A Bayesian generalized random regression model for estimating heritability using overdispersed count data

A statistical framework for calculating prospective sample sizes and classifying efficacy results for faecal egg count reduction tests in ruminants, horses and swine

The faecal egg count reduction test (FECRT) is the primary diagnostic tool used for detecting anthelmintic resistance at the farm level. It is therefore extremely important that the experimental design of a FECRT and the susceptibility classification of the result use standardised and statistically rigorous methods. Several different approaches for improving the analysis of FECRT data have been proposed, but little work has been published on how to address the issue of prospective sample size calculations. Here, we provide a complete and detailed overview of the quantitative issues relevant to a FECRT starting from basic statistical principles. We then present a new approach for determining sample size requirements for the FECRT that is built on a solid statistical framework, and provide a rigorous anthelminthic drug efficacy classification system for use with FECRT in livestock. Our approach uses two separate statistical tests, a one-sided inferiority test for resistance and a one-sided non-inferiority test for susceptibility, and determines a classification of resistant, susceptible or inconclusive based on the combined result. Since this approach is based on two independent one-sided tests, we recommend that a 90 % CI be used in place of the historically used 95 % CI. This maintains the desired Type I error rate of 5 %, and simultaneously reduces the required sample size. We demonstrate the use of this framework to provide sample size calculations that are rooted in the well-understood concept of statistical power. Tailoring to specific host/parasite systems is possible using typical values for expected pre-treatment and post-treatment variability in egg counts as well as within-animal correlation in egg counts. We provide estimates for these parameters for ruminants, horses and swine based on a re-examination of datasets that were available to us from a combination of published data and other sources. An illustrative example is provided to demonstrate the use of the framework, and parameter estimates are presented to estimate the required sample size for a hypothetical FECRT using ivermectin in cattle. The sample size calculation method and classification framework presented here underpin the sample size recommendations provided in the upcoming FECRT WAAVP guidelines for detection of anthelmintic resistance in ruminants, horses, and swine, and have also been made freely available as open-source software via our website (https://www.fecrt.com).

Estimation of Genetic Variance in Fitness, and Inference of Adaptation, When Fitness Follows a Log-Normal Distribution

Additive genetic variance in relative fitness (σA2(w)) is arguably the most important evolutionary parameter in a population because, by Fisher’s fundamental theorem of natural selection (FTNS; Fisher RA. 1930. The genetical theory of natural selection. 1st ed. Oxford: Clarendon Press), it represents the rate of adaptive evolution. However, to date, there are few estimates of σA2(w) in natural populations. Moreover, most of the available estimates rely on Gaussian assumptions inappropriate for fitness data, with unclear consequences. “Generalized linear animal models” (GLAMs) tend to be more appropriate for fitness data, but they estimate parameters on a transformed (“latent”) scale that is not directly interpretable for inferences on the data scale. Here we exploit the latest theoretical developments to clarify how best to estimate quantitative genetic parameters for fitness. Specifically, we use computer simulations to confirm a recently developed analog of the FTNS in the case when expected fitness follows a log-normal distribution. In this situation, the additive genetic variance in absolute fitness on the latent log-scale (σA2(l)) equals (σA2(w)) on the data scale, which is the rate of adaptation within a generation. However, due to inheritance distortion, the change in mean relative fitness between generations exceeds σA2(l) and equals (exp⁡(σA2(l))−1). We illustrate why the heritability of fitness is generally low and is not a good measure of the rate of adaptation. Finally, we explore how well the relevant parameters can be estimated by animal models, comparing Gaussian models with Poisson GLAMs. Our results illustrate 1) the correspondence between quantitative genetics and population dynamics encapsulated in the FTNS and its log-normal-analog and 2) the appropriate interpretation of GLAM parameter estimates.

Differentiating Wheat Genotypes by Bayesian Hierarchical Nonlinear Mixed Modeling of Wheat Root Density

Ensuring future food security for a growing population while climate change and urban sprawl put pressure on agricultural land will require sustainable intensification of current farming practices. For the crop breeder this means producing higher crop yields with less resources due to greater environmental stresses. While easy gains in crop yield have been made mostly "above ground," little progress has been made "below ground"; and yet it is these root system traits that can improve productivity and resistance to drought stress. Wheat pre-breeders use soil coring and core-break counts to phenotype root architecture traits, with data collected on rooting density for hundreds of genotypes in small increments of depth. The measured densities are both large datasets and highly variable even within the same genotype, hence, any rigorous, comprehensive statistical analysis of such complex field data would be technically challenging. Traditionally, most attributes of the field data are therefore discarded in favor of simple numerical summary descriptors which retain much of the high variability exhibited by the raw data. This poses practical challenges: although plant scientists have established that root traits do drive resource capture in crops, traits that are more randomly (rather than genetically) determined are difficult to breed for. In this paper we develop a hierarchical nonlinear mixed modeling approach that utilizes the complete field data for wheat genotypes to fit, under the Bayesian paradigm, an "idealized" relative intensity function for the root distribution over depth. Our approach was used to determine heritability: how much of the variation between field samples was purely random vs. being mechanistically driven by the plant genetics? Based on the genotypic intensity functions, the overall heritability estimate was 0.62 (95% Bayesian confidence interval was 0.52 to 0.71). Despite root count profiles that were statistically very noisy, our approach led to denoised profiles which exhibited rigorously discernible phenotypic traits. Profile-specific traits could be representative of a genotype, and thus, used as a quantitative tool to associate phenotypic traits with specific genotypes. This would allow breeders to select for whole root system distributions appropriate for sustainable intensification, and inform policy for mitigating crop yield risk and food insecurity.

Territorial aggression does not feed back on testosterone in a multiple-brooded songbird species with breeding and non-breeding season territoriality, the European stonechat

Testosterone mediates reproductive behaviours in male vertebrates. For example, breeding season territoriality depends on testosterone in many species of birds and in some, territorial interactions feed back on testosterone concentrations. However, the degree to which territorial behaviour and testosterone are associated differs even between species with seemingly similar life histories, especially between species that also defend territories outside the breeding season. Here, we investigate the link between territorial behaviour and testosterone in European stonechats. Previous studies found that territorial aggression in stonechats depends on testosterone in a breeding, but not in a non-breeding context. We investigated whether stonechats show a rise in testosterone during simulated territorial intrusions (STI) during the breeding season. Post-capture testosterone concentrations of males caught after an STI were not higher than those of males caught in a control situation regardless of breeding stage. However, most of the males would have been able to mount a testosterone response because the same individuals that did not increase testosterone during the STI showed a substantial increase in testosterone after injections of gonadotropin-releasing hormone (GnRH). GnRH-induced and post-capture testosterone concentrations were positively correlated and both decreased with successive breeding stages. Further, territory owners with a short latency to attack the decoy expressed higher post-capture testosterone concentrations than males with a longer latency to attack the decoy. Thus, there is no evidence for behavioural feedback on testosterone concentrations during male-male interactions in stonechats. In combination with previous studies our data suggest that testosterone functions as an on/off switch of high intensity territorial aggression during the breeding season in stonechats. The among-species variation in the androgen control of territorial behaviour may be only partly a result of environmental differences. Instead, potential differences in how territoriality evolved in different species may have influenced whether and how a reproductive hormone such as testosterone was co-opted into the mechanistic control of territorial behaviour.