1992). Randomization tests (Edgington 1986, Manly 1991) were used in comparison with conventional A N O V A and regression analysis. With the two-way A N O V A for the effect of location arid trap type on pupal catches, the randomization testing involved a random allocation of the samples to the location and trap type combinations. In the one-way A N O V A for the effect of trap zone on capture, the randomization testing assigned the samples to different zones within each trap type. The regression coefficient for the relationship between trap capture and open density was compared with the coefficients from random allocation of samples. 89 5.3 Results Catches of pupae in trap types A and B. Table 5. 1 shows the average pupal counts by location, burlap trap type and trap zone. The effects of locations and trap type were significant (p<0.05), but the interaction was not (Table 5.2). At five of the six locations, trap type B had twice as many pupae as trap type A; however, trap type A had smaller coefficients of variation (CV) than trap type B. Pupal density varied among different zones within trap type B (p <0.05 ), but not within trap type A (P > 0.05) (Table 5.3). In both trap types, more pupae were found on double or triple burlap layer zones than on single layer zones (Table 5.1). Surprisingly, the pocket structure did not always attract more pupating larvae as expected. Although pupal counts were generally higher inside the pockets than outside (4/6 of the locations, Table 5.1) for type A traps, it was the opposite for type B traps (Table 5.1). Single layer zones had smaller CV values than double layer zones in type A traps (4/6 of the locations, Table 5.1), but a greater CV value than three layer zones in type B traps (Table 5.1). In both trap types, zones outside the pockets had smaller CV values than those inside the pockets. Total catches of pupae in type A traps were closely related to those in type B traps (r = 0.70, p < 0.01), In addition, a high correlation of catches was found among the burlap zones within trap types A and B, respectively (Table 5.4 and 5.5). The high correlation of pupal catches between an individual zone and the entire trap denoted that pupal catches of an individual zone may be used to indicate pupal catches of the entire trap. Pupal catches outside of the pockets had the highest correlation (r = 0.95, p <0.01) with that of the entire trap. 90 0) > <v c m in o o in Â§- O Â° co .Ti X! 03 â€¢a *s co O â€¢ r H I i .5 â€¢3 CO s dl C O N 73 C CS CD dl u O >. M Dl C 3 X c g O ca m & c + .Â« <U 0 , o >. + J J XI c CO a-10 c (0 id 0 â€” u .rH o u CO a 01 10 x: â€¢ rH ai <D >H x: 10 o c > o >rH til a <D U-t 01 â€¢o CO O c ai â€¢rH CU 0 c CO J 3 i - J CO u u u c <D 3 i_) 0) Q. P- C O 10 â€¢rH IB â€¢rH o CJ f-t 1J 0) â€¢rH U ai a> lâ€”i "4-13 a <D x: 10 4 H XI 10 x: o u ai M râ€”i o u o Ci U i j 10 u u 3 10 CI II II XI u II J II II a . < XI m a . Â§r E- .^ - - O 10 < O i- t > co CN oo *-i 04 r~ i n co T H O\ \o tn t/t â€¢q" Pi <u > > c n) ai E c ID 0) E T-( O o o o o Table 5. 2. Analysis of variance of the effect of location and trap type (A and B) on pupal catches of Lambdina fiscellaria lugubrosa at six locations in the interior of British Columbia, 1993. Source DF SS MS F Pr>F Location 5 107.05 21.41 73.96 0.0001 Trap type 1 4.63 4.63 16.01 0.0001 Location x trap type 5 2.85 0.57 1.96 0.0882 Error term 150* 0.29 * pupal counts were lacking from a total of 18 traps at the six locations as these traps were destroyed by bears. Table 5. 3. Analysis of variance of the effect of burlap zone within trap types A and B on pupal catches of Lambdina fiscellaria lugubrosa in the interior of British Columbia, 1993. Trap type Source DF SS MS F Pr>F A Zone 2 2.58 1.29 1.96 0.1431 Error term 231 152.46 0.66 B Zone 3 29.49 9.83 11.19 0.0001 Error term 332 192.16 0.88 Table 5. 4. Pearson correlation coefficients for pupal counts of Lambdina fiscellaria lugubrosa among burlap zones within trap type A. a b c Total a 0.75 0.83 0.87 b 0.87 0.95 c 0.97 Total 1.00 All values are significant at the 0.01 level. Table 5.5. Pearson correlation coefficients for pupal counts of Lambdina fiscellaria lugubrosa among burlap zones within trap type B. a b c d Total a 0.61 0.72 0.64 0.75 b 0.87 0.78 0.95 c 0.80 0.97 d 0.86 Total All values are significant at the 0.01 level. 95 Catches of pupae in trap types C and D. Pupae were found in most of the type C traps at the H C and TR locations (Table 5.6), mdicating that a piece of burlap band covering part of a tree trunk can also trap pupae. The variation of population density among locations as indicated by type C traps was consistent with those indicated by trap types A and B. Type D traps successfully caught pupae at all locations (Table 5.7), with the highest counts of pupae occurring at and the lowest catches at Jumping Creek. Based on my observation in the field, most of the pupae were found on the trap surface facing towards tree trunk; only a very small proportion was found between the two layers. Pupae were found in burlap traps on both western red cedar and Engelmann spruce. In plot A, pupal counts on western hemlock were slightly higher than on western red cedar; in plot D, however, they were lower on western hemlock than on western red cedar and Engelmann spruce (Table 5.8). The effect of stand variables on trap capture varied with locations. At locations WC and HC, no significant effect of the five stand variables on pupal catches was found. At location SU, however, the effect of DBH and basal area of western hemlock was significant at the 0.05 level (Table 5.9). Burlap traps on smaller trees tended to catch more pupae. The number of pupae caught in burlap traps were closely related to the numbers of pupae found in the open bark surface unit (30cm X 40cm) of a nearby tree at the three locations (Table 5.10, Figure. 5.3). Burlap trap capture accounted for 56%, 66% and 89% of the variation of pupal counts on nearby trees at HC, WC and SU, respectively. The pooled data model explained 79% of the variation. A comparison of the predicted and actual values of pupal density based on the regression model is given in Figure 5.4. 96 Table 5. 6. Pupal catches of Lambdina fiscellaria lugubrosa in type C traps in the interior of British Columbia, 1993. Location N Empty Mean SD Min. Max. trap TR 5 2 0.2250 0.2245 0 0.5000 HC 5 1 0.1625 0.1135 0 0.3125 WR 5 4 0.0125 0.0280 0 0.0625 Mean = number of pupae per 100 cm2 burlap surface area Table 5.7. Pupal catches of Lambdina fiscellaria lugubrosa in type D traps at different locations in the interior of British Columbia, 1994. Locations Plot type No. trees Mean DBH SD Mean catches SD HC Regular 12 54.00 8.18 0.04 0.03 WC Regular 12 26.99 4.87 0.07 0.07 SU Regular 23 49.28 23.65 0.17 0.24 TR Regular 24 42.59 20.62 0.10 0.09 JC Regular 11 41.31 8.18 0.03 0.07 HC Grid 30 43.29 11.78 0.12 0.11 WC Gird 30 38.88 11.06 0.16 0.16 SU Grid 30 45.72 10.86 0.35 0.73 DBH is in cm; mean catch values refer to 100 cm2 burlap surface area 98 Table 5. 8. Pupal catches of Lambdina fiscellaria lugubrosa in type D traps on different tree species in two sample plots in the Sugar Lake area, British Columbia, 1994. Plot Tree species No. traps Mean catches SD 1 W. R.Cedar 5 0.0675 0.0605 1 W. Hemlock 5 0.0721 0.0768 1 W. R.Cedar 5 0.0435 0.0495 2 W. Hemlock 6 0.0178 0.0153 2 E. Spruce 10 0.0199 0.0191 Catch values refer to 100 cm2 burlap surface area. Table 5. 9. Analysis of covariance of the effect of stand variables on pupal catches of Lambdina fiscellaria lugubrosa in burlap traps of type D in a grid plot (60m x 200 m) in the Sugar Lake area, British Columbia, 1994. Source DF SS MS F Pr>F CCLASS 2 0.2442 0.1221 2.26 0.1292 CRATIO 3 0.2491 0.0830 1.54 0.2346 DEFOL 1 0.0820 0.0820 1.52 0.2317 DBH 1 1.9261 1.9261 35.63 0.0001 BA 1 0.3398 0.3398 6.29 0.0205 100 2.5 Figure 5. 3. Relationship of pupal density between burlap traps (x) and open bark surface units (y) for pupae of Lambdina fiscellaria lugubrosa in the interior of British Columbia. The two variables were transformed into In (x+1) and In (y+1), respectively. 101 - â€¢â€” predicted 100 "Â°" a c t u a l Figure 5. 4. Actual and predicted values of population density of pupae of Lambdina fiscellaria lugubrosa based on regression model In (y+1) = 0.62 In (x+1), where y is density in open bark surface units and x is the density in burlap traps. Pupal density is expressed as numbers of pupae per 100 cm2 burlap surface area. 102 Table 5.10. Regression models for relationships of pupal density of Lambdina fiscellaria lugubrosa between burlap traps and open bark surface units (30 cm X 40 cm) in the interior of British Columbia, 1994 Location n Regression model MSE r2 HC 30 In (y+1) = 0.76 In (x+1) 0.0099 0.56 WC 30 In (y+1) = 0.49 In (x+1) 0.0093 0.66 SU 30 In (y+1) = 0.63 In (x+1) 0.0086 0.89 Pooled 90 In (y+1) =0.62 In (x+1) 0.0079 0.79 x is the number of pupae caught in a burlap trap and y is the pupal count recorded in a 30 cm x 40 cm tree bark area of a nearby tree. When a model had an intercept which was not significant at the 0.05 level, the non-intercept model was used. 103 Randomization tests. In the two-way A N O V A for the effect of location and burlap trap types on pupal captures, the statistical significance level was similar between conventional and randomization tests for location and trap type, but not for the interaction (Table 5.11). The interaction effect was almost significant at the p<0.05 level in the conventional test, but was not significant in the randomization testing. For the effect of trap zone, randomization testing agreed with the conventional tests. Randomization testing also gave the same significance level for the relationship of pupal density between burlap traps and open tree bark units. 5.4 Discussion and conclusions The expression of pupae based on burlap surface area makes pupal density from traps of various sizes comparable. Burlap bands have also been used for population sampling for larvae of gypsy moth (Lance and Barbosa 1979, Wallner 1983, Liebhold et al, 1986), but none of them expressed insect density relative to the size of the burlap surface area. In one study (Liebhold et al. 1986), a strip of burlap (40 cm wide) was doubled over, wrapped around, and stapled at breast height on each bole and larval density was expressed as numbers of larvae per trap. Although the authors did not provide a description of the host trees (Quercus spp.), their DBH might have varied considerably. I attempted to use pockets to attract more larvae to pupate. Because the results varied between trap types A and B, the further use of pockets is not recommended. With more pupae caught on two or three layers than on a single layer, however, a burlap trap type with two layers, such as trap type D, is recommended. More than two layers would increase the quantity of burlap needed and the results may not warrant the extra cost. The 0) > at y cn at C â€¢B c > c o u L O N O o < o o O O 0 0 o o i n o o o 0 0 H H O O r - l o o i n o o o o d d <N o o o o o o CN o o o o o o â€¢J3 â€¢B to H CU 01 dl 1+ *-, ^ d (0 3 3 3 cr* cr1 cr1 to to <o c c c ed ed os QJ 0J OJ s s a 01 OS 3 c r to C at 0) 3 tr to C Of 0) at > C o â€¢43 at <" O i>Â£ x CL, at (X at y at J3 Â° Â±1 O OI C O N OI X t o < >o < > O < > o < .a â€¢S Â° O <Q u â€¢G * .Â£ - a ii w S oi . , o ^ N 0) CL, ^ S 0 u u at 01 <J Â£ C W O o Â» N 01 OH 5 X 1 o at 0) u * c W o 105 strong correlation of pupal counts among different zones within a burlap trap indicated that partial counts can be used as an indicator for the entire trap. Pupal catches in type C traps indicated that a burlap band does not have to be wrapped entirely around the bole, especially for larger trees. In some mature stands, the diameter of a western hemlock tree at breast height can be as large as 120 cm, requiring a burlap band of 753 cm in length. In addition to reducing burlap use and facilitating large tree trapping, type C traps can also be used to provide uniform sizes of sampling units, a preferred feature for sampling units (Cochran 1977, Southwood 1978). One of the disadvantages with trap type C may be its lower sensitivity to sparse population levels than a full burlap band, due to its smaller trapping area. The fact that DBH and total basal area of western hemlock had a significant effect on trap capture only at one location indicated that the effects of these factors are complex and further examination of this is required. The successful trapping of pupae on both western red cedar and Engelmann spruce indicated that western hemlock looper also uses these tree species as pupating sites. Because the sample sizes of trees for these two tree species were not large, further study is needed, with large sample size, to ascertain the differences in pupal densities among different tree species as well as their temporal and spatial associations. I was aware of the potential problem of spatial autocorrelation in the grid plot data. However, the relatively small number of subplots did not allow me to use spatial autocorrelation analysis. As suggested by Griffith (1988), the bias caused by spatial autocorrelation can be compensated by using a very high significance level. In the results, the effect of DBH was significant at the 0.0001 level and basal area at the 0.02 level. Therefore, spatial autocorrelation is not expected to be a serious problem. 106 The most significant finding of this study was the close relationship between pupae captures in burlap traps and pupal density in open bark surface units, with the pooled model accounting for 79% of the variation. The consistency of the relationship in the three grid plots indicated that type D traps should be used as a sampling tool for the management of the western hemlock looper. 107 Chapter 6 Forest roadside sampling of larvae and adults of Lambdina fiscellaria lugubrosa 6.1 Introduction Sampling methods for wildlife populations have traditionally differed from those for insect populations. However, since both insects and wildlife are mobile, some of the methods used for wildlife may also be applicable for insects. The sampling methods for wildlife included roadside census sampling, aerial census sampling, line transect sampling, distance sampling, removal sampling, and capture-recapture sampling methods (Seber 1982). Some of these methods have been applied to insects, for example, the removal sampling method for sampling looper eggs from their substrates (Shepherd and Gray 1972), the captue-recapture method for estimating gypsy moth density (Wallner et al. 1989) and the distance method for estimating grasshopper density (Seber 1982). The roadside census method, in which sampling is conducted along a road, has the advantage that large areas can be quickly covered. The method has been used for the census of cottontails (Newman 1959, Wight 1959, Kline 1965), small birds (Howell 1951), woodcocks (Kozicky et al. 1954), mourning doves (Foote et al. 1958), pheasants (Fisher et al. 1947, Kozicky et al. 1952, Hartley et al. 1955), blackbirds (Hewitt 1967), and rhesus monkeys (Southwick and Siddiqi 1968). InU. S. A. roadside census was one of the few methods used on a state-wide basis for wildlife surveys (Seber 1982). 108 The roadside sampling method has not been used for forest insects because of the concern that insect densities along forest roads may differ from those within the stands (forest edge effects). However, there are several reasons to justify roadside sampling for forest insects. First, some stands have low accessibility, especially those with abundant shrubs on the ground. Second, the operational budges for insect sampling is generally hmited as insect management is only one of the many tasks in the overall forest resource management. With large areas to be surveyed on the ground, there has to be some kind of compromise. Third, forest edge effect can be examined and roadside insect density may be used to estimate insect density within the stand. Some empirical evidence has suggested a generally higher insect density along roadsides than within the stands (Xiao Ganrou, pers. comms.), which means that roadside densities can at least provide an early indication of insect density within the stands. As western hemlock looper can quickly build its population over large areas, the feasibility of roadside sampling should be explored. In roadside sampling, information about the spatial dependence of insect counts along roadsides is useful. When insect counts at adjacent sampling points are spatially dependent, the number of sampling points can be reduced. The desirable distance should be the one which renders neighboring sampling points spatially independent in insect counts. Spatial autocorrelation of insect counts has been reported for a number of insects. In a study on egg masses of the gypsy moth, Lymantria dispar, Liebhold et al. (1991) found a spatial dependence of egg masses at distances ranging from 20 km to 100 km. He also found that the range and magnitude of the spatial dependence varied significantly among years and among sites. Midgarden et al. (1993) studied spatial correlation of adults of the 109 western corn rootworm, Diabrotica virgifera, in sticky traps and found that traps within a distance of 30 m were dependent in catches. While insects are sampled along roadsides, sampling can also be conducted within nearby stands so that comparison can be made between the roadsides and the within-stand values. The objectives of this study were to: (1) examine spatial dependence of western hemlock looper along forest roads and determine the desirable distance between adjacent sample points; and (2) examine the correlation of western hemlock looper larval and adult densities between roadside samples and those within the stands. 6.2 Methods 6.2.1 Study areas. In 1993 and 1994, male adults, caught in pheromone traps, were sampled along the main road in each of the Capilano, Seymour and Coquitlam watersheds in Vancouver, British Columbia, where western hemlock looper is a historical problem and the watershed managers were interested in a roadside sampling scheme for the looper. The Capilano Watershed is the most western watershed with a land area of 20,000 hectares, while the Seymour Watershed, covering an area of 18,000 ha, lies just to the east of the Capilano Watershed separated by a mountain ridge. The Coquitlam Watershed, at 20,050 ha, located farthest to the east, is the largest of the three. The main coniferous tree species in the three watersheds are western hemlock, Douglas-fir, Pseudotsuga menziesii, mountain hemlock, Tsuga mertensiana and Amabilis fir, Abies amabilis. 110 Western hemlock was the dominant tree species along the main sampling roads. In addition, environmental conditions were similar. In some cases, the road section for sampling was shortened to less than the actual road length to rriinimize a sudden change of environmental conditions (elevation, etc.). In 1994, roadside sampling was also conducted for larvae and male adults along the Sugar Lake Forest Road in the Kamloops Forest Region, British Columbia, where western hemlock looper was a concern. Unlike the three Vancouver watersheds, most of the western hemlock trees along the roadsides had lower branches which could be reached with a 10 m pole pruner. Thus, larvae sampling was possible. The road started at the northeastern edge of Sugar Lake and extended almost directly north for 61 km. The main coniferous tree species along the road were western hemlock, western red cedar, mountain hemlock and spruces, Picea spp. To compare insect counts along the roadsides with those within the stands, four sampling plots, A, B, C and D, were also set up within the stand at 28, 31, 35 and 45 km along the road to compare insect densities with those at the nearest roadside sampling point. The distance among the four plots was unequal, because many of the stands along the road had poor accessibility. 6.2.2 Sampling methods. Two types of pheromone traps, known as Multi-traps and Uni-traps, were used. The former were used in the Sugar Lake area, while the latter in the three watersheds. All traps were baited with 200 u.g western hemlock looper pheromone lures (containing a 1: 1 ratio of isomeric 5, 11-dimethylheptadecane and 2, 5-dimethylheptadecane) (Gries et al. 1993, Li. et al. 1993 a, b) which was provided by Phero. Tech. Inc. Vancouver. The 200 ug was used because it was the recommended dosage in 1993 (Carlson, pers. comm.). I used two types of traps, because I needed to reuse some I l l traps in storage at no cost. With difference in trap type, statistical analyses were conducted on single area basis and no comparison of captures was made between the two areas. In 1993, 20 traps were placed along the Seymour Main Road and 19 traps along the Coquitlam Main Road. In the following year, two and six more traps were placed at the extended road section of the Seymour and Coquitlam main roads respectively. In addition, 19 traps were placed along the Capilano Main Road. A l l traps were placed at 1 km intervals. In 1994, larvae were sampled at 30 points along the Sugar Lake Forest Road at 1.5 km intervals. At each point, two 45 cm branch tips were taken from the lower crown of each of two western hemlock trees by the road with a pole pruner equipped with a basket. Before adults emerged, one Multi trap was placed at each of the 30 points where larvae had been sampled. A l l pheromone traps were hung on a branch (approximately 1.5 m above the ground) under the canopy of a tree within the stand. In a few stands where no branch could be used, the trap was hung on a shrub at a similar height. 6.2.3 Statistical analyses. Spatial autocorrelation (also known as spatial dependence or spatial continuity) refers to a phenomenon where the observed value of a response variable at one locality is dependent on the values at the neighboring localities (Sokal and Oden 1978), while spatial autocorrelation analysis is a statistical technique for quantifying the degree of this dependence (Sokal and Oden 1978, Legendre and Fortin 1989, Legendre 1993). Spatial autocorrelation analysis has been used in a number of entomological studies (Schotzko and O'Keeffe 1989, 1990, Liebhold and Elkinton 1989, Liebhold et al. 1991, Gage et al. 1990, Midgarden et al. 1993). In spatial autocorrelation analysis, the autocorrelation coefficient for a response variable is generally calculated based on the Moran index, I (d) 112 (Moran, 1950): where yi and yj are values of the variable at location i and j, and y is tlie mean, wij takes the value 1 when the pair (i,j) are within distance class d (the one for which the coefficient is computed), and 0 otherwise. A distance can be divided into class by forming equal distance classes, with the number of classes approximating 1/3 of the total sample points (Legendre and Fortin 1989). W is the number of pairs (i and j) within the distance classes. For roadside sampling of western hemlock looper, equal distance classes were used in which the distance along a road was divided into equal classes. The Moran I values vary generally from -1 to +1. For insect counts, a positive I value indicates spatial continuity, whereas negative I values indicates spatial discontinuity on patchiness. These coefficients are computed for each distance class d and each value is accompanied by the probability of it not being significantly different from zero (i. e. there is no spatial autocorrelation). A correlogram is a graph where the autocorrelation values are plotted against the distances (d) among sampling localities. Correlograms can be analyzed by looking at their shapes (Legendre and Fortin 1989). Sokal (1979) and Legendre and Fortin (1989) have provided a variety of reference correlograms which help to interpret typical spatial patterns that may occur. The degree of spatial dependence of western hemlock looper density along the forest roads were calculated with the Moran I index in 113 which yi and y are insect density at locality i and j respectively and depicted with correlograms. While the Moran I value for each specific distance class was tested for significance, a correlogram as a whole was tested for significance by using the Bonferroni's method for multiple tests (Oden 1984, Legendre and Fortin 1989): P p- = -v where p' is the Bonferroni-corrected level, v is the number of distance classes and p is the assigned globally significance level. In this study, p was set at 0.05 for all correlograms. When a correlogram contains at least one distance class which is significant at the Bonferroni-corrected level, the correlogram as a whole is considered as globally significant at the 0.05 level. The correlation of western hemlock looper density between the roadside and within-stand estimates was analyzed with Pearson correlation coefficient s (Zar 1984). 6.3 Results Vancouver watersheds. A total of 14,684 male adults were trapped along the Seymour Watershed Main Road, with an average of 756 adults per trap. At the same time, 19,473 male adults were caught at the Coquitlam Watershed Main Road, averaging 928 adults per trap. Capilano Watershed had the lowest mean capture (56) per trap (Table 6.1). In 1993, as the Moran I value was significant at the Bonferroni-corrected level (p'= 0.05/19=0.003) for distance class 6, the correlogram for the Seymour Main Road was 114 Table 6.1. Sampling statistics for catches of male adults of Lambdina fiscellarialugubrosa in pheromone traps in Capilano, Seymour and Coquitlam watersheds, British Columbia, 1993-1994. Year Watershed Sample line N Mean Min. Max. SD 1993 Seymour Main Road 20 756 327 1,502 327 1993 Coquitlam Main Road 21 928 60 1,925 544 1994 Capilano Main Road 19 56 0 107 37 1994 Seymour Main Road 22 400 59 1,531 373 1994 Coquitlam Main Road 26 184 6 1,336 322 N=number of pheromone traps Table 6.2. Summary of results of spatial autocorrelation analysis of male adults of Lambdina fiscellaria lugubrosa, caught in pheromone traps along the main road in the Seymour Watershed, Vancouver, British Columbia, 1993 and 1994. Distance Upper No. pairs Moran's I Significance class boundary level 93 94 93 94 93 94 93 94 1 2.71 3 33 60 0.24 0.16 0.042 0.041 2 5.43 6 42 51 -0.13 0.03 0.497 0.204 3 8.14 9 35 42 -0.19 -0.06 0.235 0.702 4 10.86 12 19 33 0.38 -0.54 0.026 0.001 5 13.57 15 21 24 -0.17 -0.11 0.283 0.375 6 16.29 18 15 16 -0.58 -0.13 0.003 0.361 7 19.00 21 6 6 -0.03 0.42 0.521 0.101 Values for the upper boundary are in kilometers. 1 117 globally significant at the p=0.05 level. The positive and significant Moran I value for distance class 1 indicated a spatial dependence of catches between traps within 2.71 km (Table 6.2, and Figure 6.1). For the Coquitlam Watershed, as none of the Moran I values were significant at the p=0.05 level, spatial autocorrelation was not detected. In 1994, the Seymour Main Road had the highest mean capture, followed by the Coquitlam Main Road and the Capilano Main Road (Table 6.1). Catches at both the Seymour and the Coquitlam Main Roads were lower than in 1993. The Bonferroni-corrected level of the correlogram was 0.003 for Capilano Main Road and 0.002 for Seymourand Coquitlam main roads. Comparing the significance level of the Moran I index with the Bonferroni adjustment level, the correlograms for the Seymour and Coquitlam main roads were globally significant at the p=0.05 level, but the one for the Capilano Main Road was not (Table 6.3). For the Seymour Main Road, as the Moran I value for distance class 1 was positive and significant, pheromone traps separated by a distance up to 3 km were similar in catches of male adults. After that distance class, catches became less similar with increasing distance. The positive I value for distance class 7 was high, but not significant. As Capilano Main Road also had a significant and positive Moran I value for distance class 1, traps separated by a distance up to 3 km were spatially correlated. On the Coquitlam Main Road, the Moran I value was positive for distance class 1 and became negative for the remaining distance classes except for class 3. However, the positive Moran's I value for distance class 3 was too small and not significant. Apparently, traps within a distance of 3 km were spatially correlated. In summary, the numbers of male adults caught varied significantly between years and among roads, but a significant spatial continuity of catches was found in 4/5 of the Table 6.3. Summary of results for spatial autocorrelation analysis of male adults of Lambdina fiscellaria lugubrosa, caught in pheromone traps along main roads in the Capilano Watershed and Coquitlam Watershed, Vancouver, British Columbia, 1994. Distance Upper No. pairs Moran's I Significance class boundary level CAP COQ CAP COQ CAP COQ CAP COQ 1 3 3 51 69 0.22 0.25 0.021 0.001 2 6 6 42 60 -0.36 -0.03 0.005 0.826 3 9 9 33 51 0.22 0.02 0.051 0.220 4 12 12 24 42 0.08 -0.10 0.244 0.478 5 15 15 15 33 -0.59 -0.20 0.011 0.134 6 18 18 6 24 -0.95 -0.33 0.008 0.039 7 21 15 -0.58 0.005 8 24 6 -0.37 0.161 CAP=Capilano Main Road; COQ=Coquitlam Main Road Values for the upper boundary are in kilometers. 119 roads. Generally, catches of adults in pheromone traps were similar to one another at closer distances. In 3/5 of the roads, there was a significant spatial dependence of catches within a distance of 3 km, and on one road, the distance was 2.7 km which is close to 3 km. The results suggested that pheromone traps should be placed at an interval larger than 3 km along the main roads in the three Vancouver watersheds. Sugar Lake. Late larval density along the Sugar Lake Forest Road had a mean of 2.7 larvae per lOOg of dry needles, a standard deviation of 4.7, a maximum of 25 and a minimum of 0. The Bonferroni correction level for the correlograms was p'= 0.05/33 = 0.002. Moran's I was significant at the p = 0.05 level for distance classes 1, 2, 5 and 6 with classes 1, 5 and 6 being significant at the Bonferroni adjustment level (Table 6.4). Overall, the correlogram was globally significant at the 0.05 level (Figure. 6.2). As Moran's I was significant at the p = 0.05 level for distance classes 1 and 2, larval densities were spatially dependent for those sampling points which were up to 7.3 km apart. On the other hand, as the autocorrelation value for distance class 1 was greater than for distance class 2, sampling points separated by a distance of 3.6 km had a higher degree of spatial dependence than those separated by a distance between 3.6 and 7.3 km. The negative Moran's I values after distance class 2 indicated a dissimilarity of larval density for the remaining distance classes. Mean adult density was 2,117 per pheromone trap with a standard deviation of 1,524, a maximum of 3,810 and a minimum of 1,524. The Moran I values were significant at the p=0.05 level for distance classes 1, 2, 4, 5, 6 and 7 with these values exceeding the Bonferroni correction level (pv= 0.05/30 = 0.0017). Thus, the correlogram was globally significant at the p=0.05 level (Table 6.4 and Figure 6.2). Similar to the larval stage, there was spatial dependence of catches along the road for distance classes 1 and 2. Pheromone traps which were up to 7.3 km apart were spatially similar in catches. 120 Table 6.4. Summary of results for spatial autocorrelation analysis of larvae and male adults of Lambdina fiscellaria lugubrosa along the Sugar Lake Forest Road, Kamloops Forest Region, British Columbia, 1994. Larvae were sampled with a pole pruner from the lower crown of Tsuga heterophylla and adults with pheromone traps. Distance Upper No. pairs Moran's I Significance class boundary level LAR ADU LAR ADU LAR ADU LAR ADU 1 3.63 3.63 84 84 0.38 0.42 0.001 0.001 2 7.25 7.25 98 98 0.18 0.16 0.007 0.004 3 10.88 10.88 63 63 -0.08 0.08 0.493 0.239 4 14.50 14.50 70 70 -0.17 -0.41 0.104 0.001 5 18.13 18.13 54 54 -0.51 -0.53 0.001 0.001 6 21.75 21.75 30 30 -0.51 -0.52 0.002 0.061 7 25.38 25.38 26 26 -0.31 -0.50 0.060 0.070 8 29.00 29.00 10 10 0.37 0.57 0.074 0.036 LAR=larva; ADU=aduIt. Values for the upper boundary are in kilometers 121 A i . . . , 0.6 -0.6 .1 I . , . . . . 1 2 3 4 5 6 7 8 Distance class B 1 i â€¢ â€¢ â€¢ â€¢ â€¢ â€¢ 1 0.6 -0.6 -1 I â€¢ â€¢ â€¢ â€¢ â€¢ ' ' 1 2 3 4 5 6 7 8 Distance class Figure 6. 2. Spatial correlogram of late larvae (A) and adults (B) of Lambdina fiscellaria lugubrosa, along the Sugar Lake Forest Road, Kamloops Forest Region, British Columbia, 1994. Distance class intervals are 3km. 122 Spatial dependence of captures was found for both larvae and adults along the Sugar Lake Forest Road and interestingly, the degree of the dependence was similar between larvae and adults. On the other hand, as the Moran I values were generally larger in adults than in larvae for the same distance interval, adults were more spatially dependent. This can be attributed to the flight capability of adults, whereas early larvae can only be carried by wind between or within stands, and late larvae can only migrate over short distances among trees. Among the four plots used to sample densities within stands at Sugar Lake, plot A had the highest late larval density (mean = 6.7 larvae per 100 g of dry needles), followed by plot B (mean = 3.2), plot C (mean = 3.1) and plot D (mean = 1.5). The corresponding roadside mean densities were 8.3 for plot A (at 45 km), 3.2 for plot B (at 35 km), 1.0 for plot C (at 31 km) and 0 for plot D (at 28 km). Although roadside densities of late larvae were not consistently higher than the corresponding stand densities, they were closely related (r = 0.88, p < 0.05). Catches of adults at the four plots were 2,782 per trap at plot A, 1,766 at plot B, 1,312 at plot C and 585 at plot D. The corresponding roadside densities were 2,512 at 45 km, 2,129 at 35 km, 1,936 at 31 km and 175 at 28 km. Therefore, catches of adults from roadsides were also closely related to those within the stands (r = 0.97, p < 0.05). 6.4 Discussion and conclusions In this study, although a significant spatial dependence was found for adults within a distance of 2.75 km in 4 out of the 5 cases in the three watersheds, there was significant variation in the magnitude of spatial autocorrelation between years and among sites. For example, no spatial autocorrelation was detected in 1993 along the Coquitlam Main Road, 123 but a significant autocorrelation was detected in 1994. Also, the magnitude of spatial dependence varied between Sugar Lake and the three watersheds, with Sugar Lake having a stronger spatial autocorrelation. At Sugar Lake, a positive spatial autocorrelation of catches between traps was detected at a distance interval up to 8 km, whereas in the three watersheds, it was only up to 3 km. This may be attributed to density differences between the two areas, with spatial dependence more likely to occur over greater distances at higher population levels. The variability of spatial dependence in looper densities may reflect the heterogeneity of forest environments and the interaction of the insect with environmental factors, in addition to the dominant spatial pattern. The variation of spatial dependence of catches within a sampling line and among lines in the three watersheds may relate to ecological factors on a small scale such as slope. By contrast, the difference between the watersheds and Sugar Lake may have contributed to variation in other ecological factors on a larger scale (e.g. climate and topography). The difference of spatial autocorrelation between 1993 and 1994 at the Coquitlam and Seymour main roads may be explained by the temporal variation of ecological factors, such as yearly variation in precipitation. In the three watersheds, while pheromone traps are recommended to be placed at a distance interval of 3 km, the distance interval may be subject to modification. The distance interval recommended for pheromone trap placement at a specific location, ideally, may need to be modified when data from several consecutive years become available. Another useful result from this study is that roadside insect densities of western hemlock looper can be used to indicate population densities within the stands. Further study is needed to examine forest edge effects on a larger scale (more locations and over several consecutive years) so that roadside insect densities can be used to predict insect 124 densities within the stand. Obviously, such a study will have to consider the effect of other ecological factors such as stand composition and density. As many of the ecological factors are correlated each other, the approach of principal component regression (Liang and Thomson, 1994) may be applied. The fact that forest insect pest management is only one of the many tasks in the overall management of forest resources (Waters et al. 1985) requires any insect sampling plan to be cost-effective. Inaccessibility of stands and constraints of funding and manpower would prohibit attempts to set up a large number of plots in an area. Forest roadside sampling is appealing because it costs less and provides information faster. Spatial statistics provide a useful analytical tool for data from roadside sampling. Information about the spatial dependence of insect counts between neighboring localities can be incorporated into a sampling plan to determine the appropriate spacing among sampling stations. Also, it can describe the overall trend of an insect along a forest road regardless of local variability resulting from fine scale variation in environment factors. In fact, the effect of local variability can be reduced by choosing an appropriate lag distance between two successive sample stations. For example, a lag distance of 3 km will not be affected by any local variability within 3 km. Furthermore, results from a spatial analysis can provide guidelines for deterrnining the maximum extent of a study area to avoid the unwanted effects of variability on larger spatial scales. With the assistance of spatial statistics and information about forest edge effects, roadside sampling is expected to play a more important role in the monitoring and forecasting of forest insect populations. On the other hand, roadside sampling is recommended for population monitoring only and should not be abused. Many other kinds of entomological and ecological information will have to be obtained within stands. 125 Chapter 7 Population density and defoliation prediction in Lambdina fiscellaria lugubrosa 7.1 Introduction Insect population dynamics has long been a central topic in the development of integrated pest management programs for forest insects (Waters et al. 1985, Coulson and Witter 1984). Population dynamics of forest insects is largely affected by self regulation and ecological factors such as weather, parasitism, predation and disease (Price 1984, Coulson and Witter 1984, Waters et al. 1985, Speight and Wainhouse 1989). The relative importance of these factors can be determined from detailed studies of insect populations in the field and the use of life tables. A clear illustration of the life table approach is provided by Varley et al. (1973) in their study of the winter moth, Operophtera brumata (Linn.), in which winter disappearance was identified as the key factor responsible for population fluctuations of the insect. However, many problems remain in the study of life tables, including the demand of much time and effort, the difficulty of identifying some mortality factors, and the potential destruction of insect habitat caused by frequent sampling or observations (Southwood 1978, Price 1984). As a consequence, interest in the life table approach has been declining over the last two decades. The system approach, in which simulation models are used, has also been used for forest insect population dynamics (Hines 1979, Waters et al. 1985), but the practical values of simulation models for field use have yet to be proven (Chapter 2). 126 While new methodologies that incorporate a range of ecological factors are needed to reveal the underlying causes of population dynamics in forest insects, other approaches which examine insect population change based on the numeric characteristics of population density have also been explored, including time-series analysis (Royama 1981, Liang and Li 1991, Volney and McCullough 1994, Mason 1996) and regression analysis (Morris 1959, Granett 1974, Gansner et al. 1985, Shepherd et al . 1985, Fowler et al. 1987, Sanders 1988, Sweeney et al. 1990, Evenden et al. 1995). Time-series analysis generally involves the use of long term data. For example, the data for the spruce budworm study were collected over a period of 30 years (Royama 1981) and the data sets for Douglas-fir tussock moth ranged from 12 to 23 years (Mason 1996). By contrast, long term data are not required by the regression analysis approach because the average population change rate is considered spatially, not temporally. Based on short term data, which were collected over a few years, regression models have been developed for population prediction of the gypsy moth (Granett 1974, Gage et al. 1990), jack pine budworm (Fowler et al. 1987), spruce budworm (Fowler et al. 1987), Douglas-fir tussock moth (Shepherd et al. 1985), western hemlock looper (Evenden et al. 1995) and western spruce budworm (Sweeney et al. 1990). Besides population prediction, defoliation prediction has also been examined for the gypsy moth (Gansner et al. 1985, Liebhold et al. 1993) in which egg-mass density was used as a predictor variable in regression models. Evenden et al. (1995) exarriined the regression of adult catches of western hemlock looper with population estimates of eggs, larvae and pupae. Because the population estimates for larvae and pupae were relative (larval density was expressed as number of larvae per beating sheet and pupal density as number of pupae per burlap trap), the value 127 of the models to western hemlock looper management is limited. Unlike relative population estimates, basic population estimates express insect population abundance relative to the actual size of the habitat unit (Morris 1959, Southwood 1978), making them the preferred choice for developing statistical models. In this study, basic population estimates of early larvae, late larvae and pupae obtained from a common set of sample trees were used in the development of regression models. A substantial defoliation caused by insects usually reduces the photosynthetic capacity of the tree which may result in growth reduction, top kill and tree mortality in extreme cases. Prevention or reduction of defoliation has been a concern in western hemlock looper management, but there have been no published reports relating population density to defoliation. In an integrated pest management program, the establishment of quantitative relationships between looper density and defoliation may provide insect managers with the capability of predicting defoliation and, hence, the basis for making informed decisions on appropriate control measures. The objectives of this chapter were to describe the quantitative relationships between population estimates at successive life stages and between population estimates and defoliation levels. The relationships, if strong, can be used to predict population density and defoliation. 7.2 Methods The data for regression analysis were density estimates of early larvae, late larvae and pupae in 1993 and 1994. Quantitative relationships between life stages were analyzed with regression analysis in which the response variable was the population estimate at life 128 stage I and the regressor was the population estimate at life stage I-j (j =1,2). The population estimates were transformed with In (x+1) to adjust for potential violation of the assumptions of regression analysis (nonnormality and nonconstant variance) (Montgomery and Peck 1992). The analysis was conducted on the single tree and plot level, respectively. When the intercept of a regression model was not statistically significant at the 0.05 level, a regression model through origin (non-intercept model) was used (Montgomery and Peck 1992). As indicated by Kozak and Kozak (1995), a direct comparison of the r 2 value between the non-intercept model and the full model can be misleading. Therefore, mean square error (MSE) was used as a basis for comparison between the intercept and non-intercept models (Montgomery and Peck 1992). In 1994, as large numbers of western hemlock looper larvae were killed by a nuclear polyhedrosis virus disease at the Walker Creek location ( pers. obs.), this location was excluded from the analysis. Egg density was not related to densities of larvae and pupae because destructive sampling was used for eggs in the first year to examine vertical distributions of eggs within tree crowns. The relationship between looper density and defoliation class was examined at the plot level using egg and larval data. As the number of sample plots for eggs was relatively small for each individual year, the data for the three years were pooled. For larvae, both the pooled data and the 1993 data, separately, were examined. The 1994 data were not analyzed separately because only light defoliation occurred that year. The defoliation classes were assessed for each sample tree based on the percentage of crown defoliation: 1 = 0%; 2 = 1 to 25%; 3 = 26% to 50%, 4 = 51% to 75%; 5 = > 75%. The average defoliation classes per plot were classified into three groups: light (1 to 2.5), medium (2.6 to 3.5) and severe (3.6 to 5). To establish the relationship between looper density and defoliation, 129 discriminant analysis, a multivariate statistical method for identifying the key features separating sets of objects (Rao 1973, Johnson and Wichern 1992) was used. The objective of the discriminant analysis was to develop discriminant functions to predict defoliation classes from egg and larval densities. The fact that defoliation mainly occurs on mature trees suggested that host tree size may also be an important factor; thus, tree diameter at breast height (DBH) was also used as a predictor variable. The discriminant analyses followed Rao (1973) and Johnson and Wichern (1992), with the prior probabilities of the three defoliation classes proportional to group size and the minimization of total probability of misclassification as the criterion. Let A and B be the observed values of looper population density and DBH, respectively, m i and mi the mean values and 7ii the prior probability of the i defoliation class. For any defoliation class, ther linear discriminant score is Si = h A+h B + (log 7i; - 1/2 Â£ l] W j ) , i =1, 2, 3, j = 1, 2. The coefficients k and h is computed as h = a 1 1 m\ + a 1 2 mi and h = a 2 1 m i + o 2 2 m 2 , respectively, where ay is the elements in the data variance / covariance matrix. An individual tree is assigned to the group for which Si is the largest. The Wilks' lambda statistic for the overall discrimination was computed as the ratio of the determinant of the within-group variance/covariance matrix over the determinant of the total variance/covariance matrix. The values of Wilks' lambda range between 0 (perfect discrimination) to 1 (no discrirnination). 130 7.3 Results Relationships of population estimates among different life stages. In 1993, early larvae density was closely related to late larvae density at the single tree level (Table 7.1). There was also a moderate linear relationships between early larvae and pupae as well as late larvae and pupae. Early larval density accounted for 73% and 46% of the variation of late larvae and pupae, respectively (Table 7.1). However, relationships among population estimates at the single tree level were weak in 1994 (Table 7.2). The regression of population densities at the plot level was considerably stronger than those at the single tree level. In 1993, all models at the plot level had a much smaller MSE value than the corresponding models at the single tree level (Table 7.1). The change of MSE value was most significant for the early larvae-late larvae relationship, from 0.46 to 0.18 (Table 7.1). In 1994, although a weak regression was found between early and late larval density at the single tree level, there was a strong regression at the plot level (Table 7.2). Thus, the use of plot mean density significantly improved the predictive capability of the regression models. The analysis based on the pooled data of 1993 and 1994 also gave strong linear relationships between early and late larvae (r2 = 0.97, MSE = 0.18), early larvae and pupae (r2 = 0.87, MSE = 0.18), and late larvae and pupae(r2 = 0.77, MSE = 0.21) at the plot level (Table 7.3, Figure 7.1, 7.2, 7.3). At the plot level, the model predicting late larvae from early larval density had consistently high accuracy across all plots examined(Figure 7.4). However, the model using early larval density to predict pupal density tended to underestimate at higher densities and overestimate at lower population densities (Figure 7.5), although the overall trend was correctly predicted. The statistical 131 00 CO d o â€” o d C I oo d o d c cu Iâ€” 00 a o W 0 0 2S vO O N d d d oo d in O N d a 3 v. a IP | K i Â»3 IU T 3 O + O d II + + X d + o d II + X JS -5 -S d + + + X d + + x d + + x O d + JS Â£ Â£ o a. u u T3 J3 T 3 O c â€¢o c o "3 a, &si O â€” J2 Â«f -8 IB O E Â£ -2 o â€¢IS ss % H. C * <~ -i 5 ii c _a â€” cq CD H -5 -a f> c o Q . c a> - O c at cu ' i > nt a. 3 CD at a, 3 O H . at iâ€”I CD at D . 3 CL, <u at a, 3 CL, CD CD CQ oo g â€¢3 c o D. on g c u 3 S3 O E c o c 132 o o d o â€”c o o OS d oo o CO d o d W IT) oo CN CN o d d d d d o CD T3 o + p d o + Â© d â€¢ re CN d + o d + OS d II + r-oo d + CN d + o + SD d + o u > Â£ s> & t $> â€¢a o o â€¢*-Â» o CD c o co S3 > CO W CD â€¢Jo â€”1 CO CD CO 3 <D id CD CO o. 3 CD co > CD â€¢4â€”Â» co CD CO Â£ co co W co ft 3 CO > CO â€”1 CD CO ex 3 ft oo c â€¢5 Â£3 o Q . cn u b o C CD x: 5 T3 O c CD T3 C CO CD s CD CD ft o c < 133 significance levels of the regression coefficients in Table 7.1, 7.2 and 7.3 were similar to those from the corresponding randomization tests. Relationship between egg densityestimates and defoliation. The prior proba-bilities of the three defoliation classes in the pooled data of the three years were 0.53 for light, 0.29 for moderate, and 0.18 for severe defoliation, respectively. With the Wilks' Lambda being close to zero and the F-value being significant at the 0.001 level, the result of the discriminant analysis was sound (Table 7. 4). Based on a classification of the sample data values, the discriminant functions accounted for 88% of the variation in defoliation class. For an egg density of 20 eggs per 40 g lichen sample (x2 = 40) and a DBH of 45 cm (xi = 45), \j\ = 23.42, 1/2 = 20.27 and y3=13.88. Because j/i > y2 > \p, that egg density on the particular size of tree would be expected to result in light defoliation. Relationship between larval density estimates and defoliation. The Wilks' Lambda and F values indicated a satisfactory result for the discriminant analyses based on the 1993 data (Table 7.5) and that based on the pooled data of 1993 and 1994 (Table 7.6). The prior probabilities of the three defoliation classes in 1993 were: light = 0.44, moderate = 0.39 and severe = 0.17. The smaller Wilks' lambda and greater F value for the early larval density than the late larval density indicated a better discriirunation by early larval density. The pooled data of 1993 and 1994 gave a prior probability of 0.67 for light defoliation, 0.23 for moderate and 0.10 for severe defoliation. Overall, the pooled data models gave a better discrimination than the single data models. The pooled data model using early larval density and DBH as independent variables accounted for 93% of the variation in the defoliation data. For an early larval density of 5 larvae per 100 g dry needles (xi = 5) and a DBH of 35 cm (xi = 35), yi = 33.34, y 2 = 20.89 and j/ 3 = -12.05. Because xji > y2 >\fi, light 134 Table 7.3. Regression models of plot mean densities of Lambdina fiscellaria lugubrosa among different life stages in the interior of British Columbia, based on pooled data of 1993 and 1994. Response Predictor Model MSE r2 variable (y) (x) Late larvae Early larvae Pupae Early larvae Pupae Late larvae In (y+1) = 0.77 In (x+1) In (y+1) = 0.36 In (x+1) In 0+1) = 0.45 In (x+1) 0.18 0.97 0.21 0.87 0.21 0.77 135 Table 7.4. Quantitative relationships between egg density of Lambdina fiscellaria lugubrosa and defoliation in the interior of British Columbia, based on the pooled data of 1993, 1994 and 1995. yi = -28.12+ 0.06 x a + 1.12 x 2 y2 = -37.26 + 0.13 xi + 1.22 x2 y3 = -41.29 + 0.20 xi + 1.14 x 2 (Wilks' Lambda = 0.26, F = 6.36, p < 0.001) yi = light defoliation, 1/2 = moderate defoliation, 1/3 = severe defoliation, x\ - egg density and x2=DBH. 136 0 1 2 3 4 5 In ( early larval density +1) Figure 7.1. Relationship of population densities between early and late larvae of Lambdina fiscellaria lugubrosa, based on pooled data of 1993 and 1994. Larval density is expressed as numbers of larvae per 100 g dry needles. 137 2.4 1 2 3 4 5 In ( early larval density +1) Figure 7.2. Relationship of population densities between early larvae and pupae of Lambdina fiscellaria lugubrosa, based on pooled data of 1993 and 1994. Larval density is expressed as numbers of larvae per 100 g dry needles and pupal density as numbers of pupae per 100 cm2 burlap trap surface area. 0 0 1 2 3 In ( l a te larval density +1 ) 4 Figure 7.3. Relationship of population densities between late larvae and pupae of Lambdina fiscellaria lugubrosa, based on pooled data of 1993 and 1994. Larval density is expressed as numbers of larvae per 100 g dry needles and pupal density as number of pupae per 100 cm2 burlap trap surface area. Table 7.5. Quantitative relationships between larval density of Lambdina fiscellaria lugubrosa and defoliation in the interior of British Columbia, 1993. Life stage Discriminant function Early larvae i / i = -47.01 + 4.43 xi + 0.20x2 i /2= -46.76 + 4.34 xi + 0.32x2 i/3 = -54.45 + 3.53 xi + 0.70x2 (Wilks' Lambda = 0.1242, F = 12.86, p < 0.01) Late larvae yi = -44.19 +4.19xi +0.03 x2 i / 2 = -40.89 +3.94x1 +0.33 x2 y3 = -48.17+2.65 xi +1.47x2 (Wilks' Lambda = 0.0919, F =16.10, p < 0.01) i/i = light defoliation, 1/2 = moderate defoliation, 1/3 = severe defoliation, x\ = DBH of sample tree, xi = early larval density and X3 = late larval density. 140 Table 7.6 Quantitative relationships between larval density of Lambdina fiscellaria lugubrosa and defoliation in the interior of British Columbia, 1993 and 1994 pooled. Life stage Discriminant function Early larvae yi = -12.01 +1.21xi +0.06 x2 y2= -16.77 +1.26xi +0.28x2 1/3 = -50.97 + 0.94xi +1.01X2 (Wilks' Lambda = 0.06, F = 41.05, p < 0.001) Late larvae j/i = -11.89 +1.20xi + 0.06x3 y2= -15.36 +1.20xi + 0.48x3 i/3 = -53.32 + 0.71xi + 2.36x3 (Wilks' Lambda = 0.10, F = 27.83, p < 0.001) i/i = light defoliation, 1/2 = moderate defoliation, 1/3 = severe defoliation, xi = DBH of sample tree, x2 = early larval density and X3 = late larval density 141 Plot Figure 7.4. Actual and predicted density of late larvae of Lambdina fiscellari lugubrosa, based on the regression model In (y+1) = 0.97 In (x+1), where y is late larval density and x is early larval density . Larval density is expressed as numbers of larvae per 100 g dry needles. 142 2.4 T5 1-2 0.8 Actual Predicted Figure 7.5. Actual and predicted density of pupae of Lambdina fiscellari lugubrosa, based on the regression model In (y+1) = 0.36 In (x+1), where y is pupal density and x is early larval density. Larval density is expressed as numbers of larvae per 100 g dry needles while pupal density is expressed as numbers of pupae per 100 cm2 burlap trap surface area 143 defoliation is predicted. The discriminant function using late larvae and DBH as variables also accounted for 93% of the variation in defoliation. For a late larval density of 30 larvae per 100 g dry needle (x2 = 30) and a DBH of 35 cm (xi = 35), yi = 3.2, y2 = 41.02 and \p = 42.38. As j/3 > j/2 >yi, the late larval density on a tree with a DBH of 35 cm would most likely cause severe defoliation. In all discriminant functions, the signs of the coefficients for larval density and DBH were positive, suggesting that higher values of larval density and DBH will result in more defoliation. 7.4 Discussion and conclusions This study indicated strong relationships of population densities among early larvae, late larvae and pupae of the western hemlock looper, which are useful for predicting population trends. The weak relationships at the single tree level in 1994 may largely be attributed to a higher degree of between-tree movement of larvae than in 1993. Larvae tend to move from heavily defoliated trees to trees without defoliation (Koot 1994), but the movement is generally restricted within a stand. The between-tree movement of larvae may largely explain why the regression of population density based on plot mean was higher than that based on individual trees. Thus, to achieve greater accuracy of prediction, plot mean population density should be used rather than density based on individual sample trees. With a high r 2 value, the regression model for predicting late larval density from early larval density is expected to perform well in the field. While a strong regression of population density between different life stages may be used for population prediction, caution should also be exercised. The models developed here do not take catastrophic factors, such as extremes in daily temperature and epidemic insect disease into account. 144 These factors may change the quantitative relationships drastically. In fact, a predictive model only tells us what is likely to occur in the future, given the current population levels. In developing regression models for insect population prediction, the density of an earlier life stage should always be the predictor variable. In another study of western hemlock looper (Evenden et al. 1995), however, adult density was used as the response variable and the subsequent larval and pupal densities as predictor variables; thus, the models are not considered predictive. It should also be pointed out that regression analysis does not exclude long term data. In a study of spruce budworm (Sanders 1988), regression analysis was used on a data set collected over a period of 21 years. Although regression models were developed for individual years, an integrated analysis was helpful for describing population dynamics in the long term. Insect population processes that affect the rate of change of density from one period to the next, through birth and death, and through immigration and emigration, frequently are dependent on the density of previous periods. It is based on the existence of this quantitative relationship that time-series analysis and regression analysis can be used to make population prediction. Royama (1981) proposed the following model to describe an insect population process: Rt = f(Nt, Nn, , Nt-p+i) +8t, where Rt is population change rate at time period t, N is population density measured at a given life stage or generation identified by the subscript (t, t-1, etc.), and 8t is the effect of the exogenous component on the change rate Rt. In the time-series approach for insect population dynamics, rather than taking the average of R t's from a number of separate series (Ri, R2, Rt), a simple series of observations in which Rt occurs only was used. However, such an estimation is justified only if the assumption of stationarity is met. To examine stationarity, defined as no systematic-changes in the mean and the variance (Chatfield 1984), the numbers of 145 observations should be reasonably large, and in most of the cases, be at least 50. For an insect species with one generation per year, this would require a data set spanning 50 years! While the collection of data in the same area over many years should be encouraged as a long term task, current insect management also needs alternative approaches such as regression analysis which can utilize data collected over shorter time periods. Moreover, as pointed out by Royama (1981), certain types of temporal processes of insect populations can be deduced from spatially observed data. While the numerical information in population density data can be used for population prediction, the complex ecological interactions involved in the population dynamics of western hemlock looper should also be kept in mind. Indeed, a clear understanding of the population dynamics of the western hemlock looper in British Columbia is challenging and may take decades. Over the past two decades, there have had many studies of population dynamics in forest insects, but few have provided practical guidelines for insect management. Even for the most extensively studied insects such gypsy moth and spruce budwom, our knowledge about their population dynamics is still limited. In forest resource management, defoliation prediction has always been a highly desirable goal for pest managers. The use of insect density as a predictor is based on the fact that a low population density will never cause defoliation. Three studies (Campbell and Standaert 1974, Gansner et al. 1985, Williams et al. 1991) have focused on predicting defoliation from gypsy moth egg-mass density. However, because of variability in fecundity and egg survival, egg density alone did not predict subsequent defoliation with satisfactory accuracy. Liebhold et al. (1993) used additional measurements of egg-mass density including egg fecundity and survival to increase the accuracy of the prediction, but the models accounted for less than 40% of the variation in defoliation. In this study, by 146 contrast, the discriminant function using early larvae and DBH as independent variables to predict defoliation class accounted for a much higher percentage of the total variation. One of the advantages of discriminant function analysis lies in its capability of using categorical data. For example, rather than using percent defoliation, three defoliation classes were used: light, moderate and severe. The use of defoliation classes obviously reduces the effect of random errors involved in estimating percent defoliation. A similar approach to discriirunant analysis is logistic regression analysis in which the dependent variable is a categorical variable (Montgomery and Peck 1992). Based on the discrirrvinant models from this study, egg density or larval density of the western hemlock looper, togather with DBH of sample trees, can be used successfully to predict defoliation. 147 Chapter 8 General discussion 8.1 Population expression, spatial dispersion and sampling plans Basic population estimates have been the choice in many studies of forest insect defoliators (Chapter 2), but the reasons have not been well addressed. The major problem with absolute population estimates lies in the accumulative bias caused by variability in tree and stand variables. In this thesis, basic population estimates of eggs, larvae and pupae of the western hemlock looper were used to develop statistical models for population prediction. The high correlation of basic population estimates among different life stages supports the contention that basic population estimates may be a reasonably good indicator of absolute population changes over a limited period of years (Morris 1955). In fact, since absolute population estimate was introduced as a concept, no study of forest insect defoliators using this method of population expression has reported satisfactory results (Volney 1979, Batzer et al. 1995). By contrast, even some sophisticated population models for forest insect defoliators, such as time series models (Royama 1981, Volney and McCullough 1994, Mason 1996), have been developed with basic population estimates. Without underestimating the potential value of absolute population estimates for insect population dynamics studies, I suggested that the emphasis remain on basic population estimates for current insect management. Because basic population estimates are specific to each life stage, the direct comparison of survivorship rates between successive life stages, which is required in life table studies and some other ecological studies, remains unsolved. Although statistical 148 models for the precise estimation of total foliage area, total foliage biomass, total bark area, and total number of branches have been developed in the context of forest mensuration, these models may not perform well in uneven-aged and mixed species stands (Schreuder et al. 1993). Further collaboration between entomologists and researchers in forest mensuration may eventually yield greater precision in the absolute population estimates of forest insect defoliators. In mature western hemlock stands, absolute population estimates for western hemlock looper wil l require comprehensive information about the trees and other relevant stand variables. For example, to convert egg density per 40 g lichen sample to density per hectare, the total amount of lichen in a sample plot has to be estimated. This would involve the assessment of lichen abundance and distribution within and among trees and, possibly, other substrata where lichens occur. Similarly, absolute population estimates for larvae wil l need an estimation of total amount of foliage, a task which is expected to yield low precision considering the variability in age, size and vigor of trees encountered in the field. The concept of relative population estimates (Morris 1955, Southwood 1978) was expanded to relative population estimate and relative population intensity in this thesis (Chapter 2) to consider the variability in artificial sampling units. Without the expansion, pupal counts on a 60 cm burlap band wil l be considered as the same as those on a 120 cm burlap band, which is obviously misleading. For traps of different designs, such as sticky traps (Speight and Wainhouse 1989), the consideration of sampling unit size wil l also provide the means for the standardization of insect counts. The examination of spatial dispersion patterns has been the subject of numerous studies in insect sampling (Southwood 1978, Kuno 1991, Binns and Nyrop 1992). Among the approaches for mvestigating spatial dispersion, the mean-variance relationship is much 149 more popular than the others and also proved to be effective for western hemlock looper in this study. Although the Iwao model reveals further information about several specific distributions such as the Poisson, negative binomial and Neyman Type A, it does not test other distributions such as the geometric and Weibull distributions (Pielou 1977, Southwood 1978). The Weibull distribution has been used in forecasting gypsy moth defoliation (Liebhold et al. 1993). Despite the success of individual distribution models, further studies are needed for developing more comprehensive approaches for simultaneous testing of two or more distributions. For example, it may be possible to develop a method using attributes of the Poisson distribution Pk= (,\k/k!)e-\ the geometric distribution, Pk= pq k , and the Weibull distribution, F(t) = l-e-('/a). In entomology, the Taylor power law model and the Iwao patchiness regression model have been used simultaneously in many sampling studies (Kuno 1991, Binns and Nyrop 1992). Since the Iwao model can be expressed as Model (2.11), which looks very similar to the Taylor model in that it expresses variance as a function of the mean, not mean crowding, a unified model may be possible if the two parameters a and b in Model (2.3) can be related to a and B in Model (2.11). The advantage of sequential sampling over fixed sample size methods for deter-mining optimum sample sizes was demonstrated in this thesis, with the former requiring fewer samples than the latter for eggs, larvae and pupae of the western hemlock looper. It was also shown that the two sequential sampling models, the Green and the Kuno models, may give different results. For example, results from the two models agreed with each other in early and late larval stages, but not in the egg stage. Although sampling plans based on the fixed sample size method and the sequential sampling methods were provided, the binomial sampling plans will be more appealing because only the presence 150 and absence of individuals are to be recorded. Since the pioneering study by Gerrard and Chiang (1970), there has been a growing interest in the method. Because counting the tiny eggs and young larvae is tedious and time consuming, the metiiod could be particularly useful in western hemlock looper sampling. The results from this thesis indicated the great potential of using binomial sampling for western hemlock looper management. 8.2 Sampling and randomization tests Non-random samples have been used to make statistical inferences in many studies (Manly 1991). Realizing the potential problems of statistical invalidity, a large sample size is often used to compensate for the loss of randomness. However, a large sample size may be unrealistic in a situation when trees would have to be felled, such as in the examination of the vertical distribution of western hemlock looper eggs within the tree crown (Chapter 3). In that study, although the sample size, 65 trees, was larger than what was reported in a previous study (26 trees at four locations) (Shore 1990), the number of trees examined was still relatively low. Randomization tests provide a means to overcome the limitation of using small, non-random samples for statistical inference, as well as a safety check on results from conventional tests. Manly (1991) suggested that "randomization methods should be part of the data analyst's tools ". This thesis provided an example in which field data were used to compare the difference of statistical significance level between conventional statistical analyses and randomization testing. In most of the cases, such as the mean-variance, mean-mean crowding and mean-proportion relationships, results from the randomization tests were very close to those from the conventional tests. In examining the vertical distribution of 151 eggs within a tree crown and the effect of location and trap types on capture of pupae, substantial differences in significance levels between the conventional tests and randomization tests were found. However, the differences were not so large as to change the conclusions. In fact, this study supported the continued use of conventional statistical analyses on non-random insect samples. If the use of conventional statistical analyses always provide close approximations to the significance values given by randomization tests, the use of randomization tests would be of academic interest only. However, conventional analyses sometimes give significance values that differ considerably from those given by randomization tests. This makes the use of randomization tests necessary. From a biological point of view, randomization testing offers great potential in areas where destructive sampling may be a concern. For example, if only 20 trees are available to examine the vertical distribution of eggs within tree crowns, the sample size is small. But the use of randomization tests can at least tell us whether the pattern observed in the data have been arisen by chance. Moreover, real data values are used in randomization tests, which differs from some simulation studies where data values were generated under assumptions. In forestry applications where random sampling is usually not feasible, the use of randomization testing has at least three advantages: (1) it permits valid statistical inferences in the absence of random sampling; (2) it avoids the collection of an unnecessarily large sample size; and (3) it evaluates the robustness of conventional statistical analyses applied to non-random sample data. There are situations, however, such as testing a matrix correlation for significance, where randomization testing is all that is available. One area in forest insect management in which randomization testing may be of great value is statistical analysis on dichotomous variables. Many variables in forest insect management may be simply designated as falling into one of two 152 categories. Examples include recording whether trees are alive or dead, or whether an insect is present or absent. As a conventional A N O V A requires the response variables to be continuous, it can not be used for dichotomous data. On the other hand, a non-parametric analysis of variance is applicable for one treatment effect. For more than one treatment effect, randomization testing is the only choice (Edgington 1986). 8.3 The development of a population monitoring and prediction system for western hemlock looper in British Columbia The concept of integrated pest management (IPM) has been widely accepted and used in forestry (Waters et al. 1985, Coulson and Witter 1984, Speight and Wainhouse 1989). IPM refers to an integrated process in which several management strategies and tactics are used in an ecologically and economically sound manner to reduce the pest population to a tolerable level. In forestry, the introduction of IPM has ended an era in which forest managers relied solely on chemical insecticides to control insects, and population elimination was the ultimate goal. Since the early 1980s, IPM has been used as the framework for management of forest insects, with the three major bark beetles in the United States (the mountain pine beetle, the lodgepole pine beetle and the southern pine beetle ) as successful examples (Waters et al. 1985). In British Columbia, the management system for the Douglas-fir tussock moth is another example (Shepherd and Otvos 1986). With the successful development of IPM systems for other insects, it is worth considering how an IPM system for the western hemlock looper in British Columbia might be designed. Waters and Cowling (1976) proposed a system structure for IPM in forestry which is still applicable for current use. For the western hemlock looper, a complete IPM system wil l 153 f-have to include pest impact assessment, hazard rating, population monitoring and prediction, treatment tactics, and cost-benefit analysis (Waters et al. 1985). Since all these components require insect population estimates, sampling methods are the foundation. While a complete IPM system may take years to develop, a preliminary IPM system aimed at population monitoring and prediction is urgently needed before the next outbreak of the western hemlock looper. Western hemlock looper eggs are present in the field from late August or early September to the following May. This long time period makes the egg stage particularly suitable for sampling (Thomson 1958, Carolin et al. 1964, Shore 1989). However, egg sampling is expensive because of the time and effort involved in collecting, extracting and counting the tiny eggs. Furthermore, egg density, depending on its collection time, may not always be a good indicator of subsequent defoliation levels, because factors such as viability, parasitism and predation can significantly affect the proportion of eggs which hatch (Hopping 1934, Turnquist 1991), and the survival of early larvae to the more damaging later instars. The larval stage of the western hemlock looper is the feeding stage which causes tree damage through defoliation. As current biological insecticides for the insect are applied against the larval stage, larval population estimates become especially useful. In comparison to lichen samples, branch samples obtained with a pole pruner for larvae require less effort to process. In addition, larval counting is less tedious and time consuirting than egg counting. But larval sampling does not provide sufficient lead time to plan and conduct control operations. Larval sampling can be conducted at the early or late stages, with the early stage being more suitable for giving an early warning of damage, and 154 the late stage providing more useful data for evaluating the efficiency of control operations and for predicting damage in the following years. Pupal sampling for western hemlock looper can be conducted with burlap traps which are placed, for convenience, at about breast height of the trees. However, the shorter period of the pupal stage (about two weeks in British Columbia) imposes a major disadvantage on pupal sampling. As pupa-egg relationships are usually stronger (Shore 1990) than pupa-larva relationships (Evenden et al. 1995), pupal counts are more useful for predicting adults of the same generation and eggs of trie next generation than for predicting larval density and defoliation of the next generation. Pheromone traps can be easily placed along roads or in forest stands to sample adults (Evenden et al. 1995). The high sensitivity of pheromone trapping has proven to be very useful for monitoring low and sparse populations where insects may be lured in from considerable distances (Speight and Wainhouse 1989). By contrast, a burlap trap or a pole pruner only samples the pupae or larvae from a particular sample tree. There are, however, two main limitations with pheromone trapping. First, since only males are trapped, information on sex ratios is not acquired. Second, the relationship between adults and larvae is indirect and adult counts may not be a good indicator of defoliation of the subsequent season. Although sampling at a particular stage may have some advantages over other stages, population estimates are needed for all stages in an IPM system for the western hemlock looper. By mtegrating information from this and other previous studies, a prehminary population monitoring and prediction system for the western hemlock looper in British Columbia is presented below. 155 Population monitoring. Sample plots should be established in areas where mature western hemlock is the dominant species and western hemlock looper infestations have been recorded. In sparse populations, burlap traps of type D or pheromone traps should be used to monitor population change within stands. At locations where accessibility to stands is limited, pheromone traps can be placed at 3 km intervals along roads. If a substantial increase in population level is detected, egg and larval sampling should be initiated. In stands where lichen is abundant, a 40 g lichen sample can be collected from the lower crown stratum, with the optimum sample size determined by the fixed sample size or the sequential sampling plans. For sample plots measuring 100 m x 300 m, no more than 16 trees are needed to achieve a precision of 0.02 for a mean egg density of 13 eggs per 40 g lichen sample. In a sequential sampling plan, sampling can be stopped when the cumulative numbers of eggs reach 50. In larval sampling, a 45 cm branch tip should be used as the sampling unit with density expressed as number of larvae per 100 g dry needles or more practically, per 100 g fresh branch. A quick population estimation requires only the record of presence and absence of larvae in branch tip samples and the use of models (4.5, 4.6, 4.7 and 4.8). Otherwise, the sequential sampling plans should be used. Using Model 4.7 and 4.8 as examples, a 10% empty sample indicates a mean early larval density of 1.31 and a mean late larval density of 2.14. With the sequential sampling plans described in Table 4, sampling should be stopped when the cumulative number of larvae is 141 (for early larvae) or 198 (for late larvae) after examining 15 branches. Population prediction. In another study (Evenden et al. 1995) of the western hemlock looper, population estimates of eggs, larvae and pupae, obtained indirectly, were related to the numbers of male moths captured in pheromone traps and regression models were developed. However, because the population estimates for eggs, larvae and pupae 156 were relative and not basic population estimates, the reliability of the models is affected. Based on first hand data of basic population estimates, this thesis established the relationships of population density among early larvae, late larvae and pupae. In addition, relationships between insect density and defoliation were examined. With the monitoring system providing insect population estimates, the prediction models can be used to forecast future population trends and defoliation. According to the models in Table 7.3, a density of 25 early larvae per 100 g dry needles is expected to result in a density of 19 late larvae and a density of 9 pupae per 100 cm 2 burlap surface area. Similarly, 25 late larval per 100 g dry needles will give an expected pupal density of 11 per 100 cm 2 burlap surface area. Light defoliation is expected at either a density of 10 eggs per 20 g lichen sample, or 5 early larvae per 100 g dry needles on a tree with a DBH of 35 cm. Among forest insect defoliators, population monitoring and predicting systems have been developed for gypsy moth and Douglas-fir tussock moth. In gypsy moth, sampling units were examined for eggs (Thorpe and Ridgway 1992) and burlap traps were tested for larvae (Lance and Barbosa 1979, Wallner 1983, Liebhold et al. 1986). Kolodny-Hirsch (1986) fitted the Iwao patchiness regression model with gypsy moth egg data and found that egg distribution was contagious. Using parameters from the Iwao model, he developed a sequential sampling plan for gypsy moth eggs in urban woodlots. The sequential sampling plan for gypsy moth in forest habitats was developed by Carter et al. (1994). Based on parameters from the Taylor power law model, Carter and Ravlin (1995) evaluated binomial sampling plans for eggs. Recently, spatial statistics was applied to examine the spatial dependence of egg density (Liebhold et al. 1993) and pheromone trap capture of adults (Gage et al. 1990). In defoliation prediction, egg density was used as a predictor variable 157 (Campbell and Standaert 1974, Gansner et al. 1985, Williams et al. 1991, Liebhold et al. 1993). The population monitoring and predicting system for the Douglas-fir tussock moth in the USA began with the examination of spatial distribution patterns for eggs and larvae (Mason 1970) and sequential sampling plans (Mason 1969). Then binomial sampling plans (Mason 1987) and population prediction models (Mason 1996) were developed. In Canada, similar approaches have also been used (Shepherd et al. 1984, Shepherd 1985) for sampling Douglas-fir tussock moth and predicting its outbreaks. 8.4 Further work in population monitoring and prediction The implementation of an effective integrated management program for the western hemlock looper will largely depend on our capability of obtaining precise population data from which meaningful prediction can be derived. While results from this thesis provides a set of guidelines for a prelirninary population monitoring and prediction system, further work is required to improve the system. Because the population prediction models from this study were based on data from only two or three years, parameters in the prediction models are subject to adjustment with the addition of new data. In this thesis, a presence and absence sampling model was not developed for eggs, due to the low proportion of samples without an egg. Given the importance of the model, new effort is needed to develop the model with data from sparse population levels. Two other insect pests, the western blackheaded budworm and the hemlock sawfly, Neodiprion tsugae Midd., occur almost at the same time on the same host as western hemlock looper. As these insect species may have some ecological relationships with the western hemlock looper, the development of methods for simultaneous sampling of all three species should be pursued. 158 Defoliation caused by the western hemlock looper can have direct and substantial effects on timber as well as aesthetic values of western hemlock forests. One of the major impediments to an IPM approach for forest insects is the lack of an accurate yet cost-effective procedure for forecasting defoliation. For western hemlock looper, egg density is a preferred predictor variable for defoliation because it is the overwintering stage and about 8 months removed from the occurrence of defoliation and thus would provide enough time to plan and conduct a control operation. However, many factors, such as variability in egg fecundity, egg mortality, early larval mortality, larval dispersal and tree phenology, may all contribute to variance in the egg density-defoliation correlation. The use of male moth counts in pheromone traps as a predictor for defoliation is also subject to the same problems. Nevertheless, pheromone trapping remains a convenient monitoring tool and is especially effective in sparse population levels (Evenden et al. 1995). It follows that further investigations of the male adult-defoliation relationship should be conducted. Of the four statistical approaches outlined for insect population prediction in Chapter 2, the regression approach is recommended for the western hemlock looper because long term data are not required as they are for time series analysis and because the life table and system simulation approaches are likely to be too complicated to benefit current insect management. On the other hand, as time series analysis may provide more insight into the underlying population process (Berryman 1992, Volney and McCullough 1994, Mason 1996), it should also be considered for long term studies. For example, in a study of population dynamics of Douglas-fir tussock moth populations in the Pacific Northwest, Mason (1996) applied time series analysis to four data sets which came from eight permanent plots spanning a time period from 12 to 23 years. Indeed, this represents a substantial time cornmitment, but such long term studies are necessary for a fuller 159 understanding of the relationships among insect pests and their biotic and abiotic environments. Fortunately, basic population estimates are used in time series analysis (Mason 1996), thus avoiding the difficulty in obtaining absolute population estimates. Unlike life table studies in which survivorship rates between successive life stages are considered, time series analysis and regression analysis deal with population change rates among life stages. In time series analysis, the first, second and third order autoregressive models have been used (Royama 1981, Volney and McCullough 1994, Mason 1996). Similarly, in a regression analysis, insect densities of the last one life stage or two life stages can be used as independent variables. Two phenomena in insect population dynamic are beneficial to the time series analysis and the regression analysis approaches: density dependence between successive life stages or generations and synchronization of population fluctuation at different locations. In examining population dynamics of Douglas-fir tussock moth, Mason (1996) found that fluctuation in the insect populations are mostly a result of their own density dependent structure. Although environmental variables may affect the limits within which densities fluctuate, much of the numerical behavior of each population is endogenous to the population itself (Mason 1996). Synchrony in numerical behavior of tussock moth populations was also reported by Mason (1996) who found a high correlation of population change rates between sample locations, including two locations which were 250 km apart. What is implied by die synchronization is that the numbers of sample plots for population monitoring may be reduced, depending on the characteristics of the synchronization. The work involved in tliis thesis has been conducted in mature hemlock forests which are far more complex structurally and compositionally than a forest plantation or an agricultural field. As the principles of insect management were first developed in 160 agricultural systems, the greater complexity of natural forest ecosystems needs to be kept in mind when dealing with forest insects. Forest ecosystems present a much broader array of ecological variables than do agricultural systems (Waters et al. 1985). Forests not only cover a much larger area than agricultural crops, but also vary in growth rates, succession and functional processes. In addition, the interactions among organisms in a forest are far more complex than in an agricultural system (Ewing et al. 1974, Holling 1978). Despite the greater complexity of natural forests, there would be little gained by the development of more complicated sampling methods and population prediction models because of the increasing effects of random and systematic errors involved in obtaining model parameters. Thus, retaining a reasonable simplicity in the framework of IPM is the best compromise. For some years, forest and pest managers have been searching for practical methods for insect population monitoring and prediction. In this thesis, the use of basic population estimates, the development of sequential and binomial sampling plans, the exploration of roadside sampling and, finally, the analysis of short term data for population and defoliation prediction, all have been carried out with the needs of forest and pest managers clearly in rnind. 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Sampling methods and population prediction in Lambdina fiscellaria lugubrosa (Lepidoptera: geometridae)… Liang, Qiwei 1997
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Title | Sampling methods and population prediction in Lambdina fiscellaria lugubrosa (Lepidoptera: geometridae) in British Columbia |
Creator |
Liang, Qiwei |
Date Issued | 1997 |
Description | Outbreaks of Lambdina fiscellaria lugubrosa in British Columbia have always been preceded by a rapid population growth. Sampling methods and population prediction models are needed to provide forest managers with the capability of monitoring and predicting populations of the insect. I sampled eggs, larvae, pupae and adults of Lambdina fiscellaria lugubrosa at various locations in the province of British Columbia from 1992 to 1994. Population estimates of eggs and larvae, directly obtained from habitat units, were fitted to theoretical spatial distribution and mean - variance models. Sampling plans, based on fixed sample size, sequential sampling, and binomial sampling methods, were developed. Pupae were sampled with burlap traps of different designs. Because more pupae were trapped in two or three layers of burlap than in a single layer, traps with at least two layers are recommended for future use. The strong linear relationship of pupal density between burlap traps and open tree bark units validated the use of burlap traps as a sampling tool. Spatial continuity of larval and adult densities was found along forest roads, although the range and magnitude of the spatial dependence varied significantly between years and among sites. Also, larval and adult densities along the road were closely related to those within the stands. The results showed a great potential of roadside sampling for the management of this insect. Regression models showed strong quantitative relationships of population estimates between successive life stages, which can be used to predict population density. Defoliation prediction was conducted with discriminant analysis, in which defoliation classes were related to insect population estimates and tree DBH. Like many other studies in insect sampling, the insect samples were non-random in this study. Randomization tests were used to validate results from conventional statistical analyses and to examine the general necessity of using randomization tests in insect sampling. The results suggested that non-random insect samples do not seriously hamper the use of conventional statistical analyses. The implications of this study to the management of western hemlock looper and other forest insects were discussed. |
Extent | 7371628 bytes |
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Thesis/Dissertation |
Type |
Text |
FileFormat | application/pdf |
Language | eng |
Date Available | 2009-04-02 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0076933 |
URI | http://hdl.handle.net/2429/6746 |
Degree |
Doctor of Philosophy - PhD |
Program |
Interdisciplinary Studies |
Affiliation |
Graduate and Postdoctoral Studies |
Degree Grantor | University of British Columbia |
GraduationDate | 1997-05 |
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UBCV |
Scholarly Level | Graduate |
AggregatedSourceRepository | DSpace |
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