Perturbation expansions of multilocus fixation probabilities for frequency-dependent selection with applications to the Hill-Robertson effect and to the joint evolution of helping and punishment.

Natural populations are of finite size and organisms carry multilocus genotypes. There are, nevertheless, few results on multilocus models when both random genetic drift and natural selection affect the evolutionary dynamics. In this paper we describe a formalism to calculate systematic perturbation expansions of moments of allelic states around neutrality in populations of constant size. This allows us to evaluate multilocus fixation probabilities (long-term limits of the moments) under arbitrary strength of selection and gene action. We show that such fixation probabilities can be expressed in terms of selection coefficients weighted by mean first passages times of ancestral gene lineages within a single ancestor. These passage times extend the coalescence times that weight selection coefficients in one-locus perturbation formulas for fixation probabilities. We then apply these results to investigate the Hill-Robertson effect and the coevolution of helping and punishment. Finally, we discuss limitations and strengths of the perturbation approach. In particular, it provides accurate approximations for fixation probabilities for weak selection regimes only (Ns < or = 1), but it provides generally good prediction for the direction of selection under frequency-dependent selection.

Frequency-dependent selection at the amylase locus in Drosophila melanogaster

A. strain of Drosophila melanog-aster deficient in null amylase activity (Amylase ) was isolated from a wild null population of flies. The survivorship of Amylase homozygous flies is very low when the principal dietary carbohydrate source is starch. However, the survivorship of the null Amylase genotype is comparable to the wild type when the dietary starch is replaced by glucose. In addition, the null viability of the amylase-producing and Amylase strains is comparable v and very lm<] f on a medium with no carbohydrates . Furthermore, amylase-producing genotypes were shovm to excrete enzymatically active amylase protein into the food medium. The excreted amylase causes the external breakdown of dietary starch to sugar. These results led to the following null prediction: the viability of the A.mvlase genotype (fed on a starch rich diet) might increase in the presence of individuals which were amylase-producing. It was shown experimentally that such an increase in viability did in fact occur and that this increase v\Tas proportional to the number of mnylase..::producing fli.es present. These results provide a unique example of a non-"competi ti ve inter-genotype interaction, and one where the underlying physio~ logical and biochemical mechanism has been fully understood.

Frequency-Dependent Selection Predicts Patterns of Radiations and Biodiversity

Most empirical studies support a decline in speciation rates through time, although evidence for constant speciation rates also exists. Declining rates have been explained by invoking pre-existing niches, whereas constant rates have been attributed to non-adaptive processes such as sexual selection and mutation. Trends in speciation rate and the processes underlying it remain unclear, representing a critical information gap in understanding patterns of global diversity. Here we show that the temporal trend in the speciation rate can also be explained by frequency-dependent selection. We construct a frequency-dependent and DNA sequence-based model of speciation. We compare our model to empirical diversity patterns observed for cichlid fish and Darwin's finches, two classic systems for which speciation rates and richness data exist. Negative frequency-dependent selection predicts well both the declining speciation rate found in cichlid fish and explains their species richness. For groups like the Darwin's finches, in which speciation rates are constant and diversity is lower, speciation rate is better explained by a model without frequency-dependent selection. Our analysis shows that differences in diversity may be driven by incipient species abundance with frequency-dependent selection. Our results demonstrate that genetic-distance-based speciation and frequency-dependent selection are sufficient to explain the high diversity observed in natural systems and, importantly, predict decay through time in speciation rate in the absence of pre-existing niches.

Negative frequency-dependent selection maintains a dramatic flower color polymorphism in the rewardless orchid Dactylorhiza sambucina (L.) Soò

The orchid Dactylorhiza sambucina shows a stable and dramatic flower-color polymorphism, with both yellow- and purple-flowered individuals present in natural populations throughout the range of the species in Europe. The evolutionary significance of flower-color polymorphisms found in many rewardless orchid species has been discussed at length, but the mechanisms responsible for their maintenance remain unclear. Laboratory experiments have suggested that behavioral responses by pollinators to lack of reward availability might result in a reproductive advantage for rare-color morphs. Consequently, we performed an experiment varying the relative frequency of the two color morphs of D. sambucina to test whether rare morph advantage acted in the natural habitat of the species. We show here clear evidence from this manipulative experiment that rare-color morphs have reproductive advantage through male and female components. This is the first demonstration, to our knowledge, that negative frequency-dependent selection through pollinator preference for rare morphs can cause the maintenance of a flower-color polymorphism.

Cumulative frequency-dependent selective episodes allow for rapid morph cycles and rock-paper-scissors dynamics in species with overlapping generations.

Rock-paper-scissors (RPS) dynamics, which maintain genetic polymorphisms over time through negative frequency-dependent (FD) selection, can evolve in short-lived species with no generational overlap, where they produce rapid morph frequency cycles. However, most species have overlapping generations and thus, rapid RPS dynamics are thought to require stronger FD selection, the existence of which yet needs to be proved. Here, we experimentally demonstrate that two cumulative selective episodes, FD sexual selection reinforced by FD selection on offspring survival, generate sufficiently strong selection to generate rapid morph frequency cycles in the European common lizard Zootoca vivipara, a multi-annual species with major generational overlap. These findings show that the conditions required for the evolution of RPS games are fulfilled by almost all species exhibiting genetic polymorphisms and suggest that RPS games may be responsible for the maintenance of genetic diversity in a wide range of species.

Frequency-dependent social dominance in a color polymorphic cichlid fish

A mechanism commonly suggested to explain the persistence of color polymorphisms in animals is negative frequency-dependent selection. It could result from a social dominance advantage to rare morphs. We tested for this in males of red and blue color morphs of the Lake Victoria cichlid, Pundamilia. Earlier work has shown that males preferentially attack the males of their own morph, while red males are more likely to win dyadic contests with blue males. In order to study the potential contribution of both factors to the morph co-existence, we manipulated the proportion of red and blue males in experimental assemblages and studied its effect on social dominance. We then tried to disentangle the effects of the own-morph attack bias and social dominance of red using simulations. In the experiment, we found that red males were indeed socially dominant to the blue ones, but only when rare. However, blue males were not socially dominant when rare. The simulation results suggest that an own-morph attack bias reduces the social dominance of red males when they are more abundant. Thus, there is no evidence of symmetric negative frequency-dependent selection acting on social dominance, suggesting that additional fitness costs to the red morph must explain their co-existence.

Evolution of dominance under frequency-dependent intraspecific competition

A population-genetic analysis is performed of a two-locus two-allele model, in which the primary locus has a major effect on a quantitative trait that is under frequency-dependent disruptive selection caused by intraspecific competition for a continuum of resources. The modifier locus determines the degree of dominance at the trait level. We establish the conditions when a modifier allele can invade and when it becomes fixed if sufficiently frequent. In general, these are not equivalent because an unstable internal equilibrium may exist and the condition for successful invasion of the modifier is more restrictive than that for eventual fixation from already high frequency. However, successful invasion implies global fixation, i.e., fixation from any initial condition. Modifiers of large effect can become fixed, and also invade, in a wider parameter range than modifiers of small effect. We also study modifiers with a direct, frequency-independent deleterious fitness effect. We show that they can invade if they induce a sufficiently high level of dominance and if disruptive selection on the ecological trait is strong enough. For deleterious modifiers, successful invasion no longer implies global fixation because they can become stuck at an intermediate frequency due to a stable internal equilibrium. Although the conditions for invasion and for fixation if sufficiently frequent are independent of the linkage relation between the two loci, the rate of spread depends strongly on it. The present study provides further support to the view that evolution of dominance may be an efficient mechanism to remove unfit heterozygotes that are maintained by balancing selection. It also demonstrates that an invasion analysis of mutants of very small effect is insufficient to obtain a full understanding of the evolutionary dynamics under frequency-dependent selection.

EVOLUTION OF DOMINANCE UNDER FREQUENCY-DEPENDENT INTRASPECIFIC COMPETITION IN AN ASSORTATIVELY MATING POPULATION

We study the evolution of higher levels of dominance as a response to negative frequency-dependent selection. In contrast to previous studies, we focus on the effect of assortative mating on the evolution of dominance under frequency-dependent intraspecific competition. We analyze a two-locus two-allele model, in which the primary locus has a major effect on a quantitative trait that is under a mixture of frequency-independent stabilizing selection, density-dependent selection, and frequency-dependent selection caused by intraspecific competition for a continuum of resources. The second (modifier) locus determines the degree of dominance at the trait level. Additionally, the population mates assortatively with respect to similarities in the ecological trait. Our analysis shows that the parameter region in which dominance can be established decreases if small levels of assortment are introduced. In addition, the degree of dominance that can be established also decreases. In contrast, if assortment is intermediate, sexual selection for extreme types can be established, which leads to evolution of higher levels of dominance than under random mating. For modifiers with large effects, intermediate levels of assortative mating are most favorable for the evolution of dominance. For large modifiers, the speed of fixation can even be higher for intermediate levels of assortative mating than for random mating.

Frequency-dependent sexual selection with respect to offspring fitness returns is consistent with predictions from rock-paper-scissors dynamics in the European common lizard

Genetic polymorphism can be maintained over time by negative frequency-dependent (FD) selection induced by Rock-paper-scissors (RPS) social systems. RPS games produce cyclic dynamics, and have been suggested to exist in lizards, insects, isopods, plants, and bacteria. Sexual selection is predicted to accentuate the survival of the future progeny during negative FD survival selection. More specifically, females are predicted to select mates that produce progeny genotypes that exhibit highest survival during survival selection imposed by adult males. However, no empirical evidence demonstrates the existence of FD sexual selection with respect to fitness payoffs of genetic polymorphisms. Here we tested this prediction using the common lizard Zootoca vivipara, a species with three male color morphs (orange, white, yellow) that exhibit morph frequency cycles. In a first step we tested the congruence of the morph frequency change with the predicted change in three independent populations, differing in male color morph frequency and state of the FD morph cycle. Thereafter we ran standardized sexual selection assays in which we excluded alternative mechanisms that potentially induce negative FD selection, and we quantified inter-sexual behavior. The patterns of sexual selection and the observed behavior were in line with context-dependent female mate choice and male behavior played a minor role. Moreover, the strength of the sexual selection was within the magnitude of selection required to produce the observed 3-4-year and 6-8 year morph frequency cycles at low and high altitudes, respectively. In summary, the study provides the first experimental evidence that underpins the crucial assumption of the RPS games suggested to exist in lizards, insects, isopods, and plants; namely, that sexual selection produces negative-FD selection. This indicates that sexual selection, in our study exert by females, might be a crucial driver of the maintenance of genetic polymorphisms.

Evolution of foraging behavior in Drosophila by density-dependent selection

One of the rare examples of a single major gene underlying a naturally occurring behavioral polymorphism is the foraging locus of Drosophila melanogaster. Larvae with the rover allele, forR, have significantly longer foraging path lengths on a yeast paste than do those homozygous for the sitter allele, fors. These variants do not differ in general activity in the absence of food. The evolutionary significance of this polymorphism is not as yet understood. Here we examine the effect of high and low animal rearing densities on the larval foraging path-length phenotype and show that density-dependent natural selection produces changes in this trait. In three unrelated base populations the long path (rover) phenotype was selected for under high-density rearing conditions, whereas the short path (sitter) phenotype was selected for under low-density conditions. Genetic crosses suggested that these changes resulted from alterations in the frequency of the fors allele in the low-density-selected lines. Further experiments showed that density-dependent selection during the larval stage rather than the adult stage of development was sufficient to explain these results. Density-dependent mechanisms may be sufficient to maintain variation in rover and sitter behavior in laboratory populations.

Frequency band selection of radars for buried object detection

Choice of the operational frequency is one of the most responsible parts of any radar design process. Parameters of radars for buried object detection (BOD) are very sensitive to both carrier frequency and ranging signal bandwidth. Such radars have a specific propagation environment with a strong frequency-dependent attenuation and, as a result, short operational range. This fact dictates some features of the radar's parameters: wideband signal-to provide a high range resolution (fractions of a meter) and a low carrier frequency (tens or hundreds megahertz) for deeper penetration. The requirement to have a wideband ranging signal and low carrier frequency are partly in contradiction. As a result, low-frequency (LF) ultrawide-band (UWB) signals are used. The major goal of this paper is to examine the influence of the frequency band choice on the radar performance and develop relevant methodologies for BOD radar design and optimization. In this article, high-efficient continuous wave (CW) signals with most advanced stepped frequency (SF) modulation are considered; however, the main conclusions can be applied to any kind of ranging signals.

Sex-dependent selection on an autosomal melanic female ornament promotes the evolution of sex ratio bias.

Sex-dependent selection often leads to spectacularly different phenotypes in males and females. In species in which sexual dimorphism is not complete, it is unclear which benefits females and males derive from displaying a trait that is typical of the other sex. In barn owls (Tyto alba), females exhibit on average larger black eumelanic spots than males but members of the two sexes display this trait in the same range of possible values. In a 12-year study, we show that selection exerted on spot size directly or on genetically correlated traits strongly favoured females with large spots and weakly favoured males with small spots. Intense directional selection on females caused an increase in spot diameter in the population over the study period. This increase is due to a change in the autosomal genes underlying the expression of eumelanic spots but not of sex-linked genes. Female-like males produced more daughters than sons, while male-like females produced more sons than daughters when mated to a small-spotted male. These sex ratio biases appear adaptive because sons of male-like females and daughters of female-like males had above-average survival. This demonstrates that selection exerted against individuals displaying a trait that is typical of the other sex promoted the evolution of specific life history strategies that enhance their fitness. This may explain why in many organisms sexual dimorphism is often not complete.

Sex allocation and sex-dependent selection for body size in Trypoxylon rogenhoferi Kohl (Hymenoptera, Sphecidae)

Two populations of the wasp Trypoxylon rogenhoferi Kohl, 1884 from São Carlos and Luís Antônio, State of São Paulo, Brazil, were observed and sampled from May 1999 to February 2001 using trap-nests. This mass-provisioning wasp was used to test some aspects of optimal sex allocation theory. Both populations fit all the predictions of the models of Green and Brockmann and Grafen. Maternal provisions determined the size of each offspring, and females allocated well-stocked brood cells to daughters, the sex that benefits most being large. This strategy resulted in a difference in size between the sexes. In São Carlos, female weight at emergence was 1.18 times that of males, in Luís Antônio this value was 1.13. The brood cell volume was correlated with both wing length and weight at emergence in both sexes, and the chance that a given brood cell contained a male offspring decreased with increased brood cell volume. In T. rogenhoferi female body size was related to fitness. Larger females were able to collect more mass of spiders per day, the spiders they captured were heavier, and they provisioned more brood cells per day. They also produced larger daughters. For males, no relationship between body size and fitness was found, but the data were scarce. Since the patterns of provisioning were variable among different females in both study sites, it is possible that the females not follow a unique strategy for sex allocation. The sex ratio and/or investment ratio in the São Carlos population was female-biased and in Luís Antônio, male-biased. In spite of the influence of trap-nests diameters on male production in Luís Antônio, there is some evidence that in São Carlos population the local availability of prey and/or lower rate of parasitism may be major forces in determining the observed sex ratio, but further studies are necessary to verify such hypothesis.

A physical frequency-dependent compact model for RF integrated inductors

A frequency-dependent compact model for inductors in high ohmic substrates, which is based on an energy point-of-view, is developed. This approach enables the description of the most important coupling phenomena that take place inside the device. Magnetically induced losses are quite accurately calculated and coupling between electric and magnetic fields is given by means of a delay constant. The later coupling phenomenon provides a modified procedure for the computation of the fringing capacitance value, when the self-resonance frequency of the inductor is used as a fitting parameter. The model takes into account the width of every metal strip and the pitch between strips. This enables the description of optimized layout inductors. Data from experiments and electromagnetic simulators are presented to test the accuracy of the model.

Frequency-dependent attenuation as a potential indicator of oil saturation

At seismic frequencies, wave-induced fluid flow is a major cause of P-wave attenuation in partially saturated porous rocks. Attenuation is of great importance for the oil industry in the interpretation of seismic field data. Here, the effects on P-wave attenuation resulting from changes in oil saturation are studied for media with coexisting water, oil, and gas. For that, creep experiments are numerically simulated by solving Biot's equations for consolidation of poroelastic media with the finite-element method. The experiments yield time-dependent stress?strain relations that are used to calculate the complex P-wave modulus from which frequency-dependent P-wave attenuation is determined. The models are layered media with periodically alternating triplets of layers. Models consisting of triplets of layers having randomly varying layer thicknesses are also considered. The layers in each triplet are fully saturated with water, oil, and gas. The layer saturated with water has lower porosity and permeability than the layers saturated with oil and gas. These models represent hydrocarbon reservoirs in which water is the wetting fluid preferentially saturating regions of lower porosity. The results from the numerical experiments showed that increasing oil saturation, connected to a decrease in gas saturation, resulted in a significant increase of attenuation at low frequencies (lower than 2 Hz). Furthermore, replacing the oil with water resulted in a distinguishable behavior of the frequency-dependent attenuation. These results imply that, according to the physical mechanism of wave-induced fluid flow, frequency-dependent attenuation in media saturated with water, oil, and gas is a potential indicator of oil saturation.