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Hunting can have potentially significant impacts on wild turkey (Meleagris gallopavo) populations. We developed a 2-sex Leslie-type matrix model that predicts wild turkey population size for spring-summer and fall-winter periods to understand the effects of hunting on the dynamics of wild turkey populations in Virginia and West Virginia. A base model incorporates parameters derived from a large-scale radiotelemetry study (n = 1,543 hens radio-tagged) conducted over areas with different fall hunting seasons in Virginia and West Virginia from 1989 to 1994. These data made it possible to evaluate the effects of season length, season timing, and 1- versus 2-sex kills on population growth and future harvests. A sensitivity analysis confirmed that fall hunting has the strongest negative effect on the population growth rate. For the range of parameters explored, population growth rate appeared to decrease linearly with increases in fall hunting. Also, the proportion of males in the population was more sensitive to fall rather than spring hunting. These results were invariant to a wide variety of different model calibrations.

Knowledge of reproductive parameters and assessment of the relative importance of factors affecting reproductive success are essential for effective management of eastern wild turkeys (Meleagris gallopavo silvestris). We determined reproductive parameters of 599 radiomarked hens (293 for >1 yr), and the effects of age, year, region, condition (winter weight), incubation chronology (periods), land-ownership, and weather on their reproductive success in 3 Appalachian Mountain regions of Virginia and West Virginia. Average first nest incubation initiation was May 5 ± 0.6 days (x ± SE, n = 629). Production rate (poults alive 4 weeks post batch/female alive 1 Apr) averaged 1.46 ± 0.09 (n = 863). Nesting rates were lower than studies in other regions and may be limiting reproduction. Production rates increased with age (juv: 0.47 ± 0.14, 2+: 1.40 ± 0.14, 3+ 2.55 ± 0.25), but did not differ among regions, years, or weight classes of winter-trapped juvenile or adult hens. Reproduction was evaluated by quintiles (periods) of the first incubation dates by year. Hens that began incubation in the second or third periods had higher (>67%) incubation completion rates than other periods (≤50%), but potential production rates (poults alive 4 weeks post hatch/female completing incubation) were not different among incubation periods. Potential production rates were higher on private lands (3.93 ± 0.30) than public lands (2.67 ± 0.43). Nest incubation dates in Virginia were correlated with mean March temperatures (p = -0.53) and snow depth (p = 0.52). Managers should cautiously implement or increase fall either-sex hunting seasons in populations with survival and production rates similar to those we studied. Older hens play a critical role in reproductive success in the Appalachians. In areas with fall either-sex hunting, season timing and length that reduce adult vulnerability may lessen hunting impacts on reproduction and population growth.

Two main methods of estimating survival from radiotelemetry studies are the Trent and Rongstad approach and the Kaplan-Meier approach. Although these 2 methods often are applied, the effects of violation of assumptions have not been completely studied. We present a very brief evaluation of all assumptions and their violation. We also evaluated the assumption of equal censoring rates for live and dead animals by simulation and found that large biases can result if it is violated. For the Trent-Rongstad method where there is an additional assumption of constant survival rates over time, our simulations showed that violation of this assumption caused the largest bias with an early drop in survival rate as compared to other alternatives.

The effect of fall either-sex hunting on eastern wild turkey (Meleagris gallopavo silvestris) populations is a common concern of wildlife agencies. We examined the effect of fall either-sex hunting on survival of radiotagged female wild turkeys from 1989 to 1994 in Virginia and West Virginia. We tested the hypothesis that survival of female wild turkeys did not differ among areas closed to fall hunting, open to a 4-week fall season, or open to an. 8- or 9-week fall hunting season. Mean annual survival rates were higher in the area closed to fall hunting than in regions where fall hunting occurred (P = 0.05). Mean annual survival rates varied within years (P ≤ 0.05). Differences in annual survival rate among areas were attributed to legal hunting (P ≤ 0.01). Poaching was a major mortality factor. Juvenile, yearling, and adult hens had similar survival rates in the areas closed to fall hunting and with 4 weeks of fall hunting (P = 0.39), but survival rates of juveniles were lower (P = 0.03) than those of yearling and adult females in the area with an 8-9-week fall hunting season. Harvest rates of female turkeys averaged 4.3% in the 4-week fall hunted area and 12.3% on the 8-9-week fall hunted area. Higher harvests were achieved on the study area opened only to spring hunting than the combined fall-spring harvests on the other study areas. Total harvest was negatively associated with survival (r s =- 0.90, P = 0.04) on the 8-9-week fall hunted area and positively associated with survival (r s = 0.90, P = 0.04) in the area closed to fall hunting. Spring gobbler-only hunting is suggested for maximum growth in a wild turkey population. Guidelines are presented for fall harvest programs.

There are three methods that can be used to estimate population size when survey data are collected just before and just after two or more known harvests: change-in-ratio, index-removal, and catch-effort (removal) methods. In this paper, we introduce a methodology that combines all three methods. We begin by modeling the survey and removal processes as a Poisson point process and a linear death process, respectively, and then we combine the two processes. The completedata likelihood can be factored into three parts: the general likelihood function of the index-removal method, the general likelihood function of the change-in-ratio method, and the general likelihood function of the catch-effort method. We compute the maximum likelihood estimates using the Powell search algorithm. Monte Carlo simulations are used to demonstrate that the estimates from combining change-in-ratio, index-removal, and catch-effort methods are more precise than the estimates based on combining any two of them or only using a single method. An example based on snow crab data is presented to illustrate the methodology.

SUMMARY To estimate the total catch in a sport fishery sampled by a roving creel survey, we multiply an estimate of the total fishing effort by the estimated catch rate (i.e., catch per unit of fishing effort). While the statistical theory for estimating the fishing effort from instantaneous or progressive counts is well established, there is much confusion about the appropriate way to estimate the catch rate. Most studies have used the ratio of means or the mean of the ratios of individual catches and efforts. We analyzed the properties of these estimators of catch rate under the assumption that fishing is a stationary Poisson process. The ratio of means estimator has a finite second moment, while the mean ratio estimator has infinite variance. Simulation studies showed that the mean of ratios estimator tends to have high and unstable mean squared error relative to the ratio of means estimator and this is in accordance with empirical observations. We also studied the properties of the mean of ratios estimator when all interviews with people fishing for less than e minutes duration were disregarded for values of e up to 60 minutes. There was typically a marked reduction in mean squared error when the shorter trips were not included. We recommend that the mean of ratios estimator, with all trips less than 30 minutes disregarded, be used to estimate catch rate and hence total catch under the roving creel survey design. It has the correct expectation (at least approximately after the truncation) and almost always had smaller mean squared error than the ratio of means estimates in our simulations.

We conduct nonparametric maximum likelihood estimation under two common heterogeneous closed population capture-recapture models. Our models specify mixture models (as did previous researchers' models) which have a common generating distribution, say F, for the capture probabilities. Using Lindsay and Roeder's (1992, Journal of the American Statistical Association 87, 785-794) mixture model results and the EM algorithm, a nonparametric maximum likelihood estimator (MLE) of F for any specified population size N is obtained. Then, the nonparametric MLE of the (N, F) pair and thus for N is determined. Perhaps most importantly, since our MLE pair maximizes the likelihood under the entire nonparametric probability model, it provides an excellent foundation for estimating properties of estimators, conducting a goodness-of-fit test, and performing a likelihood ratio test. These are illustrated in the paper.

Traditional methods of estimating survival from radio-telemetry studies use either the Trent-Rongstad approach (Trent and Rongstad 1974, Heisey and Fuller 1985) or the Kaplan-Meier approach (Kaplan and Meier 1958; Pollock et al. 1989a,b). Both methods appear to require the assumption that relocation probability for animals with a functioning radio is 1. In practice this may not always be reasonable and, in fact, is unnecessary. The number of animals at risk (i.e., risk set) can be modified to account for uncertain relocation of individuals. This involves including only relocated animals in the risk set instead of also including animals not relocated but that were seen later. Simulation results show that estimators and tests for comparing survival curves should be based on this modification.

Survival of young is an important and poorly understood component of waterfowl productivity. We estimated survival of black brant (Branta bernicla nigricans) goslings during summers 1987-89 on the Yukon-Kuskokwim Delta, Alaska, to determine timing and magnitude of gosling mortality and to compare methods of estimating gosling survival. Eighty-two percent of radio-tagged adult females (n = 61) fledged ≥1 gosling (brood success). We estimated survival of goslings within broods by 3 methods: (1) changes in mean brood size through time, (2) observation of goslings associated with marked adults, and (3) age ratios of brant captured in banding drives. Estimates of gosling survival within successful broods averaged 81% and ranged from 66 to 92%. Combining brood success and gosling survival within successful broods yielded estimates of overall gosling survival that averaged 68%, ranging from 79% in 1987 to 56% in 1989. Eighty-two percent of gosling mortality occurred in the first 15 days. Estimates of survival on the basis of age ratios of birds captured in banding drives are biased low. Our estimates of average gosling survival are higher than reported for other species of geese.

Estimates of juvenile survival from hatch to fledging provide important information on waterfowl productivity. We develop a model for estimating survival of young waterfowl from hatch to fledging. Our model enables interchange of individuals among broods and relaxes the assumption that individuals within broods have independent survival probabilities. The model requires repeated observations of individually identifiable adults and their offspring that are not individually identifiable. A modified Kaplan-Meier procedure (Pollock et al. 1989a,b) and a modified Mayfield procedure (Mayfield 1961, 1975; Johnson 1979) can be used under this general modeling framework, and survival rates and corresponding variances of the point estimators can be determined.

Most change-in-ratio (CIR) methods for estimating fish and wildlife population sizes have been based only on assumptions about how encounter probabilities vary among population subclasses. When information on sampling effort is available, it is also possible to derive CIR estimators based on assumptions about how encounter probabilities vary over time. This paper presents a generalization of previous CIR models that allows explicit consideration of a range of assumptions about the variation of encounter probabilities among subclasses and over time. Explicit estimators are derived under this model for specific sets of assumptions about the encounter probabilities. Numerical methods are presented for obtaining estimators under the full range of possible assumptions. Likelihood ratio tests for these assumptions are described. Emphasis is on obtaining estimators based on assumptions about variation of encounter probabilities over time.

The Jolly-Seber method has been the traditional approach to the estimation of demographic parameters in long-term capture-recapture studies of wildlife and fish species. This method involves restrictive assumptions about capture probabilities that can lead to biased estimates, especially of population size and recruitment. Pollock (1982, Journal of Wildlife Management 46, 752-757) proposed a sampling scheme in which a series of closely spaced samples were separated by longer intervals such as a year. For this "robust design," Pollock suggested a flexible ad hoc approach that combines the Jolly-Seber estimators with closed population estimators, to reduce bias caused by unequal catchability, and to provide estimates for parameters that are unidentifiable by the Jolly-Seber method alone. In this paper we provide a formal modelling framework for analysis of data obtained using the robust design. We develop likelihood functions for the complete data structure under a variety of models and examine the relationship among the models. We compute maximum likelihood estimates for the parameters by applying a conditional argument, and compare their performance against those of ad hoc and Jolly-Seber approaches using simulation.

The Brownie et al. (1985) band return models have been widely used to estimate survival and recovery rates for hunted species, especially migratory waterfowl. We developed a generalization of the Brownie models that allowed incorporation of solicited and reported bands into one analysis. This is an important addition to banding model literature, which has ignored solicited bands in the model formulation. Furthermore, if a reporting rate estimate is available from, for example, a reward banding study and a retrieval rate (1 − crippling loss rate) from a hunter questionnaire survey, we show that it is possible to estimate harvest rate, kill rate, and hence natural mortality rate in the presence of hunting

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.

Change-in-ratio methods have been developed to estimate the size of populations with two or three population subclasses. Most of these methods require the often unreasonable assumption of equal sampling probabilities for individuals in all subclasses. This paper presents new models based on the weaker assumption that ratios of sampling probabilities are constant over time for populations with three or more subclasses. Estimation under these models requires that a value be assumed for one of these ratios when there are two samples; no assumptions about the values of these ratios are required when there are more than two samples. Explicit expressions are given for the maximum likelihood estimators under models for two samples with three or more subclasses and for three samples with two subclasses. A numerical method using readily available statistical software is described for obtaining the estimators and their standard errors under all of the models. Likelihood ratio tests that can be used in model selection are discussed. Emphasis is on the two-sample, three-subclass models for which Monte Carlo simulation results and an illustrative example are presented.

An important problem in line transect sampling is that objects or point clusters of objects of different sizes have different sighting probabilities. In a recent paper Drummer and McDonald (1987, Biometrics 43, 13-21) develop a bivariate sighting function. Their function is dependent on perpendicular distance and object size. One important special case is an extension of the exponential power series sighting function first proposed by Pollock (1978, Biometrics 34, 475-478). In this note empirical evidence is given for this model based on a field test of line transect sampling theory. Beer cans were used to simulate point clusters of objects with cluster sizes 1, 2, 4, and 8. To achieve approximately equal precision of parameter estimates, equal numbers of each cluster size were taken.

In this paper the problem of finding robust estimators of population size in closed K-sample capture-recapture experiments is considered. Particular attention is paid to models where heterogeneity of capture probabilities is allowed. First, a general estimation procedure is given which does not depend on any assumptions about the form of the distribution of capture probabilities. This is followed by a detailed discussion of the usefulness of the generalized jackknife technique to reduce bias. Numerical comparisons of the bias and variance of various estimators are given. Finally, a general discussion is given with several recommendations on estimators to be used in practice.

The effects of paraquat (1,1'-dimethyl-4,4'-bipyridinium dichloride) on reproduction and growth of northern bobwhite (Colinus virginianus) were studied. In the parent generation (P) paraquat was administered at 0, 20, 60, and 180 ppm for 6 weeks. Reproductive variables examined included egg production, fertility, hatchability, chick abnormalities, and chick survival and weights to 7 days of age. Untreated breeders in the second generation (F1) phase were the offspring of the various groups in the first generation phase. Reproductive variables examined included egg production, number of days to first and last egg of a 20-egg clutch, fertility, and hatchability. P hens fed 180 ppm laid fewer eggs (all differences are at P < 0.05) during treatment compared to their pre-treatment period and to controls, and had lower ovary and oviduct weights. There were no differences in P fertility nor in chick abnormalities or survival as compared to controls. Chicks from P parents fed 20 ppm paraquat were heavier than all other treatments. P male and female post-treatment weight did not differ from pre-treatment weight. F, hens from paraquat-treated parents started laying 1 week later than controls and produced eggs at a lower rate resulting in clutch completion 10 days later than controls. There were no differences in F, fertility, hatch, or relative testes, ovary, and oviduct weights. Adult F, hens from parents fed 60 and 180 ppm paraquat weighed less. J. WILDL. MANAGE. 49(4):1066-1073 Paraquat is used extensively throughout the world for the control of weeds in orchards and crop fields and as a crop desiccant. Increased use of paraquat has resulted from an increase in no-tillage agriculture. Paraquat is available in the United States primarily as paraquat dichloride, a 29.1% liquid concentrate containing 0.9 kg paraquat cation/3.8 liter. The recommended field application rate usually ranges from 0.28 to 1.12 kg paraquat cation/ha (Ortho Tech. Inf., Chevron Chem. Co., Richmond, Calif., 1974). Residues of about 30 ppm in alfalfa and 60 ppm in adventitious graminaceae have been found after paraquat treatment at a r commended field level (De Lavaur et al. 1973). Paraquat residues have been reported to be as high as 1,000 ppm in herbage on grazing plots treated with the highest recommended application level (Calderbank et al. 1968). Some wildlife species may be affected by recommended field application rates of paraquat (Ernest 1971, De Lavaur et al. 1973, Dial and Bauer 1984). De Lavaur et al. (1973) found that 50% of hares (Lepus europaeus) exposed to alThis content downloaded from 157.55.39.83 on Sun, 09 Oct 2016 05:00:36 UTC All use subject to http://about.jstor.org/terms

Visibility is also affected when animals occur in groups, because larger groups have a higher probability of being observed than smaller groups. The result is an overestimation of mean group size and an underestimation of the mean number of groups per quadrat (Cook and Martin 1974). A general sighting function is proposed that relates the probability of sighting a group to its size. When ground counts are available on some of the quadrats, it is possible to estimate the parameters of the sighting function and obtain unbiased estimation of the mean group size, the density of groups, and the density of individuals. A proposed sighting function is applied to 3 aerial surveys of the sea otter (Enhydra lutris) in California, and also compared to a more restrictive sighting function suggested by Cook and Martin (1974).

On propose des tests generaux d'ajustement pour le modele de Jolly-Seber. Ces tests sont fondes sur des raisonnements conditionnels utilisant des statistiques minimales exhaustives. Les liens de ces tests avec les autres tests existant sont examines. La procedure de test est illustree sur des donnees de capture-recapture des campagnols

We present the results of a long-term (1970-85) band recovery study of northern bobwhite quail (Colinus virginianus) at Tall Timbers Research Station, Leon County, Florida. The mean annual survival rate of male quail (18.7 ? 1.2 [SE] %) was significantly (P = 0.01) greater than that of females (14.3 ? 1.2%). The difference between survival of young (6-9 months old) and adults (>1 yr old) was 3 ? 2.2% and not significant. Survival rates varied significantly among years. The mean harvest was 23.3 ? 0.53%/year. Young male quail were harvested at a significantly higher rate than adult males (2% difference). There was no significant difference between harvest rates of young and adult females. Juvenile male and female harvest rates were not significantly different. However, adult females were harvested at a significantly higher rate than adult males (5% difference). Harvest varied among years. The mean annual kill (harvest rate + crippling loss) was approximately 30% for both sexes. Male and female natural mortality were approximately 52 and 56%, respectively. There was evidence of additivity of hunting and natural mortality for this population harvested in late winter. Our long-term study provides information on the survival processes for northern bobwhite quail that can be used to enhance management of the species. J. WILDL. MANAGE. 53(1):1-6 Although research on northern bobwhite quail began in the 1920's (Stoddard 1931, Errington 1933), studies of quail survival have been limited. Sound management requires good estimates of mortality rates. Mortality for hunted species can be estimated from band recovery data using models prepared by Brownie et al. (1985). These models also provide band recovery rate estimates. Harvest rate is easily obtained if the reporting rate of bands is known. Total kill estimates follow from harvest estimates if an estimate of crippling loss is available. With these data managers can partition hunting and natural (nonhunting) mortality. A recent series of papers questions whether hunting and natural mortality are additive (Anderson and Burnham 1976, Anderson et al. 1982, Nichols and Hines 1983, Burnham and Anderson 1984, Burnham et al. 1984, Nichols et al. 1984). Most of this work applies to waterfowl, particularly mallards (Anas platyrhynchos), for which the most band recovery data are available. We report the results of a long-term bandrecovery study of bobwhite quail at Tall Timbers Research Station, Leon County, Florida. We obtained survival estimates and test the additive and compensatory mortality hypotheses (Anderson et al. 1982). W. L. Cornelius assisted with computing and J. D. Nichols reviewed an earlier draft of the manuscript. We thank present and past coworkers and many biologists and volunteers, especially wildlife technician students at Abraham Baldwin Agricultural College, for their help. This study was supported in part by Tall Timbers Research Station, Tallahassee, Florida and by an appropriation from the Congress of the United States. Funds were administered and research coordinated under the Federal Aid in Wildlife Restoration Act and through the U.S. Fish and Wildlife Service.

SUMMARY In this paper we consider the problem where there is a randomized experimental design with several successive time measurements on each experimental unit. One approach to the analysis of such data is to treat time as the subplot treatment and to use a split-plot analysis of variance. Alternatively, the problem may be considered in a more general multivariate framework. Here we recognize the timeinduced correlations and apply an autoregressive time series modelling approach. Estimation and testing are addressed. Two examples are presented to illustrate the practicality of our procedure. Some extensions are also considered briefly. Frequently data arise from a randomized experimental design where several successive measurements over time are made on each experimental unit. There are many examples, such as the following: (i) In medical trials, observations may be taken on each subject at regular time intervals. (ii) In wildlife radio-telemetry studies, the distance moved by each animal may be tracked during successive periods of a day. (iii) In plant (animal) experiments, observations may be taken on the same plant (animal) as it grows and changes over time. In all cases, there will be a correlation between observations taken on the same experimental unit at different time points. It is also likely that there is a decay in the correlation with increasing time lags. In other words, observations on the same experimental unit which are close together should be more highly correlated than those that are far apart in time. This is contrary to the assumption of constant correlation between all time points (subplots) within a unit (whole plot) made by the traditional split-plot analysis. An alternative approach is to consider a general multivariate analysis of variance (MANOVA) model, which assumes an arbitrary covariance matrix for the observations [see Timm (1980)]. However, we believe that the multivariate model is overparametrized and also it cannot easily incorporate missing values. Therefore, we consider a time series modelling approach to the problem which serves as a compromise. We now present the time series model that we consider for analyzing such data. We denote the variable under study by the letter Y with two subscripts, where the first subscript refers to the individual experimental units and the second subscript refers to the successive measurements for the particular individual. We assume that n "individuals" are selected at random and that "measurements" are taken at ti consecutive time points on the ith individual. We consider a linear model r

The assumptions inherent in modern band-recovery models are reviewed with particular attention to homogeneity of survival and band-recovery rates for all individuals in the population. If this assumption fails, the following implications emerge: (1) the models only enable estimation of average annual survival and band-recovery rates; (2) estimators of these averages probably give underestimates; (3) the degree of underestimation in practical studies is difficult to assess, but may sometimes be important for survival estimates; (4) if sampling is nonrandom and heterogeneity of survival and recovery rates is present in the population, then any estimates could be misleading; and (5) if survival rates are homogeneous but recovery rates are heterogeneous (due perhaps to geographical variation in hunting pressure and reporting rates), then there is no bias in survival estimates. An example where data from neck-collared birds showed heterogeneity in segments of a Canada goose (Branta canadensis) population is discussed. We believe that the practical limitations of bird-banding studies deserve careful review by population biologists and managers. J. WILDL. MANAGE. 46(1):88-98 Band-recovery data have long been used to estimate mortality rates in exploited migratory bird populations. However, it is only in recent years that methods of analysis of banding data have been rigorously considered. By making certain assumptions, Seber (1970, 1971, 1972, 1973) formulated a rigorous statistical model that gave rise to explicit maximum-likelihood estimators of survivaland recovery-rate parameters. Extensions allowing for age dependence of survival and recovery rates were made by Johnson (1974), Brownie and Robson (1976), and Brownie et al. (1978), who, in a comprehensive monograph, detailed a variety of age-dependent models. Development of modern methods clearly identified the weaknesses of some of the older procedures such as the composite dynamic life table. Burnham and Anderson (1979) analyzed 45 substantial data sets from migratory waterfowl band recoveries and demonstrated that the 1 Present address: Department of Statistics, North Carolina State University, Box 5457, Raleigh, NC 27650. composite dynamic life table should no longer be used, as only 2 data sets (4%) fit the model at a = 0.05. Burnham and Anderson (1979) also found that modern methods are not necessarily always adequate for analyzing banding data, as 14 of 45 data sets (30%) did not fit. In this paper we further examine the assumptions of the modern methods. An important assumption of all recovery models is that all banded individuals of an identifiable class (e.g., by species, age, sex) in the sample have the same annual survival and recovery rates (Brownie et al. 1978:6). We consider what happens when this assumption fails, and the importance of random sampling in conjunction with homogeneity of survival and recovery rates. First, we consider a specific model (Model 1: Adults Only Banded) when the homogeneity assumption holds. We shall refer to this as the Homogeneous Population Model. This will be followed by the same model when the homogeneity assumption fails, the Heterogeneous Population Model. We discuss a populaJ. Wildl. Manage. 46(1):1982 88 HETEROGENEOUS SURVIVAL RATES Pollock and Raveling 89 tion of Canada geese for which segments with heterogeneous survival and recovery rates are known to exist from the use of individually identifiable neck-collared birds (Raveling 1978). Finally, we provide a general discussion of all the assumptions underlying modern band-recovery models, with an emphasis on the practical implications of assumption failure. We thank D. R. Anderson, D. W. Anderson, K. P. Bumham, D. S. Gilmer, D. H. Johnson, and R. M. McLandress for helpful comments on an earlier version of the manuscript. HOMOGENEOUS POPULATION MODEL Here we consider the situation where all birds are banded as adults and all birds have the same survival and recovery rates in a particular year (Model 1 of Brownie et al. 1978:15). For simplicity, we will also assume the number of years of recoveries is the same as the number of years of banding. The data matrix for observed recoveries is given in Table 1. Under this model, each row of recoveries follows a multinomial distribution, and the expected recoveries take the form given in Table 2. The maximum-likelihood estimators of the survivaland recovery-rate parameters are given by the following equations

Utility of the change-in-ratio (CIR) technique for estimating abundance of deer (Odocoileus spp.) populations was investigated by calculating the sample size requirements (n, = prehunt and n2 = posthunt) for 3 levels of accuracy (e = 0.10, 0.25, and 0.50) and a = 0.05 and by applying the technique to the deer population at Remington Farms, Maryland. The calculations indicated that a sample size of n = 1,600 was required to estimate abundance of deer populations with a skewed sex ratio (prehunt proportion of antlered bucks [P,] = 0.10) with f = 0.25. If only antlerless deer were removed from a population with a similar sex ratio and a large change in the ratio (AP = 0.20) was achieved, N, could be estimated for E = 0.25 with n = 325. Application of the technique at Remington Farms indicated that the sample sizes could be achieved for relatively high density herds in open habitat. Biases associated with applying the CIR to deer populations are discussed. J. WILDL. MANAGE. 50(1):125-129 Population estimates are an important component of deer population management, particularly when establishing harvest quotas or evaluating the impacts of previous management practices. Numerous techniques are available to estimate deer abundance, including track counts (McCaffery 1976), pellet group counts (Stormer et al. 1977), aerial counts (Floyd et al. 1979), drives (McCullough 1979), line transects (Evans 1975), remote sensing (Wyatt et al. 1980), markreobservation (Downing et al. 1977), and change-in-ratio (Hess 1985). Because most of these techniques are expensive, biased, or unproven, they have limited utility for management agencies. The CIR technique is an attractive alternative for estimating or indexing populations of white-tailed deer (0. virginianus) because few data are required to execute the method, and the precision of the estimator can be high. Only prehunt and posthunt estimates of the proportions of the population that are antlered and antlerless and the number and sex of deer killed by hunting are required to apply the CIR. Precision of the CIR depends on the prehunt and posthunt ratios and kill removals. An added advantage is the usefulness of sex ratios for establishing harvest regulations, particularly for trophy-buck production, when adjusting the sex ratio is a management goal. Our study objectives were to: (1) evaluate the theoretical precision of the estimator and to calculate the sample size requirements for a range of proportions of antlered and antlerless deer and (2) address the assumptions of the technique relative to its application. We then applied the CIR in a field example to ascertain whether the sample sizes dictated by the theoretical calculations could be achieved. We thank Remington Farms personnel, especially E. C. Soutiere and E. H. Galbreath, for their support, ideas, and encouragement. J. W. Eldrett conducted the fieldwork. Remington Arms Co., Inc., and the Natl. Rifle Assoc. provided funding. C. Powell drafted the figures. DESCRIPTION OF THE TECHNIQUE A brief description of the CIR technique follows; for more detail see Seber (1982) or Paulik and Robson (1969). We consider a closed population with 2 classes of animals, x-type and y-type. For our example, x-type are antlered and y-type are antlerless deer. If the proportion of xand y-type animals in the population changes between 2 periods due to the removal of a known number of animals (in our example by hunting), we can estimate total population size before the removal (NI) as follows: N, = R P (1) N2 P 2 where R, = the number of x-types removed (known), R = Rx + RY = the total number of animals removed (known), P, = X,1N, = the proportion of x-type animals before the removal, and

Aerial surveys, often used to estimate the density of wildlife populations, commonly underestimate population density because of animals being missed. This visibility bias can be serious. Methods of estimating visibility bias based on comparison with ground counts, use of a subpopulation of marked animals, mapping with multiple observers, line transect sampling, and multiple counts on the same area are reviewed. All of the methods are model based and the various model assumptions are discussed and compared. J. WILDL. MANAGE. 51(2):502-510 Aerial surveys are used to estimate the population size of many large birds (Caughley and Grice 1982), large terrestrial mammals (Rice and Harder 1977), and marine mammals (Burnham et al. 1980:76). They are used in conjunction with other methods of estimation or by themselves, either by choice or necessity. "Visibility bias" results from animals being missed and is exacerbated by factors such as dense vegetation, bad weather conditions, and observer fatigue. Beyond the logistics and dangers of flying surveys precisely, the principal difficulty in aerial censuses lies in estimating the visibility bias to establish a correction factor. Caughley (1977: 35) presents a table showing the visibility bias in a wide range of aerial surveys. Biologists tempted to minimize this problem should study this table where the visibility bias is often in the range of 30-50% animals missed! If absolute density estimates are to be reported there will always be the need for a correction factor. Here we review the various methods of estimating visibility bias from an applied statistician's perspective. Neither of us claim to be experts in the practicalities of running aerial

The dependence of animal capture probabilities on auxiliary variables is an important practical problem which has not been considered in the development of estimation procedures for capturerecapture and removal experiments. In this paper the linear logistic binary regression model is used to relate the probability of capture to continuous auxiliary variables. The auxiliary variables could be environmental quantities such as air or water temperature, or characteristics of individual animals, such as body length or weight. Maximum likelihood estimators of the population parameters are considered for a variety of models which all assume a closed population. Testing between models is also considered. The models can also be used when one auxiliary variable is a measure of the effort expended in obtaining the sample.

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

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.

Une facon simple d'analyser les donnees de captures-recaptures est de n'utiliser que la premiere et la derniere capture en appliquant les methodes de reconstitution de bandes de Brownie et coll. On presente la perte d'efficacite de cette approche par rapport a la methode de Jolly-Seber et a l'extension de celle-ci quand les parametres dependent de l'âge. Application a des donnees fossiles

The change-in-ratio technique is a useful practical procedure for the estimation of game animal population sizes. The major problem with this technique is failure of the assumption that both types of animals are captured or sighted with equal probabilities. Here we extend the change-in-ratio technique to the case where there are two removals with emphasis on the special situation where there are two consecutive single-type removals. The advantage of this extension is that it allows an estimation procedure which is robust to unequal capture or sighting probabilities. It is also possible to test the assumption of equal sighting probabilities. Some numerical results on mean squared error of the population size estimator for the new design and the traditional design are given. The procedure is illustrated on some juvenile grass carp data collected in a small pond where the population size is known. We believe this technique is potentially useful to wildlife and fisheries biologists and that more statistical research would be beneficial.

We describe a harvest strategy that integrates a population dynamics model, a rationale for choosing a harvest rate, a means of implementing harvesting, and a change-in-ratio (CIR) population estimation technique. The size of the harvest is determined by selecting a proportion of the postharvest (residual) population (#) chosen between about zero and the intrinsic rate of increase in a given environment (rm), with a maximum sustained yield (MSY) at about 0 = r,/2 based on logistic growth, or about i = 0.5 based on McCullough's (1979:118, 1984) studies of the George Reserve white-tailed deer (Odocoileus virginianus) herd. The advantages of proportional harvesting are that the population stabilizes for all proportions, the location of the population along the sustained yield (SY) curve is unambiguous, and proportions are naturally self-correcting because harvests are tied to population size. Taking 2 separate single-type (sex) harvests provides a means for achieving the harvest quota and also yields a CIR population estimate based on observations of the proportion of antlered deer in the population at 3 times. The 2-stage CIR technique is robust to unequal observability, a major weakness of the traditional CIR methods. Our harvest strategy is most applicable where harvests can be controlled closely, and hunting seasons are relatively short. Field experiments are required to establish the efficacy of our harvest paradigm. J. WILDL. MANAGE. 52(4):589-595 Several components are needed to provide a framework for managing harvests of white-tailed deer to attain harvest and population goals. Among these are an underlying model of population dynamics that incorporates removals due to hunting, a rationale for choosing a harvest level, a means of implementing and controlling the removals, and a procedure to evaluate the success of the harvest strategy. Our objective is to integrate these requirements into a management paradigm based on a stock-recruitment model of population responses to harvesting (McCullough 1979:123-127, 1984), on 2 separate single-type (sex) removals during the hunting season, and on a 2-stage CIR population estimation technique (Pollock et al. 1985). We present a management paradigm, based on logic and theory that incorporates the concept of proportional harvesting. The 2-stage CIR is used to estimate population size, but any suitable estimation technique could be applied. We caution that our paradigm requires testing under field conditions. Our analysis begins with a deterministic model and then expands to consider briefly stochastic variability. Our strategy is most appropriate for herds closely controlled by managers. To support our rationale, we draw upon published literature and our experiences studying the deer herd on Remington Farms, Chestertown, Maryland. O r paradigm differs from the strategy developed by Hayne and Gwynn (1977), which uses the proportion of females in the harvest as a management objective. They reasoned that if th adult male harvest is inherently limited because hunter effort declines as males become scarce, then the female harvest could also be limited at a lower level by relating it to the male harvest. Their approach does not estimate population size or incorporate a measure of productivity, yet it has apparently been misinterpreted by some deer managers to reflect recruitment or changes in herd size (Downing 1981). Furthermore, Downing (1981) showed tha , alone, the proportion of females in the kill reveals little about the status of the herd. Our paradigm differs from Hayne and Gwynn's (1977) in that ours incorporates an estimate of the population and a measure of productivity. We thank Remington Farms and especially E. C. Soutiere and E. H. Galbreath for their encouragement and support. D. A. Adams, G. Caughley, P. D. Doerr, E. C. Franklin, and D. R. McCullough reviewed earlier drafts and provided helpful comments. This is paper 11498 of the Journal Series of the North Carolina Agricultural Research Service, Raleigh. IPresent address: Florida Game and Fresh Water Fish Commission, Route 7, P.O. Box 440, Lake City, FL 32055.

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.

The Jolly-Seber model (Jolly 1965, Seber 1965) is probably the most important open population model for use in capture-recapture experiments. Because of its importance and wide use, it is desirable to have knowledge of the effects of deviations from underlying model assumptions on resulting parameter estimates. Previous investigations have considered the effects of heterogeneity of capture probability (Carothers 1973, Gilbert 1973), tag loss (Arnason and Mills 1981), temporary emigration (Balser 1981), and age-specific differences in mortality rates (Manly 1970). Trap response refers to the situation in which marking an animal causes a change in its capture or survival probability for some time after its initial capture. Robson (1969), Pollock (1975), and Brownie and Robson (1980) have generalized the JollySeber capture-recapture model to permit temporary (e.g., one or more time periods after initial capture) trap response in survival and capture probability. Although a temporary trap response seems reasonable for survival rate and in some instances for capture probability, a permanent trap response in capture probability seems likely in many situations. In this paper we examine bias in Jolly-Seber estimates of survival rate and population size resulting from permanent trap response in capture probability.

Il faut tenir compte d'une certaine perte des bagues (fixees aux oreilles) chez les Ursus americanus de Pennsylvanie pour l'analyse des populations