Fast likelihood-based inference for latent count models using the saddlepoint approximation.

Latent count models constitute an important modeling class in which a latent vector of counts, z , is summarized or corrupted for reporting, yielding observed data y=Tz where T is a known but non-invertible matrix. The observed vector y generally follows an unknown multivariate distribution with a complicated dependence structure. Latent count models arise in diverse fields, such as estimation of population size from capture-recapture studies; inference on multi-way contingency tables summarized by marginal totals; or analysis of route flows in networks based on traffic counts at a subset of nodes. Currently, inference under these models relies primarily on stochastic algorithms for sampling the latent vector z , typically in a Bayesian data-augmentation framework. These schemes involve long computation times and can be difficult to implement. Here, we present a novel maximum-likelihood approach using likelihoods constructed by the saddlepoint approximation. We show how the saddlepoint likelihood may be maximized efficiently, yielding fast inference even for large problems. For the case where z has a multinomial distribution, we validate the approximation by applying it to a specific model for which an exact likelihood is available. We implement the method for several models of interest, and evaluate its performance empirically and by comparison with other estimation approaches. The saddlepoint method consistently gives fast and accurate inference, even when y is dominated by small counts.

Genetic relatedness reveals total population size of white sharks in eastern Australia and New Zealand.

Conservation concerns exist for many sharks but robust estimates of abundance are often lacking. Improving population status is a performance measure for species under conservation or recovery plans, yet the lack of data permitting estimation of population size means the efficacy of management actions can be difficult to assess, and achieving the goal of removing species from conservation listing challenging. For potentially dangerous species, like the white shark, balancing conservation and public safety demands is politically and socially complex, often leading to vigorous debate about their population status. This increases the need for robust information to inform policy decisions. We developed a novel method for estimating the total abundance of white sharks in eastern Australia and New Zealand using the genetic-relatedness of juveniles and applying a close-kin mark-recapture framework and demographic model. Estimated numbers of adults are small (ca. 280-650), as is total population size (ca. 2,500-6,750). However, estimates of survival probability are high for adults (over 90%), and fairly high for juveniles (around 73%). This represents the first direct estimate of total white shark abundance and survival calculated from data across both the spatial and temporal life-history of the animal and provides a pathway to estimate population trend.

Microsatellite DNA markers: evaluating their potential for estimating the proportion of hatchery-reared offspring in a stock enhancement programme.

We describe a statistical method for estimating the effectiveness of a stock enhancement programme using nuclear DNA loci. It is based on knowing the population allele frequencies and the genotypes of the hatchery parents (mother only, or mother and father), and on determining the probability that a wild-born animal will by chance have a genotype consistent with hatchery origin. We show how to estimate the proportion of released animals in the wild population, and its standard error. The method is applied to a data set of eight microsatellite loci in brown tiger prawns (Penaeus esculentus), prior to the start of a possible enhancement programme. We conclude that, for this particular data set, the effectiveness of such an enhancement programme could be quantified accurately if both maternal and paternal genotypes are known, but not if maternal genotypes only are known. Full paternal genotyping would require offspring genotyping and thus would be expensive, but a partly typed paternal genotype from a mass homogenate of offspring would be almost as effective and much cheaper. The experiment would become feasible based on maternal genotypes alone, if a further three typical microsatellite loci could be found to add to the existing panel of eight. The methods detailed should be of interest to any enhancement project that relies on nuclear DNA markers to provide tags.