A quantitative genetic model for analyzing species differences in outcrossing species

A genetic model based on a two-level intra- and interspecific mating design is proposed to estimate the genetic architecture of species differences and heterosis for outcrossing species. The underlying genetic analyses make use of classical quantitative genetic theories and recent results from molecular genetic studies. Gene effects across different quantitative trait loci (QTL) can be approximated by a geometric series. Under natural selection, gene effects are often associated with allele frequencies in a particular way, which can be approximated by the gamma distribution. By incorporating these approximations into family structural analyses in the mating design, we are able to estimate a number of genetic parameters that contribute to quantitative genetic variation based on a nonlinear optimization approach. These parameters include the number of QTL, their gene effects, and their allele frequencies in the parental populations. We perform simulation studies and illustrate an example to demonstrate the statistical property and procedure of the method.     

A mixed model for the effects of single gene,polygenes and their interaction on quantitative traits

Summary A model for the effects of single gene (SG), polygenes (PG) and their interaction on quantitative traits was developed. It is a mixed model where the SG is a fixed effect and the PG is a random effect. A two-way factorial experiment, in which the SG and the PG are the main effects, is proposed. The experimental material is comprised of F₃ families derived from F₂ plants heterozygous for the SG. For this experiment an ANOVA table with expected mean square is proposed, which facilitates estimation of the components of the model and testing of their significance. A detailed method for the interpretation of results from such an experiment is proposed, with emphasis on the analysis of the SG × PG interaction. Theoretical and applied aspects of SG × PG interaction is discussed.This paper is part of a Ph.D. Thesis of the senior author to be submitted to the Hebrew University of Jerusalem     

Needs and benefits of empirical power transformations for production and quality traits in forest tree breeding

Non-normality in the distribution of individual observations of production and quality traits in forest tree breeding may cause inaccurate selection and overestimation of predicted selection gain. The distribution of individual observations of traits such as height, diameter, branch diameter, branch angle and number of branches per whorl is not always normal. We investigated how the observations were distributed and to what degree it is possible to improve normality, homogeneity of error variance and additivity by using empirical power transformations. Computer simulations showed that a seriously skewed distribution impairs selection efficiency and exaggerates selection gain expectations. If the distribution is heavily skewed, transformation might be worthwhile. It does not seem possible to offer any general advice about which varities should be transformed, but in most cases there seems to be no need of any transformation.     

A quantitative genetic model for growth,shape, reaction norms,and other infinite-dimensional characters

Infinite-dimensional characters are those in which the phenotype of an individual is described by a function, rather than by a finite set of measurements. Examples include growth trajectories, morphological shapes, and norms of reaction. Methods are presented here that allow individual phenotypes, population means, and patterns of variance and covariance to be quantified for infinite-dimensional characters. A quantitative-genetic model is developed, and the recursion equation for the evolution of the population mean phenotype of an infinite-dimensional character is derived. The infinite-dimensional method offers three advantages over conventional finite-dimensional methods when applied to this kind of trait: (1) it describes the trait at all points rather than at a finite number of landmarks, (2) it eliminates errors in predicting the evolutionary response to selection made by conventional methods because they neglect the effects of selection on some parts of the trait, and (3) it estimates parameters of interest more efficiently.     

Statistical analysis of a linkage experiment in barley involving quantitative trait loci for height and ear-emergence time and two genetic markers on chromosome 4

Summary The quantitative traits height and ear-emergence date were analyzed in the F₂ progeny of a cross between a tall winter barley cultivar (Gerbel) and a short spring barley cultivar (Heriot). The trait distributions were found to be related to the genotypes at two biochemical loci, -amylase (Bmy1) and water-soluble protein (Wsp3), which are known to lie on the long arm of chromosome 4. Linkages between each trait and the markers were investigated using normal mixture models. The two parental phenotypes and the heterozygote phenotype of Bmy1 were distinguishable so the model could be used directly to estimate linkage between Bmy1 and a quantitative trait locus (QTL) for height (Height). The Gerbel homozygote and heterozygote phenotype of Wsp3 could not be distinguished and the model was adapted accordingly. The proportion of plants requiring vernalization was consistent with control by two independent genes acting epistatically, and a normal mixture model based on a two-gene hypothesis was fitted to the distribution of ear-emergence date to estimate linkage between the marker loci and a QTL for ear-emergence date (Vrn1). The parameters of each model were the recombination fraction between the marker locus and the QTL and the means and standard deviations associated with each QTL genotype; these were estimated by maximum likelihood. The fitted distributions correspond well to those observed and the order of the loci along the chromosome is inferred to be Height — Vrn1 — Bmy1 — Wsp3, with Wsp3 being the most distal.     

A practical introduction to Random Forest for genetic association studies in ecology and evolution

Large genomic studies are becoming increasingly common with advances in sequencing technology, and our ability to understand how genomic variation influences phenotypic variation between individuals has never been greater. The exploration of such relationships first requires the identification of associations between molecular markers and phenotypes. Here, we explore the use of Random Forest (RF), a powerful machine‐learning algorithm, in genomic studies to discern loci underlying both discrete and quantitative traits, particularly when studying wild or nonmodel organisms. RF is becoming increasingly used in ecological and population genetics because, unlike traditional methods, it can efficiently analyse thousands of loci simultaneously and account for nonadditive interactions. However, understanding both the power and limitations of Random Forest is important for its proper implementation and the interpretation of results. We therefore provide a practical introduction to the algorithm and its use for identifying associations between molecular markers and phenotypes, discussing such topics as data limitations, algorithm initiation and optimization, as well as interpretation. We also provide short R tutorials as examples, with the aim of providing a guide to the implementation of the algorithm. Topics discussed here are intended to serve as an entry point for molecular ecologists interested in employing Random Forest to identify trait associations in genomic data sets.     

Sexual cannibalism in the fishing spider and a model for the evolution of sexual cannibalism based on genetic constraints

Several hypotheses have been proposed for the evolution of sexual cannibalism by females. Newman and Elgar (1991) suggested that sexual cannibalism prior to mating by virgin female spiders may have evolved as a result of female foraging considerations. According to this model, an adult female's decision to mate or cannibalize a courting male should be based on an assessment of the male's value as a meal versus his value as a mate. The current study provides an empirical test of the assumptions and predictions of this model in the sexually cannibalistic fishing spider. Adult females were subjected to different food treatments, and exposed to adult males in the laboratory. However, only one of the assumptions of the model and none of its five predictions were upheld. We failed to find any effects of female foraging, female mating status, female size, male size or time of the season on females' behaviour towards courting males. Females behaved stereotypically, and many females were left unmated despite numerous mating opportunities. We also demonstrate costs of sexual cannibalism in a natural population. We propose that the act of sexual cannibalism in the fishing spider is non-adaptive, and develop a model for the evolution of premating sexual cannibalism in spiders based on genetic constraints. According to this hypothesis, sexual cannibalism by adult females may have evolved as an indirect result of selection for high and non-discriminate aggression during previous ontogenetic stages. Genetic covariance between different components of aggressive behaviour may constrain the degree to which (1) juvenile and adult aggression and/or (2) aggression towards conspecifics and heterospecifics can vary independently. We briefly review the support for our model, and suggest several critical tests that may be used to assess the assumptions and predictions of the model.     

A multiplicative-epistatic model for analyzing interspecific differences in outcrossing species

Epistasis may play an important role in evolution and speciation. Under multiplicative interactions between different loci, an analytical model is proposed to estimate genetic parameters at the individual locus level that contribute to interspecific differences in outcrossing species. The multiplicative epistasis model, inferred from a number of animal and plant experiments, suggests that genotypes at a pair of loci have genotypic values equal to the product of genotypic values at the two different loci. By considering the genetic property of outcrossing species (i.e., high polymorphisms) in the multilevel family structure analysis for an intra- and interspecific factorial mating design, a method is developed to provide estimates for allele frequencies and additive and dominant effects at individual loci in each of the two parental populations, the genotypic values of newly formed heterozygotes through species combination each with one allele from a parental population and the second from the other parental population, and the numbers of genetic factors that lead to species differentiation. Use of clones offers a tremendous power to test the adequacy of the model. However, the utilization of the model with species that cannot be cloned is also discussed. An example with interspecific hybrids of two forest tree species is used to demonstrate the model.     

A quantitative genetic test of adaptive decoupling across metamorphosis for locomotor and life-history traits in the pacific tree frog, Hyla regilla

Metamorphosis is assumed to be beneficial because it can break developmental links between traits in the different phases of a complex life-cycle and thereby allow larval and adult phases to adapt independently. I tested the prediction that correlations between the larval and adult phases are smaller than within stages. I estimated phenotypic and additive genetic variances and correlations for tadpole swimming speed, frog jump distance, body size, and larval period in a single population of the Pacific tree frog, Hyla regilla. These traits are known or reasonably assumed to be important for survival in this and other anuran species from temporary ponds. Only the three size variables were affected by sire identity. Heritabilities for locomotor performance, larval period, and size-independent performance were low (0.00-0.23) and not significant. Body size measurements showed somewhat higher and statistically significant heritabilities (0.24-0.34). Most traits were phenotypically correlated. On average, phenotypic correlations were larger between phases than within phases (0.41 vs. 0.28). Genetic correlations involving body-size traits were positive and large, and average within- and between-phase genetic correlation coefficients were identical (0.81). These results do not support the adaptive decoupling hypothesis, and they indicate that a paucity of additive genetic variation is a likely constraint on the evolution of traits measured for this population.     

A genetic model for the endosperm balance number (EBN) in the wild potato Solanum acaule Bitt. and two related diploid species

Solanum acaule Bitt. is a disomic tetraploid potato which has been assigned two endosperm balance numbers (EBN). It readily crosses with diploids but does not cross with other tetraploid species, although exceptions have been reported. The genetic basis of this behavior was studied in intra- and interspecific crosses involving plants of four introductions of this species and plants of one introduction of 2x S. commersonii Dun., one of 2x S. gourlayi Haw., and two of 4x S. gourlayi Haw., which have been assigned one EBN, two EBN, and four EBN respectively. Some of the pollinated pistils were used to analyze pollen-pistil compatibility reactions; the rest were left in the plants for seed production. At harvest, seeds were sorted according to size and plumpness, and the ploidy of the resulting plantlets determined from root tips. A model is proposed to explain the results of these crosses as well as the exceptions previously reported. It is based on the presence of two independent loci controlling the EBN, with two alleles in homozygosity: 1/2 and 0. This model, which is extended to cmm and grl, also explains the behavior of 3x (cmm x grl) hybrids in crosses with one-EBN, two-EBN, and four-EBN species reported in a previous work.