Computational aspects of N-mixture models.

The N-mixture model is widely used to estimate the abundance of a population in the presence of unknown detection probability from only a set of counts subject to spatial and temporal replication (Royle, 2004, Biometrics 60, 105-115). We explain and exploit the equivalence of N-mixture and multivariate Poisson and negative-binomial models, which provides powerful new approaches for fitting these models. We show that particularly when detection probability and the number of sampling occasions are small, infinite estimates of abundance can arise. We propose a sample covariance as a diagnostic for this event, and demonstrate its good performance in the Poisson case. Infinite estimates may be missed in practice, due to numerical optimization procedures terminating at arbitrarily large values. It is shown that the use of a bound, K, for an infinite summation in the N-mixture likelihood can result in underestimation of abundance, so that default values of K in computer packages should be avoided. Instead we propose a simple automatic way to choose K. The methods are illustrated by analysis of data on Hermann's tortoise Testudo hermanni.

Computational methods for yeast prion curing curves.

If the chemical guanidine hydrochloride is added to a dividing culture of yeast cells in which some of the protein Sup35p is in its prion form, the proportion of cells that carry replicating units of the prion, termed propagons, decreases gradually over time. Stochastic models to describe this process of 'curing' have been developed in earlier work. The present paper investigates the use of numerical methods of Laplace transform inversion to calculate curing curves and contrasts this with an alternative, more direct, approach that involves numerical integration. Transform inversion is found to provide a much more efficient computational approach that allows different models to be investigated with minimal programming effort. The method is used to investigate the robustness of the curing curve to changes in the assumed distribution of cell generation times. Matlab code is available for carrying out the calculations.

The power of monitoring: optimizing survey designs to detect occupancy changes in a rare amphibian population.

Biodiversity conservation requires reliable species assessments and rigorously designed surveys. However, determining the survey effort required to reliably detect population change can be challenging for rare, cryptic and elusive species. We used a tropical bromeliad-dwelling frog as a model system to explore a cost-effective sampling design that optimizes the chances of detecting a population decline. Relatively few sampling visits were needed to estimate occupancy and detectability with good precision, and to detect a 30% change in occupancy with 80% power. Detectability was influenced by observer expertise, which therefore also had an effect on the sampling design - less experienced observers require more sampling visits to detect the species. Even when the sampling design provides precise parameter estimates, only moderate to large changes in occupancy will be detected with reliable power. Detecting a population change of 15% or less requires a large number of sites to be surveyed, which might be unachievable for range-restricted species occurring at relatively few sites. Unless there is high initial occupancy, rare and cryptic species will be particularly challenging when it comes to detecting small population changes. This may be a particular issue for long-term monitoring of amphibians which often display low detectability and wide natural fluctuations.

Efficient occupancy model-fitting for extensive citizen-science data.

Appropriate large-scale citizen-science data present important new opportunities for biodiversity modelling, due in part to the wide spatial coverage of information. Recently proposed occupancy modelling approaches naturally incorporate random effects in order to account for annual variation in the composition of sites surveyed. In turn this leads to Bayesian analysis and model fitting, which are typically extremely time consuming. Motivated by presence-only records of occurrence from the UK Butterflies for the New Millennium data base, we present an alternative approach, in which site variation is described in a standard way through logistic regression on relevant environmental covariates. This allows efficient occupancy model-fitting using classical inference, which is easily achieved using standard computers. This is especially important when models need to be fitted each year, typically for many different species, as with British butterflies for example. Using both real and simulated data we demonstrate that the two approaches, with and without random effects, can result in similar conclusions regarding trends. There are many advantages to classical model-fitting, including the ability to compare a range of alternative models, identify appropriate covariates and assess model fit, using standard tools of maximum likelihood. In addition, modelling in terms of covariates provides opportunities for understanding the ecological processes that are in operation. We show that there is even greater potential; the classical approach allows us to construct regional indices simply, which indicate how changes in occupancy typically vary over a species' range. In addition we are also able to construct dynamic occupancy maps, which provide a novel, modern tool for examining temporal changes in species distribution. These new developments may be applied to a wide range of taxa, and are valuable at a time of climate change. They also have the potential to motivate citizen scientists.

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.