Instituto Venezolano de Investigaciones Científicas and Universidad Simón Bolívar
Apartado 89000, Caracas 1080, Venezuela
Fax : 582-9063624, e-mail : firstname.lastname@example.org
Using computer simulations I studied the conditions under which sex is evolutionary stable. The parameters that showed relevance to the stability of sex were: variable environments, mutation rates, ploidy, number of loci subject to evolution, mate selection strategy, reproductive system and number of gametes (spermatozoa). The simulations showed that mutants for sex and recombination are evolutionarily stable, displacing alleles for monosexuality when more than one of the following conditions were fulfilled simultaneously: selection pressure was variable, mate selection was not random, ploidy was two, the reproductive strategy was haplo-dipoid, diploid or hermaphroditic, the complexity of the genome was large (more than 4 loci suffered adaptation), and gamete selection occurred. The results suggest that at least four phenomena, related to sex, have convergent adaptive values: Diploidy, sexual reproduction (recombination), gamete selection and the segregation of sexes. The results suggest that the emergence of sex had to be preceded by the emergence of diploid monosexual organisms and provide an explanation for the emergence and maintenance of sex among diploids and for the scarcity of sex among haploid organisms. The divergence of the evolutionary adaptation of the sexes should be a derived consequence of the emergence of sex. I postulate that for a harmonious evolution of complex genomes, optimal levels of genetic variation are required. Sex with random mating provides genetic variation but in excess, and thus has to be modulated by mate and gamete selection mechanisms. Generalizing, the dynamic advantages of sexual reproduction are that it allows evolving organisms to modulate the genetic variance (assortative mating), it opens the way for new levels of selection (mate and gamete selection), and it allows for divergent adaptations of the sexes. (female and male)
What selective forces maintain sexual reproduction and genetic recombination in nature? The answer to this question has been an elusive mystery (Maynard-Smith 1978, Judson and Normak 1996, Hurst and Peck 1996). Asexual reproduction is theoretically much more likely to occur than sexual one due to at least three inherent advantages: parthenogenic females do not need to find mates; they produce twice as many daughters and four times as many granddaughters compared to the average sexual ones; and natural selection drives adaptation and thus selection of relevant genetic traits much faster in asexual organisms compared to sexual ones (Maynard-Smith 1978, Jaffe 1996). Despite these relative theoretical advantages of asexuality, most of the higher organisms are sexual. The various hypotheses put forward to explain this mystery can be grouped into three broad categories:
1- The ecological genetic models and the Red Queen Hypothesis which postulate that sex is adaptive in variable environments or variable parasite pressure because it enables genetic variation and the rapid spread and creation of advantageous traits (Bell and Maynard-Smith 1987, Hamilton et al 1990, Ebert and Hamilton 1996, Howard and Lively 1994). This model has been shown to be incomplete in explaining the emergence and maintenance of sex (Ochoa and Jaffe, 1999 for example)
2- The mutation-accumulation models (Muller 1964, Hill and Robertson 1966, Kondrashov 1984, 1988, 1994, Taylor and Williams 1982, Heisler 1984), which suggest that sex is adaptive because it performs the efficient removal of deleterious mutations or DNA repair. Experimental results have shown that this model can not explain the genetic dynamics of extant sexual organisms (Cutter and Payseur 2002 for example).
3- The mate selection (and gamete selection) models, which assume that sex allows for the selection of 'good genes' by orientating the evolutionary process towards the fixation of beneficial traits (Kodric-Brown and Brown 1987, Jaffe 1996, 1999). Specifically, assortative mating has been shown to be very successful in increasing the fitness of sexual species (Davis 1995, Jaffe 1998, 2000). Here I want to explore this last model further.
The model Biodynamica used here (Jaffe 1996, 1998, 1999, 2000, 2001), has been "validated" by showing to have heuristic properties in explaining or predicting experimental data. It explains many aspects of the emergence of genetic resistance to antibiotics and pesticides (Jaffe et al 1997), it predicted divergent behavior of production of males in facultative sexual nematodes (Rincones et al. 2001), and the importance of economic aspects in the evolution of social behavior (Silva and Jaffe 2002). Thus it seems promising in uncovering some remaining mysteries of sex.
The simulation model Biodynamica, described many times elsewhere (see Jaffe 1996, 1998, 1999, 2000, 2001, Jaffe et al 1997) was used. In this multi-agent, adaptive model, each individual is simulated as an autonomous agent that interacts with the environment and with other individuals according to five evolutionary steps (see below) and to the alleles it carries in its various loci as given in Table 1. Simulations consisted of competitions between agents possessing alleles coding for different strategies. The population of agents (organisms) after being created with a random distribution of alleles, suffered a 5 step evolutionary process which mathematically speaking is equivalent to the following:
Mate selection: Females of bisexual species choose a male of the same species, whereas hermaphrodites mated with any conspecific individual. When random mating was simulated, females and hermaphrodites mated with a randomly chosen mate, whereas in assortative mating females and hermaphrodites mated with the genetically most similar mate among 20 randomly chosen individuals (This number had been shown to be close to the optimal for asortative mating to work under the present set of parameters, see Jaffe 1999). Genetic similarity was estimated by comparing the phenotypes of both individuals. When no sexually mature mate was found by a females or hermaphrodites, the individual did not reproduce during that time step if bisexual, or reproduced monosexually if hermaphrodite.
Reproduction: The reproductive strategy applied for haploid or diploid organisms. If sexual (i.e. not monosexual) organisms could mate randomly or assortatively . Monosexuals simulated parthenogenesis or thelytoky. That is, monosexual organisms did not mate. In monosexual haploids, the individual transmitted all its genes to the offspring (cloning) with no variance except that allowed by mutations, simulating asexuality. Monosexual diploids did not mate and produced offspring by uniform random crossovers of the alleles in each loci of the parent. Bisexuals produced equal numbers of males and females randomly. Males could mate several times each time step. Hermaphrodites produced only females and reproduced similar to bisexuals if finding another hermaphroditic female, or else reproduced as the corresponding monosexuals. Hermaphrodites thus, mated assortatively with females having the same disposition for sex, even when mating randomly regarding all other loci. In haplo-diploid reproduction, males were haploid and females diploid.
Females produced offspring according to their phenotypically determined clutch size (see Table 1), transmitting their genes following Mendelian rules of reproduction (free recombination). If sexual, each parent provided half of its alleles to the newborn, so that for each locus, one allele came from each parent if diploid, or each parent had a probability of 0.5 to transmit its allele to each locus if the organism was haploid or the offspring a haplo-diploid male
Variation: In each offspring, randomly selected genes mutated, changing their allelic value randomly. The probability of a mutation occurring in a given offspring was determined by the allele in gene 2 (Table 1).
Phenotypic expression: As commonly done with genetic algorithms (and as it is known to occur frequently in real organisms), total allelic dominance was simulated. That is, in diploid organisms, only one allele per loci was expressed phenotypically during the lifetime of each organism. The allele to be expressed phenotypically was selected randomly at birth. Selection: The model did not assume any simplified expression of fitness but reproduction and individual survival were decomposed into different aspects for selection to act. Individuals were excluded from the population at the end of each time step when their age exceeded their genetically prefixed life span. The survival of individuals was in addition dependent on population density, where survival probability was 0 if r1 * Nt ³ ops * r2 and 1 if r1 * Nt < ops * r2 ; where ops is the optimal population size, Nt the population size at time-step t and r1 and r2 are random numbers between 0 and 1
3- Individuals not possessing the resistant phenotype of genes 6 to 8 in Table 1 were killed randomly, with probabilities that varied randomly each time step from 0 to 0.9, simulating an environment in which two different biocides or parasites trimmed the population by killing non resistant individuals. Optimal size of populations was 800 and the initial size of the populations was 200 individuals for each reproductive strategy to be contested.
Table 1: Genes and their possible alleles defining the agents-organisms. Simulations of genes with allelic variance allowed mutant alleles to appear in the range given below. Initial populations had individuals possessing any of the alleles indicated in that range. In simulations in which some genes had no allelic variance, the default allele, indicated in parenthesis, was assigned to all the corresponding loci in all organisms.
Gene Range Effect on phenotype
0 1-2 Ploidy. Either haploid or diploid.
1 1-6 Reproductive strategy
2 0-10 Mutation rate: from 0.2 to 10 -7 mutations per gene in logarithmic
3 0-10 Maximum life span coding for life spans from 0 to 10 time steps (5)
4 0-10 Clutch size from 0 to 10 offspring (5)
5 0-5 Minimum age for initiating reproduction of females in t-steps (0)
6 0-10 Resistance to biocide 1: Only allele 0 was resistant to that biocide (0)
7 0-10 Resistance to biocide 2: Idem as gene 6 but for biocide 2 (0)
8 0-10 Resistance to biocide 3: Idem as gene 6 but for biocide 3 (0)
9 0-10 Number of spermatozoa produced by males
Figure 1 shows some results of tournament between a population of organisms with a given reproductive systems and a population of monosexual diploid organisms reproducing by thelytoky. Initially, both alleles were carried by 50% of the population and individuals of the different populations interbred. After 20 time steps the percentage of alleles of the reproductive strategy to be tested was calculated (shorter simulations produced results closer to the 50% line and longer simulations produced results more distanced from that line, reducing the visibility of the differences). The results confirm previous work that low mutations, greater variance in male reproductive success, assortative mating, mating with males possessing ‘good genes’, and hermaphrodites increase the adaptive value of bisexuals, being the strategies that could fix more alleles in the population than monosexual diploids. A surprising result was the strong positive effect of sperm selection. This strategy, when combined with others, was the only able to out-compete asexual organisms (monosexual haploids reproducing by cloning) in 66 % of the tournaments in less than 20 time steps (n = 2000 simulations).
Figure 1: Percent of alleles of the given reproductive strategy present in a population of 800 agents in relation to alleles coding for monosexual diploids (thelytoky). Bars smaller than 50% indicate strategies less efficient than monosexuual diploids; bars larger than 50% indicate stategies successful thanb Each bar is the average of 2000 simulations using the agent based computer simulation Biodynamica (Jaffe, 1995). Tournaments were run, starting with populations having a 50/50 proportion of alleles for monosexuality and for the ones indicated in the y axis. All reproductive systems were modelled as indicated elsewhere (Jaffe, 2000), except for sperm selection (Sp) which was modelled for the first time in two different formats: Sp(10,3) male produced 10 haploid spermatozoa, each containing one allele per loci taken from the father’s diploid genome at random. The spermatozoa possessing the largest number of alleles that were resistant to the simulated parasites (maximum 3), was used to fuse with a randomly chosen haploid gamete from the female, following the rules of meiosis (see Jaffe, 2000). Sp(30,5) male produced 30 spermatozoa that were selected based on the 3 loci for parasite resistance, plus one for large clutch size and another for long life span. Abbreviations indicate: Bi: bisexual, Haplo-Diploid: females are diploid and males haploid, Am: assortative mating, Gg: females select males for good genes, Mv: reproductive variance in males was twice hat for females, Lm: low mutation rate was 0.008 mutations per loci, Hm: high mutation rate was 0.2 mutations per loci. Else 0.04 random mutations per loci were simulated. The results can be obtained independently by downloading the program Biodynamica at http://atta.labb.usb.ve/Klaus/klaus.htm and running the file Demo19.prm.
The results show that the more selection there is on the genome (through gamete selection or mate selection), prior to fertilization, the more efficient the evolutionary process becomes. I postulated earlier (Jaffe 2000) that the genetic variance produced by sex differs from that produced by random mutations in that sex with assortative mating produces a better blend of variation, allowing faster adaptation in scenarios with very large genetic combinatorial possibilities, if compared to random mating. That is, sex slows the speed of evolution (Jaffe 1996) as advantageous mutations are not always transmitted to the offspring and are often mixed with disadvantageous alleles in other loci during recombination. Assortative mating reduces the extent to which this "dilution effect" of advantageous mutations occurs (Jaffe 1999), by reducing the variance of allelic composition between mates and thus producing offspring which have a greater likelihood of possessing the advantageous genes of their parents. Thus, assortative mating accelerates the fixation of advantageous alleles in the population canceling the effect of sex in slowing evolution. On the other hand, the long term advantage of sex is that it can produce advantageous blends of alleles faster than asexual reproduction does, but only if the number of loci is large (Jaffe 1998). For genomes with low genetic complexity (number of loci), mutations together with asexual reproduction is faster than sex in achieving optimal allelic combinations in the genome. Thus, the advantage of sex will be evidenced only if organisms do not mate randomly and the simulated genome has sufficient complexity (Ochoa and Jaffe 1999).
In addition, sexual reproduction allows gamete selection to occur. The present simulations suggest that this feature seems to be the one providing the greatest adaptive value to sexual reproduction. Yet, the adaptive value of sex seems to be rather a combination of features, as the present simulations suggest that various features of sex have additive properties regarding their adaptive value.
In the light of the numerous theoretical studies about the adaptive value of sex, it could be interesting to ask why other researchers have not reached these conclusions. Here I present a list of some plausible reasons, based on the fact that most studies on the emergence and maintenance of sex have focused on models using or modeling:
Cutter, A.D. and B.A. Payseur 2002. Implications of the deleterious mutation rate in three Caenorhabditis species for the evolution of sex. http://www.u.arizona.edu/~acutter/abstracts.htm
Ebert D. and W.D. Hamilton 1996. Sex against virulence: The coevolution of parasitic diseases. Trend. Ecol. Evol, 11 : 79-82.
Hamilton W.D., R. Axelrod and R. Tanese, 1990. Sexual reproduction as an adaptation to resist parasites (A review). Proc. Nat. Acad. Sci. (USA), 87: 3566-3573
Heisler, I.L. 1984. A quantitative genetic model for the origin of mating preferences. Evolution 36: 1283.
Hill W.G. and A. Robertson 1966. The effect of linkage on limits to artificial selection. Genet. Res. 8: 269-294.
Howard R.S. and C.M. Lively 1994. Parasitism, mutation accumulation and the maintenance of sex. Nature, 367 : 554-556 .
Hurst L.D. and J.R. Peck 1996. Recent advances in the understanding of the evolution and maintenance of sex. Trend. Ecol. Evol. 11: 46-52.
Jaffe K. 1996. The dynamics of the evolution of sex: Why the sexes are, in fact, always two? Interciencia 21: 259-267 and errata in 22: 48.
Jaffe, K. 1998. Sex, mate selection and evolution. In : Lecture Notes in Computer Science 1447 : Evolutionary Programming VII, Springer Verlag, V.W. Porto, N. Saravanan, D. Waagen and A.E. Eiben (Eds.), pp. 483-492.
Jaffe, K. 1999. On the adaptive value of some mate selection strategies. Acta Biotheoretica 47: 29-40.
Jaffe, K. 2000. Emergence and maintenance of sex among diploid organisms aided by assortative mating. Acta Biotheoretica 48: 137-147.
Jaffe K. 2001. On the relative importance of Haplo-Diploidy, Assortative Mating and Social Synergy on the Evolutionary Emergence of Social Behavior. Acta Biotheoretica 49: 29-42.
Jaffe K., S. Issa, E. Daniels and D. Haile 1997. Dynamics of the emergence of genetic resistance to pesticides among asexual and sexual organisms. J. Theor. Biol. 188: 289-299.
Judson O.P. and B.B. Normak 1996. Ancient asexual scandals. Trend. Ecol. Evol. 11: 41-46 .
Kodric-Brown, A. and J.H. Brown 1987. Anisogamy, sexual selection, and the evolution and maintenance of sex. Evolut. Ecol. 1 : 95-105.
Kondrashov, A.S. 1984. Deleterious mutations as an evolutionary factor. I. the advantage of recombinations. Genet. Res. 44: 199.
Kondrashov, A.S. 1988. Deleterious mutations as an evolutionary factor. III. Mating preferences and some general remarks. J. Theor. Biol. 131: 487-496.
Kondrashov, A.S. 1994. The asexual ploidy cycle and the origin of sex. Nature, 370 : 213-216.
Maynard-Smith J.M. 1978. The Evolution of Sex. Cambridge University Press, U.K.
Muller H.J. 1964. The relation of recombination to mutational change. Mut. Res., 1:2-9.
Ochoa G. and Jaffe K. 1999. On sex, mate selection and the Red Queen. J. Theor. Biol 199: 1-9.
Rincones J., Mauleon H., Jaffe K. 2001. Bacteria modulate the degree of ampimix of their symbiotic entomopathogenic nematodes in response to nutritional stress. Naturwissenschaften 88: 310-312.
Silva E.R. and Jaffe K. 2002. Expanded food choice as a possible factor in the evolution of eusociality in Vespidae Sociobiology 39:25-36, 2002
Taylor P.D. and Williams G.C. 1982. The lek paradox is not resolved. Theor. Pop. Biol. 22: 392