The effect of linkage on sample size determination for multiple trait selection

Sufficient sample sizes are needed in breeding programs to be confident, with a specified probability , of obtaining a specified number of plants of a desired genotype in segregating populations. We develop a method of determining the minimum sample size needed to produce, with specified probability , at least m individuals of a desired genotype. This method takes into consideration factors affecting differential selection of gametes, segregation at a single locus, and linkage among the loci of interest. We first consider the effects in the gametophyte (haploid level) of fitness and linkage on the frequencies of alleles at two linked loci, then at three or more linked loci. The probability of obtaining at least m successes, or occurrences of the desired allele, among n gametes is given by a formula based on the binomial distribution. This probability is affected by fitness and linkage through their impact on the probability that a single randomly chosen gamete is of the desired type. Using an extension of this approach, we examine the effects of the altered allelic frequencies on the likelihood of obtaining the desired genotype from a randomly chosen pair of gametes in the sporophyte (diploid level). A table and a figure show the sample size required to produce, with probability 0.95, m individuals of the desired g enotype or phenotype, as a function of m and the probability that a randomly selected individual is of the desired type.BU-1031-MC in the Technical Report Series of the Biometrics Unit, Cornell University, Ithaca, New York 14853     

A comparison of methods for adaptive treatment selection

Traditionally drug development is generally divided into three phases which have different aims and objectives. Recently so-called adaptive seamless designs that allow combination of the objectives of different development phases into a single trial have gained much interest. Adaptive trials combining treatment selection typical for Phase II and confirmation of efficacy as in Phase III are referred to as adaptive seamless Phase II/III designs and are considered in this paper. We compared four methods for adaptive treatment selection, namely the classical Dunnett test, an adaptive version of the Dunnett test based on the conditional error approach, the combination test approach, and an approach within the classical group-sequential framework. The latter two approaches have only recently been published. In a simulation study we found that no one method dominates the others in terms of power apart from the adaptive Dunnett test that dominates the classical Dunnett by construction. Furthermore, scenarios under which one approach outperforms others are described.     

Capwire: a R package for estimating population census size from non‐invasive genetic sampling

Non‐invasive genetic sampling is an increasingly popular approach for investigating the demographics of natural populations. This has also become a useful tool for managers and conservation biologists, especially for those species for which traditional mark–recapture studies are not practical. However, the consequence of collecting DNA indirectly is that an individual may be sampled multiple times per sampling session. This requires alternative statistical approaches to those used in traditional mark–recapture studies. Here we present the R package capwire , an implementation of the population size estimators of Miller et al. (Molecular Ecology 2005; 14 : 1991), which were designed to deal specifically with this type of sampling. The aim of this project is to enable users across platforms to easily manipulate their data and interact with existing R packages. We have also provided functions to simulate data under a variety of scenarios to allow for rigorous testing of the robustness of the method and to facilitate further development of this approach.     

Long-term paternity skew and the opportunity for selection in a mammal with reversed sexual size dimorphism

Most mammalian groups are characterized by male-biased sexual size dimorphism, in which size-dependent male-male competition and reproductive skew are tightly linked. By comparison, little is known about the opportunity for sexual selection in mammalian systems without male-biased dimorphism, where the traits under sexual selection might be less obvious. We examined 10 years of parentage data in a colony of greater horseshoe bats (Rhinolophus ferrumequinum) to determine the magnitude of male reproductive skew and the opportunity for sexual selection in a mammal in which females are the larger sex. Annual paternity success was weakly skewed but consistent patterns led to strong longitudinal paternity skew among breeders. Just three males accounted for a third of all paternity assignments, representing at least a fifth of all colony offspring born in a decade. Paternity success was in part determined by age but was not influenced by dispersal status. Our results show that paternity skew and the opportunity for sexual selection in a species with reversed sexual size dimorphism can approach levels reported for classical examples of species with polygyny and male-biased dimorphism, even where the traits under sexual selection are not known.     

Importance of a pilot study for non-invasive genetic sampling: genotyping errors and population size estimation in red deer

Population size information is critical for managing endangered or harvested populations. Population size can now be estimated from non-invasive genetic sampling. However, pitfalls remain such as genotyping errors (allele dropout and false alleles at microsatellite loci). To evaluate the feasibility of non-invasive sampling (e.g., for population size estimation), a pilot study is required. Here, we present a pilot study consisting of (i) a genetic step to test loci amplification and to estimate allele frequencies and genotyping error rates when using faecal DNA, and (ii) a simulation step to quantify and minimise the effects of errors on estimates of population size. The pilot study was conducted on a population of red deer in a fenced natural area of 5440 ha, in France. Twelve microsatellite loci were tested for amplification and genotyping errors. The genotyping error rates for microsatellite loci were 0–0.83 (mean=0.2) for allele dropout rates and 0–0.14 (mean=0.02) for false allele rates, comparable to rates encountered in other non-invasive studies. Simulation results suggest we must conduct 6 PCR amplifications per sample (per locus) to achieve approximately 97% correct genotypes. The 3% error rate appears to have little influence on the accuracy and precision of population size estimation. This paper illustrates the importance of conducting a pilot study (including genotyping and simulations) when using non-invasive sampling to study threatened or managed populations.     

Sexual selection for size and symmetry in a diversifying secondary sexual character in Drosophila bipectinata Duda (Diptera: Drosophilidae)

Results of intrapopulation studies of sexual selection and genetic variation and covariation underlying elements of the sex comb of Drosophila bipectinata are presented. The magnitude of the sex comb, a sexual ornament, varies significantly among Australasian populations, motivating research into the evolutionary mechanisms responsible for its incipient diversification. The comb is composed of stout black teeth on the front legs of males arranged in three distinct segments: C1, C2, and C3. Significant sexual selection in field populations in northeastern Queensland, Australia, was detected for increasing C2 and body size, and simultaneously for reducing comb positional fluctuating asymmetry. In contrast, sexual selection was not detected for other comb segments, nor for sternopleural bristle number or symmetry. Selection intensities for C2 and comb positional fluctuating asymmetry were similar in magnitude, and although they were opposite in sign, values across twelve sampling dates, or selection episodes, were uncorrelated. Heritability estimates for C2 were high and significant across years, whereas heritability estimates for comb positional asymmetry were small, and generally nonsignificant. The major sex comb segments (C1 and C2) were significantly and positively correlated genetically, indicating the potential for correlated evolution of these components of the comb under sexual selection. The original finding of a significant positive genetic correlation between the magnitude of this sex trait and its positional asymmetry indicates that the counteracting and independent selection pressures detected could contribute to the maintenance of genetic variation sustaining sexual selection. The study documents the simultaneous presence of sexual selection in nature and of heritable genetic variation underlying expression of the sex comb, fundamental conditions necessary for its adaptive diversification. Drosophila bipectinata may be a valuable model for studies of adaptive diversification and incipient speciation by sexual selection.     

Genome‐wide evidence for divergent selection between populations of a major agricultural pathogen

The genetic and environmental homogeneity in agricultural ecosystems is thought to impose strong and uniform selection pressures. However, the impact of this selection on plant pathogen genomes remains largely unknown. We aimed to identify the proportion of the genome and the specific gene functions under positive selection in populations of the fungal wheat pathogen Zymoseptoria tritici. First, we performed genome scans in four field populations that were sampled from different continents and on distinct wheat cultivars to test which genomic regions are under recent selection. Based on extended haplotype homozygosity and composite likelihood ratio tests, we identified 384 and 81 selective sweeps affecting 4% and 0.5% of the 35 Mb core genome, respectively. We found differences both in the number and the position of selective sweeps across the genome between populations. Using a XtX‐based outlier detection approach, we identified 51 extremely divergent genomic regions between the allopatric populations, suggesting that divergent selection led to locally adapted pathogen populations. We performed an outlier detection analysis between two sympatric populations infecting two different wheat cultivars to identify evidence for host‐driven selection. Selective sweep regions harboured genes that are likely to play a role in successfully establishing host infections. We also identified secondary metabolite gene clusters and an enrichment in genes encoding transporter and protein localization functions. The latter gene functions mediate responses to environmental stress, including interactions with the host. The distinct gene functions under selection indicate that both local host genotypes and abiotic factors contributed to local adaptation.