Non-random Mating Populations Research Articles

Random and non-random mating populations: Evolutionary dynamics in meiotic drive

Game theoretic tools are utilized to analyze a one-locus continuous selection model of sex-specific meiotic drive by considering nonequivalence of the viabilities of reciprocal heterozygotes that might be noticed at an imprinted locus. The model draws attention to the role of viability selections of different types to examine the stable nature of polymorphic equilibrium. A bridge between population genetics and evolutionary game theory has been built up by applying the concept of the Fundamental Theorem of Natural Selection. In addition to pointing out the influences of male and female segregation ratios on selection, configuration structure reveals some noted results, e.g., Hardy–Weinberg frequencies hold in replicator dynamics, occurrence of faster evolution at the maximized variance fitness, existence of mixed Evolutionarily Stable Strategy (ESS) in asymmetric games, the tending evolution to follow not only a 1:1 sex ratio but also a 1:1 different alleles ratio at particular gene locus. Through construction of replicator dynamics in the group selection framework, our selection model introduces a redefining bases of game theory to incorporate non-random mating where a mating parameter associated with population structure is dependent on the social structure. Also, the model exposes the fact that the number of polymorphic equilibria will depend on the algebraic expression of population structure.

Chemical polymorphism in male femoral gland secretions matches polymorphic coloration in common wall lizards (Podarcis muralis)

Previous studies showed that common wall lizards (Podarcis muralis) are polymorphic in colour, both sexes showing three main ventral morphs (white, yellow and red) within the same population and that the three morphs correlate with many life-history traits, including a positive assortative mating according to colour. Chemical communication plays a key role in intra-specific recognition and in social organization of lizards; thus chemical cues might be involved in morph recognition and mate choice. We used gas chromatography–mass spectrometry (GC–MS) to investigate possible differences in the lipophilic fraction of femoral gland secretions between size/age classes and to explore whether chemical secretions match male colour morphs. As expected, most males shared the same compounds, but smaller males showed significantly higher proportions of aldehydes, alcohols and ketones and significantly lower proportions of tocopherols than larger males. Interestingly, inter-morph differences in the proportion of some compounds (especially tocopherols and furanones) matched ventral colour polymorphism. Pairwise comparisons showed that white lizards had significantly different chemical profiles than both the yellow and red ones, whereas differences between yellow and red males were only marginal. A further canonical analysis of principal coordinates correctly classified 67.2 % on average of the chemical profiles according to colour morph (white 85.0 %, red 60.9 %, yellow 57.1 %). We hypothesized that chemical differences associated with colour polymorphism may play a central role in intra-specific communication and even in sexual selection, allowing individuals to choose their partners according to their age, and more interestingly according to their colour morph, in a non-random mating population system.

Reply to ten Kate et al

We thank Prof ten Kate et al1 for the useful observations, which will allow us to clarify some aspects of the HI method.2, 3 With regard to the inclusion of mutations with relative frequency below 1% in the formula, we may notice how these negligibly affect the final result, with a gene frequency increasing from 1.90 to 1.95%. This corresponds to an even smaller increase in the prevalence of the disease (from 3.65 × 10−4 to 3.8 × 10−4, if we assume P=q2 to simplify). With reference to the exclusion of heterozygous patients from the formula, this is a conservative choice that we made under the basic assumption of strict recessive inheritance in the model, as including them would mean to (erroneously) assume that they are all compound heterozygotes. We also underline that, in this specific study, every sample was first investigated for the six most common reported mutations in Sardinia, and then, if no mutation was found, by single-strand conformation polymorphisms and Sanger sequencing of all exons and of the flanking intronic regions in the ATP7B gene. This makes it highly unlikely that a mutation already found in the Sardinian population was undetected. Finally, we agree that in a non-random mating population q→P (instead of P=q2, as per Hardy–Weinberg equilibrium). However, the current Sardinian population is characterized by high endogamy more than by high frequency of consanguineous matings. Under this scenario, also known as ‘random inbreeding',4 the chance that an individual will mate with a genetically related one will be higher, and will finally lead to P≈q2, as already discussed in a recent letter published in this Journal.5 Nonetheless, we acknowledge that this is an unavoidable approximation and we always mentioned the gene frequency (q) of a recessive disorder instead of the Prevalence (P) as the main output of the HI method, inferring P only when required for a comparison with other epidemiological methods.2, 3 In summary, we agree with ten Kate et al1 that all of these details only slightly affect the final result but we disagree that they will jointly create a big discrepancy between our q estimate and the real one, as also demonstrated by the factual equivalence between our q and the one estimated by Zappu et al6 through a classical and reliable neonatal molecular screening. What is more important, the main purpose of the HI method is not to make a precise inference of the prevalence of a given recessive disorder in a population (as variables like the inbreeding coefficient can still be a source of error), but to produce ‘a ranking order of the prevalence of autosomal recessive disorders, thus establishing priorities for genetic testing at the population level'.2, 3 Our wish is that the HI method becomes of common use by public health institutions, especially in those country characterized by highly endogamous/consanguineous populations, and that it can be improved by making use of precise estimates of the inbreeding coefficient based on the analysis of genomic patterns of homozygosity.7

Molecular Characterization of Fusarium Head Blight Pathogens Sampled from a Naturally Infected Disease Nursery Used for Wheat Breeding Programs in China.

Fusarium head blight (FHB) is an important disease of wheat and barley worldwide. The disease is primarily caused by members of the Fusarium graminearum species complex, consisting of at least 14 phylogenetically distinct species. To determine the population structure of the FHB pathogens in a naturally infected disease nursery located at Jianyang, Fujian province, China, 160 isolates of the F. graminearum complex were recovered from symptomatic wheat spike samples collected in two consecutive years (2008 and 2009) and characterized using species- and chemotype-specific polymerase chain reaction as well as variable number tandem repeat (VNTR) markers. All isolates analyzed were identified as F. asiaticum except for one isolate, which was identified as F. avenaceum. Among the 159 F. asiaticum isolates, 126 (79%) isolates were of the nivalenol (NIV) type while 29 (18%) isolates were of the 15-acetyl deoxynivalenol type and only 4 (3%) isolates were of the 3-acetyl deoxynivalenol type. The 10 VNTR markers revealed 124 distinct haplotypes and 76 polymorphic alleles across the whole population. The two subpopulations (FA-08 and FA-09) grouped based on the year of collection exhibited low genetic differentiation (Fst = 0.032) and high gene flow (Nm = 15.13). However, a significant genetic differentiation was found within the NIV-type isolates as revealed by the Structure software. The pairwise linkage disequilibrium tests did not support the hypothesis of random mating in the population because half (48.8%) of the locus pairs showed a linkage disequilibrium (P > 0.05). Our results suggest that FHB in this nursery was caused by a genetically homogenous and non-random mating population of F. asiaticum in 2008 and 2009, which consisted of all three trichothecene types with various levels of aggressiveness.

Neutral and Stable Equilibria of Genetic Systems and the Hardy–Weinberg Principle: Limitations of the Chi-Square Test and Advantages of Auto-Correlation Functions of Allele Frequencies

Since the foundations of Population Genetics the notion of genetic equilibrium (in close analogy with Classical Mechanics) has been associated with the Hardy–Weinberg (HW) principle and the identification of equilibrium is currently assumed by stating that the HW axioms are valid if appropriate values of χ2 (p < 0.05) are observed in experiments. Here we show by numerical experiments with the genetic system of one locus/two alleles that considering large ensembles of populations the χ2-test is not decisive and may lead to false negatives in random mating populations and false positives in non-random mating populations. This result confirms the logical statement that statistical tests cannot be used to deduce if the genetic population is under the HW conditions. Furthermore, we show that under the HW conditions populations of any size evolve in time according to what can be identified as neutral dynamics to which the very notion of equilibrium is unattainable for any practical purpose. Therefore, under the HW conditions the identification of equilibrium properties needs a different approach and the use of more appropriate concepts. We also show that by relaxing the condition of random mating the dynamics acquires all the characteristics of asymptotic stable equilibrium. As a consequence our results show that the question of equilibrium in genetic systems should be approached in close analogy to non-equilibrium statistical physics and its observability should be focused on dynamical quantities like the typical decay properties of the allelic auto-correlation function in time. In this perspective one should abandon the classical notion of genetic equilibrium and its relation to the HW proportions and open investigations in the direction of searching for unifying general principles of population genetic transformations capable to take in consideration these systems in their full complexity.

Forward-time simulations of non-random mating populations using simuPOP

Computer simulations play an important role in studies of non-random mating populations. Because of implementation difficulties, only very limited types of non-random mating schemes are provided in the currently available simulation programs. Starting with version 0.8.5, simuPOP provides a few mating schemes that can be used to simulate arbitrary non-random mating models. This article describes the concepts and methods behind these mating schemes and demonstrates their uses in a few examples, including partial self-mating, positive assortative mating, non-random outbreeding, and simulation of overlapping generations in age-structured populations. simuPOP is freely available at http://simupop.sourceforge.net, distributed under a GPL license. Cited examples are in the doc/cookbook directory of a simuPOP distribution.

Competitive divergence in non-random mating populations

A haploid model of frequency-dependent selection and assortative mating is introduced and analyzed for the case of a single multiallelic autosomal locus. Frequency-dependent selection is due to intraspecific competition mediated by a quantitative character under stabilizing or directional selection. Assortment is induced by the same trait. We analyze the equilibrium structure and the local stability properties of all possible equilibria. In the limit of weak selection we obtain global stability properties by finding a Lyapunov function. We provide necessary and sufficient conditions for the maintenance of polymorphism in terms of the strength of stabilizing selection, intraspecific competition and assortment. Our results also include criteria for the ability of extreme types to invade the population. Furthermore, we study the occurrence of disruptive selection and provide necessary and sufficient conditions for intraspecific divergence to occur.

Introgressive hybridization of tilapias in Zimbabwe

Three species of tilapia native to Zimbabwe, Oreochromis mossambicus, O. mortimeri and O. macrochir are not naturally sympatric, but because of transplantation they have been brought into sympatry. Allozymes of fish examined from Lakes Kariba, Kyle and Chivero showed evidence of introgressive hybridization. The data showed non-random mating populations in Lakes Kariba and Kyle. All three reservoirs displayed individuals with intermediate principal component scores and hybrid index scores indicating hybridization.

Inbreeding coefficient and effective size for an X-linked locus in nonrandom mating populations

Formulae are given for equilibrium inbreeding coefficients for an X-linked locus in infinite populations under partial full-sib, half-sib and parent-offspring matings, respectively. An exact recurrence equation for the inbreeding coefficient for an X-linked locus is derived for a finite population with equal numbers of males and females under partial full-sib mating. Following the approach of variance of change in gene frequency, two general equations for effective size for an X-linked locus are obtained. The equations consider an arbitrary distribution of family size, unequal numbers of males and females and nonrandom mating. For some special cases, the equations reduce to the simple expressions derived by previous authors. Comparisons are made between expressions for effective size for an X-linked locus and those for an autosomal locus. Some interesting conclusions are drawn from the analysis and discussed.

A Two‐Stage Test for Distinguishing Random, Pseudo‐Random and Nonrandom Mating Populations

AbstractThere is no such an implication that a population in Hardy‐Weinberg equilibrium must have undergone random mating. Therefore, it is unequivocal that the usual tests for “Hardy‐Weinberg equilibrium” are indeed tests for “random union of gametes” but not for “random mating”. In this paper, utilizing population characteristics expressed in equilibrium state (equilibrium or disequilibrium) and mating behavior (random or nonrandom), a two‐stage testing procedure for distinguishing random, pseudo‐random and nonrandom mating populations is proposed. At the first stage, a population is tested for Hardy‐Weinberg equilibrium. If insignificant result (i.e., in equilibrium) is obtained, then to a second stage the population is further tested for mating behavior. Random mating‐pairs data are needed here for analysis instead of random individuals for usual Hardy‐Weinberg equilibrium tests. Since distinguishing the three types of mating populations depends on the combined results of two stages, the probability of correct determination of the two‐stage tests is discussed by simulation studies.

Effective size of nonrandom mating populations.

Nonrandom mating whereby parents are related is expected to cause a reduction in effective population size because their gene frequencies are correlated and this will increase the genetic drift. The published equation for the variance effective size, Ne, which includes the possibility of nonrandom mating, does not take into account such a correlation, however. Further, previous equations to predict effective sizes in populations with partial sib mating are shown to be different, but also incorrect. In this paper, a corrected form of these equations is derived and checked by stochastic simulation. For the case of stable census number, N, and equal progeny distributions for each sex, the equation is [formula: see text], where Sk2 is the variance of family size and alpha is the departure from Hardy-Weinberg proportions. For a Poisson distribution of family size (Sk2 = 2), it reduces to Ne = N/(1 + alpha), as when inbreeding is due to selfing. When nonrandom mating occurs because there is a specified system of partial inbreeding every generation, alpha can be substituted by Wright's FIS statistic, to give the effective size as a function of the proportion of inbred mates.

On Nonrandom Mating Systems for Attaining Hardy‐Weinberg Equilibrium

AbstractLI (1988) showed that random mating is a sufficient, not a necessary condition for the Hardy‐Weinberg principle. A nonrandom mating population that behaves like a random mating population is thus called a ‘pseudo‐random mating population’ by him. The pseudo‐random mating system studied by him has been focused on those populations in which the parental generation is in Hardy‐Weinberg proportions. In other words, the mating type frequency deviations from random mating for each parental genotype add up to zero. In this article these restrictions are relaxed and new pseudo‐random mating systems that immediately yield Hardy‐Weinberg offspring are also obtained. This is possible because reciprocal crosses have identical segregation probabilities for an autosomal locus, and the manipulation of the combined frequency of reciprocal crosses does not change the gene frequency of the population. A comparison of these new patterns with that of Li is given in the Discussion.

Pseudo-random mating populations. In celebration of the 80th anniversary of the Hardy-Weinberg law.

That random mating leads to Hardy-Weinberg distribution of genotypes is well known. This report is to show that, if the deviations from random mating are of a certain pattern, the offspring generation will also be in Hardy-Weinberg proportions. This brings out the fact that random mating is a sufficient condition, not a necessary one, for the attainment of the Hardy-Weinberg proportions. Such nonrandom-mating populations are tentatively said to be pseudo-random mating. Pseudo-random-mating populations exist for both autosomal and sex-linked systems with two or multiple alleles. This report covers the basic case of a two-allele autosomal locus in detail, but the possible extension to two loci and cytonuclear systems have also been mentioned in discussion.

Sufficient Conditions for Multiple Niche Polymorphism

Sufficient Conditions for Multiple Niche Polymorphism