Variance estimation for integrated population models

Abstract State-space models are widely used in ecology. However, it is well known that in practice it can be difficult to estimate both the process and observation variances that occur in such models. We consider this issue for integrated population models,which incorporate state-space models for population dynamics. To some extent, the mechanism of integrated population models protects against this problem, but it can still arise, and two illustrations are provided, in each of which the observation variance is estimated as zero. In the context of an extended case study involving data on British Grey herons, we consider alternative approaches for dealing with the problem when it occurs. In particular, we consider penalised likelihood, a method based on fitting splines and a method of pseudo-replication, which is undertaken via a simple bootstrap procedure. For the case study of the paper, it is shown that when it occurs, an estimate of zero observation variance is unimportant for inference relating to the model parameters of primary interest. This unexpected finding is supported by a simulation study

Exact inference for integrated population modelling

Integrated population modelling is widely used in statistical ecology. It allows data from population time series and independent surveys to be analysed simultaneously. In classical analysis the time‐series likelihood component can be conveniently approximated using Kalman filter methodology. However, the natural way to model systems which have a discrete state space is to use hidden Markov models (HMMs). The proposed method avoids the Kalman filter approximations and Monte Carlo simulations. Subject to possible numerical sensitivity analysis, it is exact, flexible, and allows the use of standard techniques of classical inference. We apply the approach to data on Little owls, where the model is shown to require a one‐dimensional state space, and Northern lapwings, with a two‐dimensional state space. In the former example the method identifies a parameter redundancy which changes the perception of the data needed to estimate immigration in integrated population modelling. The latter example may be analysed using either first‐ or second‐order HMMs, describing numbers of one‐year olds and adults or adults only, respectively. The use of first‐order chains is found to be more efficient, mainly due to the smaller number of one‐year olds than adults in this application. For the lapwing modelling it is necessary to group the states in order to reduce the large dimension of the state space. Results check with Bayesian and Kalman filter analyses, and avenues for future research are identified

Bayesian analysis of Jolly-Seber type models; Incorporating heterogeneity in arrival and departure

We propose the use of finite mixtures of continuous distributions in modelling the process by which new individuals, that arrive in groups, become part of a wildlife population. We demonstrate this approach using a data set of migrating semipalmated sandpipers (Calidris pussila) for which we extend existing stopover models to allow for individuals to have different behaviour in terms of their stopover duration at the site. We demonstrate the use of reversible jump MCMC methods to derive posterior distributions for the model parameters and the models, simultaneously. The algorithm moves between models with different numbers of arrival groups as well as between models with different numbers of behavioural groups. The approach is shown to provide new ecological insights about the stopover behaviour of semipalmated sandpipers but is generally applicable to any population in which animals arrive in groups and potentially exhibit heterogeneity in terms of one or more other processes

Estimating survival and transition rates from aggregate sightings of animals

We compare and contrast two methods for fitting probability models to data which arise when animals are marked in batches, without individual identification, and live in several different sites or states. The methods are suitable for populations in which animals are marked at birth and then resighted over several sites/states, for small animals going through several growth stages (insects, amphibiae, etc.), as well as for the follow-up of animals released after laboratory colour-marking, for example. The methods we consider include a multi-state model for resightings of batch-marked animals, allowing us to estimate survival, transitions, and sighting probabilities. One method is based on the EM algorithm, and the second uses the Kalman filter for computing likelihoods. The methods are illustrated on real data from a cohort of Great Cormorants Phalacrocorax carbo, and their performance is evaluated using simulation. We recommend identifying the batches, for instance in the case of sites, by using a different colour on each site at the time of marking, and in general the use of the Kalman filter rather than the EM-based approach

An Integrated Population Model From Constant Effort Bird-Ringing Data

Data from annual bird-ringing programs, in which catch effort is standardized, are routinely used to index abundance, productivity, and adult survival. Efficient models have been developed for each. Such monitoring schemes, based on ringing across a number of sites, are perhaps unique in providing this combination of demographic information and make the data particularly amenable to an integrated approach to population modeling. We develop a Bayesian approach and a deterministic population model uniting abundance, productivity, and survival. The method is applied to sedge warbler Acrocephalus schoenobaenus data from the British Trust for Ornithology’s Constant Effort Sites scheme. The possibility of “transient” birds needs to be incorporated within this analysis. We demonstrate how current methodology can efficiently be extended to use additional data from multiple within year recaptures when controlling for transience. Supplemental materials for this article are available online

A threshold model for heron productivity

We demonstrate the potential of conditionally Gaussian state-space models in integrated population modeling, when certain model parameters may be functions of previous observations. The approach is applied to a heron census, and the data are best described by a model with three population-size thresholds which determine the population productivity. The model provides an explanation of how the population rebounds rapidly after major falls in size, which are characteristic of the data. By contrast, a simple logarithmic regression of productivity on population size was not significant. The results are of ecological interest, and suggest hypotheses for further investigation

A Bayesian approach to fitting Gibbs processes with temporal random effects

This work is partially supported by Research Councils UKWe consider spatial point pattern data that have been observed repeatedly over a period of time in an inhomogeneous environment. Each spatial point pattern can be regarded as a “snapshot” of the underlying point process at a series of times. Thus, the number of points and corresponding locations of points differ for each snapshot. Each snapshot can be analyzed independently, but in many cases there may be little information in the data relating to model parameters, particularly parameters relating to the interaction between points. Thus, we develop an integrated approach, simultaneously analyzing all snapshots within a single robust and consistent analysis. We assume that sufficient time has passed between observation dates so that the spatial point patterns can be regarded as independent replicates, given spatial covariates. We develop a joint mixed effects Gibbs point process model for the replicates of spatial point patterns by considering environmental covariates in the analysis as fixed effects, to model the heterogeneous environment, with a random effects (or hierarchical) component to account for the different observation days for the intensity function. We demonstrate how the model can be fitted within a Bayesian framework using an auxiliary variable approach to deal with the issue of the random effects component. We apply the methods to a data set of musk oxen herds and demonstrate the increased precision of the parameter estimates when considering all available data within a single integrated analysis.PostprintPeer reviewe