Parameter redundancy in Jolly-Seber tag loss models.

Capture-recapture experiments are conducted to estimate population parameters such as population size, survival rates, and capture rates. Typically, individuals are captured and given unique tags, then recaptured over several time periods with the assumption that these tags are not lost. However, for some populations, tag loss cannot be assumed negligible. The Jolly-Seber tag loss model is used when the no-tag-loss assumption is invalid. Further, the model has been extended to incorporate group heterogeneity, which allows parameters to vary by group membership. Many mark-recapture models become overparameterized resulting in the inability to independently estimate parameters. This is known as parameter redundancy.We investigate parameter redundancy using symbolic methods. Because of the complex structure of some tag loss models, the methods cannot always be applied directly. Instead, we develop a simple combination of parameters that can be used to investigate parameter redundancy in tag loss models.The incorporation of tag loss and group heterogeneity into Jolly-Seber models does not result in further parameter redundancies. Furthermore, using hybrid methods we studied the parameter redundancy caused by data through case studies and generated tag histories with different parameter values.Smaller capture and survival rates are found to cause parameter redundancy in these models. These problems resolve when applied to large populations.

Estimating age-dependent survival from age-aggregated ringing data-extending the use of historical records.

Bird ring-recovery data have been widely used to estimate demographic parameters such as survival probabilities since the mid-20th century. However, while the total number of birds ringed each year is usually known, historical information on age at ringing is often not available. A standard ring-recovery model, for which information on age at ringing is required, cannot be used when historical data are incomplete. We develop a new model to estimate age-dependent survival probabilities from such historical data when age at ringing is not recorded; we call this the historical data model. This new model provides an extension to the model of Robinson, 2010, Ibis, 152, 651-795 by estimating the proportion of the ringed birds marked as juveniles as an additional parameter. We conduct a simulation study to examine the performance of the historical data model and compare it with other models including the standard and conditional ring-recovery models. Simulation studies show that the approach of Robinson, 2010, Ibis, 152, 651-795 can cause bias in parameter estimates. In contrast, the historical data model yields similar parameter estimates to the standard model. Parameter redundancy results show that the newly developed historical data model is comparable to the standard ring-recovery model, in terms of which parameters can be estimated, and has fewer identifiability issues than the conditional model. We illustrate the new proposed model using Blackbird and Sandwich Tern data. The new historical data model allows us to make full use of historical data and estimate the same parameters as the standard model with incomplete data, and in doing so, detect potential changes in demographic parameters further back in time.

Removal models accounting for temporary emigration.

Removal of protected species from sites scheduled for development is often a legal requirement in order to minimize the loss of biodiversity. The assumption of closure in the classic removal model will be violated if individuals become temporarily undetectable, a phenomenon commonly exhibited by reptiles and amphibians. Temporary emigration can be modeled using a multievent framework with a partial hidden process, where the underlying state process describes the movement pattern of animals between the survey area and an area outside of the study. We present a multievent removal model within a robust design framework which allows for individuals becoming temporarily unavailable for detection. We demonstrate how to investigate parameter redundancy in the model. Results suggest the use of the robust design and certain forms of constraints overcome issues of parameter redundancy. We show which combinations of parameters are estimable when the robust design reduces to a single secondary capture occasion within each primary sampling period. Additionally, we explore the benefit of the robust design on the precision of parameters using simulation. We demonstrate that the use of the robust design is highly recommended when sampling removal data. We apply our model to removal data of common lizards, Zootoca vivipara, and for this application precision of parameter estimates is further improved using an integrated model.

Parameter redundancy in discrete state-space and integrated models.

Discrete state-space models are used in ecology to describe the dynamics of wild animal populations, with parameters, such as the probability of survival, being of ecological interest. For a particular parametrization of a model it is not always clear which parameters can be estimated. This inability to estimate all parameters is known as parameter redundancy or a model is described as nonidentifiable. In this paper we develop methods that can be used to detect parameter redundancy in discrete state-space models. An exhaustive summary is a combination of parameters that fully specify a model. To use general methods for detecting parameter redundancy a suitable exhaustive summary is required. This paper proposes two methods for the derivation of an exhaustive summary for discrete state-space models using discrete analogues of methods for continuous state-space models. We also demonstrate that combining multiple data sets, through the use of an integrated population model, may result in a model in which all parameters are estimable, even though models fitted to the separate data sets may be parameter redundant.

Does your species have memory? Analyzing capture-recapture data with memory models.

We examine memory models for multisite capture-recapture data. This is an important topic, as animals may exhibit behavior that is more complex than simple first-order Markov movement between sites, when it is necessary to devise and fit appropriate models to data. We consider the Arnason-Schwarz model for multisite capture-recapture data, which incorporates just first-order Markov movement, and also two alternative models that allow for memory, the Brownie model and the Pradel model. We use simulation to compare two alternative tests which may be undertaken to determine whether models for multisite capture-recapture data need to incorporate memory. Increasing the complexity of models runs the risk of introducing parameters that cannot be estimated, irrespective of how much data are collected, a feature which is known as parameter redundancy. Rouan et al. (JABES, 2009, pp 338-355) suggest a constraint that may be applied to overcome parameter redundancy when it is present in multisite memory models. For this case, we apply symbolic methods to derive a simpler constraint, which allows more parameters to be estimated, and give general results not limited to a particular configuration. We also consider the effect sparse data can have on parameter redundancy and recommend minimum sample sizes. Memory models for multisite capture-recapture data can be highly complex and difficult to fit to data. We emphasize the importance of a structured approach to modeling such data, by considering a priori which parameters can be estimated, which constraints are needed in order for estimation to take place, and how much data need to be collected. We also give guidance on the amount of data needed to use two alternative families of tests for whether models for multisite capture-recapture data need to incorporate memory.

Parameter redundancy in mark-recovery models.

We provide a definitive guide to parameter redundancy in mark-recovery models, indicating, for a wide range of models, in which all the parameters are estimable, and in which models they are not. For these parameter-redundant models, we identify the parameter combinations that can be estimated. Simple, general results are obtained, which hold irrespective of the duration of the studies. We also examine the effect real data have on whether or not models are parameter redundant, and show that results can be robust even with very sparse data. Covariates, as well as time- or age-varying trends, can be added to models to overcome redundancy problems. We show how to determine, without further calculation, whether or not parameter-redundant models are still parameter redundant after the addition of covariates or trends.

The number and transmission of [PSI] prion seeds (Propagons) in the yeast Saccharomyces cerevisiae.

BACKGROUND: Yeast (Saccharomyces cerevisiae) prions are efficiently propagated and the on-going generation and transmission of prion seeds (propagons) to daughter cells during cell division ensures a high degree of mitotic stability. The reversible inhibition of the molecular chaperone Hsp104p by guanidine hydrochloride (GdnHCl) results in cell division-dependent elimination of yeast prions due to a block in propagon generation and the subsequent dilution out of propagons by cell division. PRINCIPAL FINDINGS: Analysing the kinetics of the GdnHCl-induced elimination of the yeast [PSI+] prion has allowed us to develop novel statistical models that aid our understanding of prion propagation in yeast cells. Here we describe the application of a new stochastic model that allows us to estimate more accurately the mean number of propagons in a [PSI+] cell. To achieve this accuracy we also experimentally determine key cell reproduction parameters and show that the presence of the [PSI+] prion has no impact on these key processes. Additionally, we experimentally determine the proportion of propagons transmitted to a daughter cell and show this reflects the relative cell volume of mother and daughter cells at cell division. CONCLUSIONS: While propagon generation is an ATP-driven process, the partition of propagons to daughter cells occurs by passive transfer via the distribution of cytoplasm. Furthermore, our new estimates of n(0), the number of propagons per cell (500-1000), are some five times higher than our previous estimates and this has important implications for our understanding of the inheritance of the [PSI+] and the spontaneous formation of prion-free cells.

Cell division is essential for elimination of the yeast [PSI+] prion by guanidine hydrochloride.

Guanidine hydrochloride (Gdn.HCl) blocks the propagation of yeast prions by inhibiting Hsp104, a molecular chaperone that is absolutely required for yeast prion propagation. We had previously proposed that ongoing cell division is required for Gdn.HCl-induced loss of the [PSI+] prion. Subsequently, Wu et al.[Wu Y, Greene LE, Masison DC, Eisenberg E (2005) Proc Natl Acad Sci USA 102:12789-12794] claimed to show that Gdn.HCl can eliminate the [PSI+] prion from alpha-factor-arrested cells leading them to propose that in Gdn.HCl-treated cells the prion aggregates are degraded by an Hsp104-independent mechanism. Here we demonstrate that the results of Wu et al. can be explained by an unusually high rate of alpha-factor-induced cell death in the [PSI+] strain (780-1D) used in their studies. What appeared to be no growth in their experiments was actually no increase in total cell number in a dividing culture through a counterbalancing level of cell death. Using media-exchange experiments, we provide further support for our original proposal that elimination of the [PSI+] prion by Gdn.HCl requires ongoing cell division and that prions are not destroyed during or after the evident curing phase.