Evolutionary limits to the frequency of aggression between related or unrelated conspecifics in diploid species with simple mendelian inheritance

Game theory has been used by some authors to analyse evolutionary limits to the expression of aggression in theoretical haploid parthenogenetic species. Others have examined frequency dependent selection, of which aggression may be a case, by applying population genetic models to diploid species. A model is presented which attempts to combine these two approaches. Game theory is used to determine evolutionarily stable strategies and corresponding stable polymorphisms for a two-strategy game played by members of a diploid sexual species, when choice of strategy is determined by two alleles at a single locus. Results are given for dominant, co-dominant and recessive determination of choice of the more aggressive of two strategies, for two levels of relationship: unrelated players and sibs. It is found that for a range of models of single locus inheritance the evolutionarily stable strategy (ESS) determined for haploid species remains the stable population strategy for diploid sexual species, when players are unrelated. In sibling contestants aggression is reduced. The mixed strategy haploid ESS underestimates, but the pure strategy haploid ESS provides a good indication of the degree to which relatedness lessens aggression in diploid species. For both haploid and diploid species there may be a considerable advantage to confining conflicts to kin.     

A simple fitness proxy for structured populations with continuous traits, with case studies on the evolution of haplo-diploids and genetic dimorphisms

For structured populations in equilibrium with everybody born equal, ln(R (0)) is a useful fitness proxy for evolutionarily steady strategy (ESS) and most adaptive dynamics calculations, with R (0) the average lifetime number of offspring in the clonal and haploid cases, and half the average lifetime number of offspring fathered or mothered for Mendelian diploids. When individuals have variable birth states, as is, for example, the case in spatial models, R (0) is itself an eigenvalue, which usually cannot be expressed explicitly in the trait vectors under consideration. In that case, Q(Y| X):=-det (I-L(Y| X)) can often be used as fitness proxy, with L the next-generation matrix for a potential mutant characterized by the trait vector Y in the (constant) environment engendered by a resident characterized by X. If the trait space is connected, global uninvadability can be determined from it. Moreover, it can be used in all the usual local calculations like the determination of evolutionarily singular trait vectors and their local invadability and attractivity. We conclude with three extended case studies demonstrating the usefulness of Q: the calculation of ESSs under haplo-diploid genetics (I), of evolutionarily steady genetic dimorphisms (ESDs) with a priori proportionality of macro- and micro-gametic outputs (an assumption that is generally made but the fulfilment of which is a priori highly exceptional) (II), and of ESDs without such proportionality (III). These case studies should also have some interest in their own right for the spelled out calculation recipes and their underlying modelling methodology.     

Causes and consequences of extreme variation in reproductive strategy and vegetative growth among invasive populations of a clonal aquatic plant, <Emphasis Type="Italic">Butomus umbellatus</Emphasis> L. (Butomaceae)

The mode of reproduction may influence the spread of invasive species by affecting evolutionary potential and dispersal ability. We sampled 51 introduced North American populations of the clonal aquatic plant Butomus umbellatus L. (flowering rush) and found extreme variation in sexual fertility caused by polyploidy. Populations consisted of diploids that produced thousands of viable seeds or of sexually sterile triploids. Although a trade-off between sexual and clonal reproduction predicts that the sexual sterility of triploids would be compensated for by greater clonal reproduction, a greenhouse experiment involving eight diploid and 10 triploid populations showed that diploid plants not only invest substantially in sexual structures but also make hundreds of tiny clonal bulbils on both rhizomes and inflorescences. In contrast, triploids do not make bulbils and have very limited scope for clonal multiplication and dispersal. Diploid populations were more frequent than triploid populations, especially in the Great Lakes region. This is probably because of the difference between cytotypes in clonal rather than sexual reproduction, as genetic analyses indicate a general lack of sexual recruitment in North America. Although triploids were less common, they have a wider geographical distribution. This could be due to a greater ecological tolerance resulting from polyploidy. However, genetic evidence suggests that triploids have become widespread via their use in and escape from horticulture. North America is being colonized by two distinct forms of B. umbellatus that differ strongly in reproductive strategy as well as the vectors and pathways of invasion.     

The contribution of haploids, diploids and clones to fine-scale population structure in the seaweed Cladophoropsis membranacea (Chlorophyta)

Local populations of Cladophoropsis membranacea exist as mats of coalesced thalli composed of free-living haploid and diploid plants including clonally reproduced plants of either phase. None of the phases are morphologically distinguishable. We used eight microsatellite loci to explore clonality and fine-scale patch structure in C. membranacea at six sites on the Canary Islands. Mats were always composites of many individuals; not single, large clones. Haploids outnumbered diploids at all sites (from 2:1 to 10:1). In both haploid and diploid plants, genetic diversity was high and there was no significant difference in allele frequencies. Significant heterozygote deficiencies were found in the diploid plants at five out of six sites and linkage disequilibrium was associated with the haploid phase at all sites. Short dispersal distances of gametes/spores and small effective population sizes associated with clonality probably contribute to inbreeding. Spatial autocorrelation analysis revealed that most clones were found within a radius of approximately 60 cm and rarely further than 5 m. Dominance of the haploid phase may reflect seasonal shifts in the relative frequencies of haploids and diploids, but may alternatively reflect superiority of locally adapted and competitively dominant, haploid clones; a strategy that is theoretically favoured in disturbed environments. Although sexual reproduction may be infrequent in C. membranacea, it is sufficient to maintain both life history phases and supports theoretical modelling studies that show that haploid-diploid life histories are an evolutionarily stable strategy.     

A quasispecies approach to the evolution of sexual replication in unicellular organisms

This study develops a simplified model describing the evolutionary dynamics of a population composed of obligate sexually and asexually reproducing, unicellular organisms. The model assumes that the organisms have diploid genomes consisting of two chromosomes, and that the sexual organisms replicate by first dividing into haploid intermediates, which then combine with other haploids, followed by the normal mitotic division of the resulting diploid into two new daughter cells. We assume that the fitness landscape of the diploids is analogous to the single-fitness-peak approach often used in single-chromosome studies. That is, we assume a master chromosome that becomes defective with just one point mutation. The diploid fitness then depends on whether the genome has zero, one, or two copies of the master chromosome. We also assume that only pairs of haploids with a master chromosome are capable of combining so as to produce sexual diploid cells, and that this process is described by second-order kinetics. We find that, in a range of intermediate values of the replication fidelity, sexually reproducing cells can outcompete asexual ones, provided the initial abundance of sexual cells is above some threshold value. The range of values where sexual reproduction outcompetes asexual reproduction increases with decreasing replication rate and increasing population density. We critically evaluate a common approach, based on a group selection perspective, used to study the competition between populations and show its flaws in addressing the evolution of sex problem.     

Reconciling theoretical approaches to stochastic patch-occupancy metapopulation models

There appear to be two different kinds of theoretical results about stochastic patch-occupancy metapopulation models: those recently proposed by Gyllenberg and Silvestrov about metapopulations including a very stable patch, and those by Darroch and Seneta about more general metapopulations. Based on the spectral theory of linear operators, it is shown that the results by Gyllenberg and Silvestrov are a limiting case of those by Darroch and Seneta. Taking the examples proposed by Gyllenberg and Silvestrov as a case study, the application and relevance of these results are discussed, with a particular stress to their bearing on real metapopulations.     

Evolution of unconditional dispersal in periodic environments

Organisms modulate their fitness in heterogeneous environments by dispersing. Prior work shows that there is selection against 'unconditional' dispersal in spatially heterogeneous environments. 'Unconditional' means individuals disperse at a rate independent of their location. We prove that if within-patch fitness varies spatially and between two values temporally, then there is selection for unconditional dispersal: any evolutionarily stable strategy (ESS) or evolutionarily stable coalition (ESC) includes a dispersive phenotype. Moreover, at this ESS or ESC, there is at least one sink patch (i.e. geometric mean of fitness less than one) and no sources patches (i.e. geometric mean of fitness greater than one). These results coupled with simulations suggest that spatial-temporal heterogeneity is due to abiotic forcing result in either an ESS with a dispersive phenotype or an ESC with sedentary and dispersive phenotypes. In contrast, the spatial-temporal heterogeneity due to biotic interactions can select for higher dispersal rates that ultimately spatially synchronize population dynamics.     

Mitotic recombination accelerates adaptation in the fungus Aspergillus nidulans

Understanding the prevalence of sexual reproduction in eukaryotes is a hard problem. At least two aspects still defy a fully satisfactory explanation, the functional significance of genetic recombination and the great variation among taxa in the relative lengths of the haploid and diploid phases in the sexual cycle. We have performed an experimental study to explore the specific advantages of haploidy or diploidy in the fungus Aspergillus nidulans. Comparing the rate of adaptation to a novel environment between haploid and isogenic diploid strains over 3,000 mitotic generations, we demonstrate that diploid strains, which during the experiment have reverted to haploidy following parasexual recombination, reach the highest fitness. This is due to the accumulation of recessive deleterious mutations in diploid nuclei, some of which show their combined beneficial effect in haploid recombinants. Our findings show the adaptive significance of mitotic recombination combined with flexibility in the timing of ploidy level transition if sign epistasis is an important determinant of fitness.     

The role of vegetative spread and seed dispersal for optimal life histories of clonal plants: a simulation study

Sexual and vegetative reproduction of clonal plants phenotypically differ in dispersal distance, in the phenology of offspring production and establishment, and in the success of establishment. We applied a combination of analytical and of spatially explicit individual-based simulation modelling to calculate long-term fitness. We predicted optimal clonal plant life histories in a parameter space spanned by stolon number, stolon internode length, and relative allocation to sexual and vegetative reproduction. For a given allocation to sexual reproduction and number of stolons, fitness was optimised for rather short internode lengths under small disturbances, and for the longest possible internodes under larger disturbances. A trade-off between length and number of vegetative spacers drew parameters away from their unrestricted optima. Now, intermediate length and number of spacers led to maximum fitness under large disturbances. Simultaneous trade-offs between sexual and vegetative reproduction and between the length and number of spacers could also lead to fitness optima at intermediate parameter values, depending on the success of seedling establishment. We demonstrated that spatial habitat structure (1) selects for an efficient use of available space either by optimum internode length or by investment into seeds, which disperse farther than vegetative spacers, and (2) leads to an interaction between trade-offs. We conclude, that dispersal distance, i.e. a spatial life-history component, and trade-offs must be included in considerations on adaptive evolution of clonal life histories.     

Two fitness measures for clonal plants and the importance of spatial aspects

The capability of clonal plants to reproduce both sexually and vegetatively and their resulting hierarchical organisation into ramets and genets pose problems for the determination of fitness. We develop ramet-based measures of clonal plant fitness including both modes of reproduction. To this end we use simple population-dynamic equations accounting for limited space, limited dispersal, and disturbance. Neglecting interactions among ramets (r-selection regime) we derive an expression for initial growth rate r as a fitness measure. At higher densities interactions among ramets lead to density control (K-selection regime) and competitive exclusion of genotypes or species may occur. In this case we apply an invasibility criterion to derive an abundance fitness measure: competitiveness C. The optimum of C corresponds to an evolutionary stable strategy. C increases with the proportion of reproductive adults, with inverse module mortality, and with the sum of sexual and vegetative reproduction. The latter are defined as the product of the rate of module production and two correction factors accounting for juvenile mortality before establishment and for the efficiency of space exploitation by propagules. Thus C is equivalent to potential life-time offspring production, in contrast to realized life-time offspring production R₀. Because the correction factor for space exploitation cannot be expressed analytically we obtain it from complementary spatially-explicit individual-based simulations. To illustrate an application of the fitness measure C we predict optimal allocation to vegetative and sexual reproduction. In a homogeneous habitat an intermediate allocation may maximize fitness only if there is a non-linear trade-off between the modes of reproduction. However even if this trade-off is linear, spatially heterogenous disturbances can lead to an intermediate optimum of allocation because seed dispersal with subsequent vegetative spread improves the utilization of available space for recruitment if the spatial extent of single disturbances is much larger than the distance of vegetative dispersal. Thus, our study underlines the importance of spatial features for fitness measures especially of clonal plants.     

Meiotic hybridogenesis in triploid Misgurnus loach derived from a clonal lineage

Triploid loaches Misgurnus anguillicaudatus are derived from unreduced diploid gametes produced by an asexual clonal lineage that normally undergoes gynogenetic reproduction. Here, we have investigated the reproductive system of two types of triploids: the first type carried maternally inherited clonal diploid genomes and a paternally inherited haploid genome from the same population; the second type had the same clonal diploid genomes but a haploid genome from another, genetically divergent population. The germinal vesicles of oocytes from triploid females (3n=75) contained only 25 bivalents, that is, 50 chromosomes. Flow cytometry revealed that the majority of the progeny resulting from fertilization of eggs from triploid females with normal haploid sperm were diploid. This indicates that triploid females mainly produced haploid eggs. Microsatellite analyses of the diploid progeny of triploid females showed that one allele of the clonal genotype was not transmitted to haploid eggs. Moreover, the identity of the eliminated allele differed between the two types of triploids. Our results demonstrate that there is preferential pairing of homologous chromosomes as well as the elimination of unmatched chromosomes in the course of haploid egg formation, that is, meiotic hybridogenesis. Two distinct genomes in the clone suggest its hybrid origin.     

Synthesis of clonality and polyploidy in vertebrate animals by hybridization between two sexual species

Because most clonal vertebrates have hybrid genomic constitutions, tight linkages are assumed among hybridization, clonality, and polyploidy. However, predictions about how these processes mechanistically relate during the switch from sexual to clonal reproduction have not been validated. Therefore, we performed a crossing experiment to test the hypothesis that interspecific hybridization per se initiated clonal diploid and triploid spined loaches (Cobitis) and their gynogenetic reproduction. We reared two F1 families resulting from the crossing of 14 pairs of two sexual species, and found their diploid hybrid constitution and a 1:1 sex ratio. While males were infertile, females produced unreduced nonrecombinant eggs (100%). Synthetic triploid females and males (96.3%) resulted in each of nine backcrossed families from eggs of synthesized diploid F1s fertilized by haploid sperm from sexual males. Five individuals (3.7%) from one backcross family were genetically identical to the somatic cells of the mother and originated via gynogenesis; the sperm of the sexual male only triggered clonal development of the egg. Our reconstruction of the evolutionary route from sexuality to clonality and polyploidy in these fish shows that clonality and gynogenesis may have been directly triggered by interspecific hybridization and that polyploidy is a consequence, not a cause, of clonality.     

The reproductive biology of Polytrichum formosum: clonal structure and paternity revealed by microsatellites

Using highly polymorphic microsatellite markers, we assessed clonal structure and paternity in a population of the bryophyte species Polytrichum formosum. Identical multilocus genotypes of individual shoots were almost never observed in spatially separated cushions, but were found to be highly clustered within moss cushions. Therefore, asexual reproduction through dispersal of gametophyte fragments is not very important in P. formosum. However, asexual reproduction on a very localized scale through vegetative growth of genets (branching of gametophytes via clonal growth of rhizomes) is very extensive. The patchy spatial distribution of genets and the absence of intermingling among genets suggest that this species follows a 'phalanx' clonal growth strategy. Vegetative proliferation of genets will increase their size, and, consequently, will have considerable fitness consequences for individuals in terms of increased genet longevity and reproductive output. Although paternity analysis of sporophytes confirmed male genet size, i.e. gamete production, to be an important determinant of male reproductive fitness, it also showed that the spatial distance to female genets is the predominant factor that governs male reproductive success. Moreover, we showed that male gamete dispersal distances in P. formosum are much further than generally assumed, and are in the order of metres rather than centimetres. Combining the findings, we conclude that the high genotypic diversity observed for this facultatively clonal species is most likely explained by a preponderance of sexual reproduction over clonal reproduction.     

ESSs with two types of players II (intra- and interspecific competition between haploid species)

The investigation of strategy evolution resulting from animal behavior is continued using a new approach to multispecies evolutionary games. A different interpretation of the known result that contestants in asymetrical games choose pure strategies is proven. This leads to a classification of all evolutionarily stable strategies (ESS) when there is no selection from interspecific competitions. In case the dimension of the strategy space is restricted as in a diallelic haploid model, the phase portrait of the evolutionary dynamics is illustrated. The results are then compared with the previous approach and to models of sex dependent selection in randomly mating diploid species.     

DOES THE TRADE-OFF BETWEEN GROWTH AND REPRODUCTION SELECT FOR FEMALE-BIASED SEXUAL ALLOCATION IN COSEXUAL PLANTS?

We analyzed sexual allocation in cosexual plants while taking the trade-off between growth and reproduction into consideration and showed that this trade-off does not select for female-biased sexual allocation. There are two problems in sexual allocation: optimizing the amount of resources allocated to reproduction in a growing season and equalizing the resources allocated to the male and the female functions. If these two are possible at the same time, equal resource allocation to the male and the female functions is the evolutionarily stable strategy (ESS; given that the fitness gains through the male and the female functions are proportional to the amount of the resources allocated to these functions). Biased sexual allocation only occurs when constraints make it impossible to simultaneously optimize allocation to reproduction and allocation to male and female functions. However, even if female-biased sexual allocation occurs due to the addition of other constraints, the trade-off between growth and reproduction itself is not an important factor that selects for female-biased sexual allocation.     

Optimum reproduction and dispersal strategies of a clonal plant in a metapopulation: a simulation study with Hieracium pilosella

Clonal spread is favoured in many plants at the expense of seed production in order to expand rapidly into open habitats or to occupy space by forming dense patches. However, for the dynamics of a population in a patchy landscape seed dispersal remains important even for clonal plants. We used a spatially explicit individual-based metapopulation model to examine the consequences of two trade-offs in Hieracium pilosella L: first, between vegetative and sexual reproduction, and second, between short and far-distance dispersal of seeds. Our main question was, what are the environmental conditions that cause a mixed strategy of vegetative and sexual reproduction to be optimal. The model was parameterised with field data on local population dynamics of H. pilosella. Patch dynamics were given firstly by disturbance events that opened patches in a matrix of a clonal grass that were colonisable for H. pilosella, and secondly by the gradual disappearance of H. pilosella patches due to the expanding grass. Simulations revealed opposing selection pressures on traits determined by the two trade-offs. Vegetative reproduction is favoured by local dynamics, i.e. the need for maintenance and expansion of established populations, whereas seed production is favoured by the necessity to colonise empty habitats. Similar pressures act on the proportion of seeds dispersed over short and far distances. Optimum reproductive and dispersal strategies depended on habitat quality (determined by seedling establishment probability), the fraction of dispersed seeds, and the fraction of seeds lost on unsuitable ground. Under habitat conditions supporting moderate to low seedling establishment, between 20% and 40% of reproductive effort in H. pilosella should be devoted to sexual reproduction with at least 10% of the seeds dispersed over distances suitable to attain empty patches. We conclude that in a spatially heterogeneous landscape sexual seed production in a clonal plant is advantageous even at the expense of local vegetative growth.     

Evolution of flowering strategies in Oenothera glazioviana: an integral projection model approach

The timing of reproduction is a key determinant of fitness. Here, we develop parameterized integral projection models of size-related flowering for the monocarpic perennial Oenothera glazioviana and use these to predict the evolutionarily stable strategy (ESS) for flowering. For the most part there is excellent agreement between the model predictions and the results of quantitative field studies. However, the model predicts a much steeper relationship between plant size and the probability of flowering than observed in the field, indicating selection for a 'threshold size' flowering function. Elasticity and sensitivity analysis of population growth rate lambda and net reproductive rate R(0) are used to identify the critical traits that determine fitness and control the ESS for flowering. Using the fitted model we calculate the fitness landscape for invading genotypes and show that this is characterized by a ridge of approximately equal fitness. The implications of these results for the maintenance of genetic variation are discussed.     

Evolution of seed dormancy due to sib competition: effect of dispersal and inbreeding

The effect of dispersal and inbreeding on the evolution of seed dormancy to avoid sib competition is theoretically investigated, using a model which assumes a plant population with patchy spatial structure in a constant environment. Applying the inclusive fitness method, the evolutionarily stable dormancy rates are analytically derived for three cases: (a) an asexual haploid population, (b) a diploid-hermaphrodite population in which the dormancy rate is controlled by seeds, and (c) a diploid-hermaphrodite population in which the dormancy rate is controlled by mother plants. The evolutionarily stable dormancy rates decrease in the order of case (c), case (a), and case (b). In all the cases, the evolutionarily stable dormancy rates increase with decreasing the dispersal rate. Although inbreeding generally increases the evolutionarily stable dormancy rates, inbreeding due to selfing reduces the rate exceptionally in case (c).     

Computer experiments on the evolution of sex: the haploid case

We have conducted a set of computer experiments that investigate the conditions under which sexual reproduction can evolve. In these experiments, haploid genomes are treated as integer strings able to undergo mutation and, in the case of sexual strings, recombination, with string sequence (the genotype) determining fitness. Our results indicate that the likelihood of a rare sexual mutant spreading through an otherwise asexual population is small when sexual reproduction entails the classical two-fold cost of males. However, our results indicate that when mutation rates are not excessively high, sexual reproduction constitutes a more efficient fitness optimization algorithm, allowing a sexual population to adapt more quickly to its environment than an asexual population.     

Triploid bridge and role of parthenogenesis in the evolution of autopolyploidy

Autopolyploidization is considered to play an important role in plant evolution. In polyploidization, the polyploid evolves from the original diploid cytotype, in which the triploid state is considered to mediate the process (triploid bridge). Nevertheless, the fitness of triploid individuals seems to be too low to facilitate the polyploidization process (triploid block). The evolutionary condition of autopolyploidy was analyzed using a mathematical model focusing on the role of parthenogenesis in triploid and tetraploid individuals. In addition, offspring were assumed to arise by sexual reproduction by conjugations between haploid, diploid, and triploid gametes produced by diploid, tetraploid, and triploid individuals. According to the analysis, even if triploid block suppresses the fitness of sexually produced triploids, the polyploidization process can proceed when parthenogenesis occurs frequently. If only triploids frequently reproduce parthenogenetically, the evolutionary consequences tend to depend on the fitness of the tetraploid individuals. On the basis of a predetermined parameter set, if tetraploid fitness is relatively low, all three ploidies can coexist. Otherwise, tetraploidization occurs. In this case, triploid parthenogenesis promotes not only triploidization but also tetraploidization. However, if both triploids and tetraploids frequently reproduce parthenogenetically, the ploidy levels with the highest fitness are likely to dominate in the population through direct competition among cytotypes.