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.

Kinetic models of guanidine hydrochloride-induced curing of the yeast [PSI+] prion.

A population of [PSI(+)] Saccharomyces cerevisiae cells can be cured of the [PSI(+)] prion by the addition of guanidine hydrochloride (GdnHCl). In this paper we extend existing nucleated polymerisation simulation models to investigate the mechanisms that might underlie curing. Our results are consistent with the belief that prions are dispersed through the cells at division following GdnHCl addition. A key feature of the simulation model is that the probability that a polymer is transmitted from mother to daughter during cell division is dependent upon the length of the polymer. The model is able to reproduce the essential features of data from several different experimental protocols involving addition and removal of GdnHCl.

Determining the parametric structure of models.

In this paper we develop a comprehensive approach to determining the parametric structure of models. This involves considering whether a model is parameter redundant or not and investigating model identifiability. The approach adopted makes use of exhaustive summaries, quantities that uniquely define the model. We review and generalise previous work on evaluating the symbolic rank of an appropriate derivative matrix to detect parameter redundancy, and then develop further tools for use within this framework, based on a matrix decomposition. Complex models, where the symbolic rank is difficult to calculate, may be simplified structurally using reparameterisation and by finding a reduced-form exhaustive summary. The approach of the paper is illustrated using examples from ecology, compartment modelling and Bayes networks. This work is topical as models in the biosciences and elsewhere are becoming increasingly complex.

Modeling survival at multi-population scales using mark-recapture data.

The demography of vertebrate populations is governed in part by processes operating at large spatial scales that have synchronizing effects on demographic parameters over large geographic areas, and in part, by local processes that generate fluctuations that are independent across populations. We describe a statistical model for the analysis of individual monitoring data at the multi-population scale that allows us to (1) split up temporal variation in survival into two components that account for these two types of processes and (2) evaluate the role of environmental factors in generating these two components. We derive from this model an index of synchrony among populations in the pattern of temporal variation in survival, and we evaluate the extent to which environmental factors contribute to synchronize or desynchronize survival variation among populations. When applied to individual monitoring data from four colonies of the Atlantic Puffin (Fratercula arctica), 67% of between-year variance in adult survival was accounted for by a global spatial-scale component, indicating substantial synchrony among colonies. Local sea surface temperature (SST) accounted for 40% of the global spatial-scale component but also for an equally large fraction of the local-scale component. SST thus acted at the same time as both a synchronizing and a desynchronizing agent. Between-year variation in adult survival not explained by the effect of local SST was as synchronized as total between-year variation, suggesting that other unknown environmental factors acted as synchronizing agents. Our approach, which focuses on demographic mechanisms at the multi-population scale, ideally should be combined with investigations of population size time series in order to characterize thoroughly the processes that underlie patterns of multi-population dynamics and, ultimately, range dynamics.

Approximations for expected generation number.

A deterministic formula is commonly used to approximate the expected generation number of a population of growing cells. However, this can give misleading results because it does not allow for natural variation in the times that individual cells take to reproduce. Here we present more accurate approximations for both symmetric and asymmetric cell division. Based on the first two moments of the generation time distribution, these approximations are also robust. We illustrate the improved approximations using data that arise from monitoring individual yeast cells under a microscope and also demonstrate how the approximations can be used when such detailed data are not available.

New approximations to the Malthusian parameter.

Approximations to the Malthusian parameter of an age-dependent branching process are obtained in terms of the moments of the lifetime distribution, by exploiting a link with renewal theory. In several examples, the new approximations are more accurate than those currently in use, even when based on only the first two moments. The new approximations are extended to include a form of asymmetric cell division that occurs in some species of yeast. When used for inference, the new approximations are shown to have high efficiency.

Semiparametric regression in capture-recapture modeling.

Capture-recapture models were developed to estimate survival using data arising from marking and monitoring wild animals over time. Variation in survival may be explained by incorporating relevant covariates. We propose nonparametric and semiparametric regression methods for estimating survival in capture-recapture models. A fully Bayesian approach using Markov chain Monte Carlo simulations was employed to estimate the model parameters. The work is illustrated by a study of Snow petrels, in which survival probabilities are expressed as nonlinear functions of a climate covariate, using data from a 40-year study on marked individuals, nesting at Petrels Island, Terre Adélie.

Factors influencing soay sheep survival: a Bayesian analysis.

This article presents a Bayesian analysis of mark-recapture-recovery data on Soay sheep. A reversible jump Markov chain Monte Carlo technique is used to determine age classes of common survival, and to model the survival probabilities in those classes using logistic regression. This involves environmental and individual covariates, as well as random effects. Auxiliary variables are used to impute missing covariates measured on individual sheep. The Bayesian approach suggests different models from those previously obtained using classical statistical methods. Following model averaging, features that were not previously detected, and which are of ecological importance, are identified.

Estimating the number of prions in yeast cells.

Certain yeast cells contain proteins that behave like the mammalian prion PrP and are called yeast prions. The yeast prion protein Sup35p can exist in one of two stable forms, giving rise to phenotypes [PSI(+)] and [psi(-)]. If the chemical guanidine hydrochloride (GdnHCl) is added to a culture of growing [PSI(+)] cells, the proportion of [PSI(+)] cells decreases over time. This process is called curing and is due to a failure to propagate the prion form of Sup35p. We describe how curing can be modelled, and improve upon previous models for the underlying processes of cell division and prion segregation; the new model allows for asymmetric cell division and unequal prion segregation. We conclude by outlining plans for future experimentation and modelling.

Models for yeast prions.

The cytoplasmic heritable determinant [PSI+] of the yeast Saccharomyces cerevisiae exhibits prion-like properties. The properties of yeast prions are studied in the hope that this will enhance the understanding of mammalian prions, which cause mad-cow, Creutzfeldt-Jakob, and related neurodegenerative diseases. When host cells divide, the yeast prions distribute themselves without loss over the daughter cells. Experimental data provide information on how the proportion of cells with prions decreases over time when priori replication is inhibited. One feature of scientific interest is the unknown mean number, n0, of prions assumed to be present in the cells at the start of the experiment. We develop several stochastic models and by fitting them to the data, we obtain substantially larger estimates of n0 compared with a previous analysis. An interesting feature of a model with constant cell generation times is that the predicted proportion of cells with prions varies over time as a sequence of linked hyperbolic curves. Avenues for future research are outlined, which relax simplifying assumptions made in the models. We make several recommendations for the design of future experiments.

The analysis of ring-recovery data using random effects.

We show how random terms, describing both yearly variation and overdispersion, can easily be incorporated into models for mark-recovery data, through the use of Bayesian methods. For recovery data on lapwings, we show that the incorporation of the random terms greatly improves the goodness of fit. Omitting the random terms can lead to overestimation of the significance of weather on survival, and overoptimistic prediction intervals in simulations of future population behavior. Random effects models provide a natural way of modeling overdispersion-which is more satisfactory than the standard classical approach of scaling up all standard errors by a uniform inflation factor. We compare models by means of Bayesian p-values and the deviance information criterion (DIC).

Integrating mark-recapture-recovery and census data to estimate animal abundance and demographic parameters.

In studies of wild animals, one frequently encounters both census and mark-recapture-recovery data. We show how a state-space model for census data in combination with the usual multinomial-based models for ring-recovery data provide estimates of productivity not available from either type of data alone. The approach is illustrated on two British bird species. For the lapwing, we calibrate how its recent decline could be due to a decrease in productivity. For the heron, there is no evidence for a decline in productivity, and the combined analysis increases significantly the strength of logistic regressions of survival on winter severity.