Kenneth H. Pollock

Bio: Kenneth H. Pollock is an academic researcher from North Carolina State University. The author has contributed to research in topics: Population & Mark and recapture. The author has an hindex of 70, co-authored 256 publications receiving 20366 citations. Previous affiliations of Kenneth H. Pollock include Murdoch University & United States Fish and Wildlife Service.

Survival analysis in telemetry studies: the staggered entry design

Abstract: The estimation of survival distributions for radio-tagged animals is important to wildlife ecologists. Allowance must be made for animals being lost (or censored) due to radio failure, radio loss, or emigration of the animal from the study area. The Kaplan-Meier procedure (Kaplan and Meier 1958), widely used in medical studies subject to censoring, can be applied to this problem. We developed a simple modification of the Kaplan-Meier procedure that allows for new animals to be added after the study has begun. We present 2 examples using telemetry data collected from northern bobwhite quail (Colinus virginianus) to show the simplicity and utility of the Kaplan-Meier procedure and its modifications. The log rank test used to compare 2 survival distributions can also be modified to allow for additions during the study. Simple computer programs that can be run on a personal computer are available from the authors. J. WILDL. MANAGE. 53(1):7-15 Radio-tagged animals are used to study survival. Present techniques for analyzing data from these studies assume that each survival event (typically an animal surviving a day) is independent and has a constant probability over all animals and all periods (Trent and Rongstad 1974, Bart and Robson 1982, Heisey and Fuller 1985). We believe these assumptions are often unrealistic and restrictive. White (1983) generalized discrete approaches using the same framework as that of band return models (Brownie et al. 1985) and he developed a flexible computer program (SURVIV) for use with his approach. Heisey and Fuller (1985) generalized the Trent and Rongstad (1974) approach to allow mortality from different causes (e.g., predation, starvation) and developed a microcomputer program called MICROMORT. Typically an animal's exact survival time (at least to within 1-2 days) is known unless that survival time is right censored (i.e., only known to be greater than some value). Pollock (1984) and Pollock et al. (1989) suggested a useful approach based on continuous survival models allowing right censoring that is widely used in medicine and engineering (Kalbfleisch and Prentice 1980, Cox and Oakes 1984) and provided examples of the Kaplan-Meier procedure. The Kaplan-Meier procedure does not require specification of a particular parametric continuous distribution; e.g., the exponential or Weibull. Related ecological papers using survival methods include Muenchow (1986), Pyke and Thompson (1986), Kurzejeski et al. (1987), and White et al. (1987). We present a simple description of the Kaplan-Meier procedure with an example using northern bobwhite quail survival data collected by PDC. We then generalize the Kaplan-Meier procedure to allow gradual (or staggered) entry of animals into the study. The calculations are illustrated with an example from the quail data. Finally, we present the log-rank test for comparison of survival distributions (modified for staggered entry of animals) with an example. We also present a discussion of model assumptions and directions for future research. We thank J. D. Nichols and W. L. Link for helpful comments on an earlier draft of this paper. We acknowledge G. C. White and D. M. Heisey for their helpful reviews that improved the final version. THE KAPLAN-MEIER OR PRODUCT LIMIT PROCEDURE The Kaplan-Meier or product limit estimator was developed by Kaplan and Meier (1958) and is d scussed by Cox and Oakes (1984:48) and Kalbfleisch and Prentice (1980:13). The survival function (S[t]) is the probability of an arbitrary animal in a population surviving t units of time from the beginning of the study. A nonparametric estimator of the survival function can be obtained by restricting ourselves to the discrete time points when deaths occur a1, a2, ..., ag. We define r, . . . , rg to be the numbers of an-

A Capture-Recapture Design Robust to Unequal Probability of Capture

Abstract: At the basis of many capture-recapture sampling models is the assumption that all animals are equally likely to be caught in each sample (The Equal Catchability Assumption). This assumption is often violated in wildlife populations (Seber 1973:81) and 2 general types of alternatives exist (Pollock 1981): (1) Heterogeneity: The probability of capture in any sample is a property of the animal and may vary over the population. That is, animals may vary in capture probabilities according to age, sex, social status, and many other factors. (2) Trap response: The probability of capture in any sample depends on the animal's prior history of capture. That is, animals may become "trap shy" or "trap happy" depending upon the type of trapping method used. Either 1 or both of these 2 types of alternatives may be acting in a particular animal population. The traditional capture-recapture model used by biologists for closed populations (populations closed to additions or deletions) in short-term studies is the Schnabel Model (Schnabel 1938) that requires The Equal Catchability Assumption. In recent years there has been substantial research on models for closed populations that allow heterogeneity and/or trap response of the capture probabilities. Otis et al. (1978) published an important monograph on these models that allows their routine use by biologists. The capture-recapture model becoming used by biologists for open populations in long-term studies is the Jolly-Seber Model (Seber 1973). This model requires The Equal Catchability Assumption and the complexity of open population models is likely to preclude general models that allow heterogeneity and/or trap response. During the preparation of a review of capture-recapture methods (Pollock 1981), I realized that statisticians have drawn a sharp distinction between closed and open population models that is perhaps rather artificial. Here I describe a design for long-term studies that is robust to heterogeneity and/or trap response. It allows an analysis that uses methodology from closed and open population models. There is a brief examination of its robustness properties using simulation and an example is given in detail to illustrate the methodology for biologists.

Capture-recapture studies for multiple strata including non-markovian transitions

Abstract: We consider capture-recapture studies where release and recapture data are available from each of a number of strata on every capture occasion. Strata may, for example, be geographic locations or physiological states. Movement of animals among strata occurs with unknown probabilities, and estimation of these unknown transition probabilities is the objective. We describe a computer routine for carrying out the analysis under a model that assumes Markovian transitions and under reducedparameter versions of this model. We also introduce models that relax the Markovian assumption and allow "memory" to operate (i.e., allow dependence of the transition probabilities on the previous state). For these models, we suggest an analysis based on a conditional likelihood approach. Methods are illustrated with data from a large study on Canada geese (Branta canadensis) banded in three geographic regions. The assumption of Markovian transitions is rejected convincingly for these data, emphasizing the importance of the more general models that allow memory.

The Theory of Island Biogeography

Abstract: Preface to the Princeton Landmarks in Biology Edition vii Preface xi Symbols Used xiii 1. The Importance of Islands 3 2. Area and Number of Speicies 8 3. Further Explanations of the Area-Diversity Pattern 19 4. The Strategy of Colonization 68 5. Invasibility and the Variable Niche 94 6. Stepping Stones and Biotic Exchange 123 7. Evolutionary Changes Following Colonization 145 8. Prospect 181 Glossary 185 References 193 Index 201

Program MARK: survival estimation from populations of marked animals

Abstract: MARK provides parameter estimates from marked animals when they are re-encountered at a later time as dead recoveries, or live recaptures or re-sightings. The time intervals between re-encounters do not have to be equal. More than one attribute group of animals can be modelled. The basic input to MARK is the encounter history for each animal. MARK can also estimate the size of closed populations. Parameters can be constrained to be the same across re-encounter occasions, or by age, or group, using the parameter index matrix. A set of common models for initial screening of data are provided. Time effects, group effects, time x group effects and a null model of none of the above, are provided for each parameter. Besides the logit function to link the design matrix to the parameters of the model, other link functions include the log—log, complimentary log—log, sine, log, and identity. The estimates of model parameters are computed via numerical maximum likelihood techniques. The number of parameters that are...

Effects of Habitat Fragmentation on Biodiversity

Abstract: ■ Abstract The literature on effects of habitat fragmentation on biodiversity is huge. It is also very diverse, with different authors measuring fragmentation in different ways and, as a consequence, drawing different conclusions regarding both the magnitude and direction of its effects. Habitat fragmentation is usually defined as a landscape-scale process involving both habitat loss and the breaking apart of habitat. Results of empirical studies of habitat fragmentation are often difficult to interpret because (a) many researchers measure fragmentation at the patch scale, not the landscape scale and (b) most researchers measure fragmentation in ways that do not distinguish between habitat loss and habitat fragmentation per se, i.e., the breaking apart of habitat after controlling for habitat loss. Empirical studies to date suggest that habitat loss has large, consistently negative effects on biodiversity. Habitat fragmentation per se has much weaker effects on biodiversity that are at least as likely to be positive as negative. Therefore, to correctly interpret the influence of habitat fragmentation on biodiversity, the effects of these two components of fragmentation must be measured independently. More studies of the independent effects of habitat loss and fragmentation per se are needed to determine the factors that lead to positive versus negative effects of fragmentation per se. I suggest that the term “fragmentation” should be reserved for the breaking apart of habitat, independent of habitat loss.

Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness

Abstract: Species richness is a fundamental measurement of community and regional diversity, and it underlies many ecological models and conservation strategies. In spite of its importance, ecologists have not always appreciated the effects of abundance and sampling effort on richness measures and comparisons. We survey a series of common pitfalls in quantifying and comparing taxon richness. These pitfalls can be largely avoided by using accumulation and rarefaction curves, which may be based on either individuals or samples. These taxon sampling curves contain the basic information for valid richness comparisons, including category‐subcategory ratios (species-to-genus and species-toindividual ratios). Rarefaction methods ‐ both sample-based and individual-based ‐ allow for meaningful standardization and comparison of datasets. Standardizing data sets by area or sampling effort may produce very different results compared to standardizing by number of individuals collected, and it is not always clear which measure of diversity is more appropriate. Asymptotic richness estimators provide lower-bound estimates for taxon-rich groups such as tropical arthropods, in which observed richness rarely reaches an asymptote, despite intensive sampling. Recent examples of diversity studies of tropical trees, stream invertebrates, and herbaceous plants emphasize the importance of carefully quantifying species richness using taxon sampling curves.