Analysis of partial assortative mating and sexual selection models for a polygamous species involving a trait based on levels of heterozygosity

The consequences of preferential mating in the presence of partial assortative and sexual selection mechanisms are ascertained for a two-allele one-locus trait involving two phenotype classes C₁ = {all homozygotes} and C₂ = {heterozygotes}. Relevant biological cases may include Burley (1977, Proc. Nat. Acad. Sci. USA74, 3476–3479), Wilbur et al. (1978, Evolution32, 264–270), and Singh and Zouros (1978, Evolution32, 342–353). When the preference rate for the heterozygote exceeds that for homozygotes, it is established that the unique stable state is the central Hardy-Weinberg equilibrium. The rate of approach is faster with sexual selection than for the corresponding model of assortative mating. When the preference rates favor the homozygotes then in this symmetric model of sexual selection two asymmetric Hardy-Weinberg polymorphisms can evolve, and which succeeds depends on initial conditions. The models are also analyzed with natural selection acting on phenotypes superimposed on assortative mating. In this case we can have up to three coexisting stable states involving both fixation alternatives and a central polymorphism. The corresponding model with sexual selection maintains either the central equilibrium as in assortative mating or two asymmetric polymorphic equilibria.     

Comparisons of positive assortative mating and sexual selection models

A series of theoretical models of positive assortative mating and sexual selection are contrasted. It is established that for a dominant trait partial positive assortative mating generally implies some fixation, whereas sexual selection exhibits a unique globally stable polymorphism exhibiting Hardy-Weinberg proportions. The effects of monogamy against polygamy do not qualitatively alter the equilibrium outcomes, although the rate of evolutionary change is generally slowed with monogamy vis-à-vis polygamy. For sexual selection the influence of timing of random mating as against preferential mating causes no change in the equilibrium states, although the rates of convergence can be slowed if sexual selection occurs late in the breeding season. Under assortative mating the timing can alter the equilibrium outcomes. The amount of heterozygosity is always deficient in cases of assortative mating, but always exhibits Hardy-Weinberg ratios under a sexual selection mechanism. This suggests that observations consistent with Hardy-Weinberg equilibrium states cannot preclude ipso facto certain forms of selection forces, including mating patterns and some natural selection structures.     

A novel method for estimating the strength of positive mating preference by similarity in the wild

Mating preference can be a driver of sexual selection and assortative mating and is, therefore, a key element in evolutionary dynamics. Positive mating preference by similarity is the tendency for the choosy individual to select a mate which possesses a similar variant of a trait. Such preference can be modelled using Gaussian‐like mathematical functions that describe the strength of preference, but such functions cannot be applied to empirical data collected from the field. As a result, traditionally, mating preference is indirectly estimated by the degree of assortative mating (using Pearson's correlation coefficient, r) in wild captured mating pairs. Unfortunately, r and similar coefficients are often biased due to the fact that different variants of a given trait are nonrandomly distributed in the wild, and pooling of mating pairs from such heterogeneous samples may lead to “false–positive” results, termed “the scale‐of‐choice effect” (SCE). Here we provide two new estimators of mating preference (C_rough and C_scaled) derived from Gaussian‐like functions which can be applied to empirical data. Computer simulations demonstrated that r coefficient showed robust estimations properties of mating preference but it was severely affected by SCE, C_rough showed reasonable estimation properties and it was little affected by SCE, while C_scaled showed the best properties at infinite sample sizes and it was not affected by SCE but failed at biological sample sizes. We recommend using C_rough combined with the r coefficient to infer mating preference in future empirical studies.     

Rules for assortative mating in relation to selection for linear merit functions

Summary This study examined how assortative mating (without selection) based on linear combinations of two traits could be used to change genetic parameters so as to increase efficiency of selection. The efficiency of the Smith-Hazel index for improvement of multiple traits is a function of phenotypic and genetic variances and covariances, and of the relative economic values of the traits involved. Assortative mating is known to change genetic variances and covariances. Recursive formulae were derived to obtain these variances and covariances after t generations of assortative mating on linear combinations (mating rules) of phenotypic values for two traits, with a given correlation between mates. Selection efficiency after t generations of assortative mating without selection was expressed as a function of random mating genetic parameters, economic values, the mating rule, and the correlation between mates. Selection efficiency was maximized with respect to the coefficients in the mating rule. Because the objective function was nonlinear, a computer routine was used for maximizing it. Two cases were considered. When random mating heritabilities for the two traits were h _X ² =0.25 and h _Y ² =0.50, the genetic correlation r_XY=-0.60, and the economic values were a_X=3 and a_Y=1, continued assortative mating based on the optimal mating rule for 31 generations (with a correlation of 0.80 between mates) increased selection efficiency by 29%. Heritabilities changed to 0.38 and 0.66, respectively, and the genetic correlation became – 0.79. When h _X ² =0.60, h _Y ² =0.60, r_XY=– 0.20, a₁=1 and a₂=1, 36 generations of continued assortative mating with the optimal mating rule increased the efficiency of selection by 17%, heritabilities became h _X ² = h _Y ² =0.71, and the genetic correlation changed to 0.25. Only three generations of assortative mating were required to change the sign of the genetic correlation.     

The average frequency of private alleles in a partially isolated population

An analytic model is developed to explore the relationship between gene flow, selection, and genetic drift. We assume that a single copy of a mutant allele appears in a finite, partially isolated population and allow for the effects of immigration, genic selection, and mutation on the frequency of the mutant. Our concern is with the distribution of the mutant's frequency before it either is lost from the population or emigrates. Before either of these events, the allele will be a “private allele” and would be found in only one of several populations in a larger collection. Slatkin [(1985) Evolution 39, 53–65] found several simple properties of private alleles in his simulations. We use the method developed by Karlin and Tavaré [(1980) Genet. Res. 37, 33–46; (1981a), Theor. Pop. Biol. 19, 187–214; (1981b) Theor. Pop. Biol. 19, 215–229] for a model similar to ours to obtain a diffusion equation with a “killing term” and obtain the mean and variance of the mutant's frequency and its expected frequency in samples of a specified size. There is only fair agreement between the analytic results from this model and those from Slatkin's (loc. cit.) simulations. The rescaling method used to obtain the results indicates that if emigration is relatively frequent, the distribution of rare alleles is governed largely by the balance between genetic drift and emigration, with selection, mutation, and immigration playing a lesser role.     

Emergence and loss of assortative mating in sympatric speciation

We have studied an agent model which presents the emergence of sexual barriers through the onset of assortative mating, a condition that might lead to sympatric speciation. In the model, individuals are characterized by two traits, each determined by a single locus A or B. Heterozygotes on A are penalized by introducing an adaptive difference from homozygotes. Two niches are available. Each A homozygote is adapted to one of the niches. The second trait, called the marker trait has no bearing on the fitness. The model includes mating preferences, which are inherited from the mother and subject to random variations. A parameter controlling recombination probabilities of the two loci is also introduced. We study the phase diagram by means of simulations, in the space of parameters (adaptive difference, carrying capacity, recombination probability). Three phases are found, characterized by (i) assortative mating, (ii) extinction of one of the A alleles and (iii) Hardy-Weinberg like equilibrium. We also make perturbations of these phases to see how robust they are. Assortative mating can be gained or lost with changes that present hysteresis loops, showing the resulting equilibrium to have partial memory of the initial state and that the process of going from a polymorphic panmictic phase to a phase where assortative mating acts as sexual barrier can be described as a first-order transition.     

On the role of sexual selection in ecological divergence: a test of body‐size assortative mating in the eastern newt Notophthalmus viridescens

Speciation processes initiated by divergent selection often fail to complete; yet, how sexual selection is involved in the progress of ecological speciation is rarely understood. Intraspecific body‐size variation affects mate preference and male–male competition, which can consequently lead to assortative mating based on body size. In the present study, we tested the importance of body size difference in the potential of assortative mating between the two eastern newt subspecies, larger Notophthalmus viridescens viridescens and smaller Notophthalmus viridescens dorsalis. Through differential expression of life‐cycle polyphenism, these two subspecies are adapted to contrasting environments, which has likely led to the subspecific body‐size difference. We found that males of both subspecies preferred larger females of N. v. viridescens as mates presumably because of the fecundity advantage of larger females. On the other hand, no evidence of female choice was found. Larger males of N. v. viridescens exhibited greater competitive ability and gained primary access to larger females of their own kind. However, smaller males were able to overcome their inferior competitive ability by interfering with larger males' spermatophore transfer and sneakily mating with larger females. Thus, the subspecific body‐size difference importantly affected sexual selection processes, resulting in nonrandom but not completely assortative mating patterns between the larger and smaller subspecies. Although life‐cycle polyphenism facilitates the intraspecific ecological divergence within N. v. viridescens sexual selection processes, namely smaller males' mate preference for larger females and sexual interference during spermatophore transfer, may be halting completion of the ecological speciation. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2010, 101 , 884–897.     

Frequency-dependent selection and the evolution of assortative mating

A long-standing goal in evolutionary biology is to identify the conditions that promote the evolution of reproductive isolation and speciation. The factors promoting sympatric speciation have been of particular interest, both because it is notoriously difficult to prove empirically and because theoretical models have generated conflicting results, depending on the assumptions made. Here, we analyze the conditions under which selection favors the evolution of assortative mating, thereby reducing gene flow between sympatric groups, using a general model of selection, which allows fitness to be frequency dependent. Our analytical results are based on a two-locus diploid model, with one locus altering the trait under selection and the other locus controlling the strength of assortment (a "one-allele" model). Examining both equilibrium and nonequilibrium scenarios, we demonstrate that whenever heterozygotes are less fit, on average, than homozygotes at the trait locus, indirect selection for assortative mating is generated. While costs of assortative mating hinder the evolution of reproductive isolation, they do not prevent it unless they are sufficiently great. Assortative mating that arises because individuals mate within groups (formed in time or space) is most conducive to the evolution of complete assortative mating from random mating. Assortative mating based on female preferences is more restrictive, because the resulting sexual selection can lead to loss of the trait polymorphism and cause the relative fitness of heterozygotes to rise above homozygotes, eliminating the force favoring assortment. When assortative mating is already prevalent, however, sexual selection can itself cause low heterozygous fitness, promoting the evolution of complete reproductive isolation (akin to "reinforcement") regardless of the form of natural selection.     

Sexual selection and assortative mating: an experimental test

Mate choice and mate competition can both influence the evolution of sexual isolation between populations. Assortative mating may arise if traits and preferences diverge in step, and, alternatively, mate competition may counteract mating preferences and decrease assortative mating. Here, we examine potential assortative mating between populations of Drosophila pseudoobscura that have experimentally evolved under either increased (‘polyandry’) or decreased (‘monogamy’) sexual selection intensity for 100 generations. These populations have evolved differences in numerous traits, including a male signal and female preference traits. We use a two males: one female design, allowing both mate choice and competition to influence mating outcomes, to test for assortative mating between our populations. Mating latency shows subtle effects of male and female interactions, with females from the monogamous populations appearing reluctant to mate with males from the polyandrous populations. However, males from the polyandrous populations have a significantly higher probability of mating regardless of the female's population. Our results suggest that if populations differ in the intensity of sexual selection, effects on mate competition may overcome mate choice.     

Variation in complex mating signals in an “island” hybrid zone between Stenobothrus grasshopper species

Two grasshopper species Stenobothrus rubicundus and S. clavatus were previously shown to meet in a narrow hybrid zone on Mount Tomaros in northern Greece. The species are remarkable for their complex courtship songs accompanied by conspicuous movements of antennae and wings. We analyzed variations in forewing morphology, antenna shape, and courtship song across the hybrid zone using a geographic information system, and we documented three contact zones on Mount Tomaros. All male traits and female wings show abrupt transitions across the contact zones, suggesting that these traits are driven by selection rather than by drift. Male clines in antennae are displaced toward S. clavatus, whereas all clines in wings are displaced toward S. rubicundus. We explain cline discordance as depending on sexual selection via female choice. The high covariance between wings and antennae found in the centers of all contact zones results from high levels of linkage disequilibria among the underlying loci, which in turn more likely results from assortative mating than from selection against hybrids. The covariance is found to be higher in clavatus‐like than rubicundus‐like populations, which implies asymmetric assortative mating in parental‐like sites of the hybrid zone and a movement of the hybrid zone in favor of S. clavatus.     

The effect of positive assortative mating at one locus on a second linked locus

Summary A model for positive assortative mating based on genotype for one locus is employed to investigate the effect of this mating system on the genotypic structure of a second linked locus as well as on the joint genotypic structure of these two loci. It is shown that the second locus does not attain a precise positive assortative mating structure, but yet it shares a property that is characteristic of positive assortative mating, namely an increase in the frequency of homozygotes over that typically found in panmictic structures. Given any arbitrary genotypic structure for the parental population, the resulting offspring generation possesses a structure at the second locus that does not depend on the recombination frequency, while the joint structure of course does. In case assortative mating as well as linkage are not complete, there exists a unique joint equilibrium state for the two loci, which is characterized by complete stochastic independence between the two loci as well as by Hardy-Weinberg proportions at the second locus. For the second locus alone, Hardy-Weinberg equilibrium is realized if and only if gametic linkage equilibrium and an additionally specified condition are realized.     

Assortative mating,sexual selection,and their consequences for gene flow in Littorina

When divergent populations are connected by gene flow, the establishment of complete reproductive isolation usually requires the joint action of multiple barrier effects. One example where multiple barrier effects are coupled consists of a single trait that is under divergent natural selection and also mediates assortative mating. Such multiple-effect traits can strongly reduce gene flow. However, there are few cases where patterns of assortative mating have been described quantitatively and their impact on gene flow has been determined. Two ecotypes of the coastal marine snail, Littorina saxatilis, occur in North Atlantic rocky-shore habitats dominated by either crab predation or wave action. There is evidence for divergent natural selection acting on size, and size-assortative mating has previously been documented. Here, we analyze the mating pattern in L. saxatilis with respect to size in intensively sampled transects across boundaries between the habitats. We show that the mating pattern is mostly conserved between ecotypes and that it generates both assortment and directional sexual selection for small male size. Using simulations, we show that the mating pattern can contribute to reproductive isolation between ecotypes but the barrier to gene flow is likely strengthened more by sexual selection than by assortment.     

Asymmetric mating in the brachypterous grasshopper Podisma sapporensis

Crossing of genetically differentiated populations often results in assortative mating within populations. However, asymmetric sexual isolation or negative assortative mating has occasionally been reported. Previous studies suggested that sexual selection or sexual conflicts would lead to asymmetric mating when local populations are crossed. In order to evaluate the extent of assortative or disassortative mating in population crosses, we conducted laboratory crosses using the flightless grasshopper Podisma sapporensis. Crossing was conducted for all pairwise combinations of three populations, 150–240 km from one another – Teine, Shimokawa, and Akan. We found evidence for asymmetric mating for all the pairs of the populations. In particular, when the Teine and Akan populations were crossed, mating in the Teine male–Akan female cross was significantly more frequent than mating in both within‐population crosses, whereas mating in the Teine female–Akan male cross was significantly less frequent than mating in both within‐population crosses. We examined whether these results can be explained by any of the three hypotheses: (1) Kaneshiro's hypothesis, (2) differentiation in attractiveness, or (3) coevolution between male vigor and female receptivity. All the results were consistent with male vigor differing between populations balanced by different female potential to reject males. The available evidence suggests that antagonistic coevolution between the sexes has led local populations to different equilibria and that crossing of populations at different equilibria has resulted in asymmetry in mating frequencies.     

Structure toxicity relationships of synthetic azaspiracid-1 and analogs in mice

Synthetic azaspiracid-1 (AZA-1, 1), 6-, 10-, 13-, 14-, 16-, 17-, 19-, 20-epi-azaspiracid-1 (C₁–C₂₀-epi-AZA-1, 2), and twelve truncated azaspiracid-1 analogs (3–14) were synthesized and tested for their toxicity effects in mice. Of these compounds only AZA-1 (1) and its diastereomer C₁–C₂₀-epi-AZA-1 (2) exhibited significant toxicity in mice with the latter compound (2) being one-fourth as toxic as the former (1). The lack of toxicity exhibited by the severely truncated analogs (3–14) implies that the entire or at least a major part of the structure of AZA-1 (1) is required for biological activity.     

Sexual size dimorphism and assortative mating for morphological traits in Passer domesticus

In this study, assortative mating for different morphological traits was studied in a captive population of house sparrows (Passer domesticus). Males were larger than females. Assortative mating was found for tail length, wing length and general body size. Males with larger badge size mated with females with longer tails. The strongest assortative mating occurred for tail length (r=0.77), and this assortative mating remained significant after controlling for wing length, mass and tarsus length, suggesting that it was not an artefact of assortative mating for body size. The possibility of sexual selection for tail length in the house sparrow is discussed.     

3-(1′,1′-Dimethylbutyl)-1-deoxy-Δ-THC and related compounds: synthesis of selective ligands for the CB2 receptor

The synthesis and pharmacology of 15 1-deoxy-Δ⁸-THC analogues, several of which have high affinity for the CB₂ receptor, are described. The deoxy cannabinoids include 1-deoxy-11-hydroxy-Δ⁸-THC (5), 1-deoxy-Δ⁸-THC (6), 1-deoxy-3-butyl-Δ⁸-THC (7), 1-deoxy-3-hexyl-Δ⁸-THC (8) and a series of 3-(1′,1′-dimethylalkyl)-1-deoxy-Δ⁸-THC analogues (2, n=0–4, 6, 7, where n=the number of carbon atoms in the side chain−2). Three derivatives (17–19) of deoxynabilone (16) were also prepared. The affinities of each compound for the CB₁ and CB₂ receptors were determined employing previously described procedures. Five of the 3-(1′,1′-dimethylalkyl)-1-deoxy-Δ⁸-THC analogues (2, n=1–5) have high affinity (K_i=<20 nM) for the CB₂ receptor. Four of them (2, n=1–4) also have little affinity for the CB₁ receptor (K_i=>295 nM). 3-(1′,1′-Dimethylbutyl)-1-deoxy-Δ⁸-THC (2, n=2) has very high affinity for the CB₂ receptor (K_i=3.4±1.0 nM) and little affinity for the CB₁ receptor (K_i=677±132 nM).

Scheme 3. (a) (C₆H₅)₃PCH₃⁺ Br⁻, n-BuLi/THF, 65°C; (b) LiAlH₄/THF, 25°C; (c) KBH(sec-Bu)₃/THF, −78 to 25°C then H₂O₂/NaOH.     

Seeking signatures of reinforcement at the genetic level: a hitchhiking mapping and candidate gene approach in the house mouse

Reinforcement is the process by which prezygotic isolation is strengthened as a response to selection against hybridization. Most empirical support for reinforcement comes from the observation of its possible phenotypic signature: an accentuated degree of prezygotic isolation in the hybrid zone as compared to allopatry. Here, we implemented a novel approach to this question by seeking for the signature of reinforcement at the genetic level. In the house mouse, selection against hybrids and enhanced olfactory‐based assortative mate preferences are observed in a hybrid zone between the two European subspecies Mus musculus musculus and M. m. domesticus, suggesting a possible recent reinforcement event. To test for the genetic signature of reinforcing selection and identify genes involved in sexual isolation, we adopted a hitchhiking mapping approach targeting genomic regions containing candidate genes for assortative mating in mice. We densely scanned these genomic regions in hybrid zone and allopatric samples using a large number of fast evolving microsatellite loci that allow the detection of recent selection events. We found a handful of loci showing the expected pattern of significant reduction in variability in populations close to the hybrid zone, showing assortative odour preference in mate choice experiments as compared to populations further away and displaying no such preference. These loci lie close to genes that we pinpoint as testable candidates for further investigation.     

Some population genetic models combining artificial and natural selection pressures in the presence of assortative mating

Summary We have attempted quantitatively through a series of assortative mating models to gain insight into the interaction between the usually antagonistic tendencies of artificial and natural selection pressures. We summarize some of the robust conclusions. In cases where natural selection is expressed only through the phenotype and acts in the opposite direction to the culling incline, then fixation of the dominant or recessive type can be achieved and which occurs depends critically on the initial composition of the population and the magnitude of the degree of culling compared to the selection coefficients.With traits determined at two loci in the case that the double heterozygote is the desired kind, the effect of selfing can only be overcome by very strong artificial selection pressures (high culling order). The degree of culling to achieve its objective can be relaxed with weakening of linkage. The relevant comparison is r ₂ + (1 – r)₂ < (1 – c)indicating the precise extent of culling needed, to prevent fixation. The relationships are more complex when natural selection forces are also involved (see Model IV).Supported in part by NIH Grant USPHS 10452-09.     

m-Alkyl, α,α,α-trifluoroacetophenones: A new class of potent transition state analog inhibitors of acetylcholinesterase

A series of m-alkyl α,α,α-trifluoroacetophenones (1–5) was synthesized and evaluated as inhibitors of acetylcholinesterase from Torpedo california. All ketones (1–5) were found to be potent inhibitors of the enzyme; m-t-butyl α,α,α-trifluoroacetophenone (4) was the most potent inhibitor with a K_i value of 3.7 pM.     

Origin and evolution of assortative mating in actively speciating mole rats

The origin and evolution of positive assortative mating in the actively speciating subterranean mole rats of the Spalax ehrenbergi superspecies in Israel, may be deciphered by comparing female mate preference in the laboratory between ancestral and derivative species. Estrous females of the recent derivative of speciation (chromosomal species 2n = 60) showed trimodal mate preference distribution significantly differing from a normal curve. Females consisted of three phenotypes, comprising negative, low positive, and high positive preference for homospecific males. By contrast, mate preference in encounters of ancestral species (2n = 52, 54, and 58) showed a prevalence of a positive homospecific mate preference. It is suggested that the three modal distribution is explicable even on the basis of one major gene with three genotypes. The evolution of ethological reproductive isolation proceeded presumably from a high polymorphism in the most recent derivative of speciation towards increasing monomorphism of positive assortative mating among ancestral species. If an assortative mating locus combines with sexual selection of the frequent male adapted optimally to the local environment, then speciation and adaptation will be tightly linked in the evolution of mole rats.