Scott R. Winterstein

Survival analysis in telemetry studies: The staggered entry design

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 animals 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-

Estimation and analysis of survival distributions for radio-tagged animals

We present results on the estimation of survival distributions for an important problem in animal ecology. The problem involves estimation of survival distributions using radio-tagged animals. It requires allowance for censored observations due to radio failure, emigration from the study area, and animals surviving past the end of the study period. We show that survival analysis techniques already used in medical and engineering studies may be applied to this problem. Emphasis is placed on the model assumptions and the need for further research. An example to illustrate the strengths and weaknesses of this approach is presented.

Epidemiology of Mycobacterium bovis in free-ranging white-tailed deer, Michigan, USA, 1995–2000

An endemic area of bovine tuberculosis (TB) (Mycobacterium bovis) currently affecting wild white-tailed deer (Odocoileus virginianus) in northern lower Michigan, USA, constitutes the first self-sustaining outbreak of the infection in free-ranging North American cervids. Given this precedent, epidemiologic insights gained from the outbreak afford the opportunity to guide not only current surveillance and intervention but also control efforts for future outbreaks involving wildlife reservoirs. Our specific objectives were to evaluate retrospective data from field surveillance conducted from 1995 to 2000 to determine apparent prevalence, trends in apparent prevalence, and the effects of various factors on the odds of being M. bovis positive. Data were gathered from post-mortem examinations of 62,560 wild deer collected from all 83 Michigan counties. Records of survey method, sex, age, geographic area and infection status as determined by mycobacterial culture were subjected to trend analysis and multivariable logistic regression. Apparent prevalence for the period was 0.54% (336/62,560) statewide. Prevalence varied widely with geographic area, but significantly decreased since 1995 in the core area of the outbreak-which coincided with implementation of control strategies. Significant risk factors were geographic area, sex, age, and the sex-by-age interaction. The survey method by which deer were obtained for testing was not a predictor of infection. Our results to date suggest an outbreak characterized by broad areas of very low prevalence surrounding focal areas where prevalence is sometimes orders-of-magnitude higher (e.g., deer originating from the core area were up to 147 times more likely to be TB positive than deer from other areas). Our results also identify older male deer as most likely to be M. bovis positive (OR=11.3, 95% CI 3.2, 40.3 for bucks > or =5 years vs. does < or =1.5 years)-an observation consistent with the biology and behavior of the species. Synthesizing these results with those of other ongoing investigations, we hypothesize a two-stage model of disease transmission where TB is maintained at very low prevalence in matriarchal groups, with primary dissemination of the disease attributable to the dispersal and movements of bucks (as well as to the large aggregations of animals created by human activities).

Analysis of Survival Data from Radiotelemetry Studies

Publisher Summary An animal is captured, fitted with a radio transmitter, and released. From the time of release, the animals unique radio signal is monitored to determine the animals fate at more or less regular intervals. For each animal, the investigator must know the date it was radio-marked and released, the date it was last located, and its status when last located. At each location time, the status of each animal is recorded as alive, dead, or missing. Missing animals are considered censored, meaning that the event of interest cannot be observed. This type of censoring is generally referred to as “right censoring” and is caused by such factors as radio failure, topography that inhibits signal reception, and permanent or temporary emigration. As the field of spatial analysis grows, there is a need to integrate survival and spatial analyses. As the ability to assess actual and potential habitat quality improves, the impact of an animals movements must be modeled through the use of a mosaic of habitat types on its survival. There is also a need to develop stage-structured survival models. These models will, in many cases, mimic time-dependent models, allowing the examination of the impact on survival of an animal moving into a new age class or moving to a lower or higher quality territory.

Noninvasive Estimation of Black Bear Abundance Incorporating Genotyping Errors and Harvested Bear

Abstract Estimating black bear (Ursus americanus) population size is a difficult but important requirement when justifying harvest quotas and managing populations. Advancements in genetic techniques provide a means to identify individual bears using DNA contained in tissue and hair samples, thereby permitting estimates of population abundance based on established mark–capture–recapture methodology. We expand on previous noninvasive population-estimation work by geographically extending sampling areas (36,848 km2) to include the entire Northern Lower Peninsula (NLP) of Michigan, USA. We selected sampling locations randomly within biologically relevant bear habitat and used barbed wire hair snares to collect hair samples. Unlike previous noninvasive studies, we used tissue samples from harvested bears as an additional sampling occasion to increase recapture probabilities. We developed subsampling protocols to account for both spatial and temporal variance in sample distribution and variation in sample quality using recently published quality control protocols using 5 microsatellite loci. We quantified genotyping errors using samples from harvested bears and estimated abundance using statistical models that accounted for genotyping error. We estimated the population of yearling and adult black bears in the NLP to be 1,882 bears (95% CI = 1,389–2,551 bears). The derived population estimate with a 15% coefficient of variation was used by wildlife managers to examine the sustainability of harvest over a large geographic area.

Avian Abundance in CRP and Crop Fields during Winter in the Midwest

Abstract We compared the abundance and species composition of birds in Conservation Reserve Program (CRP) fields with the same aspects in row-crop fields during the winter (January and February) over several years (1992–1995) for six midwestern states (Indiana, Iowa, Kansas, Michigan, Missouri and Nebraska). Field techniques were standardized in all states. CRP fields consisted of either permanent introduced grasses and legumes (CP1) or permanent native grasses (CP2), and the plant species seeded in CRP fields differed within and among states. Vegetation characteristics of CRP fields varied considerably from state to state, but vertical density and total canopy cover (primarily grasses) were particularly high in Nebraska. Mean annual total bird abundance ranged from 0.1 to 5.1 birds per km of transect in CRP fields and from 0.1 to 24.2 in row-crop fields. The total number of bird species recorded in CRP fields in the six states ranged from 6 to 32; the range for row-crop fields was 8 to 18. The most abundant species in CRP fields differed among states but included the ring-necked pheasant, American tree sparrow, northern bobwhite, dark-eyed junco and American goldfinch. The most abundant species in row-crop fields included the horned lark, American tree sparrow, European starling, mourning dove, lapland longspur, meadowlarks and Canada goose. Some of the most abundant bird species wintering on CRP fields have been undergoing long-term population declines, thus this program has the potential to mitigate population losses.

A capture± recapture survival analysis model for radio-tagged animals

In recent years, survival analysis of radio-tagged animals has developed using methods based on the Kaplan-Meier method used in medical and engineering applications (Pollock et al. , 1989a,b). An important assumption of this approach is that all tagged animals with a functioning radio can be relocated at each sampling time with probability 1. This assumption may not always be reasonable in practice. In this paper, we show how a general capture-recapture model can be derived which allows for some probability (less than one) for animals to be relocated. This model is not simply a Jolly-Seber model because it is possible to relocate both dead and live animals, unlike when traditional tagging is used. The model can also be viewed as a generalization of the Kaplan-Meier procedure, thus linking the Jolly-Seber and Kaplan-Meier approaches to survival estimation. We present maximum likelihood estimators and discuss testing between submodels. We also discuss model assumptions and their validity in practice. An exa...

GEOGRAPHICAL GENETICS: CONCEPTUAL FOUNDATIONS AND EMPIRICAL APPLICATIONS OF SPATIAL GENETIC DATA IN WILDLIFE MANAGEMENT

Abstract Molecular-genetic technology and statistical methods based on principles of population genetics provide valuable information to wildlife managers. Genetic data analyzed in a hierarchical, spatial context among individuals and among populations at micro- and macro-geographic scales has been widely used to provide information on the degree of population structure and to estimate rates of dispersal. Our goals were to (1) provide an overview of spatial statistics commonly used in empirical population genetics, and (2) introduce analytical designs that can be employed to extend hypothesis-testing capabilities by incorporating space-time interactions and by using information on habitat quality, distribution, and degree of connectivity. We show that genetics data can be used to quantify the degree of habitat permeability to dispersal and to qualify the negative consequences of habitat loss. We highlight empirical examples that use information on spatial genetic structure in areas of harvest derivation for admixed migratory species, wildlife disease, and habitat equivalency analysis.

Cause-Specific Mortality and Survival of White-Tailed Deer Fawns in Southwestern Lower Michigan

Abstract Understanding white-tailed deer (Odocoileus virginianus) fawn survival is critical for managing herd dynamics and setting effective harvest regulations. We fitted white-tailed deer fawns with radiocollars during spring 2001 (n = 35) and 2002 (n = 40) to quantify cause-specific mortality, survival, and home-range size and composition in the southwestern Lower Peninsula of Michigan, USA. We monitored fawns a minimum of twice a week until they died, were censored, or the tracking period ended. Seventeen of 75 fawns died. The primary causes of mortality were legal hunting (n = 5) and deer–vehicle collisions (n = 5). Other causes included dehydration, bacterial infection, suspected coyote (Canis latrans) predation, drowning, and malnutrition. Survival probabilities for 2001 and 2002 radiocollared fawns to 30 days postcapture were 0.97 and 0.93, respectively. Capture-to-prehunt (127 days) fawn-survival probabilities were 0.91 for 2001 fawns and 0.90 for 2002 fawns. Posthunt (220 days) fawn survival probabilities were 0.76 for 2001 fawns and 0.85 for 2002 fawns. Annual estimated fawn-survival probabilities were 0.76 for 2001 and 0.75 for 2002. Mean annual home-range size for fawns was 75.36 ha. Habitat quality and land cover and use were potential factors that contributed to our high fawn survival. Our results can aid wildlife biologists in developing, refining, and validating deer population models as well as devising and balancing white-tailed deer population management decisions in an agroforested landscape.

Regulating Hunter Baiting for White-Tailed Deer in Michigan: Biological and Social Considerations

Abstract Eradication of bovine tuberculosis (TB) from free-ranging white-tailed deer (Odocoileus virginianus) requires mortality rates of infected deer exceed the rate of new infection. Efforts to reduce TB transmission in Michigan, USA, are based on 2 assumptions: 1) deer mortality may be increased through recreational hunting, and 2) encounter rates between infected and noninfected deer may be reduced by prohibiting baiting and supplemental feeding. Spatial correlation of TB-infected deer and supplemental feeding sites detected using aerial surveys validated a ban on artificial feeding in Michigan. Similar analysis could not be used to evaluate the effects of a baiting ban because bait distribution was unknown. Furthermore, a ban on deer baiting could confound attempts to increase deer mortality through reduced hunter participation or efficacy. We reviewed the process used to evaluate a strategy for regulating bait use by hunters. This review included an assessment of 5 factors: statewide spatial analysis of apparent TB prevalence, deer intraspecific interactions at bait sites, effects of bait on hunter harvest rates, impacts of disease presence and practice of eradication efforts on hunting participation in the infected area, and input from law enforcement personnel. Our analysis suggested that restricting baiting to a limited, consistent region incurred less biological risk than allowing bait to be used statewide and less political risk than a statewide ban.