A Bayesian estimate of harbour seal survival using sparse photo-identification data

Survival rates have rarely been estimated for pinniped populations due to the constraints of obtaining unbiased sample data. In this paper, we present an approach for estimating survival probabilities from individual recognition data in the form of photographic documentation of pelage patterns. This method was applied to estimate adult (age 2+) survival for harbour seals in the Moray Firth, NE Scotland. An astronomical telescope was used to obtain digital images of individual seals, and high-quality images were used to document the annual presence or absence of individuals at a single haul-out site over a 4-year period. A total of 95 females, 10 males and 57 individuals of unknown sex were photographically documented during the study period. Survival and recapture probabilities were estimated using Jolly–Seber mark–recapture models in a Bayesian statistical framework. Computer-intensive Markov Chain Monte Carlo methods were used to estimate the probability distributions for the survival and recapture probabilities, conveying the full extent of the uncertainty resulting from unavoidably sparse observational data. The deviance information criterion was used to identify a best-fitting model that accounted for variation in the probability of capture between sexes, with constant survival. The model estimated adult survival as 0.98 (95% probability interval of 0.94–1.00) using our photo-identification data alone, and 0.97 (0.92–0.99) with the use of an informative prior distribution based on previously published estimates of harbour seal survival. This paper represents the first survival estimate for harbour seals in the UK, and the first survival estimate using photo-identification data in any species of pinniped.     

Point and interval estimates of marker location in radiation hybrid mapping.

Radiation hybrid (RH) mapping is a powerful method for ordering loci on chromosomes and for estimating the distances between them. RH mapping is currently used to construct both framework maps, in which all markers are ordered with high confidence (e.g., 1,000:1 relative maximum likelihood), and comprehensive maps, which include markers with less-confident placement. To deal with uncertainty in the order and location of markers, marker positions may be estimated conditional on the most likely marker order, plausible intervals for nonframework markers may be indicated on a framework map, or bins of markers may be constructed. We propose a statistical method for estimating marker position that combines information from all plausible marker orders, gives a measure of uncertainty in location for each marker, and provides an alternative to the current practice of binning. Assuming that the prior distribution for the retention probabilities is uniform and that the marker loci are distributed independently and uniformly on an interval of specified length, we calculate the posterior distribution of marker position for each marker. The median or mean of this distribution provides a point estimate of marker location. An interval estimate of marker location may be constructed either by using the 100(alpha/2) and 100(1-alpha)/2 percentiles of the distribution to form a 100(1-alpha) % posterior credible interval or by calculating the shortest 100(1-alpha) % posterior credible interval. These point and interval estimates take into account ordering uncertainty and do not depend on the assumption of a particular marker order. We evaluate the performance of the estimates on the basis of results from simulated data and illustrate the method with two examples.     

Survival of bowhead whales,Balaena mysticetus,estimated from 1981-1998 photoidentification data

Annual survival probability of bowhead whales, Balaena mysticetus, was estimated using both Bayesian and maximum likelihood implementations of Cormack and Jolly-Seber (JS) models for capture-recapture estimation in open populations and reduced-parameter generalizations of these models. Aerial photographs of naturally marked bowheads collected between 1981 and 1998 provided the data. The marked whales first photographed in a particular year provided the initial 'capture' and 'release' of those marked whales and photographs in subsequent years the 'recaptures'. The Cormack model, often called the Cormack-Jolly-Seber (CJS) model, and the program MARK were used to identify the model with a single survival and time-varying capture probabilities as the most appropriate for these data. When survival was constrained to be one or less, the maximum likelihood estimate computed by MARK was one, invalidating confidence interval computations based on the asymptotic standard error or profile likelihood. A Bayesian Markov chain Monte Carlo (MCMC) implementation of the model was used to produce a posterior distribution for annual survival. The corresponding reduced-parameter JS model was also fit via MCMC because it is the more appropriate of the two models for these photoidentification data. Because the CJS model ignores much of the information on capture probabilities provided by the data, its results are less precise and more sensitive to the prior distributions used than results from the JS model. With priors for annual survival and capture probabilities uniform from 0 to 1, the posterior mean for bowhead survival rate from the JS model is 0.984, and 95% of the posterior probability lies between 0.948 and 1. This high estimated survival rate is consistent with other bowhead life history data.     

Testing the consistency of wildlife data types before combining them: the case of camera traps and telemetry

Wildlife data gathered by different monitoring techniques are often combined to estimate animal density. However, methods to check whether different types of data provide consistent information (i.e., can information from one data type be used to predict responses in the other?) before combining them are lacking. We used generalized linear models and generalized linear mixed-effects models to relate camera trap probabilities for marked animals to independent space use from telemetry relocations using 2 years of data for fishers (Pekania pennanti) as a case study. We evaluated (1) camera trap efficacy by estimating how camera detection probabilities are related to nearby telemetry relocations and (2) whether home range utilization density estimated from telemetry data adequately predicts camera detection probabilities, which would indicate consistency of the two data types. The number of telemetry relocations within 250 and 500 m from camera traps predicted detection probability well. For the same number of relocations, females were more likely to be detected during the first year. During the second year, all fishers were more likely to be detected during the fall/winter season. Models predicting camera detection probability and photo counts solely from telemetry utilization density had the best or nearly best Akaike Information Criterion (AIC), suggesting that telemetry and camera traps provide consistent information on space use. Given the same utilization density, males were more likely to be photo-captured due to larger home ranges and higher movement rates. Although methods that combine data types (spatially explicit capture–recapture) make simple assumptions about home range shapes, it is reasonable to conclude that in our case, camera trap data do reflect space use in a manner consistent with telemetry data. However, differences between the 2 years of data suggest that camera efficacy is not fully consistent across ecological conditions and make the case for integrating other sources of space-use data.     

Estimating chronic wasting disease effects on mule deer recruitment and population growth

Chronic wasting disease (CWD), a prion disease of mule deer (Odocoileus hemionus), accelerates mortality and in so doing has the potential to influence population dynamics. Although effects on mule deer survival are clear, how CWD affects recruitment is less certain. We studied how prion infection influenced the number of offspring raised to weaning per adult (≥2 yr old) female mule deer and subsequently the estimated growth rate (λ) of an infected deer herd. Infected and presumably uninfected radio-collared female deer were observed with their fawns in late summer (August-September) during three consecutive years (2006-2008) in the Table Mesa area of Boulder, Colorado, USA. We counted the number of fawns accompanying each female, then used a fully Bayesian model to estimate recruitment by infected and uninfected females and the effect of the disease on λ. On average, infected females weaned 0.95 fawns (95% credible interval=0.56-1.43) whereas uninfected females weaned 1.34 fawns (95% credible interval=1.09-1.61); the probability that uninfected females weaned more fawns than infected females was 0.93). We used estimates of prevalence to weight recruitment and survival parameters in the transition matrix of a three-age, single-sex matrix model and then used the matrix to calculate effects of CWD on λ. When effects of CWD on both survival and recruitment were included, the modeled λ was 0.97 (95% credible interval = 0.82-1.09). Effects of disease on λ were mediated almost entirely by elevated mortality of infected animals. We conclude that although CWD may affect mule deer recruitment, these effects seem to be sufficiently small that they can be omitted in estimating the influences of CWD on population growth rate.     

The effect of aquatic and terrestrial habitat characteristics on occurrence and breeding probability in a montane amphibian: insights from a spatially explicit multistate occupancy model

Understanding species distribution and predicting range shifts are major goals of ecology and biogeography. Obtaining reliable predictions of how species distribution might change in response to habitat change requires knowledge of habitat availability, occupancy, use for breeding, and spatial autocorrelation in these parameters. Amphibians in alpine areas provide an excellent model system for disentangling habitat drivers of occupancy from that of breeding while explicitly accounting for spatial autocorrelation. We focused on the widespread common frog (Rana temporaria) inhabiting alpine lakes in the Southern Carpathians, Romania. We used single season multistate occupancy models developed to account for imperfect detection and spatial autocorrelation to estimate the occupancy and breeding probabilities and to evaluate their response to habitat characteristics. We found that frogs do not occur in all water bodies [occupancy probability: 0.697; 95% credible interval (0.614, 0.729)] and do not breed in a substantial proportion of water bodies where they occur [breeding probability conditional on occupancy: 0.707; 95% credible interval (0.670, 0.729)]. Habitat characteristics explain water body occupancy but not breeding probability; and altitude, water body surface area, water body sinuosity and permanency, presence of invertebrates, and grazing along the banks all had positive effects on occupancy. We also detected strong spatial autocorrelation in occupancy and breeding probabilities. Thus, our results indicate that habitat choice by montane amphibians is influenced by both spatial autocorrelation and habitat characteristics. Because spatial autocorrelations matter and because the presence of adults is not the same as the presence of a reproducing population, it will be difficult to predict the effects of habitat change on high altitude amphibian populations.     

Effect of Pre-Harvest Mortality on Harvest Rates and Derived Population Estimates

Banding waterfowl, in combination with the citizen science provided by hunters that report marks from harvested birds, is a long-standing, institutionalized practice for estimating probabilities of survival and exploitation (i.e., legal harvest from such populations). Range-wide population abundance can also be estimated by combining the number of banded individuals with the number harvested from the population. Waterfowl marking with uniquely identifiable bands done during late summer in North America is often referred to as pre-season banding. For example, mass capture of arctic geese for pre-season banding is normally done in July (nonbreeders) or August (failed breeders and breeders with young) during flightless molt of respective groups. An important assumption for proper inference about harvest probability provided from such samples is that there is no mortality, natural or otherwise, during the interval between when individuals are marked and when hunting seasons begin. We evaluated the effect of variable mortality that could occur between marking and subsequent hunting seasons on estimates of survival, recovery, and harvest probabilities using simulation pertinent to a typical waterfowl species. We fit a Brownie tag-recovery model to the simulated data and calculated the estimator bias that resulted from various pre-harvest mortality scenarios. There was no effect on survival probability during the interval between annual banding in subsequent years, but recovery probability, and thus estimated harvest probability, was directly and inversely related to pre-harvest mortality of juveniles. The magnitude of negative bias in harvest probability of juveniles increased further as the fraction of the population sampled declined. If the probability of pre-harvest mortality differs between marked and unmarked individuals, the negative bias in harvest probability results in overestimates of derived abundance that increases as the proportion of marked individuals in the population declines. We used our observed results to propose an explanation for occasional biologically improbable estimates of abundance of juvenile lesser snow geese (Anser caerulescens). © 2021 The Authors. The Journal of Wildlife Management published by Wiley Periodicals LLC on behalf of The Wildlife Society.     

Estimating genotypes with independently sampled descent graphs

A method for estimating genotypic and identity-by-descent probabilities in complex pedigrees is described. The method consists of an algorithm for drawing independent genotype samples which are consistent with the pedigree and observed genotype. The probability distribution function for samples obtained using the algorithm can be evaluated up to a normalizing constant, and combined with the likelihood to produce a weight for each sample. Importance sampling is then used to estimate genotypic and identity-by-descent probabilities. On small but complex pedigrees, the genotypic probability estimates are demonstrated to be empirically unbiased. On large complex pedigrees, while the algorithm for obtaining genotype samples is feasible, importance sampling may require an infeasible number of samples to estimate genotypic probabilities with accuracy.     

Estimation of Bayesian confidence intervals for the product of conditional survival probabilities

A model is derived to estimate the survival probability of a time interval when censorings occur. The time interval is divided into partial intervals in order to obtain the conditional survival probabilities, each of which is a parameter of a Binomial distributed random variable. To allow for the dependence between the events in the different intervals these parameters are transformed. Corresponding a priori density functions are formulated regarding both the Bayesian uniform distribution and the special model. The a posteriori density function is derived for the product of the conditional survival probabilities, and formulae for the BAYE sian confidence interval and the expectation are given. Lower and upper bounds for the confidence interval and the expectation are derived. Some examples are given to compare the results with other methods.     

Adjusting survival estimates for premature transmitter failure: a case study from the Sacramento-San Joaquin Delta

In telemetry studies, premature tag failure causes negative bias in fish survival estimates because tag failure is interpreted as fish mortality. We used mark-recapture modeling to adjust estimates of fish survival for a previous study where premature tag failure was documented. High rates of tag failure occurred during the Vernalis Adaptive Management Plan’s (VAMP) 2008 study to estimate survival of fall-run Chinook salmon (Oncorhynchus tshawytscha) during migration through the San Joaquin River and Sacramento-San Joaquin Delta, California. Due to a high rate of tag failure, the observed travel time distribution was likely negatively biased, resulting in an underestimate of tag survival probability in this study. Consequently, the bias-adjustment method resulted in only a small increase in estimated fish survival when the observed travel time distribution was used to estimate the probability of tag survival. Since the bias-adjustment failed to remove bias, we used historical travel time data and conducted a sensitivity analysis to examine how fish survival might have varied across a range of tag survival probabilities. Our analysis suggested that fish survival estimates were low (95% confidence bounds range from 0.052 to 0.227) over a wide range of plausible tag survival probabilities (0.48–1.00), and this finding is consistent with other studies in this system. When tags fail at a high rate, available methods to adjust for the bias may perform poorly. Our example highlights the importance of evaluating the tag life assumption during survival studies, and presents a simple framework for evaluating adjusted survival estimates when auxiliary travel time data are available.     

A Markov formulation of the repair-misrepair model of cell survival

Tobias' repair-misrepair (RMR) model of cell survival is formulated as a Markov process, a sequence of discrete repair steps occurring at random times, and the probability of a sequence of viable repairs is calculated. The Markov formulation describes the time evolution of the probability distribution for the number of lesions in a cell. The probability of cell survival is calculated from the distribution of the initial number of lesions and the probabilities of the repair events. The production of lesions is formulated in accordance with the principles of microdosimetry, and the distribution of the initial number of lesions is obtained as an approximation for high and low linear energy transfer cases. The Markov formulation of the RMR model uses the same biological hypotheses as the original version with two statistical approximations deleted. These approximations are the neglect of the effect of statistical fluctuations in calculating the average rate of repair of lesions and the assumption that the final number of unrepaired and lethally misrepaired lesions has a Poisson distribution. The quantitative effect of these approximations is calculated, and a basis is provided for an alternative approach to calculating survival probabilities.     

On the survival probability of a slightly advantageous mutant gene in a multitype population: A multidimensional branching process model

The estimated survival probability of a slightly supercritical Galton-Watson process is generalized to a multitype branching process. The result is used to estimate the probability of initial success of a mutant gene whose effect on the individual carrier depends on the carrier's sex, class, etc. The probability of initial success is also estimated in a case where the effect of the mutation is manifested in terms of the distribution of types within one's progeny, e.g. in a case of a change in the sex ratio.     

Evaluation of several methods for estimating phylogenetic trees when substitution rates differ over nucleotide sites

Several maximum likelihood and distance matrix methods for estimating phylogenetic trees from homologous DNA sequences were compared when substitution rates at sites were assumed to follow a gamma distribution. Computer simulations were performed to estimate the probabilities that various tree estimation methods recover the true tree topology. The case of four species was considered, and a few combinations of parameters were examined. Attention was applied to discriminating among different sources of error in tree reconstruction, i.e., the inconsistency of the tree estimation method, the sampling error in the estimated tree due to limited sequence length, and the sampling error in the estimated probability due to the number of simulations being limited. Compared to the least squares method based on pairwise distance estimates, the joint likelihood analysis is found to be more robust when rate variation over sites is present but ignored and an assumption is thus violated. With limited data, the likelihood method has a much higher probability of recovering the true tree and is therefore more efficient than the least squares method. The concept of statistical consistency of a tree estimation method and its implications were explored, and it is suggested that, while the efficiency (or sampling error) of a tree estimation method is a very important property, statistical consistency of the method over a wide range of, if not all, parameter values is prerequisite.     

Spatial patterns in age- and colony-specific survival in a long-lived seabird across 14 contrasting colonies

Demographic rates such as recruitment and survival probability can vary considerably among populations of the same species due to variation in underlying environmental processes. If environmental processes are spatially correlated, nearby populations are expected to have more similar demographic rates than those further apart. Breeding populations and foraging ranges are spatially segregated in colonial seabirds, making them ideal for studying spatial patterns in demographic rates and their effects on local population dynamics. Here we explored variation in age-dependent survival probabilities across 14 colonies of Herring Gulls Larus argentatus breeding along the Dutch North Sea coast. We used long-term mark–recapture data of marked fledglings to estimate survival, and estimated spatial autocorrelation of survival probabilities. We assessed whether survival until recruitment age or until 10 years old (close to their expected lifespan) explained variation in population trajectories of each colony. Juvenile and adult survival showed a strong, but different, north-to-south gradient in survival probability, with lower juvenile but higher adult survival in northern colonies than southern colonies, whereas the spatial pattern of immature survival was less distinct. Neither recruitment nor the proportion of 10-year-old adults alive predicted whether a colony collapsed, declined, remained stable or increased. The distinct spatial pattern in survival suggests variation in regional food availability, which do not seem to drive local population dynamics. The absence of a link between survival and colony trajectories implies that connectivity between populations plays an important role affecting population dynamics.     

Probability distribution of molecular evolutionary trees: A new method of phylogenetic inference

A new method is presented for inferring evolutionary trees using nucleotide sequence data. The birth-death process is used as a model of speciation and extinction to specify the prior distribution of phylogenies and branching times. Nucleotide substitution is modeled by a continuous-time Markov process. Parameters of the branching model and the substitution model are estimated by maximum likelihood. The posterior probabilities of different phylogenies are calculated and the phylogeny with the highest posterior probability is chosen as the best estimate of the evolutionary relationship among species. We refer to this as the maximum posterior probability (MAP) tree. The posterior probability provides a natural measure of the reliability of the estimated phylogeny. Two example data sets are analyzed to infer the phylogenetic relationship of human, chimpanzee, gorilla, and orangutan. The best trees estimated by the new method are the same as those from the maximum likelihood analysis of separate topologies, but the posterior probabilities are quite different from the bootstrap proportions. The results of the method are found to be insensitive to changes in the rate parameter of the branching process. Correspondence to: Z. Yang     

Estimating Survival for Elusive Juvenile Pond-Breeding Salamanders

Juvenile vital rates have important effects on population dynamics for many species, but this demographic is often difficult to locate and track. As such, we frequently lack reliable estimates of juvenile survival, which are necessary for accurately assessing population stability and potential management approaches to conserve biodiversity. We estimated survival rates for elusive juveniles of 3 species, the ringed salamander (Ambystoma annulatum), spotted salamander (A. maculatum), and small-mouthed salamander (A. texanum), using 2 approaches. First, we conducted an 11-month (2016–2017) mark-recapture study within semi-natural enclosures and used Bayesian Cormack-Jolly-Seber models to estimate survival and recapture probabilities. Second, we inferred the expected annual juvenile survival rate given published vital rates for pre-metamorphic and adult ambystomatids assuming stable population growth. For all 3 species, juvenile survival probabilities were constant across recapture occasions, whereas recapture probability estimates were time-dependent. Further, survival and recapture probabilities among study species were similar. Post-study sampling revealed that the initial study period median estimate of annual survival probability (0.39) underestimated the number of salamanders known alive at 11 months. We therefore appended approximately 1 year of opportunistic data, which produced a median annual survival probability of 0.50, encompassing salamanders that we knew to have been alive. Calculation from literature values suggested a mean annual terrestrial juvenile ambystomatid survival probability of 0.49. Similar results among our approaches indicated that juvenile survival estimates for the study species were robust and likely comparable to rates in nature. These estimates can now be confidently applied to research, monitoring, and management efforts for the study species and ecologically similar taxa. Our findings indicated that similarly robust vital rate estimates for subsets of ecologically and phylogenetically similar species can provide reasonable surrogate demographic information that can be used to reveal key factors influencing population viability for data-deficient species. © 2020 The Wildlife Society.     

A Bayesian method to estimate the optimal threshold of a longitudinal biomarker

The objective of this study was to develop methods to estimate the optimal threshold of a longitudinal biomarker and its credible interval when the diagnostic test is based on a criterion that reflects a dynamic progression of that biomarker. Two methods are proposed: one parametric and one non‐parametric. In both the cases, the Bayesian inference was used to derive the posterior distribution of the optimal threshold from which an estimate and a credible interval could be obtained. A numerical study shows that the bias of the parametric method is low and the coverage probability of the credible interval close to the nominal value, with a small coverage asymmetry in some cases. This is also true for the non‐parametric method in case of large sample sizes. Both the methods were applied to estimate the optimal prostate‐specific antigen nadir value to diagnose prostate cancer recurrence after a high‐intensity focused ultrasound treatment. The parametric method can also be applied to non‐longitudinal biomarkers.     

The parasite capacity of the host population

The estimation of parasitic pressure on the host populations is frequently required in parasitological investigations. The empirical values of prevalence of infection are used for this, however the latter one as an estimation of parasitic pressure on the host population is insufficient. For example, the same prevalence of infection can be insignificant for the population with high reproductive potential and excessive for the population with the low reproductive potential. Therefore the development of methods of an estimation of the parasitic pressure on the population, which take into account the features the host population, is necessary. Appropriate parameters are to be independent on view of the researcher, have a clear biological sense and be based on easily available characteristics. The methods of estimation of parasitic pressure on the host at the organism level are based on various individual viability parameters: longevity, resistance to difficult environment etc. The natural development of this approach for population level is the analysis of viability parameters of groups, namely, the changing of extinction probability of host population under the influence of parasites. Obviously, some critical values of prevalence of infection should exist; above theme the host population dies out. Therefore the heaviest prevalence of infection, at which the probability of host population size decreases during the some period is less than probability of that increases or preserves, can serve as an indicator of permissible parasitic pressure on the host population. For its designation the term "parasite capacity of the host population" is proposed. The real parasitic pressure on the host population should be estimated on the comparison with its parasite capacity. Parasite capacity of the host population is the heaviest possible prevalence of infection, at which, with the generation number T approaching infinity, there exists at least one initial population size ni(0) for which the probability of size decrease through T generations is less than the probability of its increase. [formula: see text] The estimation of the probabilities of host population size changes is necessary for the parasite capacity determination. The classical methods for the estimation of extinction probability of population are unsuitable in this case, as these methods require the knowledge of population growth rates and their variances for all possible population sizes. Thus, the development methods of estimate of extinction probability of population, based on the using of available parameters (sex ratio, fecundity, mortality, prevalence of infection PI) is necessary. The population size change can be considered as the Markov process. The probabilities of all changes of population size for a generation in this case are described by a matrix of transition probabilities of Markov process (pi) with dimensions Nmax x Nmax (maximum population size). The probabilities of all possible size changes for T generations can be calculated as pi T. Analyzing the behaviour matrix of transition at various prevalence of infection, it is possible to determine the parasite capacity of the host population. In constructing of the matrix of transition probabilities, should to be taken into account the features the host population and the influence of parasites on its reproductive potential. The set of the possible population size at a generation corresponds to each initial population size. The transition probabilities for the possible population sizes at a generation can be approximated to the binomial distribution. The possible population sizes at a generation nj(t + 1) can be calculated as sums of the number of survived parents N1 and posterities N2; their probabilities--as P(N1) x P(N2). The probabilities of equal sums N1 + N2 and nj(t + 1) > or = Nmax are added. The number of survived parents N1 may range from 0 to (1-PI) x ni(t). The survival probabilities can be estimated for each N1 as [formula: see text] The number of survived posterities N2 may range from 0 to N2max (the maximum number of posterities). N2max is [formula: see text] and the survival probabilities for each N2, is defined as [formula: see text] where [formula: see text], ni(t) is the initial population size (including of males and infected specimens of host), PI is the prevalence of infection, Q1 is the survival probabilities of parents, Pfemales is the frequency of females in the host population, K is the number of posterities per a female, and Q2 is the survival probabilities of posterities. When constructing matrix of transition probabilities of Markov process (pi), the procedure outlined above should be repeated for all possible initial population size. Matrix of transition probabilities for T generations is defined as pi T. This matrix (pi T) embodies all possible transition probabilities from the initial population sizes to the final population sizes and contains a wealth of information by itself. From the practical point of view, however, the plots of the probability of population size decrease are more suitable for analysis. They can be received by summing the probabilities within of lines of matrix from 0 to ni--1 (ni--the population size, which corresponds to the line of the matrix). Offered parameter has the number of advantages. Firstly, it is independent on a view of researcher. Secondly, it has a clear biological sense--this is a limit of prevalence, which is safe for host population. Thirdly, only available parameters are used in the calculation of parasite capacity: population size, sex ratio, fecundity, mortality. Lastly, with the availability of modern computers calculations do not make large labour. Drawbacks of this parameter: 1. The assumption that prevalence of infection, mortality, fecundity and sex ratio are constant in time (the situations are possible when the variability of this parameters can not be neglected); 2. The term "maximum population size" has no clear biological sense; 3. Objective restrictions exist for applications of this mathematical approach for populations with size, which exceeds 1000 specimens (huge quantity of computing operations--order Nmax 3*(T-1), work with very low probabilities). The further evolution of the proposed approach will allow to transfer from the probabilities of size changes of individual populations to be probabilities of size changes of population systems under the influence of parasites. This approach can be used at the epidemiology and in the conservation biology.     

Monitoring Svalbard rock ptarmigan: Distance sampling and occupancy modeling

The only resident terrestrial herbivorous bird species in high-Arctic Svalbard, Norway is the endemic Svalbard rock ptarmigan (Lagopus muta hyperborea) of which little is known of its population dynamics. We assessed temporal and spatial variability of the pre-breeding population of Svalbard rock ptarmigan males using: 1) distance sampling to estimate density (2000–2009) and 2) occupancy modeling to determine the proportion of survey points being occupied in relation to a habitat index for ptarmigan habitat suitability (2005–2009). Data were collected using a point-transect sampling design. We split the analysis according to type of survey point (non-random, random, and survey points combined). Our estimated spring densities were low (1.3–3.1 territorial male/km², non-random survey points, 2000–2009) with limited annual variability. The best models describing occupancy rates of territorial males at 2 different spatial scales (ptarmigan males observed ≤250 m and ≤450 m from the sampling point) were independent of spatial scales and the type of survey points. Occupancy dynamics were related to the habitat index whereas detection probability was year dependent. Extinction probability was negatively related to habitat quality (good habitats had lower extinction probability). We could not estimate the habitat effect on colonization precisely because initial occupancy rates were high at both spatial scales (estimated average initial occupancy at scale ≤250 m = 0.96; scale ≤450 m = 0.97). Colonization appeared to be positively related to the habitat index for the random survey points (including mainly marginal habitats), but the small sample size led to large uncertainty in the parameter estimate. Detection probabilities varied greatly between study years, thus demonstrating the importance of estimating detection probability annually. We recommend that future surveys are stratified with respect to habitat quality and to integrate the 2 methodologies in population monitoring of Svalbard rock ptarmigan. © 2011 The Wildlife Society.     

Symmetric tests and confidence intervals for survival probabilities and quantiles of censored survival data

We describe existing tests and introduce two new tests concerning the value of a survival function. These tests may be used to construct a confidence interval for the survival probability at a given time or for a quantile of the survival distribution. Simulation studies show that error rates can differ substantially from their nominal values, particularly at survival probabilities close to zero or one. We recommend our new constrained bootstrap test for its good overall performance.