Genetic basis of between-individual and within-individual variance of docility

Funded by Alces Software UCLA Academic Senate Division of Life Sciences National Geographic Society National Science Foundation. Grant Numbers: IDBR-0754247, DEB-1119660, DBI-0242960, DBI-0731346 University of Aberdeen Data deposited at Dryad: doi:10.5061/dryad.11vf0.Peer reviewedPostprin

Harvest-induced disruptive selection increases variance in fitness-related traits

The form of Darwinian selection has important ecological and management implications. Negative effects of harvesting are often ascribed to size truncation (i.e. strictly directional selection against large individuals) and resultant decrease in trait variability, which depresses capacity to buffer environmental change, hinders evolutionary rebound and ultimately impairs population recovery. However, the exact form of harvest-induced selection is generally unknown and the effects of harvest on trait variability remain unexplored. Here we use unique data from the Windermere (UK) long-term ecological experiment to show in a top predator (pike, Esox lucius) that the fishery does not induce size truncation but disruptive (diversifying) selection, and does not decrease but rather increases variability in pike somatic growth rate and size at age. This result is supported by complementary modelling approaches removing the effects of catch selectivity, selection prior to the catch and environmental variation. Therefore, fishing most likely increased genetic variability for somatic growth in pike and presumably favoured an observed rapid evolutionary rebound after fishery relaxation. Inference about the mechanisms through which harvesting negatively affects population numbers and recovery should systematically be based on a measure of the exact form of selection. From a management perspective, disruptive harvesting necessitates combining a preservation of large individuals with moderate exploitation rates, and thus provides a comprehensive tool for sustainable exploitation of natural resources

Monopoly Pricing in a Vertical Market with Demand Uncertainty

We study a vertical market with an upsteam supplier and multiple downstream retailers. Demand uncertainty falls to the supplier who acts first and sets a uniform wholesale price before the retailers observe the realized demand and engage in retail competition. Our focus is on the supplier's optimal pricing decision. We express the price elasticity of expected demand in terms of the mean residual demand (MRD) function of the demand distribution. This allows for a closed form characterization of the points of unitary elasticity that maximize the supplier's profits and the derivation of a mild unimodality condition for the supplier's objective function that generalizes the widely used increasing generalized failure rate (IGFR) condition. A direct implication is that optimal prices between different markets can be ordered if the markets can be stochastically ordered according to their MRD functions or equivalently to their elasticities. Based on this, we apply the theory of stochastic orders to study the response of the supplier's optimal price to various features of the demand distribution. Our findings challenge previously established economic insights about the effects of market size, demand transformations and demand variability on wholesale prices and indicate that the conclusions largely depend on the exact notion that will be employed. We then turn to measure market performance and derive a distribution free and tight bound on the probability of no trade between the supplier and the retailers. If trade takes place, our findings indicate that ovarall performance depends on the interplay between demand uncertainty and level of retail competition

Statistical Modeling of Epistasis and Linkage Decay using Logic Regression

Logic regression has been recognized as a tool that can identify and model non-additive genetic interactions using Boolean logic groups. Logic regression, TASSEL-GLM and SAS-GLM were compared for analytical precision using a previously characterized model system to identify the best genetic model explaining epistatic interaction for vernalization-sensitivity in barley. A genetic model containing two molecular markers identified in vernalization response in barley was selected using logic regression while both TASSEL-GLM and SAS-GLM included spurious associations in their models. The results also suggest the logic regression can be used to identify dominant/recessive relationships between epistatic alleles through its use of conjugate operators

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

Background: Faecal egg counts are a common indicator of nematode infection and since it is a heritable trait, it provides a marker for selective breeding. However, since resistance to disease changes as the adaptive immune system develops, quantifying temporal changes in heritability could help improve selective breeding programs. Faecal egg counts can be extremely skewed and difficult to handle statistically. Therefore, previous heritability analyses have log transformed faecal egg counts to estimate heritability on a latent scale. However, such transformations may not always be appropriate. In addition, analyses of faecal egg counts have typically used univariate rather than multivariate analyses such as random regression that are appropriate when traits are correlated. We present a method for estimating the heritability of untransformed faecal egg counts over the grazing season using random regression. Results: Replicating standard univariate analyses, we showed the dependence of heritability estimates on choice of transformation. Then, using a multitrait model, we exposed temporal correlations, highlighting the need for a random regression approach. Since random regression can sometimes involve the estimation of more parameters than observations or result in computationally intractable problems, we chose to investigate reduced rank random regression. Using standard software (WOMBAT), we discuss the estimation of variance components for log transformed data using both full and reduced rank analyses. Then, we modelled the untransformed data assuming it to be negative binomially distributed and used Metropolis Hastings to fit a generalized reduced rank random regression model with an additive genetic, permanent environmental and maternal effect. These three variance components explained more than 80 % of the total phenotypic variation, whereas the variance components for the log transformed data accounted for considerably less. The heritability, on a link scale, increased from around 0.25 at the beginning of the grazing season to around 0.4 at the end. Conclusions: Random regressions are a useful tool for quantifying sources of variation across time. Our MCMC (Markov chain Monte Carlo) algorithm provides a flexible approach to fitting random regression models to non-normal data. Here we applied the algorithm to negative binomially distributed faecal egg count data, but this method is readily applicable to other types of overdispersed data

Geo-additive models of Childhood Undernutrition in three Sub-Saharan African Countries

We investigate the geographical and socioeconomic determinants of childhood undernutrition in Malawi, Tanzania and Zambia, three neighboring countries in Southern Africa using the 1992 Demographic and Health Surveys. We estimate models of undernutrition jointly for the three countries to explore regional patterns of undernutrition that transcend boundaries, while allowing for country-specific interactions. We use semiparametric models to flexibly model the effects of selected so-cioeconomic covariates and spatial effects. Our spatial analysis is based on a flexible geo-additive model using the district as the geographic unit of anal-ysis, which allows to separate smooth structured spatial effects from random effect. Inference is fully Bayesian and uses recent Markov chain Monte Carlo techniques. While the socioeconomic determinants generally confirm what is known in the literature, we find distinct residual spatial patterns that are not explained by the socioeconomic determinants. In particular, there appears to be a belt run-ning from Southern Tanzania to Northeastern Zambia which exhibits much worse undernutrition, even after controlling for socioeconomic effects. These effects do transcend borders between the countries, but to a varying degree. These findings have important implications for targeting policy as well as the search for left-out variables that might account for these residual spatial patterns