Sensitivity of Bayes estimators to hyper-parameters with an application to maximum yield from fisheries

Priors are seldom unequivocal and an important component of Bayesian modeling is assessment of the sensitivity of the posterior to the specified prior distribution. This is especially true in fisheries science where the Bayesian approach has been promoted as a rigorous method for including existing information from previous surveys and from related stocks or species. These informative priors may be highly contested by various interest groups. Here, formulae for the first and second derivatives of Bayes estimators with respect to hyper-parameters of the joint prior density are given. The formula for the second derivative provides a correction to a previously published result. The formulae are shown to reduce to very convenient and easily implemented forms when the hyper-parameters are for exponential family marginal priors. For model parameters with such priors it is shown that the ratio of posterior variance to prior variance can be interpreted as the sensitivity of the posterior mean to the prior mean. This methodology is applied to a nonlinear state-space model for the biomass of South Atlantic albacore tuna and sensitivity of the maximum sustainable yield to the prior specification is examined.     

Unified maximum likelihood estimates for closed capture-recapture models using mixtures

Agresti (1994, Biometrics 50, 494-500) and Norris and Pollock (1996a, Biometrics 52, 639-649) suggested using methods of finite mixtures to partition the animals in a closed capture-recapture experiment into two or more groups with relatively homogeneous capture probabilities. This enabled them to fit the models Mh, Mbh (Norris and Pollock), and Mth (Agresti) of Otis et al. (1978, Wildlife Monographs 62, 1-135). In this article, finite mixture partitions of animals and/or samples are used to give a unified linear-logistic framework for fitting all eight models of Otis et al. by maximum likelihood. Likelihood ratio tests are available for model comparisons. For many data sets, a simple dichotomy of animals is enough to substantially correct for heterogeneity-induced bias in the estimation of population size, although there is the option of fitting more than two groups if the data warrant it.     

Stage‐specific probabilistic phenology model of Cydia pomonella (Lepidoptera: Tortricidae) using laboratory maximum likelihood parameter estimates

In this study, a probabilistic degree‐day phenology model has been developed for the codling moth, Cydia pomonella, and calibrated using data from laboratory growth studies. The model is further used to predict the succession and overlapping of certain biological events of C. pomonella in probabilistic‐physiological time scale in northern Greece fruit orchards. The model satisfactorily predicts the stage‐specific pest population dynamics, including egg laying and hatching, the occurrence of larvae and pupae stages and the emergence of adults. According to the model projections for the adult flights, there is a very high probability, p = 0.999, of observing adults of the first flight generation until 333 degree‐days (DD), but a very low probability of finding adults of the second flight generation. Moreover, at 575 DD, the probability of finding an individual to lay eggs is p = 0.15. However, there is nearly the same probability of egg hatch, p = 0.36, and larval completion p = 0.313, while at the same time, the probability of pupal completion is very low, p = 0.001. The above model predictions were validated using field data for the adult stage emergence as well as for the percentage of larval damage providing satisfactory results considering that larval emergence prediction was close to actual fruit damage observed in field. This information is very important considering that IPM programs rely on the use of biorational compounds, such as IGRs and bio‐toxins which are stage selective and often have a shorter residual activity than the preceding broad‐spectrum insecticides.     

Description of an approach based on maximum likelihood to adjust an excess hazard model with a random effect

Objective: To adjust an excess hazard regression model with a random effect associated with a geographical level, the Département in France, and compare its parameter estimates with those obtained using a “fixed-effect” excess hazard regression model. Methods: An excess hazard regression model with a piecewise constant baseline hazard was used and a normal distribution was assumed for the random effect. Likelihood maximization was performed using a numerical integration technique, the Quadrature of Gauss–Hermite. Results were obtained with colon-rectum and thyroid cancer data from the French network of cancer registries. Result: The results were in agreement with what was theoretically expected. We showed a greater heterogeneity of the excess hazard in thyroid cancers than in colon-rectum cancers. The hazard ratios for the covariates as estimated with the mixed-effect model were close to those obtained with the fixed-effect model. However, unlike the fixed-effect model, the mixed-effect model allowed the analysis of data with a large number of clusters. The shrinkage estimator associated with Département is an optimal measure of Département-specific excess risk of death and the variance of the random effect gave information on the within-cluster correlation. Conclusion: An excess hazard regression model with random effect can be used for estimating variation in the risk of death due to cancer between many clusters of small sizes.     

Managed relocation as an adaptation strategy for mitigating climate change threats to the persistence of an endangered lizard

The distributional ranges of many species are contracting with habitat conversion and climate change. For vertebrates, informed strategies for translocations are an essential option for decisions about their conservation management. The pygmy bluetongue lizard, Tiliqua adelaidensis, is an endangered reptile with a highly restricted distribution, known from only a small number of natural grassland fragments in South Australia. Land‐use changes over the last century have converted perennial native grasslands into croplands, pastures and urban areas, causing substantial contraction of the species' range due to loss of essential habitat. Indeed, the species was thought to be extinct until its rediscovery in 1992. We develop coupled‐models that link habitat suitability with stochastic demographic processes to estimate extinction risk and to explore the efficacy of potential climate adaptation options. These coupled‐models offer improvements over simple bioclimatic envelope models for estimating the impacts of climate change on persistence probability. Applying this coupled‐model approach to T. adelaidensis, we show that: (i) climate‐driven changes will adversely impact the expected minimum abundance of populations and could cause extinction without management intervention, (ii) adding artificial burrows might enhance local population density, however, without targeted translocations this measure has a limited effect on extinction risk, (iii) managed relocations are critical for safeguarding lizard population persistence, as a sole or joint action and (iv) where to source and where to relocate animals in a program of translocations depends on the velocity, extent and nonlinearities in rates of climate‐induced habitat change. These results underscore the need to consider managed relocations as part of any multifaceted plan to compensate the effects of habitat loss or shifting environmental conditions on species with low dispersal capacity. More broadly, we provide the first step towards a more comprehensive framework for integrating extinction risk, managed relocations and climate change information into range‐wide conservation management.     

Using functional trait diversity to infer community assembly mechanisms: an exclosure experiment as an example

AimsThe Qinghai-Tibetan Plateau has a mean altitude exceeding 4000 m and covers about 2.5 million km2. More than 60% of this area is alpine grassland. Exclosures have been widely used in this region to study the sustainable use of grassland resources. We used patterns of functional trait diversity to infer the effects of exclosures on community assembly in alpine meadows.     

A statistical approach to study the dynamics of micropropagation rates, using banana (Musa spp.) as an example

The use of micropropagation to obtain large numbers of high-quality planting material has increased in recent years. Behavior in culture, mainly in terms of multiplication rate, varies among genotypes, directly affecting plant production planning. To study multiplication rates over time, suckers of banana, Musa spp., cv. Maçã, were collected in the field and the shoot apex introduced in vitro for micropropagation. The number of new shoots produced in each of the six multiplication cycles was recorded and the data analyzed statistically. Variability in total shoot production and differences in multiplication rates was considerable among families, which consisted of the initial explant and its progeny. Moreover, the adjusted Poisson regression models for the number of shoots showed that the multiplication rate in this cultivar tends to decrease with time: after the seventh subculture, new shoots may form at a very low rate. Interpretation of the first and second derivatives of the regression model allowed determination of the maximum speed of multiplication and the time at which the multiplication rate begins to decline.     

Resampling-based empirical Bayes multiple testing procedures for controlling generalized tail probability and expected value error rates: focus on the false discovery rate and simulation study

This article proposes resampling-based empirical Bayes multiple testing procedures for controlling a broad class of Type I error rates, defined as generalized tail probability (gTP) error rates, gTP (q,g) = Pr(g (V(n),S(n)) > q), and generalized expected value (gEV) error rates, gEV (g) = E [g (V(n),S(n))], for arbitrary functions g (V(n),S(n)) of the numbers of false positives V(n) and true positives S(n). Of particular interest are error rates based on the proportion g (V(n),S(n)) = V(n) /(V(n) + S(n)) of Type I errors among the rejected hypotheses, such as the false discovery rate (FDR), FDR = E [V(n) /(V(n) + S(n))]. The proposed procedures offer several advantages over existing methods. They provide Type I error control for general data generating distributions, with arbitrary dependence structures among variables. Gains in power are achieved by deriving rejection regions based on guessed sets of true null hypotheses and null test statistics randomly sampled from joint distributions that account for the dependence structure of the data. The Type I error and power properties of an FDR-controlling version of the resampling-based empirical Bayes approach are investigated and compared to those of widely-used FDR-controlling linear step-up procedures in a simulation study. The Type I error and power trade-off achieved by the empirical Bayes procedures under a variety of testing scenarios allows this approach to be competitive with or outperform the Storey and Tibshirani (2003) linear step-up procedure, as an alternative to the classical Benjamini and Hochberg (1995) procedure.