Condition-dependence,genotype-by-environment interactions and the lek paradox

The lek paradox states that maintaining genetic variation necessary for 'indirect benefit' models of female choice is difficult, and two interrelated solutions have been proposed. 'Genic capture' assumes condition-dependence of sexual traits, while genotype-by-environment interactions (GEIs) offer an additional way to maintain diversity. However, condition-dependence, particularly with GEIs, implies that environmental variation can blur the relationship between male displays and offspring fitness. These issues have been treated separately in the past. Here we combine them in a population genetic model, and show that predictions change not only in magnitude but also in direction when the timing of dispersal between environments relative to the life cycle is changed. GEIs can dramatically improve the evolution of costly female preferences, but also hamper it if much dispersal occurs between the life history stage where condition is determined and mating. This situation also arises if selection or mutation rates are too high. In general, our results highlight that when evaluating any mechanism promoted as a potential resolution of the lek paradox, it is not sufficient to focus on its effects on genetic variation. It also has to be assessed to what extent the proposed mechanism blurs the association between male attractiveness and offspring fitness; the net balance of these two effects can be positive or negative, and often strongly context-dependent.     

Interpreting genotype-by-environment interaction using redundancy analysis

Summary Methods for the interpretation of genotype-by-environment interaction in the presense of explicitly measured environmental variables can be divided into two groups. Firstly, methods that extract environmental characterizations from the data itself, which are subsequently related to measured environmental variables, e.g., regression on the mean or singular value decomposition of the matrix of residuals from additivity, followed by correlation, or regression, methods. Secondly, methods that incorporate measured environmental variables directly into the model, e.g., multiple regression of individual genotypical responses on environmental variables, or factorial regression in which a genotype-by-environment matrix is modelled in terms of concomitant variables for the environmental factor. In this paper a redundancy analysis is presented, which can be derived from the singular-value decomposition of the residuals from additivity by imposing the restriction on the environmental scores of having to be linear combinations of environmental variables. At the same time, redundancy analysis is derivable from factorial regression by rotation of the axes in the space spanned by the fitted values of the factorial regression, followed by a reduction of dimensionality through discarding the least explanatory axes. Redundancy analysis is a member of the second group of methods, and can be an important tool in the interpretation of genotype-by-environment interaction, especially with reference to concomitant environmental information. A theoretical treatise of the method is given, followed by a practical example in which the results of the method are compared to the results of the other methods mentioned.     

Fair-balance paradox, star-tree paradox, and Bayesian phylogenetics

The star-tree paradox refers to the conjecture that the posterior probabilities for the three unrooted trees for four species (or the three rooted trees for three species if the molecular clock is assumed) do not approach 1/3 when the data are generated using the star tree and when the amount of data approaches infinity. It reflects the more general phenomenon of high and presumably spurious posterior probabilities for trees or clades produced by the Bayesian method of phylogenetic reconstruction, and it is perceived to be a manifestation of the deeper problem of the extreme sensitivity of Bayesian model selection to the prior on parameters. Analysis of the star-tree paradox has been hampered by the intractability of the integrals involved. In this article, I use Laplacian expansion to approximate the posterior probabilities for the three rooted trees for three species using binary characters evolving at a constant rate. The approximation enables calculation of posterior tree probabilities for arbitrarily large data sets. Both theoretical analysis of the analogous fair-coin and fair-balance problems and computer simulation for the tree problem confirmed the existence of the star-tree paradox. When the data size n --> infinity, the posterior tree probabilities do not converge to 1/3 each, but they vary among data sets according to a statistical distribution. This distribution is characterized. Two strategies for resolving the star-tree paradox are explored: (1) a nonzero prior probability for the degenerate star tree and (2) an increasingly informative prior forcing the internal branch length toward zero. Both appear to be effective in resolving the paradox, but the latter is simpler to implement. The posterior tree probabilities are found to be very sensitive to the prior.     

A potential resolution to the lek paradox through indirect genetic effects

Females often prefer males with elaborate traits, even when they receive no direct benefits from their choice. In such situations, mate discrimination presumably has genetic advantages; selective females will produce offspring of higher genetic quality. Over time, persistent female preferences for elaborate secondary-sexual traits in males should erode genetic variance in these traits, eventually eliminating any benefit to the preferences. Yet, strong female preferences persist in many taxa. This puzzle is called the lek paradox and raises two primary questions: do females obtain genetic benefits for offspring by selecting males with elaborate secondary-sexual characteristics and, if so, how is the genetic variation in these male traits maintained? We suggest that indirect genetic effects may help to resolve the lek paradox. Maternal phenotypes, such as habitat selection behaviours and offspring provisioning, often influence the condition and the expression of secondary-sexual traits in sons. These maternal influences are commonly genetic based (i.e. they are indirect genetic effects). Females choosing mates with elaborate traits may receive ‘good genes’ for daughters in the form of effective maternal characteristics. Recognizing the significance of indirect genetic effects may be important to our understanding of the process and consequences of sexual selection.     

Environmental heterogeneity,genotype-by-environment interactions and the reliability of sexual traits as indicators of mate quality

Exaggerated sexual displays are often supposed to indicate the indirect benefits females may receive from sexual reproduction with displaying males, but empirical evidence for positive relationships between the genetic quality and sexual trait quality is scant. The explanation for this might lie in the fact that mixing of reproductive individuals whose development has been influenced by genotype-by-environment interactions (GEIs) can blur the relationship between the individual male genetic quality and phenotype as perceived by females. Strong GEIs can generate an ecological crossover, where different genotypes are superior in environments that are separated either in space or time. Here, we use a stochastic simulation model to show that even a weak GEI, which does not generate an obvious ecological crossover, can neutralize or even reverse the relationship between genetic quality and sexual trait size in the presence of environmental heterogeneity during development. Our model highlights the importance of developmental selection in evolution of traits and allows us to predict the situations in which sexual displays might not be reliable indicators of genetic quality.     

Genic capture and resolving the lek paradox

The genic capture hypothesis offers a resolution to the question of how genetic variation in male sexually selected traits is maintained in the face of strong female preferences. The hypothesis is that male display traits are costly to produce and hence depend upon overall condition, which itself is dependent upon genes at many loci. Few attempts have been made to test the assumptions and predictions of the genic capture hypothesis rigorously and, in particular, little attention has been paid to determining the genetic basis of condition. Such tests are crucial to our understanding of the maintenance of genetic variation and in the evaluation of recent models that propose a role for sexual selection in the maintenance of sex. Here, we review approaches to testing the link between genetically determined condition and levels of sexual trait expression and consider the probable importance of deleterious mutations.     

Mate choice for non-additive genetic benefits: a resolution to the lek paradox

In promiscuous mating systems, females often show a consistent preference to mate with one or a few males, presumably to acquire heritable genetic benefits for their offspring. However, strong directional selection should deplete additive genetic variation in fitness and consequently any benefit to expressing the preference by females (referred to as the lek paradox). Here, we provide a novel resolution that examines non-additive genetic benefits, such as overdominance or inbreeding, as a source of genetic variation. Focusing on the inbreeding coefficient f and overdominance effects, we use dynamic models to show that (1) f can be inherited from sire to offspring, (2) populations with females that express a mating preferences for outbred males (low f) maintain higher genetic variation than populations with females that mate randomly, and (3) preference alleles for outbred males can invade populations even when the alleles are associated with a fecundity cost. We show that non-additive genetic variation due to overdominance can be converted to additive genetic variation and becomes “heritable” when the frequencies of alternative homozygous genotypes at fitness loci deviate from equality. Unlike previous models that assume an infinite population size, we now show that genetic drift in finite populations can lead to the necessary deviations in the frequencies of homozygous genotypes. We also show that the “heritability of f,” and hence the benefit to a mating preference for non-additive genetic benefits, is highest in small populations and populations in which a smaller number of loci contribute to fitness via overdominance. Our model contributes to the solution of the lek paradox.     

Red Queen dancing in the lek: effects of mating skew on host–parasite interactions

The RQH (Red Queen hypothesis), which argues that hosts need to be continuously finding new ways to avoid parasites that are able to infect common host genotypes, has been at the center of discussions on the maintenance of sex. This is because diversity is favored under the host–parasite coevolution based on negative frequency‐dependent selection, and sexual reproduction is a mechanism that generates genetic diversity in the host population. Together with parasite infections, sexual organisms are usually under sexual selection, which leads to mating skew or mating success biased toward males with a particular phenotype. Thus, strong mating skew would affect genetic variance in a population and should affect the benefit of the RQH. However, most models have investigated the RQH under a random mating system and not under mating skew. In this study, I show that sexual selection and the resultant mating skew may increase parasite load in the hosts. An IBM (individual‐based model), which included host–parasite interactions and sexual selection among hosts, demonstrates that mating skew influenced parasite infection in the hosts under various conditions. Moreover, the IBM showed that the mating skew evolves easily in cases of male–male competition and female mate choice, even though it imposes an increased risk of parasite infection on the hosts. These findings indicated that whether the RQH favored sexual reproduction depended on the condition of mating skew. That is, consideration of the host mating system would provide further understanding of conditions in which the RQH favors sexual reproduction in real organisms.     

Female choice via indicator traits easily evolves in the face of recombination and migration

Species that exist in heterogeneous environments experience selection for specialization that is opposed by the homogenizing forces of migration and recombination. Migration tends to reduce associations between alleles and habitats, whereas recombination tends to break down associations among loci. The idea that heterogeneity should favor the evolution of isolating mechanisms has motivated evolutionary studies of reduced migration, habitat preference, and assortative mating. However, costly female choice of high-quality males can also evolve in heterogeneous populations and is not hindered by either recombination or migration. When information on male fitness is available through indicator traits, female choice based on these traits increases associations between female choice alleles and locally adapted alleles. Not only does female choice evolve in a heterogeneous environment, it acts to enhance the level of genetic variation and is thus self-reinforcing. The amount of female choice at equilibrium depends on how well mixed the habitats are, how much information on male genotype is available, and how different the habitats are. Female choice reaches the highest levels for intermediate levels of heterogeneity, because at such levels of heterogeneity there is both a high risk and high cost of mismating.     

Borders,paradox and power

Border studies have grappled with, on the one hand, the need for the use of common themes or concepts while, on the other, the need for contextual specificity. Borders are sites that embody different potentialities: division and contact, conflict and cooperation, security and anxiety, creativity and oppression, among others. In short, they are sites of the paradoxical. Paradox, it is argued, is the common overarching conceptual characteristic of borders but which specific potentialities are embodied in a border and what prevails as a result of the ensuing power struggles requires contextual specificity. Cyprus, a divided island lying on various border lines, partly inside and partly outside the EU, presents a useful socio-political space in order to illustrate this argument by outlining the specific paradoxical aspects of its own border and the results of the ensuing power struggles.     

Sex-specific genotype-by-environment interactions for cuticular hydrocarbon expression in decorated crickets, Gryllodes sigillatus: implications for the evolution of signal reliability

Phenotypic traits that convey information about individual identity or quality are important in animal social interactions, and the degree to which such traits are influenced by environmental variation can have profound effects on the reliability of these cues. Using inbred genetic lines of the decorated cricket, Gryllodes sigillatus, we manipulated diet quality to test how the cuticular hydrocarbon (CHC) profiles of males and females respond across two different nutritional rearing environments. There were significant differences between lines in the CHC profiles of females, but the effect of diet was not quite statistically significant. There was no significant genotype-by-environment interaction (GEI), suggesting that environmental effects on phenotypic variation in female CHCs are independent of genotype. There was, however, a significant effect of GEI for males, with changes in both signal quantity and content, suggesting that environmental effects on phenotypic expression of male CHCs are dependent on genotype. The differential response of male and female CHC expression to variation in the nutritional environment suggests that these chemical cues may be under sex-specific selection for signal reliability. Female CHCs show the characteristics of reliable cues of identity: high genetic variability, low condition dependence and a high degree of genetic determination. This supports earlier work showing that female CHCs are used in self-recognition to identify previous mates and facilitate polyandry. In contrast, male CHCs show the characteristics of reliable cues of quality: condition dependence and a relatively higher degree of environmental determination. This suggests that male CHCs are likely to function as cues of underlying quality during mate choice and/or male dominance interactions.     

Persistence, spread and the drift paradox

We derive conditions for persistence and spread of a population where individuals are either immobile or dispersing by advection and diffusion through a one-dimensional medium with a unidirectional flow. Reproduction occurs only in the stationary phase. Examples of such systems are found in rivers and streams, marine currents, and areas with prevalent wind direction. In streams, a long-standing question, dubbed 'the drift paradox', asks why aquatic insects faced with downstream drift are able to persist in upper stream reaches. For our two-phase model, persistence of the population is guaranteed if, at low population densities, the local growth rate of the stationary component of the population exceeds the rate of entry of individuals into the drift. Otherwise the persistence condition involves all the model parameters, and persistence requires a critical (minimum) domain size. We calculate the rate at which invasion fronts propagate up- and downstream, and show that persistence and ability to spread are closely connected: if the population cannot advance upstream against the flow, it also cannot persist on any finite spatial domain. By studying two limiting cases of our model, we show that residence in the immobile state always enhances population persistence. We use our findings to evaluate a number of mechanisms previously proposed in the ecological literature as resolutions of the drift paradox.     

Temperature-dependent costs of parasitism and maintenance of polymorphism under genotype-by-environment interactions

The maintenance of genetic variation for infection-related traits is often attributed to coevolution between hosts and parasites, but it can also be maintained by environmental variation if the relative fitness of different genotypes changes with environmental variation. To gain insight into how infection-related traits are sensitive to environmental variation, we exposed a single host genotype of the freshwater crustacean Daphnia magna to four parasite isolates (which we assume to represent different genotypes) of its naturally co-occurring parasite Pasteuria ramosa at 15, 20 and 25 degrees C. We found that the cost to the host of becoming infected varied with temperature, but the magnitude of this cost did not depend on the parasite isolate. Temperature influenced parasite fitness traits; we found parasite genotype-by-environment (G x E) interactions for parasite transmission stage production, suggesting the potential for temperature variation to maintain genetic variation in this trait. Finally, we tested for temperature-dependent relationships between host and parasite fitness traits that form a key component of models of virulence evolution, and we found them to be stable across temperatures.     

The analysis of the NSW wheat variety database. II. Variance component estimation

The efficiency of various trialling systems for wheat variety evaluation in New South Wales (NSW) is considered. This involved the estimation of the variance components due to genotype, genotype-by-year, genotype-by-location and genotype-by-year-by-location. It is shown that there is a significant reduction in the magnitude of these variance components by the inclusion of the interaction of genotype maturity, winter habit and aluminium tolerance with environment.     

Assessing non-specificity of resistance in wheat to head blight caused by inoculation with European strains of Fusarium culmorum,F. graminearum and F. nivale using a multiplicative model for interaction

To determine whether resistance to Fusarium head blight in winter wheat is horizontal and non-species specific, 25 genotypes from five European countries were tested at six locations across Europe in the years 1990, 1991, and 1992. The five genotypes from each country had to cover the range from resistant to susceptible. The locations involved were Wageningen, Vienna, Rennes, Hohenheim, Oberer Lindenhof, and Szeged. In total, 17 local strains of Fusarium culmorum, F. graminearum, and F. nivale were used for experimental inoculation. One strain, F. culmorum IPO 39-01, was used at all locations. Best linear unbiased predictions (BLUPs) for the head blight ratings of the genotypes were formed within each particular location for each combination of year and strain. The BLUPs over all locations were collected in a genotype-by environment table in which the genotypic dimension consisted of the 25 genotypes, while the environmental dimension was made up of 59 year-by-strain-by-location combinations. A multiplicative model was fitted to the genotype by-environment interaction in this table. The inverses of the variances of the genotype-by-environment BLUPs were used as weights. Interactions between genotypes and environments were written as sums of products between genotypic scores and environmental scores. After correction for year-by-location influence very little variation in environmental scores could be ascribed to differences between strains. This provided the basis for the conclusion that the resistance to Fusarium head blight in winter wheat was of the horizontal and non-species specific type. There was no indication for any geographical pattern in virulence genes. Any reasonable aggressive strain, a F. culmorum strain for the cool climates and a F. graminearum strain for the warmer humid areas, should be satisfactory for screening purposes.     

Reaction norm variants for male calling song in populations of Achroia grisella (Lepidoptera: Pyralidae): toward a resolution of the lek paradox

Significant additive genetic variance often occurs for male advertisement traits in spite of the directional selection imposed by female choice, a problem generally known in evolutionary biology as the lek paradox. One hypothesis, which has limited support from recent studies, for the resolution of this paradox is the role of genotype x environment interaction in which no one genotype exhibits the superior performance in all environments--a crossover of reaction norms. However, these studies have not characterized the actual variation of reaction norms present in natural populations, and the extent to which crossover maintains genetic variance remains unknown. Here, we present a study of genotype x environment interaction for the male calling song in populations of Achroia grisella (Lepidoptera: Pyralidae; lesser waxmoth). We report significant variance among reaction norms for male calling song in two North American populations of A. grisella as measured along temperature, food availability, and density gradients, and there is a relatively high incidence of crossover of the temperature reaction norms. This range of reaction norm variants and their crossover may reflect the co-occurrence of plastic and canalized genotypes, and we argue that the different responses of these variants along environmental gradients may contribute toward the maintenance of genetic variance for male song.     

Women,resources, and dispersal in nineteenth-century Sweden

In a recent study, female dispersal in nineteenth-century Sweden has been found to correlate negatively with access to resources: women with limited access to local resources tended to migrate more frequently. In this paper I review the literature to explore whether this observed correlation was derived from a relationship in which a woman’s limited access to resources worsened her position in the marriage market and led to migration, as a strategy to improve resources and this position. Many studies within a variety of disciplines indicate that a woman’s propensity to disperse from her parish of birth variedinversely with her propensity to inherit resources. My review of the literature suggests that the less likely a woman was to inherit resources, the lower her probability of marriage, the later her expected age at marriage, and the earlier she left home, presumably to improve her resource base for marriage. This work was funded in part by the Population and Environment Dynamics Program and by the Evolution and Human Behavior Program, University of Michigan. Alice L. Clarke is a doctoral candidate in the School of Natural Resources and Environment, University of Michigan, Ann Arbor. Her dissertation research examines the ecology of human dispersal in nineteenth-century Sweden. Her broader research interests include the ecological basis of human demography and resource use.     

Life history,immunity, Peto's paradox and tumours in birds

Cancer and tumours may evolve in response to life‐history trade‐offs between growth and duration of development on one hand, and between growth and maintenance of immune function on the other. Here, we tested whether (i) bird species with slow developmental rates for their body size experience low incidence of tumours because slow development allows for detection of rapid proliferation of cell lineages. We also test whether (ii) species with stronger immune response during development are more efficient at detecting tumour cells and hence suffer lower incidence of tumours. Finally, we tested Peto's paradox, that there is a positive relationship between tumour incidence and body mass. We used information on developmental rates and body mass from the literature and of tumour incidence (8468 birds) and size of the bursa of Fabricius for 7659 birds brought to a taxidermist in Denmark. We found evidence of the expected negative relationship between incidence of tumours and developmental rates and immunity after controlling for the positive association between tumour incidence and body size. These results suggest that evolution has modified the incidence of tumours in response to life history and that Peto's paradox may be explained by covariation between body mass, developmental rates and immunity.