Estimating abundance for a savanna elephant population using mark–resight methods: a case study for the Tembe Elephant Park, South Africa

Elephants living in dense woodlands are difficult to count. Many elephant populations in Africa occur in such conditions. Estimates of these populations based on total counts, aerial counts and dung counts often lack information on precision and accuracy. We use standard mark–recapture field methods to obtain estimates of population size with associated confidence limits. We apply this approach to a closed elephant population in the Tembe Elephant Park (300 km²), South Africa. A registration count completed in 4 months gives a known population size. We evaluate mark–recapture models against the known population size. Individual identification profiles obtained for elephants during the registration count and mark–recapture events indicate that at least 167 elephants live in the park. We consider this value as an estimate of the minimum number alive. We include 189 sightings of bulls and 37 sightings of breeding herds in the mark–recapture modelling. Of the models we test (Petersen, Schnabel, Schumacher, Jolly–Seber, Bowden's, Poisson and negative binomial), Bowden's gives an estimate closest to the registration count. Assumptions of the model are not violated. For all models except one (negative binomial), our estimates improve with increased sampling intensity. Confidence intervals do not improve with increased effort except for the Schnabel model. Mark–recapture methods should be considered as reliable estimators of population size for elephants occurring in dense woodlands and forests when other methods cannot be relied on.     

Simultaneous estimation of mortality and dispersal rates of an artificially released population

Mark-recapture methods cannot estimate both mortality and dispersal rates of a wild population simultaneously. However, when an artificially cultured population is released into an area, the initial population size and the initial population distribution are usually known. If artificially cultured individuals are released with marks or distinguished from wild individuals or if no wild individual exists in the study area, we can estimate both the mortality and dispersal rates of the artificial population. The numbers of dispersed and dead individuals are estimated from the dispersal rate from the diffusion model and the total decreasing rate estimated from a mark-recapture data. We can estimate both the time-dependent and time-independent dispersal rates from the data. We choose the best fit model that has the smallest value of Akaike's Information Criteria. We also consider ‘concentric circles approximation” of spatial distribution, in which the cumulative and frequency distributions are analytically obtained.     

The Minimum Capture Proportion for Reliable Estimation in Capture–Recapture Models

Summary .   We derive estimates of the minimum capture proportion required to obtain a reliable estimate of the population size for several continuous and discrete-time capture–recapture models. The models considered are     , and     in the notation of Otis et al. , (1978, Wildlife Monograph 62 , 1–135). Numerical results with simulation studies are given, and two real examples for the model     are also considered. Potential applications of these results are suggested.     

Population size and trends of the Galápagos Penguin Spheniscus mendiculus

We applied a capture–mark–resight (CMR) method to estimate the population size of the Galápagos Penguin Spheniscus mendiculus . In 1999, we estimated 1198 individuals, with lower and upper 95% confidence limits of 1054 and 1403 individuals, respectively, and estimated that approximately 57% of the total population was counted in an annual census. Applying this estimate to the 2003 census, we estimated that the population size for the whole archipelago was 1351 individuals. We also applied the correction factor derived from the 1999 CMR data to other censuses carried out between 1970 and 2003 and estimated a maximum population of about 4000 individuals in 1971 when the highest numbers of Penguins were counted. Although the Penguin population size has fluctuated in the last 33 years, the overall trend shows larger populations in 1970–80 followed by relatively smaller populations and a slow recovery rate in 1983–2003. The data set also shows two major population declines (in 1983 and 1998), which are coincident with El Niño episodes.     

Estimating the population size of an endangered shorebird, the Madagascar plover, using a habitat suitability model

The Madagascar plover Charadrius thoracicus is a shorebird endemic to western Madagascar, currently classified as globally vulnerable. It is restricted to specialized wetland habitats that are increasingly threatened by humans. To inform future conservation measures for this poorly known species, we develop a predictive habitat suitability map and use this map to estimate the size of the Madagascar plover population. We integrate spatially referenced presence-only observations of Madagascar plovers with Landsat data, elevation data and measures of distance to settlements and the coast to produce a habitat suitability model using ecological niche factor analysis. Validation of this model using a receiver operating characteristic plot suggests that it is at least 84% accurate in predicting suitable sites. We then use our estimate of total area of suitable habitat above a critical suitability threshold and data on Madagascar plover density in suitable sites to estimate the total population size to derive a total population estimate of 3100±396 standard error individuals. Finally, we explore the conservation applications of our model.     

Population growth of human Y chromosomes: a study of Y chromosome microsatellites

We use variation at a set of eight human Y chromosome microsatellite loci to investigate the demographic history of the Y chromosome. Instead of assuming a population of constant size, as in most of the previous work on the Y chromosome, we consider a model which permits a period of recent population growth. We show that for most of the populations in our sample this model fits the data far better than a model with no growth. We estimate the demographic parameters of this model for each population and also the time to the most recent common ancestor. Since there is some uncertainty about the details of the microsatellite mutation process, we consider several plausible mutation schemes and estimate the variance in mutation size simultaneously with the demographic parameters of interest. Our finding of a recent common ancestor (probably in the last 120,000 years), coupled with a strong signal of demographic expansion in all populations, suggests either a recent human expansion from a small ancestral population, or natural selection acting on the Y chromosome.     

Population assessment without individual identification using camera-traps: A comparison of four methods

The use of camera traps to estimate population size when animals are not individually recognizable is gaining traction in the ecological literature, because of its applicability in population conservation and management.We estimated population size of synthetic animals with four camera trap sampling-based statistical models that do not rely on individual recognition. Using a realistic model of animal movement to generate synthetic data, we compared the random encounter model, the random encounter and staying time model, the association model and the time-to-event-model and we investigated the impact of violation of assumptions on the population size estimates.While under ideal conditions these models provide reliable population estimates, when synthetic animal movements were characterised by differences in speed (due to diverse behaviours such as locomotion, grazing and resting) none of the model provided both unbiased and precise density estimates. The random encounter model and the time-to-event-model provided precise results but tended to overestimate population size, while the random encounter and staying time model was less precise and tended to underestimate population size. Lastly, the association model was unable to provide precise results. We found that each tested model was very sensitive to the method used to estimate the range of the field-of-view of camera traps. Density estimates from both random encounter model and time-to-event-model were also very sensitive to biases in the estimate of animals’ speed. We provide guidelines on how to use these statistical models to get population size estimates that could be useful to wildlife managers and practitioners.     

Postprocessing of genealogical trees

We consider inference for demographic models and parameters based upon postprocessing the output of an MCMC method that generates samples of genealogical trees (from the posterior distribution for a specific prior distribution of the genealogy). This approach has the advantage of taking account of the uncertainty in the inference for the tree when making inferences about the demographic model and can be computationally efficient in terms of reanalyzing data under a wide variety of models. We consider a (simulation-consistent) estimate of the likelihood for variable population size models, which uses importance sampling, and propose two new approximate likelihoods, one for migration models and one for continuous spatial models.     

内蒙古农牧交错带长爪沙鼠种群存活的季节格局及其动态机制

了解动物种群存活特征以及相关环境因子对其变化的独立或整合作用过程,有助于阐明动物种群动态的生态学机制。长爪沙鼠（Meriones unguiculatus）是分布于我国北方典型草原、荒漠草原及其毗邻的农牧交错带的优势鼠种之一。2000年10月至2004年10月通过标志重捕法研究了栖息于内蒙古农牧交错区草地生境的种群动态。本文通过MARK软件包中的CJS和MS模型分析了长爪沙鼠半自然围栏种群表观存活率（Φ,简称存活率）的性别（g）差异和年龄（as）特征表现及其季节变化格局,并对种群存活变化的密度和气候效应加以分析,旨在检验长爪沙鼠种群存活显示季节变化特征,并受密度制约和气候条件反馈调节的假设。结果发现,长爪沙鼠种群存活率初始最优模型Φ(t)p(g*t)中重捕时序（t）效应显著（ANODEV,F _27,47 =11.05,P <0.001）,月季效应最优模型Φ(month)p(g*t)也显示存活率 季节变化明显（ANODEV,F _5,69 =31.69,P <0.001）,总体呈现从春季到冬季经历下降再升高的“V”字型动态模式。在无环境因子限制条件下,雌鼠（0.788±0.013）和雄鼠（0.781±0.013）存活率差异不明显;存活率年龄差异表现明显的季节特征（ANODEV,F _5,246 = 67.85,P < 0.001）,繁殖消耗在一定时期影响成年个体的存活。长爪沙鼠种群存活的季节格局反映其生活史对策中适应高纬度气候和食物等资源季节波动的重要特征。进一步统计发现种群存活率受密度制约、与降水负相关,其中密度制约效应具有一定的时滞,降水作用是即时的,上述效应的作用强度在雌、雄鼠的存活反应上有所差异。这些结果暗示密度制约整合水热条件介导最适栖息地环境变化,引发雌、雄鼠存活率差异性反应,进而影响其它种群参数变化,调节种群增长。这可能是北半球高纬度地区小哺乳动物种群调节的一个重要机制。     

Effective population size estimation on Sardina pilchardus in the Bay of Biscay using a temporal genetic approach

Over three consecutive years, we surveyed the temporal variability in genetic structure of sardine populations in the Bay of Biscay and effective population size. Based on individual age, the genetic structure of year classes of the fishes was also surveyed, showing that populations of sardines have weak but significant genetic differences between sampling years and between year classes. We used two different methods to assess effective population size. The methods resulted in different values but a similar range, indicating a low effective population for Sardina pilchardus . Effective population size decreased over the 3 years, probably resulting from an abundance of fish in the Bay. Based on these results, we conclude that temporal variability in the genetic structure of the sardine population and effective size are likely related to environmental conditions in the Bay. Finally, we propose to use effective population size to estimate biomass of sardines in the Bay.  © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 90 , 591–602.     

A model of physiologically structured population dynamics with a nonlinear individual growth rate

In this article we consider a size structured population model with a nonlinear growth rate depending on the individual's size and on the total population. Our purpose is to take into account the competition for a resource (as it can be light or nutrients in a forest) in the growth of the individuals and study the influence of this nonlinear growth in the population dynamics. We study the existence and uniqueness of solutions for the model equations, and also prove the existence of a (compact) global attractor for the trajectories of the dynamical system defined by the solutions of the model. Finally, we obtain sufficient conditions for the convergence to a stationary size distribution when the total population tends to a constant value, and consider some simple examples that allow us to know something about their global dynamics.This work was partially supported by DGICYT PB90-0730-C02-01 and PB91-0497.     

Parametric Models for Estimating the Number of Classes

We consider parametric distributions intended to model heterogeneity in population size estimation, especially parametric stochastic abundance models for species richness estimation. We briefly review (conditional) maximum likelihood estimation of the number of species, and summarize the results of fitting 7 candidate models to frequency‐count data, from a database of >40000 such instances, mostly arising from microbial ecology. We consider error estimation, goodness‐of‐fit assessment, data subsetting, and other practical matters. We find that, although the array of candidate models can be improved, finite mixtures of a small number of components (point masses or simple diffuse distributions) represent a promising direction. Finally we consider the connections between parametric models for abundance and incidence data, again noting the usefulness of finite mixture models. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Playback point counts and N-mixture models suggest higher than expected abundance of the critically endangered blond titi monkey in northeastern Brazil

Effective management of threatened species requires accurate population size estimation and monitoring. However, reliable population size estimates are lacking for many endangered species. The critically endangered blond titi monkey (Callicebus barbarabrownae) is an endemic primate of the Caatinga biome in Northeastern Brazil. A previous assessment based on presence-only data estimated a minimum population size of 260 mature individuals in 2,636 km², and studies based on visual records suggested very low local relative abundance. However, this cryptic species is known to be difficult to visually detect. We played back recordings of C. barbarabrownae loud calls to count the number of responding groups in 34 sampling sites during 9 consecutive days in a 221-km² study area. Repeated group counts at sites were used in N-mixture models, which account for imperfect detection, to estimate the number of groups in relation to dry forest area and distance to villages. We estimated a total of 91 groups in the study area. Considering the mean number of adults per group as three, we estimated a population of 273 adult individuals, resulting in a density of 2.3 individuals/km² in the dry forest habitat. Detection probability was four times higher for surveys conducted between sunrise to midmorning than between midmorning to sunset. We also found that C. barbarabrownae abundance increases with increasing dry forest area and increasing distance to the nearest village, indicating the need to promote dry forest restoration in the Caatinga. As our results suggest a larger population of C. barbarabrownae than had been previously estimated for its entire distribution, our results suggest a need for similar assessments in other areas to reliably estimate the total population size. This study demonstrates how playback surveys coupled with N-mixture models can be used to estimate population sizes of acoustically-responsive primates, and thus contribute to more effective conservation management.     

Evaluating the Adequacy of Gravity Models as a Description of Human Mobility for Epidemic Modelling

Gravity models have a long history of use in describing and forecasting the movements of people as well as goods and services, making them a natural basis for disease transmission rates over distance. In agent-based micro-simulations, gravity models can be directly used to represent movement of individuals and hence disease. In this paper, we consider a range of gravity models as fits to movement data from the UK and the US. We examine the ability of synthetic networks generated from fitted models to match those from the data in terms of epidemic behaviour; in particular, times to first infection. For both datasets, best fits are obtained with a two-piece ‘matched’ power law distance distribution. Epidemics on synthetic UK networks match well those on data networks across all but the smallest nodes for a range of aggregation levels. We derive an expression for time to infection between nodes in terms of epidemiological and network parameters which illuminates the influence of network clustering in spread across networks and suggests an approximate relationship between the log-likelihood deviance of model fit and the match times to infection between synthetic and data networks. On synthetic US networks, the match in epidemic behaviour is initially poor and sensitive to the initially infected node. Analysis of times to infection indicates a failure of models to capture infrequent long-range contact between large nodes. An assortative model based on node population size captures this heterogeneity, considerably improving the epidemiological match between synthetic and data networks.     

Population dynamics of Microtus pennsylvanicus in corridor-linked patches

Corridors have become a key issue in the discussion of conservation planning; however, few empirical data exist on the use of corridors and their effects on population dynamics. The objective of this replicated, population level, capture-recapture experiment on meadow voles was to estimate and compare population characteristics of voles between (1) corridor-linked fragments, (2) isolated or non-linked fragments, and (3) unfragmented areas. We conducted two field experiments involving 22 600 captures of 5700 individuals. In the first, the maintained corridor study, corridors were maintained at the time of fragmentation, and in the second, the constructed corridor study, we constructed corridors between patches that had been fragmented for some period of time. We applied multistate capture-recapture models with the robust design to estimate adult movement and survival rates, population size, temporal variation in population size, recruitment, and juvenile survival rates. Movement rates increased to a greater extent on constructed corridor-linked grids than on the unfragmented or non-linked fragmented grids between the pre- and post-treatment periods. We found significant differences in local survival on the treated (corridor-linked) grids compared to survival on the fragmented and unfragmented grids between the pre- and post-treatment periods. We found no clear pattern of treatment effects on population size or recruitment in either study. However, in both studies, we found that unfragmented grids were more stable than the fragmented grids based on lower temporal variability in population size. To our knowledge, this is the first experimental study demonstrating that corridors constructed between existing fragmented populations can indeed cause increases in movement and associated changes in demography, supporting the use of constructed corridors for this purpose in conservation biology.     

Augmenting superpopulation capture-recapture models with population assignment data

Summary Ecologists applying capture–recapture models to animal populations sometimes have access to additional information about individuals' populations of origin (e.g., information about genetics, stable isotopes, etc.). Tests that assign an individual's genotype to its most likely source population are increasingly used. Here we show how to augment a superpopulation capture–recapture model with such information. We consider a single superpopulation model without age structure, and split each entry probability into separate components due to births in situ and immigration. We show that it is possible to estimate these two probabilities separately. We first consider the case of perfect information about population of origin, where we can distinguish individuals born in situ from immigrants with certainty. Then we consider the more realistic case of imperfect information, where we use genetic or other information to assign probabilities to each individual's origin as in situ or outside the population. We use a resampling approach to impute the true population of origin from imperfect assignment information. The integration of data on population of origin with capture–recapture data allows us to determine the contributions of immigration and in situ reproduction to the growth of the population, an issue of importance to ecologists. We illustrate our new models with capture–recapture and genetic assignment data from a population of banner‐tailed kangaroo rats Dipodomys spectabilis in Arizona.     

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.     

The equilibrium assumption in estimating the parameters of metapopulation models

1.  The construction of a predictive metapopulation model includes three steps: the choice of factors affecting metapopulation dynamics, the choice of model structure, and finally parameter estimation and model testing.
2.  Unless the assumption is made that the metapopulation is at stochastic quasi-equilibrium and unless the method of parameter estimation of model parameters uses that assumption, estimates from a limited amount of data will usually predict a trend in metapopulation size.
3.  This implicit estimation of a trend occurs because extinction-colonization stochasticity, possibly amplified by regional stochasticity, leads to unequal numbers of observed extinction and colonization events during a short study period.
4.  Metapopulation models, such as those based on the logistic regression model, that rely on observed population turnover events in parameter estimation are sensitive to the implicit estimation of a trend.
5.  A new parameter estimation method, based on Monte Carlo inference for statistically implicit models, allows an explicit decision about whether metapopulation quasi-stability is assumed or not.
6. Our confidence in metapopulation model parameter estimates that have been produced from only a few years of data is decreased by the need to know before parameter estimation whether the metapopulation is in quasi-stable state or not.
7. The choice of whether metapopulation stability is assumed or not in parameter estimation should be done consciously. Typical data sets cover only a few years and rarely allow a statistical test of a possible trend. While making the decision about stability one should consider any information about the landscape history and species and metapopulation characteristics.     

A size-structured model of bacterial growth and reproduction

We consider a size-structured bacterial population model in which the rate of cell growth is both size- and time-dependent and the average per capita reproduction rate is specified as a model parameter. It is shown that the model admits classical solutions. The population-level and distribution-level behaviours of these solutions are then determined in terms of the model parameters. The distribution-level behaviour is found to be different from that found in similar models of bacterial population dynamics. Rather than convergence to a stable size distribution, we find that size distributions repeat in cycles. This phenomenon is observed in similar models only under special assumptions on the functional form of the size-dependent growth rate factor. Our main results are illustrated with examples, and we also provide an introductory study of the bacterial growth in a chemostat within the framework of our model.     

Consequences of the founder effect in the genetic structure of introduced island coral reef fish populations

Between 1955 and 1961, the Division of Fish and Game of the State of Hawaii (USA) undertook an introduction program which brought 11 species of families Serranidae and Lutjanidae (Pisces) from French Polynesia to the coral reefs off Oahu and Big Island in Hawaii. Only three— Cephalopholis argus, Lutjanus fulvus and Lutjanus kasmira —for which we have records of locations and number offish released, are known to have become established. Comparison of allozyme distribution of C. argus and L. kasmira between individuals collected in Hawaiian and Polynesian populations provided a unique opportunity to estimate the impact of genetic drift and selection processes caused by a founder event. We used temporal variance of allelic frequencies to estimate and validate effective population size within marine fish populations. Despite the fact that only 571 C. argus and 2435 L. kasmira were released, we did not observe major changes in polymorphism and heterozygosity. Using different models to estimate effective population size from temporal variance in allelic frequencies and the number of generations, we estimate that the effective population size is about 1–5% of the total population size. Such reduced effective population size explains why most of the species introduced in Hawaii (8/11) failed to become established. Our results have implications for conservation biology because they emphasize that in spite of the fact that only a few individuals bequeathed their characteristics to subsequent generations, no significant change in genetic diversity was observed; success of introduced species is therefore limited by the number of fish released.