Computer modeling of joint selection response of MGE patterns and a polygenic system]

Using computer simulation, selection response of three genome patterns--polygenes, mobile genetic elements (MGEs), and labels of identity by origin (LIOs)--were studied. In each generation of selection, variability of each pattern type was described by on UPGMA tree. Stringent positive truncation selection on an additive polygenic trait and recombination between segments of the genetic map were considered. MGEs were classified into three groups: modifiers (enhancers) of the polygenic expression, markers, and independent copies. It was shown that at generations 30 to 40, 95-96% and 70-80% of respectively enforced and non-enforced active polygenic alleles were fixed (2-3% and 16-17% lost). In all generations, Hkn < or = Dkn of the length of the maximal route along the tree. At the same time, modifier MGEs were fixed for 85-88% (lost for 11-12%); marker MGEs, for 60-70 (lost for 21-25%); and independent copies, for 30-40 (lost for 50-60%). The behavior of independent MGE copies was generally consistent with the predictions of the genetic drift theory, modifier MGEs behaved similarly to the modified polygenes, and marker MGEs exhibited intermediate properties. The LIO patterns showed rapid homozygotization: their variability dropped dramatically between generations 10 and 30. In F50, the final consensus pattern of polygenes included 16 out of 18 enforced and 18 out of 21 non-enforced polygenic alleles. The fixation/loss ratios were 16:3 for modifier MGEs, 15:6 for marker MGEs, and 25:28 (with 7 polymorphic) for independent copies. The LIO consensus pattern contained 13 out of 100 original markers, which formed 26 fragments of one to ten map segments in size; 21 fragments contained active polygenic alleles, and 14 of them had also modifier MGEs. Recombinational shuffling of patterns was not completed. In the course of selection, active polygenic alleles take along adjacent segments, including those containing modifier MGEs and markers. These constitute the conservative part of all consensus patterns while the remaining segments are random.     

Population trajectories for single locus additive fecundity selection and related selection models

A selection model which comprises models of additive fecundities as well as models of viability, fecundity, or differential mating selection acting only in one sex, is investigated for an autosomal gene locus in a population reproducing in nonoverlapping generations. The recurrence equations and basic properties of the genotypic population trajectories and equilibrium points are formulated for the multiallelic case. For the diallelic case, the trajectory development is discussed in more detail, and it is proven that every population trajectory converges to a Hardy-Weinberg equilibrium point.     

Epistasis in polygenic traits and the evolution of genetic architecture under stabilizing selection

We consider the effects of epistasis in a polygenic trait in the balance of mutation and stabilizing selection. The main issues are the genetic variation maintained in equilibrium and the evolution of the mutational effect distribution. The model assumes symmetric mutation and a continuum of alleles at all loci. Epistasis is modeled proportional to pairwise products of the single-locus effects. A general analytical formalism is developed. Assuming linkage equilibrium, we derive results for the equilibrium mutation load and the genetic and mutational variance in the house of cards and the Gaussian approximation. The additive genetic variation maintained in mutation-selection balance is reduced by any pattern of the epistatic interactions. The mutational variance, in contrast, is often increased. Large differences in mutational effects among loci emerge, and a negative correlation among (standard mean) locus mutation effects and mutation rates is predicted. Contrary to the common view since Waddington, we find that stabilizing selection in general does not lead to canalization of the trait. We propose that canalization as a target of selection instead occurs at the genic level. Here, primarily genes with a high mutation rate are buffered, often at the cost of decanalization of other genes. An intuitive interpretation of this view is given in the discussion.     

Linkage disequilibrium mapping of quantitative trait loci under truncation selection

As a dense map of single nucleotide polymorphism (SNP) markers are available, population-based linkage disequilibrium (LD) mapping or association study is becoming one of the major tools for identifying quantitative trait loci (QTL) and for fine gene mapping. However, in many cases, LD between the marker and trait locus is not very strong. Approaches that maximize the potential of detecting LD will be essential for the success of LD mapping of QTL. In this paper, we propose two strategies for increasing the probability of detecting LD: (1) phenotypic selection and (2) haplotype LD mapping. To provide the foundations for LD mapping of QTL under selection, we develop analytic tools for assessing the impact of phenotypic selection on allele and haplotype frequencies, and LD under three trait models: single trait locus, two unlinked trait loci, and two linked trait loci with or without epistasis. In addition to a traditional chi(2) test, which compares the difference in allele or haplotype frequencies in the selected sample and population sample, we present multiple regression methods for LD mapping of QTL, and investigate which methods are effective in employing phenotypic selection for QTL mapping. We also develop a statistical framework for investigating and comparing the power of the single marker and multilocus haplotype test for LD mapping of QTL. Finally, the proposed methods are applied to mapping QTL influencing variation in systolic blood pressure in an isolated Chinese population.     

On the fixation of genes of large effects due to continued truncation selection in small populations of polygenic systems with linkage

Summary The proportion of fixed loci for desirable genes and the time required for fixation is studied in simulated diploid populations, which have initially aHardy-Weinberg structure. A symmetric ten-locus system of additive or dominant genes is simulated with linkages between adjacent loci varying as .005, .05, or .5. A constant degree of upper truncation selection within a population is considered over the generations. In different populations the intensity of truncation is varied asN/N,N/N+2,N/N+4, ..., whereN is the parental population size, specified as 2,4,8 or 16. The selection differential in initial generation, , thereby varies from zero to more than two standard deviations in some cases. The initial mean gene frequency,p, simulated in an initial population is .1 or .5.It is pointed out that when selective advantage of a gene is large and is changing with gene frequency, diffusion approximations assuming constant selective advantage, gives higher values for proportion of fixed genes in the case ofp equal to .1 and lower values forp equal to .5. With parental population size of 16 or less, a relation withN alone does not give the proportion of fixed genes. Higher order terms ofN appear to be involved in the relation. For the sameN , the proportion is much higher for lowN.The depressing effect of low recombinations between loci is of different magnitude for differentN andp for a givenN . The increase in the proportion of fixed genes due to increasingN is not as large when is low. High intensity of selection offsets considerably the effects of population size and linkage when gene effects are large. It appears that with increased inbreeding and selection intensity, almost all the genes of large effects and at intermediate frequencies can be rapidly fixed regardless of linkage.Linkage has been shown to cause faster fixation of genes in the absence of selection. With selection, linkage tends to delay fixation. But in the case of very low recombinations, there appears to be a level of population size and selection intensity, below which there is more rapid fixation because of linkage. Selection for dominant genes in the case of very close linkage, delays fixation for a number of generations and this delay results in reducing the depressing effect of linkage.

---

Zusammenfassung Der Anteil fixierter Loci für erwünschte Gene und die für die Fixierung erforderliche Zeit werden in einer simulierten diploiden Population untersucht, wobei eine ursprünglicheHardy-Weinberg-Struktur angenommen wird. Es wird ein symmetrisches 10-Locus-System von additiven oder dominanten Genen mit Koppelung zwischen benachbarten Loci, die von 0,005 über 0,05 bis zu 0,5 variiert wird, simuliert. Hierbei wird ein konstantes Ausmaß von trunkierender (stutzender) Selektion für die Obergrenze der Verteilung in der Population betrachtet. In verschiedenen Populationen wird die Intensität der Verteilungsstutzung variiert in der folgenden FormN/N,N/N+2,N/N+4, ..., wobeiN die elterliche Populationsgröße ist, die mit 2,4,8 oder 16 spezifiziert wird. Das Selektionsdifferential der Ursprungsgeneration,i, variiert hierbei in einigen Fällen von 0 bis auf mehr als 2 Standardabweichungen. Die ursprüngliche mittlege Genfrequenz,p, die in einer Ausgangspopulation simuliert wird, ist 0,1 oder 0,5.Es wird gezeigt, daß, im Vergleich zu großem selektivem Vorteil eines Gens und frequenzabhängiger Änderung des Selektionskoeffizienten, Diffusionsnäherungen, die konstante selektive Vorteile voraussetzen, höhere Werte für den Anteil fixierter Gene im Fallp=0,1 und niedrigere Werte fürp=0,5 ergeben. Mit einer elterlichen Population der Größe 16 oder kleiner ergibt die BeziehungNi allein nicht den Anteil fixierter Gene, da Termini höherer Ordnung vonNi in die Bezichung einbezogen sind. Bei gleichemNi ist der Anteil bei kleinemN viel höher. Der reduzierende Effekt einer niederen Rekombinationsrate zwischen den Loci ist von unterschiedlicher Größenordnung bei verschiedenemN und bei einem gegebenenNi. Der Zuwachs im Anteil fixierter Gene infolge eines wachsendenN ist nicht so groß, wennp niedrig ist. Eine hohe Intensität der Selektion gleicht die Wirkungen der Populationsgröße und Koppelung erheblich aus, wenn die Genwirkungen groß sind. Es zeigt sich, daß praktisch alle Gene mit großer Wirkung und intermediärer Frequenz unabhängig von der Koppelung schnell fixiert werden können, wenn eine zunehmende Inzucht und Selektionsintensität vorliegt.Koppelung hat sich als eine Ursache für eine schnellere Fixierung von Genen in der Abwesenheit von Selektion erwiesen. Mit Selektion tendiert Kopplung dazu, die Fixierung zu verzögern. Es zeigt sich jedoch im Falle einer sehr niederen Rekombinationsrate, daß es für die Populationsgröße und Selektionsintensität einen Schwellenwert zu geben scheint, unterhalb dessen eine schnellere Fixierung als Folge der Koppelung auftritt. Eine Selektion auf dominante Gene verzögert im Fall der sehr engen Koppelung die Fixierung für eine Anzahl von Generationen und diese Verzögerung führt dazu, daß der verlangsamende Effekt der Koppelung reduziert wird.

---

---

On leave from West Pakistan Agricultural University, Lyallpur.

---

Journal paper No. 5870, Iowa Agriculture and Home Economics Experiment Station, Ames, supported by National Institute of Health Grant No. GM 13827.     

Multilocus dynamics under haploid selection

 A general haploid selection model with arbitrary number of multiallelic loci and arbitrary linkage distribution is considered. The population is supposed to be panmictic. A dynamically equivalent diploid selection model is introduced. There is a position effect in this model if the original haploid selection is not multiplicative. If haploid selection is additive then the fundamental theorem is established even with an estimate for the change in the mean fitness. On this basis exponential convergence to an equilibrium is proved. As rule, the limit states are single-gamete ones. If, moreover, linkage is tight, then the single-gamete state with maximal fitness attracts the population for almost all initial states. Received 27 November 1995; received in revised form 17 January 1996     

QTL mapping under truncation selection in homozygous lines derived from biparental crosses

In plant breeding, a large number of progenies that will be discarded later in the breeding process must be phenotyped and marker genotyped for conducting QTL analysis. In many cases, phenotypic preselection of lines could be useful. However, in QTL analyses even moderate preselection can have a significant effect on the power of QTL detection and estimation of effects of the target traits. In this study, we provide exact formulas for quantifying the change of allele frequencies within marker classes, expectations of marker contrasts and the variance of the marker contrasts under truncation selection, for the general case of two QTL affecting the target trait and a correlated trait. We focused on homozygous lines derived at random from biparental crosses. The effects of linkage between the marker and the QTL under selection as well as the effect of selection on a correlated trait can be quantified with the given formulas. Theoretical results clearly show that depending on the magnitude of QTL effects, high selection intensities can lead to a dramatic reduction in power of QTL detection and that approximations based on the infinitesimal model deviate substantially from exact solutions. The presented formulas are valuable for choosing appropriate selection intensity when performing QTL mapping experiments on the data on phenotypically preselected traits and enable the calculation and bias correction of the effects of QTL under selection. Application of our theory to experimental data revealed that selection-induced bias of QTL effects can be successfully corrected.     

Population dynamics and evolutionary processes: the manifold roles of habitat selection

Summary Any character that has a substantial effect on a species' distribution and abundance can exert a variety of indirect effects on evolutionary processes. It is suggested that an organism's capacity for habitat selection is just such a character. Habitat selection can constrain the selective environment experienced by a population. Habitat selection can also indirectly influence the relative importance of natural selection, drift, and gene flow, through its effect on population size and growth rate. In many circumstances (but not all), habitat selection increases population size and growth rate, and thereby makes selection in a local environment more effective than drift and gene flow.     

The divergence of a polygenic system subject to stabilizing selection, mutation and drift

Polygenic variation can be maintained by a balance between mutation and stabilizing selection. When the alleles responsible for variation are rare, many classes of equilibria may be stable. The rate at which drift causes shifts between equilibria is investigated by integrating the gene frequency distribution W2N II (pq)4N mu-1. This integral can be found exactly, by numerical integration, or can be approximated by assuming that the full distribution of allele frequencies is approximately Gaussian. These methods are checked against simulations. Over a wide range of population sizes, drift will keep the population near an equilibrium which minimizes the genetic variance and the deviation from the selective optimum. Shifts between equilibria in this class occur at an appreciable rate if the product of population size and selection on each locus is small (Ns alpha 2 less than 10). The Gaussian approximation is accurate even when the underlying distribution is strongly skewed. Reproductive isolation evolves as populations shift to new combinations of alleles: however, this process is slow, approaching the neutral rate (approximately mu) in small populations.     

Cytonuclear dynamics in selfing populations under selection

We develop a mathematical model to delimit the role of natural selection in maintaining nuclear and cytoplasmic polymorphisms in selfing populations. We provide explicit time-dependent solutions for joint cytonuclear frequencies under any combination of constant fertility, viability, and gametic selection and exact analytical conditions for the maintenance of polymorphisms under joint cytonuclear selection. The equilibrium structure is determined by the relative magnitude of echo fitnesses, defined as the rate at which individuals survive and produce offspring with their own genotype. Both nuclear and cytoplasmic polymorphisms can be maintained under biologically meaningful conditions, although the majority of the parameter combinations will lead to fixation. The theoretical framework developed here should be very useful in formally dissecting the form and strength of selection on cytonuclear genotypes in populations with negligible levels of outcrossing.     

Population genetics of polymorphism and divergence under fluctuating selection

Current methods for detecting fluctuating selection require time series data on genotype frequencies. Here, we propose an alternative approach that makes use of DNA polymorphism data from a sample of individuals collected at a single point in time. Our method uses classical diffusion approximations to model temporal fluctuations in the selection coefficients to find the expected distribution of mutation frequencies in the population. Using the Poisson random-field setting we derive the site-frequency spectrum (SFS) for three different models of fluctuating selection. We find that the general effect of fluctuating selection is to produce a more "U"-shaped site-frequency spectrum with an excess of high-frequency derived mutations at the expense of middle-frequency variants. We present likelihood-ratio tests, comparing the fluctuating selection models to the neutral model using SFS data, and use Monte Carlo simulations to assess their power. We find that we have sufficient power to reject a neutral hypothesis using samples on the order of a few hundred SNPs and a sample size of approximately 20 and power to distinguish between selection that varies in time and constant selection for a sample of size 20. We also find that fluctuating selection increases the probability of fixation of selected sites even if, on average, there is no difference in selection among a pair of alleles segregating at the locus. Fluctuating selection will, therefore, lead to an increase in the ratio of divergence to polymorphism similar to that observed under positive directional selection.     

Population dynamics under parasitic sex ratio distortion.

We analyse the population dynamic effects of sex ratio distortion by vertically transmitted, feminizing parasites. We show that, for diploid hosts, sex ratio distortion may lead to extinction as males become too rare to maintain the host population through reproduction. Feminizers can magnify Allee effects, broadening the range of conditions leading to extinction of small populations. Depending on male mating constraints and strength of density dependence, feminizers may either increase or decrease the equilibrium host density. Under conditions leading to deterministic host extinction, stochastic elimination of the parasite may allow the host population to recover. Hence, infection by parasitic sex ratio distorters may be transient in finite populations. We consider the implications of this process for parasite prevalence, host population regulation, and sex ratio evolution.     

Population dynamics of host-parasite interactions in a cockroach-oxyuroid system

Host-parasite interactions of an urban cockroach, Blattella germanica , and its oxyuroid parasite, Blatticola blattae , were investigated. Life history data of host and parasites were collected under laboratory conditions. These data were used to model the effect of the parasite on the population dynamics of the host in order to understand the parasite's impact on the host population. The aggregation of parasites within a host was under-dispersed. Hosts normally were found to be infected with only one male and one female and rarely two or three. However, the primary sex ratio after hatching was 1.1 (males/females). Female parasite longevity equalled the life span of its host. B. blattae had a significant impact on the survival rate of the cockroach larvae and their time to reach maturity, but no effect on the survival rate of the adults. Infected host females produced fewer first oothecae than uninfected ones. Using the population parameters a simple model was developed to estimate the parasite's effect on the population dynamics of its host. According to the model the parasite suppresses the cockroach populations by ca 11%. Hence, the effect of the parasite does not appear strong enough to be used as a biological control agent by itself.     

Population structure analysis using polygenic traits: estimation of migration matrices

Many studies of subdivided populations have attempted to determine the underlying migration rates that generate observed patterns of genetic differentiation. Most previous analyses have yielded only qualitative inferences about migration. In this paper I present a new method for estimating the full migration matrix from information on polygenic trait variation. The method employs multivariate quantitative genetic theory to provide a matrix formulation of the expected covariance structure in multigenerational subdivided populations for which information is available at different points in the life cycle. I develop a restricted maximum likelihood technique (REML) to take account of this additional life-cycle information and to estimate both the migration matrix and the ratio of effective population size to census size. To make the problem computationally tractable, the migration matrix is modeled as a log-linear function of a few covariates, such as subdivision size and geographic distance. I apply the technique to data on dermatoglyphic ridge counts for 1015 individuals of the Jirel population of east Nepal, considering two different age cohorts. In the adult cohort (individuals over 21 years of age) I examine data by both birthplace and residence and for the subadult cohort (under 21 years of age), by birthplace. Results from the REML technique reveal that the best-fitting migration model is a finite island model with an estimated endemicity of 0.730 +/- 0.105 and an estimated ratio of effective size to census size of 0.287 +/- 0.095. Both estimates are reasonable given known demographic data. In addition, Fst values predicted by the migration model are concordant with REML estimates obtained directly from the dermatoglyphic variation.     

Neural dynamics under noise in the olfactory system

A study is made of the dynamical properties of mammalian olfactory bulb which is represented by a set of nonlinear differential equations. It is shown that when the system of the periglomerular population receives a stationary independent stochastic input from the primary olfactory nerves, the level of ongoing mean pulse rate depends only on the expected value of the input. It is also shown that if the mitral-tufted and granule population receives stationary independent stochastic inputs both from the primary olfactory nerves and centrifugal axons, then there exists a limit cycle detectable in the EEG and the phase of the limit cycle depends only on the expected values of the inputs.