MULTISITE MARK-RECAPTURE FOR CETACEANS: POPULATION ESTIMATES WITH BAYESIAN MODEL AVERAGING

Mark-recapture techniques are widely used to estimate the size of wildlife populations. However, in cetacean photo-identification studies, it is often impractical to sample across the entire range of the population. Consequently, negatively biased population estimates can result when large portions of a population are unavailable for photographic capture. To overcome this problem, we propose that individuals be sampled from a number of discrete sites located throughout the population's range. The recapture of individuals between sites can then be presented in a simple contingency table, where the cells refer to discrete categories formed by combinations of the study sites. We present a Bayesian framework for fitting a suite of log-linear models to these data, with each model representing a different hypothesis about dependence between sites. Modeling dependence facilitates the analysis of opportunistic photo-identification data from study sites located due to convenience rather than by design. Because inference about population size is sensitive to model choice, we use Bayesian Markov chain Monte Carlo approaches to estimate posterior model probabilities, and base inference on a model-averaged estimate of population size. We demonstrate this method in the analysis of photographic mark-recapture data for bottlenose dolphins from three coastal sites around NE Scotland.     

Spatially-explicit wildlife surveillance to prove freedom from diseases or pests

Surveillance undertaken to prove freedom from a disease has traditionally focussed on sampling a specified proportion of the population to determine the presence of the infective agent. Based on a sample of individuals testing negative for disease, standard probability theory using the binomial or hypergeometric distribution can be used to make inference about the probability of disease being absent. However, if the disease agent involves a wildlife host, then determining what proportion of the population was sampled becomes problematic as it requires an estimate of population abundance, which may be difficult and expensive to obtain. Surveillance during the eradication of pests such as feral ungulates often make use of the Judas technique, whereby radio-collared individuals are released and followed in the hope that the sociality of the individuals will betray the locations of conspecifics, which can then be dispatched. Data collected during such surveillance is explicitly spatial, containing information about the ‘search area’ of the Judas animal. However, there has been no attempt to use such data to make inference about the probability of the area being free of the pest, given Judas animals fail to detect any conspecifics. We present a framework for making specific use of the spatial nature of such wildlife surveillance data to make inference about the probability of freedom from the disease or pest. Underlying the sampling framework is a model of the detection process by sampled individuals. Estimates of individual detection probability are spatially smoothed using the extent of individual movements to produce a spatially- explicit detection surface. Bayes theorem is then used to combine this 2-dimensional surface with prior information on the probability of pest or disease presence, prior to sampling, to estimate the probability that the area is free from the disease or pest, given surveillance fails to detect evidence of their presence. We illustrate the method with examples of the detection of bovine Tb in wildlife in New Zealand and the detection of pigs (Sus scrofa) using the Judas technique during the feral pig eradication programme on Santa Cruz Island, California.     

Accounting for imperfect detection of groups and individuals when estimating abundance

If animals are independently detected during surveys, many methods exist for estimating animal abundance despite detection probabilities <1. Common estimators include double‐observer models, distance sampling models and combined double‐observer and distance sampling models (known as mark‐recapture‐distance‐sampling models; MRDS). When animals reside in groups, however, the assumption of independent detection is violated. In this case, the standard approach is to account for imperfect detection of groups, while assuming that individuals within groups are detected perfectly. However, this assumption is often unsupported. We introduce an abundance estimator for grouped animals when detection of groups is imperfect and group size may be under‐counted, but not over‐counted. The estimator combines an MRDS model with an N‐mixture model to account for imperfect detection of individuals. The new MRDS‐Nmix model requires the same data as an MRDS model (independent detection histories, an estimate of distance to transect, and an estimate of group size), plus a second estimate of group size provided by the second observer. We extend the model to situations in which detection of individuals within groups declines with distance. We simulated 12 data sets and used Bayesian methods to compare the performance of the new MRDS‐Nmix model to an MRDS model. Abundance estimates generated by the MRDS‐Nmix model exhibited minimal bias and nominal coverage levels. In contrast, MRDS abundance estimates were biased low and exhibited poor coverage. Many species of conservation interest reside in groups and could benefit from an estimator that better accounts for imperfect detection. Furthermore, the ability to relax the assumption of perfect detection of individuals within detected groups may allow surveyors to re‐allocate resources toward detection of new groups instead of extensive surveys of known groups. We believe the proposed estimator is feasible because the only additional field data required are a second estimate of group size.     

Recommendations for estimating mark rate of cetaceans in photo-ID research: A critique of field sampling protocols and variance estimation

Mark rate, or the proportion of the population with unique, identifiable marks, must be determined in order to estimate population size from photographic identification data. In this study we address field sampling protocols and estimation methods for robust estimation of mark rate and its uncertainty in cetacean populations. We present two alternatives for estimating the variance of mark rate: (1) a variance estimator for clusters of unequal sizes (SRCS) and (2) a hierarchical Bayesian model (SRCS-Bayes), and compare them to the simple random sampling (SRS) variance estimator. We tested these variance estimators using a simulation to see how they perform at varying mark rates, number of groups sampled, photos per group, and mean group sizes. The hierarchical Bayesian model outperformed the frequentist variance estimators, with the true mark rate of the population held in its 95% HDI 91.9% of the time (compared with coverage of 79% for the SRS method and 76.3% for the SRCS-Cochran method). The simulation results suggest that, ideally, mark rate and its precision should be quantified using hierarchical Bayesian modeling, and researchers should attempt to sample as many unique groups as possible to improve accuracy and precision.     

Asymmetry within social groups: division of labour and intergroup competition

Social animals vary in their ability to compete with group members over shared resources and also vary in their cooperative efforts to produce these resources. Competition among groups can promote within‐group cooperation, but many existing models of intergroup cooperation do not explicitly account for observations that group members invest differentially in cooperation and that there are often within‐group competitive or power asymmetries. We present a game theoretic model of intergroup competition that investigates how such asymmetries affect within‐group cooperation. In this model, group members adopt one of two roles, with relative competitive efficiency and the number of individuals varying between roles. Players in each role make simultaneous, coevolving decisions. The model predicts that although intergroup competition increases cooperative contributions to group resources by both roles, contributions are predominantly from individuals in the less competitively efficient role, whereas individuals in the more competitively efficient role generally gain the larger share of these resources. When asymmetry in relative competitive efficiency is greater, a group's per capita cooperation (averaged across both roles) is higher, due to increased cooperation from the competitively inferior individuals. For extreme asymmetry in relative competitive efficiency, per capita cooperation is highest in groups with a single competitively superior individual and many competitively inferior individuals, because the latter acquiesce and invest in cooperation rather than within‐group competition. These predictions are consistent with observed features of many societies, such as monogynous Hymenoptera with many workers and caste dimorphism.     

Recommendations for photo‐identification methods used in capture‐recapture models with cetaceans

Capture‐recapture methods are frequently employed to estimate abundance of cetaceans using photographic techniques and a variety of statistical models. However, there are many unresolved issues regarding the selection and manipulation of images that can potentially impose bias on resulting estimates. To examine the potential impact of these issues we circulated a test data set of dorsal fin images from bottlenose dolphins to several independent research groups. Photo‐identification methods were generally similar, but the selection, scoring, and matching of images varied greatly amongst groups. Based on these results we make the following recommendations. Researchers should: (1) determine the degree of marking, or level of distinctiveness, and use images of sufficient quality to recognize animals of that level of distinctiveness; (2) ensure that markings are sufficiently distinct to eliminate the potential for “twins” to occur; (3) stratify data sets by distinctiveness and generate a series of abundance estimates to investigate the influence of including animals of varying degrees of markings; and (4) strive to examine and incorporate variability among analysts into capture‐recapture estimation. In this paper we summarize these potential sources of bias and provide recommendations for best practices for using natural markings in a capture‐recapture framework.     

A computer program to simulate multilocus genotype data with spatially autocorrelated allele frequencies

Many models for inference of population genetic parameters are based on the assumption that the data set at hand consists of groups displaying within-group Hardy-Weinberg equilibrium at individual loci and linkage equilibrium between loci. This assumption is commonly violated by the presence of within-group spatial structure arising from nonrandom mating of individuals due to isolation by distance (IBD). This paper proposes a model and simulation method implemented in a computer program to flexibly simulate data displaying such patterns. The program permits displaying of smooth spatial variations of allele frequencies due to IBD and more abrupt variations due to presence of strong barriers to gene flow. It is useful in assessing performance of various statistical inference methods and in designing spatial sampling schemes. This is shown by a simulation study aimed at assessing the extent to which IBD patterns affect accuracy of cluster inferences performed in models assuming panmixia. The program is also used to study the effects of spatial sampling scheme (e.g. sampling individuals in clumps or uniformly across the spatial domain). The accuracy of such inferences is assessed in terms of number of inferred populations, assignment of individuals to populations and location of borders between populations. The effect of spatial sampling was weak while the effect of IBD may be substantial, leading to the inference of spurious populations, especially when IBD was strong with respect to the size of the sampling domain. The model and program are new and have been embedded in the R package Geneland, for user convenience and compliance with existing data formats.     

Modeling Developmental Class Provides Insights into Individual Contributions to Infant Survival in Callitrichids

Cooperative breeders live in social groups in which individuals in an age–sex class vary in reproductive development due to reproductive dominance by a few individuals in each group. Among callitrichids, adult males have been implicated in driving group reproductive output, but uneven sampling efforts, the underlying effects of group size, and pseudoreplication at the group and species levels are confounding variables in these analyses. We examined the drivers of group reproductive output in callitrichids by 1) conducting a meta-analysis of published studies of callitrichid group composition; 2) assigning developmental class based on reproductive morphology; and 3) using multivariate modeling to test whether the proportion of individuals of each developmental class predicts the presence and the number of surviving offspring among free-ranging Weddell’s saddleback tamarins (Leontocebus weddelli) and emperor tamarins (Saguinus imperator) in Peru. The meta-analysis revealed that the number of adult females and group size, but not the number of adult males, are significantly correlated with group reproductive output. Statistical models of the new dataset revealed that the proportion of primary breeding males, primary breeding females, and group size predicted whether groups had surviving infants, and that only the proportion of primary breeding females and group size predicted the number of surviving infants. Thus, primary breeding males appear to be necessary for groups to raise any infants, but a higher proportion of primary breeding females and a larger group size increase group reproductive output overall.     

A Bayesian Approach to Inferring Rates of Selfing and Locus-Specific Mutation

We present a Bayesian method for characterizing the mating system of populations reproducing through a mixture of self-fertilization and random outcrossing. Our method uses patterns of genetic variation across the genome as a basis for inference about reproduction under pure hermaphroditism, gynodioecy, and a model developed to describe the self-fertilizing killifish Kryptolebias marmoratus. We extend the standard coalescence model to accommodate these mating systems, accounting explicitly for multilocus identity disequilibrium, inbreeding depression, and variation in fertility among mating types. We incorporate the Ewens sampling formula (ESF) under the infinite-alleles model of mutation to obtain a novel expression for the likelihood of mating system parameters. Our Markov chain Monte Carlo (MCMC) algorithm assigns locus-specific mutation rates, drawn from a common mutation rate distribution that is itself estimated from the data using a Dirichlet process prior model. Our sampler is designed to accommodate additional information, including observations pertaining to the sex ratio, the intensity of inbreeding depression, and other aspects of reproduction. It can provide joint posterior distributions for the population-wide proportion of uniparental individuals, locus-specific mutation rates, and the number of generations since the most recent outcrossing event for each sampled individual. Further, estimation of all basic parameters of a given model permits estimation of functions of those parameters, including the proportion of the gene pool contributed by each sex and relative effective numbers.     

Primates and Cameras

Field-based primate studies often make population inferences using count-based indices (e.g., individuals/plot) or distance sampling; the first does not account for the probability of detection and thus can be biased, while the second requires large sample sizes to obtain precise estimates, which is difficult for many primate studies. We discuss photographic sampling and occupancy modeling to correct for imperfect detection when estimating system states and dynamics at the landscape level, specifically in relation to primate ecology. We highlight the flexibility of the occupancy framework and its many applications to studying low-density primate populations or species that are difficult to detect. We discuss relevant sampling and estimation procedures with special attention to data collection via photographic sampling. To provide tangible meaning to terminology and clarify subtleties, we use illustrative examples. Photographic sampling can have many advantages over observer-based sampling, especially when studying rare or elusive species. Combining photographic sampling with an occupancy framework allows inference to larger scales than is common in primate studies, addresses uncertainty due to the observation process, and allows researchers to examine questions of how landscape-level anthropogenic changes affect primate distributions.     

Inferring recent migration rates from individual genotypes

We present a novel and straightforward method for estimating recent migration rates between discrete populations using multilocus genotype data. The approach builds upon a two-step sampling design, where individual genotypes are sampled before and after dispersal. We develop a model that estimates all pairwise backwards migration rates ( m_ij , the probability that an individual sampled in population i is a migrant from population j ) between a set of populations. The method is validated with simulated data and compared with the methods of BayesAss and Structure. First, we use data for an island model and then we consider more realistic data simulations for a metapopulation of the greater white-toothed shrew ( Crocidura russula ). We show that the precision and bias of estimates primarily depend upon the proportion of individuals sampled in each population. Weak sampling designs may particularly affect the quality of the coverage provided by 95% highest posterior density intervals. We further show that it is relatively insensitive to the number of loci sampled and the overall strength of genetic structure. The method can easily be extended and makes fewer assumptions about the underlying demographic and genetic processes than currently available methods. It allows backwards migration rates to be estimated across a wide range of realistic conditions.     

Studies on the effects of bait and sampling intensity on trapping and estimating Wood mice, Apodemus sylvaticus

The effects of baiting a Longworth trap with whole oats and the density of traps on an area, or sampling intensity, on trapping and estimating Wood mice were studied on two neighbouring woodland plots in November 1971. Standard capture-mark-recapture (CMR) methods were used for two weeks followed by five nights of removal trapping.
The presence of bait significantly increased the likelihood of capturing marked and unmarked animals. By increasing the sampling intensity a greater proportion of the population was sampled, although the number of animals captured per trap night decreased. These results have been related to the "effective" number of traps on an area.
Observations on population structure, weather, movement and capturing marked and unmarked animals have been made. CMR population estimates closely resembled the cumulative number of individuals captured in each study and were for the main part lower than the estimates from the removal trapping carried out at the end of the studies.     

Sampling Strategies in Antimicrobial Resistance Monitoring: Evaluating How Precision and Sensitivity Vary with the Number of Animals Sampled per Farm

Because antimicrobial resistance in food-producing animals is a major public health concern, many countries have implemented antimicrobial monitoring systems at a national level. When designing a sampling scheme for antimicrobial resistance monitoring, it is necessary to consider both cost effectiveness and statistical plausibility. In this study, we examined how sampling scheme precision and sensitivity can vary with the number of animals sampled from each farm, while keeping the overall sample size constant to avoid additional sampling costs. Five sampling strategies were investigated. These employed 1, 2, 3, 4 or 6 animal samples per farm, with a total of 12 animals sampled in each strategy. A total of 1,500 Escherichia coli isolates from 300 fattening pigs on 30 farms were tested for resistance against 12 antimicrobials. The performance of each sampling strategy was evaluated by bootstrap resampling from the observational data. In the bootstrapping procedure, farms, animals, and isolates were selected randomly with replacement, and a total of 10,000 replications were conducted. For each antimicrobial, we observed that the standard deviation and 2.5–97.5 percentile interval of resistance prevalence were smallest in the sampling strategy that employed 1 animal per farm. The proportion of bootstrap samples that included at least 1 isolate with resistance was also evaluated as an indicator of the sensitivity of the sampling strategy to previously unidentified antimicrobial resistance. The proportion was greatest with 1 sample per farm and decreased with larger samples per farm. We concluded that when the total number of samples is pre-specified, the most precise and sensitive sampling strategy involves collecting 1 sample per farm.     

Lanchester's attrition models and fights among social animals

Lanchester's models of attrition during warfare have servedas the basis for several predictions about conflicts betweengroups of animals. These models and their extensions describerates of mortality during battles as functions of the numberand fighting abilities of individuals in each group, allowinganalysis of the determinants of group strength and of the cumulativenumbers of casualties. We propose modifications to Lanchester'smodels to improve their applicability to social animals. Inparticular, we suggest that the per-capita mortality rate ofa group is a decreasing function of the fighting abilities ofits members, that the mortality rate is an increasing functionof the number of individuals in both groups, and that therewill often be diminishing returns for increasing numerical advantage.Models incorporating these assumptions predict that the abilityof social animals to win fights depends less on group size andmore on individual prowess than under Lanchester's originalmodels. We discuss how data on casualties can be used to distinguishamong alternative attrition models.     

Sequential hypothesis testing with spatially correlated presence-absence data

A pest management decision to initiate a control treatment depends upon an accurate estimate of mean pest density. Presence-absence sampling plans significantly reduce sampling efforts to make treatment decisions by using the proportion of infested leaves to estimate mean pest density in lieu of counting individual pests. The use of sequential hypothesis testing procedures can significantly reduce the number of samples required to make a treatment decision. Here we construct a mean-proportion relationship for Oligonychus perseae Tuttle, Baker, and Abatiello, a mite pest of avocados, from empirical data, and develop a sequential presence-absence sampling plan using Bartlett's sequential test procedure. Bartlett's test can accommodate pest population models that contain nuisance parameters that are not of primary interest. However, it requires that population measurements be independent, which may not be realistic because of spatial correlation of pest densities across trees within an orchard. We propose to mitigate the effect of spatial correlation in a sequential sampling procedure by using a tree-selection rule (i.e., maximin) that sequentially selects each newly sampled tree to be maximally spaced from all other previously sampled trees. Our proposed presence-absence sampling methodology applies Bartlett's test to a hypothesis test developed using an empirical mean-proportion relationship coupled with a spatial, statistical model of pest populations, with spatial correlation mitigated via the aforementioned tree-selection rule. We demonstrate the effectiveness of our proposed methodology over a range of parameter estimates appropriate for densities of O. perseae that would be observed in avocado orchards in California.     

The establishment and nature of the dominance hierarchy in the domesticated pig

The dominance hierarchy was studied by direct observation within a total of forty-four groups of pigs aged between 8 and 30 weeks. The groups were usually made up of eight animals and included both castrated males and immature females. On the introduction of preveiously unacquainted pigs vigorous fighting occurred, usually between pairs of animals. More than one encounter was often seen to occur simultaneously. This ceased within about 24 hr and the group could be ranked by 48 hr. The top animal in the dominance hierarchy, however, was identifiable within 30 to 60 min. Social rank was not correlated with sex and weight, and it is suggested that rank is a resultant of the interaction of a number of factors. The dominant animals directed most of their aggression to the rank immediately below. The basic structure of the hierarchy results from the summation of the strong, stable relationships which seem to develop between animals immediately adjacent to each other in the social hierarchy.     

Photographic identification of individuals of a free‐ranging,small terrestrial vertebrate

Recognition of individuals within an animal population is central to a range of estimates about population structure and dynamics. However, traditional methods of distinguishing individuals, by some form of physical marking, often rely on capture and handling which may affect aspects of normal behavior. Photographic identification has been used as a less‐invasive alternative, but limitations in both manual and computer‐automated recognition of individuals are particularly problematic for smaller taxa (<500 g). In this study, we explored the use of photographic identification for individuals of a free‐ranging, small terrestrial reptile using (a) independent observers, and (b) automated matching with the Interactive Individual Identification System (I³S Pattern) computer algorithm. We tested the technique on individuals of an Australian skink in the Egernia group, Slater's skink Liopholis slateri, whose natural history and varied scale markings make it a potentially suitable candidate for photo‐identification. From ‘photographic captures’ of skink head profiles, we designed a multi‐choice key based on alternate character states and tested the abilities of observers — with or without experience in wildlife survey — to identify individuals using categorized test photos. We also used the I³S Pattern algorithm to match the same set of test photos against a database of 30 individuals. Experienced observers identified a significantly higher proportion of photos correctly (74%) than those with no experience (63%) while the I³S software correctly matched 67% as the first ranked match and 83% of images in the top five ranks. This study is one of the first to investigate photo identification with a free‐ranging small vertebrate. The method demonstrated here has the potential to be applied to the developing field of camera‐traps for wildlife survey and thus a wide range of survey and monitoring applications.     

Differential expression in SAGE: accounting for normal between-library variation

MOTIVATION: In contrasting levels of gene expression between groups of SAGE libraries, the libraries within each group are often combined and the counts for the tag of interest summed, and inference is made on the basis of these larger 'pseudolibraries'. While this captures the sampling variability inherent in the procedure, it fails to allow for normal variation in levels of the gene between individuals within the same group, and can consequently overstate the significance of the results. The effect is not slight: between-library variation can be hundreds of times the within-library variation. RESULTS: We introduce a beta-binomial sampling model that correctly incorporates both sources of variation. We show how to fit the parameters of this model, and introduce a test statistic for differential expression similar to a two-sample t-test.     

Mixture models for estimating the size of a closed population when capture rates vary among individuals

We develop a parameterization of the beta-binomial mixture that provides sensible inferences about the size of a closed population when probabilities of capture or detection vary among individuals. Three classes of mixture models (beta-binomial, logistic-normal, and latent-class) are fitted to recaptures of snowshoe hares for estimating abundance and to counts of bird species for estimating species richness. In both sets of data, rates of detection appear to vary more among individuals (animals or species) than among sampling occasions or locations. The estimates of population size and species richness are sensitive to model-specific assumptions about the latent distribution of individual rates of detection. We demonstrate using simulation experiments that conventional diagnostics for assessing model adequacy, such as deviance, cannot be relied on for selecting classes of mixture models that produce valid inferences about population size. Prior knowledge about sources of individual heterogeneity in detection rates, if available, should be used to help select among classes of mixture models that are to be used for inference.     

Mark‐recapture abundance estimate of tucuxi dolphins (Sotalia fluviatilis) in a lake system of the Central Amazon

The tucuxi (Sotalia fluviatilis) is a small dolphin endemic to the Amazon River basin. Because the abundance and trends are currently unknown for the species, this study aimed to estimate its abundance in a lake system of the Central Amazon. A total of 10 two‐day sampling periods were carried out from March to June of 2013 throughout a 13.5 km² area in the Mamirauá Reserve. In the 104 encounters with the species, a minimum number of 389 dolphins were sighted and photographed, which allowed the positive identification of 49 individuals. Mark‐recapture models were used to estimate an abundance of 119 individuals (95% CI = 105–150) (corrected for the proportion of identifiable individuals). This is the first estimation of S. fluviatilis abundance using mark‐recapture analyses and, together with the photo‐id catalog made available, provides a useful reference for future studies regarding tucuxi dolphins.