On the relation between gene flow theory and genetic gain

In conventional gene flow theory the rate of genetic gain is calculated as the summed products of genetic selection differential and asymptotic proportion of genes deriving from sex-age groups. Recent studies have shown that asymptotic proportions of genes predicted from conventional gene flow theory may deviate considerably from true proportions. However, the rate of genetic gain predicted from conventional gene flow theory was accurate. The current note shows that the connection between asymptotic proportions of genes and rate of genetic gain that is embodied in conventional gene flow theory is invalid, even though genetic gain may be predicted correctly from it.     

世代重叠群体多个QTL最优化选择

一种扩展的方法能够在一个世代重叠的群体内对多个数量性状位点选择进行最优化,目的是为了在整个计划期内获得最大的累积反应加权和。该模型允许群体有多个性别年龄组、公母畜间有不同的年龄组数、各年龄组有不同的遗传贡献。整个最优化问题被描述成一个多阶段系统优化控制问题,通过一个向前和向后的迭代循环解决。用一个世代重叠的实际育种猪群的参数来评价该方法的选择效果,并和标准QTL选择和常规BLUP选择进行比较。模拟结果表明,优化选择要优于标准QTL选择和常规BLUP选择。群体结构对优化选择的影响比较明显。优化QTL选择和标准QTL选择在世代重叠的群体内比在世代离散的群体内的选择优势更明显,相对于常规BLUP选择,能够获得更大的选择优势。在世代重叠群体内随着2岁公畜遗传贡献的增大,优化选择相对于常规BLUP选择的优势越明显。     

Non-random mating for selection with restricted rates of inbreeding and overlapping generations

Minimum coancestry mating with a maximum of one offspring per mating pair (MC1) is compared with random mating schemes for populations with overlapping generations. Optimum contribution selection is used, whereby ΔF is restricted. For schemes with ΔF restricted to 0.25% per year, 256 animals born per year and heritability of 0.25, genetic gain increased with 18% compared with random mating. The effect of MC1 on genetic gain decreased for larger schemes and schemes with a less stringent restriction on inbreeding. Breeding schemes hardly changed when omitting the iteration on the generation interval to find an optimum distribution of parents over age-classes, which saves computer time, but inbreeding and genetic merit fluctuated more before the schemes had reached a steady-state. When bulls were progeny tested, these progeny tested bulls were selected instead of the young bulls, which led to increased generation intervals, increased selection intensity of bulls and increased genetic gain (35% compared to a scheme without progeny testing for random mating). The effect of MC1 decreased for schemes with progeny testing. MC1 mating increased genetic gain from 11–18% for overlapping and 1–4% for discrete generations, when comparing schemes with similar genetic gain and size.     

Optimizing Selection on Multiple Identified Quantitative Trait Loci in Population with Overlapping Generations

A method was developed to model and optimize selection on multiple identified quantitative trait loci (QTLs) and polygenic estimated breeding value, in order to maximize a weighted sum of cumulative response to selection over multiple years in a population with overlapping generations. The model allows for a population with multiple sex-age classes, different number of age class between sires and dams, and varied genetic contribution of the age class. The optimization problem was formulated as a multiple-stage optimal control problem and solved by a forward and backward iteration loop. The practical utility of this method was illustrated in an example of pig breeding population with overlapping generations. The selection response of this method was compared with standard QTL selection and conventional best linear unbiased prediction (BLUP) selection. Simulation results show that optimal selection achieved greater selection response than either standard QTL or conventional BLUP selections. The influence of population structure on optimal selection was significant. Optimal QTL selection and standard QTL selection were more favorable in a population with overlapping generations than discrete generations, and obtained more benefits relative to conventional BLUP selection in a population with overlapping generations. Optimal QTL selection relative to conventional BLUP selection is also more favorable following increase of genetic contribution of two-year-old boars and sows in a population with overlapping generations.     

Optimal mass selection policies for schemes with overlapping generations and restricted inbreeding

Optimum breeding schemes for maximising the rate of genetic progress with a restriction on the rate of inbreeding (per year or per generation) are investigated for populations with overlapping generations undergoing mass selection. The optimisation is for the numbers of males and females to be selected and for their distribution over age classes. Expected rates of genetic progress (ΔG) are combined with expected rates of inbreeding (ΔF) in a linear objective function (Φ = ΔG - λΔF) which is maximised. A simulated annealing algorithm is used to obtain the solutions. The restriction on inbreeding is achieved by increasing the number of parents and, in small schemes with severe restrictions, by increasing the generation interval. In the latter case the optimum strategy for obtaining the maximum genetic gain is far from truncation selection across age classes. In most situations, the optimum mating ratio is one but the differences in genetic gain obtained with different mating ratios are small. Optimisation of schemes when restricting the rate of inbreeding per generation leads to shorter generation intervals than optimisation when restricting the rate of inbreeding per year.     

Long-time behavior of continuous time models in genetic algebras

In [2] the solutions of Andreoli's differential equation in genetic algebras with genetic realization were shown to converge to equilibria. Here we derive an explicit formula for these limits.     

Allele frequency covariance among cohorts and its use in estimating effective size of age-structured populations

A general expression for the covariance of allele frequencies among cohorts in age-structured populations is derived. The expression is used to extend the so-called temporal method for estimating effective population size from allele frequency shifts among samples from cohorts born any number of years apart. Computer simulations are used to check on the accuracy and precision of the method, and an application to coastal Atlantic cod is presented.     

On continuous time models in genetic and Bernstein algebras

We discuss the long-time behavior of Andreoli's differential equation for genetic algebras and for Bernstein algebras and show convergence to an equilibrium in both cases. For a class of Bernstein algebras this equilibrium is determined explicitly.     

Methods for minimizing the loss of genetic diversity in conserved populations with overlapping generations

Minimization of the average coancestry in a population has been theoretically proven to be the most efficient method to preserve genetic diversity. In the present study, based on a population genetic model, two methods to minimize the average coancestry in populations with overlapping generations were developed. For a given parental coancestry structure, the first method (OG) minimizes the average coancestry in the next generation, and the second method (LT) is designed to minimize the long-term accumulation of coancestry. The efficiencies of the two methods were examined by stochastic simulation. Compared to random choice of parents, the annual effective population sizes under the two proposed methods increased 2–3 folds. The difference among the two methods was small in a population with short generation interval. For populations with long generation intervals, the OG method showed a slightly larger annual effective size in an initial few years. However, in the subsequent years, the LT method gave a 5–15% larger annual effective size than the OG method. From these results, it is suggested that the LT method would be preferred to the OG method in most practical situations.     

Environmental and genetic control of the larval diapause of the Southwestern corn borer, Diatraea grandiosella

ABSTRACT. The interaction of photoperiod and temperature in the regulation of the induction and termination of the larval diapause of the Southwestern corn borer, Diatraea grandiosella Dyar (Lepidoptera), was examined. A population originating from south-eastern Missouri had critical daylengths for diapause induction of about 15h 5min (ecological threshold) and llh (physiological threshold). The ecological threshold was more stable than was the physiological threshold at temperatures lower than 25°C. Above 25°C the diapause response was suppressed. The insect appears to measure photoperiods in a stationary manner since a stepwise increase or decrease in photoperiod did not affect the incidence of diapause. In the critical region of the photoperiodic response curve, a higher incidence of diapause was found among females than among males. Females entered diapause later than did males, but resumed active development earlier than males. The rate of diapause development was more temperature dependent than was the rate of diapause induction, yet it was also clearly under photoperiodic control. The temperature coefficient (Q₁₀) for this process was about 4. Several other factors including sex-linkage, age, and geographic adaptations are involved in controlling the rate of diapause development, even more so than they are in controlling diapause induction. In the laboratory, the intensity of diapause declined gradually without larvae being exposed to non-diapause inducing conditions. Incubation of field-collected larvae revealed that their sensitivity to diapause maintaining photoperiods had ended by January. Three generations of selection of a Mississippi population of D. grandiosella at 30°C and LD 12:12 led to the production of an essentially diapause-free strain and a diapause strain.     

Evolution of dispersal in a stepping-stone population with overlapping generations

We use Hamilton's inclusive fitness method to calculate the evolutionarily stable dispersal rate in 1- and 2-dimensional stepping-stone populations. This extends previous results by introducing a positive probability for adults to survive into the next generation and breed again. Relatedness between nearby individuals generally decreases with increasing survival, decreasing competition with kin and favouring greater dispersal rates.