Inheritance of Fusarium wilt resistance introgressed from Solanum aethiopicum Gilo and Aculeatum groups into cultivated eggplant (S. melongena) and development of associated PCR-based markers

The two eggplant relatives Solanum aethiopicum gr. Gilo and Solanum aethiopicum gr. Aculeatum (=Solanum integrifolium) carry resistance to the fungal wilt disease caused by Fusarium oxysporum f. sp. melongenae, a worldwide soil-borne disease of eggplant. To introgress the resistance trait into cultivated eggplant, the tetraploid somatic hybrids S. melongena + S. aethiopicum and S. melongena + S. integrifolium were used. An inheritance study of the resistance was performed on advanced anther culture-derived androgenetic backcross progenies from the two somatic hybrids. The segregation fitted a 3 resistant (R): 1 susceptible (S) ratio in the selfed populations and a 1R:1S ratio in the backcross progenies for the trait derived from S. aethiopicum and S. integrifolium. These ratios are consistent with a single gene, which we designated as Rfo-sa1, controlling the resistance to Fusarium oxysporum f. sp. melongenae. The allelic relationship between the resistance genes from S. aethiopicum and S. integrifolium indicate that these two genes are alleles of the same locus. Bulked Segregant Analysis (BSA) was performed with RAPD markers on the BC₃/BC₅ resistant advanced backcross progenies, and three RAPD markers associated with the resistance trait were identified. Cleaved Amplified Polymorphic Sequences (CAPSs) were subsequently obtained on the basis of the amplicon sequences. The evaluation of the efficiency of these markers in predicting the resistant phenotype in segregating progenies revealed that they represent useful tools for indirect selection of Fusarium resistance in eggplant.     

Construction of Selection Indexes with Restrictions

In this paper the problem of unistage selection with inequality constraints is formulated. If the predictor and criterion variables are all normally distributed, this problem can be written as a convex programming problem, with a linear objective function and with linear constraints and a quadratic constraint. Using the duality theory, for convex nonlinear programming it is proved, that its dual problem can be transformed into a convex minimization problem with non-negativity conditions. Good computational methods are known for solving this problem. By the help of the dual problem sufficient conditions for a solution of the original primal problem are derived and illustrated by an example of practical interest.     

Expected early genetic gain from selection for milk yield in dairy cattle

Summary A matrix program to predict short term genetic gain from single trait selection for milk yield was developed. Rate of genetic gain was calculated as the annual change in the mean breeding value of all producing females. Several parameters sets representing various selection policies were used to examine situations pertinent to dairy populations of the United States. Approach to the asymptotic rates of genetic gain within the model varied with the choice of parameters, but even with consistent selection policies, predicted total genetic gain in the first 10 years was only half of the expected from classical theory. Considerable year to year variation in the rate of gain occurred. Early gains were more dependent on female selection decisions than gains during the steady state. In a two-phase model, the approach to the linear rate of gain in the second phase was accelerated by starting with an ongoing improvement program, but considerable delays still existed. Selection for sex- limited traits such as milk yield, which require pedigree selection and a waiting time for progeny test results reached asymptotic rates more slowly than previously assumed.     

Combined S2 and crossbred family selection in full-sib reciprocal recurrent selection

Summary A method (CRRS) that combines S₂ and crossbred family selection in full-sib reciprocal recurrent selection (FSRRS) is proposed. The method requires four generations per cycle in single-eared maize populations. Selection is based on performance of S₂ and full-sib families by applying selection index theory. Equations to estimate the coefficients included in the index are given. These estimates are functions of the genetic and phenotypic variances and covariances among and between the two kinds of families. Comparisons of FSRRS and CRRS under equivalent amount of effort show that CRRS has some advantage over FSRRS for low heritability of the trait being selected (e.g., maize yield) and when only one or two locations with two replications are involved in the selection experiment.Joint contribution: Institute Nacional de Investigaciones Agrarias, La Coruna, Spain; and Agricultural Research, Science and Education Administration, U.S. Department of Agriculture, and Journal Paper No. J-10118 of the Iowa Agriculture and Home Economics Experiment Station, Ames, IA 50011. Project 2194     

Critical manifolds,travelling waves,and an example from population genetics

A generalized Morse index theory is used to study travelling waves in a natural selection-migration model for a diploid organism when the selective strength is weak.     

Computing the selection gradient and evolutionary response of an infinite-dimensional trait

 Following the results developed in a previous paper, an equation describing the evolutionary response to selection is extended from finite- to infinite-dimensional traits. The selection gradient and evolutionary response are then computed for a large class of infinite-dimensional traits of broad biological interest. In this framework, traits are modeled as Gaussian processes, and reproducing kernel Hilbert spaces constitute a primary tool. Received 12 September 1996     

The distribution of rare alleles

Population geneticists have long been interested in the behavior of rare variants. The definition of a rare variant has been the subject of some debate, centered mainly on whether alleles with small relative frequency should be considered rare, or whether alleles with small numbers should be. We study the behavior of the counts of rare alleles in samples taken from a population genetics model that allows for selection and infinitely-many-alleles mutation structure. We show that in large samples the counts of rare alleles — those represented once, twice, ... — are approximately distributed as a Poisson process, with a parameter that depends on the total mutation rate, but not on the selection parameters. This result is applied to the problem of estimating the fraction of neutral mutations.     

Fitness consequences of egg-size variation in the lesser snow goose

We investigated the relationship between eggsize variation and (a) egg hatching success, (b) chick survival to fledging and recruitment, and (c) adult female survival, over 12 years in the lesser snow goose (Anser caerulescens caerulescens). By comparing the means and variances of egg size for successful and unsuccessful eggs, our aim was to assess the relative fitness of eggs of different sizes and to determine the type of selection operating on egg size in this species. As both egg size and reproductive success vary with age in the lesser snow goose we controlled for the effects of female age. Egg-size variation is very marked in this population, varying by up to 52% for eggs hatching successfully. However, there was no relationship between egg size and post-hatching survival of goslings to fledging or recruitment, either within or between broods, pooling across years. Egg size varied significantly between successful and unsuccessful clutches in only 2 of 33 individual year comparisons. First-laid eggs surviving to onset of incubation, and eggs hatching successfully, were on average larger than unsuccessful eggs, but this was probably due to the confounding effects of female age-specific and sequence-specific egg survival. Variance of egg size differed significantly between successful and unsuccessful eggs in only 3 of 24, and 0 of 21, individual year comparisons for pre- and post-hatching survival respectively. We therefore found little evidence for a relationship between egg-size variation and offspring fitness, or for strong directional, normalising or diversifying selection operating on egg size, in the lesser snow goose. In addition, there was only weak support for the hypothesis that egg-size variation is maintained by temporal variation in selection pressure (sensu Ankney and Bisset 1973). It is likely that egg-size variation represents the pleiotropic expression of alleles affecting more general physiological or metabolic processes. While this does not rule out the existence of alleles with more direct effects on egg size we suggest that their contribution to heritable egg size is small.     

Evolution of insecticide resistance in Culex pipiens populations: The Corsican paradox

Culex pipiens mosquitoes from Corsica have been subject to insecticide treatments since 1971, using temephos (an organophosphate). After 17 years, resistance has not developed beyond a 14-fold level. This relatively low resistance is due to the presence of several identified resistance genes, including the insensitive target ( Ace^R ) and overproduced esterases (A1, A4 and B4). The fact that only a low resistance has developed after 17 years of treatment and that this low resistance level is the result of a relatively large number of resistance genes constitute a paradox. To understand this situation and explain why a higher temephos resistance level has not evolved in Corsica as in other parts of the world, it is proposed that the occurrence (through mutation or migration) of efficient resistance genes was a limiting step, and that the only resistance genes available at that time through migration from the surrounding Mediterranean countries had a low cross-resistance to temephos. The local situation of Corsica is discussed in the light of recent data on the world distribution of the known organophosphate resistance genes in this species, and the relative role of mutation and migration in the evolution of insecticide resistance in natural populations.     

Equilibria and dynamics of selection at a diallelic autosomal locus in the Nagylaki-Crow continuous model of a monoecious population

Let birth rates and death rates be constant, birth rates positive, fertilities additive, and each birth rate not larger than twice any other birth rate. Global convergence to equilibria is proved for the model in the title. There is at most one polymorphic equilibrium or there are a continuum of equilibria. The phase portraits are given. If there is a polymorphic equilibrium, then the largest negatively invariant set in the state space is a continuous curve connecting the two fixation equilibria. This curve coincides with the Hardy-Weinberg manifold exactly when the death rate is additive. Disregarding extinction, the polymorphic equilibria are the same for the continuous model as for the corresponding discrete model exactly when the death rate is additive.