Journal of Theoretical Biology, 199: 1-9, 1999
On Sex, Mate
Selection and the Red Queen
Gabriela Ochoa
Departamento de Computación
Universidad Simón Bolívar
Klaus Jaffé
Departamento de Biología de Organismos
Universidad Simón Bolívar, Apartado 89000, Caracas 10801A, Venezuela
E-mail: kjaffe@usb.ve
Abstract
The widespread occurrence of sexual reproduction despite the twofold disadvantage of producing males, is still an unsolved mystery in evolutionary biology. One explanatory theory, called the 'Red Queen' hypothesis, states that sex is an adaptation to escape from parasites. A more recent hypothesis, the mate selection hypothesis, assumes that non-random mating, possible only with sex, accelerates the evolution of beneficial traits. This paper tests these two hypotheses, using an agent-based or ‘micro-analytic’ evolutionary algorithm where host-parasite interaction is simulated adhering to biological reality. While previous simpler models testing the 'Red Queen' hypothesis considered mainly haploid hosts, stable population density, random mating and simplified expressions of fitness, our more realistic model allows diploidy, mate selection, live history constraints and variable population densities. Results suggest that the Red Queen hypothesis is not valid for more realistic evolutionary scenarios and that each of the two hypotheses tested seem to explain partially but not exhaustively the adaptive value of sex. Based on the results we suggest that sexual populations in nature should avoid both, maximising outbreeding or maximising inbreeding, and should acquire mate selection strategies which favour optimal ranges of genetic mixing in accordance to environmental challenges.
Introduction
Sex remains an
enigma within a mystery as there is
still no widely accepted consensus for the existence and maintenance of sex
(Maynard Smith, 1971, Judson and Normak 1996). The
central question stated by John Maynard Smith is as follows: “what selective
forces maintain sexual reproduction and genetic recombination in nature?”
(Maynard Smith, 1978). If males provide little or no aid to offspring, a high
(up to twofold) extra average fitness has to emerge as a property of sexual
parentage if sex is to be stable. Maynard Smith explains the twofold
disadvantage of producing males in the following terms:
“Suppose that, in a sexual species, with equal numbers of males and
females, a mutation occurs causing females to produce only parthenogenetic
females like themselves. The number of eggs laid by a female, k, will not normally depend on whether
she is parthenogenetic or not, but only on how much
food she can accumulate over and above that needed to maintain herself.
Similarly, the probability, S, that
an egg will survive to breed will not normally depend on whether it is parthenogenetic. With these assumptions the following
changes occur in one generation:
Adults Eggs Adults in next generation
Parthenogenetic EE n Õ kn Õ Skn
EE N Õ ½kN Õ ½SkN
Sexual 5
GG N Õ ½kN Õ ½SkN
Hence, in one
generation, the proportion of parthenogenetic females
increases from n/(2N+n)
to n/(N+n) ;
when n is small, this is a doubling
in each generation.”
Thus, an obligate parthenogenetic (asexual) female would produce twice as
many daughters - and four times as many granddaughters - as the average sexual
female.
Elucidating the
nature of the suspected advantage of sex is one of the major challenges of
evolutionary biology. Several alternative models of explanation have been
presented (Jusdon and Normak,
1996). However, two broad classes seem to predominate (Hurst & Peck, 1996).
First we have the ecological genetic models which postulate that sex is adaptive
in variable environments because it enables the rapid spread and creation of
advantageous traits. Second there are the mutation-accumulation models, which
suggest that sex is adaptive because it performs the efficient removal of
deleterious genes.
Enclosed within the first category, are three
major hypotheses. Two of which emphasize the importance of variation in the
physical environment. The third hypothesis, called the Red Queen hypothesis
(Hamilton, 1980 for example), emphasizes the importance of frequency-dependent
selection resulting from interspecific interactions,
such as those between hosts and their parasites. The Red Queen hypothesis
states that sex is an adaptation to escape from parasites. Under this
hypothesis, obligate asexuality is believed not to be viable because high rate
coevolving parasites efficiently adapt their strategies for infiltrating host
defenses. As asexuals often stay genetically the same
over several generations, unless a mutation occurs, an obligate asexual lineage
would accumulate coadapted harmful parasites.
Previous computer models have been proposed to test the Red Queen hypothesis.
(e.g. Bell & Maynard Smith, 1987; Hamilton et al., 1990) These models used
simplified analytical methods or game theoretical versions of host-parasite interaction, with fixed
population sizes and fixed patterns of parasite infection. Most of these models
considered only haploid organisms, random mating and a simplified expression of
fitness.
In addition to these
traditional approaches, there is mounting evidence that non random mate
selection mechanisms may provide benefits to sex which are not appreciated when
considering only random mating (Kodric-Brown and
Brown 1987, Davis
1995). Specifically, Jaffe (1996,
1998, 1999) claims that sex allows the emergence of non-random mate selection mechanisms, which
in turn restrict excess genetic variability in relevant traits, specially among
diplods, accelerating adaptation of these relevant
traits. This advantage of sex with mate selection in computer simulations
emerges only after organisms of a minimum genetic complexity (adaptation of
multiple loci and diploidy) are simulated and
increases with the number of loci subjected to adaptation in the simulated
organisms. The most successful mate selection strategies found through
simulations were selection of “good genes” and assortative
mating (Jaffe 1999). Yet, dissortative mating based
on specific phenotypic features is known to occur in nature (Wedekind et al. 1995 for example). Thus, organisms should
chose their mates using a blend of
criteria, possibly including dissortative
mating, depending on the ecological setting and/or features favored through
mate selection.
On the other hand, an important criticisms concerning the use of models in biology, is the fact that biological and ecological systems are too complex to characterise analytically (Levin et. al. 1997). Analytical models do not allow for the simultaneous analysis of various dynamic processes such as natural selection and sexual selection. This criticism is hard to refute given the large and currently increasing evidence of the emergence of unexpected properties from complex system simulations (e.g. Cliff and Miller 1994; Jefferson et al. 1991; Kauffman and Johnson 1991; Ray 1991). In this respect, evolutionary computer simulations are ideal tools for studying co-evolution. They allow modelling of more complex and realistic genotypes, phenotypes and interactions than population-genetic or evolutionary game theory models. Moreover, they allow researchers to make detailed measurements during and after co-evolution, revealing much more information than conventional methods. Within the Artificial Life community, the use of computer simulation methods has been shown to be important in understanding the dynamics of co-evolution (Cliff and Miller 1995; Hillis 1991; Kauffman and Johnson 1991). Computer simulation has also been shown to be useful in understanding the reciprocal interactions within species between mate preferences and sexually selected traits (Jaffe 1996; 1999 ; Miller and Todd 1993). Additionally, from the point of view of epidemiology, a simulation model allows the monitoring of single hosts or parasites, even when they are inside hosts.
The aim of this work is to create an 'agent-based' simulation model of host-parasite interaction as close as possible to biological reality, including non-random mating. Then to study the performance of different host reproductive strategies to evolve defences against multiple parasites under the 'Red Queen' effect. Finally, compare the results with those previously reported in the literature so as to uncover factors which are dependent on particular simulation assumptions and/or simplifications.
Methods
The model was based
on features of Hamilton´s (1990) model, but includes
variable population sizes, diploidy, mate selection,
and more realistic patterns of infection by parasites and density dependent
natural selection. The computer model simulated the interaction of mating,
reproduction, selection, and parasite infection on randomly generated virtual
populations of parasites and hosts. The two separated populations competed and
co-evolved against each other. Parasites were modeled based on the life cycle
of pathogenic nematodes, having life stages inside and outside the host.
Outside hosts they lived as free-living larvae, inside hosts they had a
three-stage life: egg, larva and adult. They reproduced only as adults, and
pre-adult larva infected hosts if they randomly encountered a host and if the
relation between the virulence of the parasite and the resistance of the host
was adequate. If the infection was successful, the parasite penetrated into the
host, fed on it and reproduced asexually. The progeny continued to feed and
reproduce in the host as long as there remained food to be eaten. Each parasite
consumed a fixed quantity of the hosts biomass at each simulation step. When
this biomass was exhausted, the host was eliminated and the parasite larvae
dispersed, increasing the external larval parasite population. In addition,
some parasite larvae dispersed from the hosts at a fixed rate during the host’s
lifetime.
Hosts could be
sexual or asexual (all female and parthenogenetic).
Sexual hosts were hermaphroditic, and when they reach the reproductive age they
choose a mate from among all members of the population. Thus, in the
simulations, asexuals and sexuals
had equal fertility, simplifying the analysis, as was done by Hamilton et al.
(1990) . Asexual diploid organisms were simulated so that there was crossover
between the two allele copies in each loci (i.e. they were monosexual
diploids as in Jaffe 1996). Asexual haploids had no crossover.
Simulations started normally with 500
parasites and 100 hosts, then
populations were free to grow, restricted by the parasite-host interaction and
by a density-dependent selection mechanism. The organism's genotype consisted
of several loci, each with one (if haploid) or two (if diploid) alleles. In
hosts, one locus was used to model the reproductive strategy (sexual, asexual),
another to model the mate selection criteria (random, similar, dissimilar) and
the rest to model resistance. In parasites, one locus accounted for parasite
type and another for virulence. Randomly selected genes coding for these traits
mutated, changing their allelic values at random within a predetermined
range for each gene. Mutations occurred
according to a fixed mutation rate. All other traits, i.e., life span,
reproductive age, clutch size and mutation rate, were fixed and equal for all
organisms, although different for hosts and parasites. The parameter values used for the simulations
reported were:
|
Parameter |
Parasites |
Host |
|
Life span (time steps) |
5 |
6 |
|
Clutch size
(offspring / breeding season) |
4 |
2 |
|
Reproductive age (time steps) |
3 |
3 |
|
Biomass
(units equivalent to one parasite egg) |
4 |
100 |
|
Mutation rate (per locus per generation) |
0.04; 0.0016 |
0.04; 0.0016 |
Life span of
parasites refers to the maximum number of time steps they may live as larvae
outside a host. Inside hosts they always passed through a three-stage life (egg, larva, and adult) and
reproduce as adults. Free living larvae became adults one time step after
infecting a host. The clutch size and the amount of food available inside host controled the number of offspring produced by a parasite.
Mating and Reproduction of Hosts. Hosts were either sexual
hermaphrodites or asexual parthenogenetic females.
Sexual hosts selected their mates following one of the following criteria;
random mating, assortative mating (favoring similar
organisms) and dissortative mating (favoring
dissimilar organisms). Additionally, two different genotypes; haploid and
diploid were modeled. Hosts reproduced for the first time when they reached
their reproductive age, and then continued to reproduce at each simulation step
. When a reproductive event occurred, the number of descendants produced was
determined by their clutch size. For asexual reproduction, the genes of the
offspring were identical to those of their single parent, unless changed by
mutations. In the case of sexual reproduction, hosts chose a mate according to
their mate selection criterion. For random mating, a mate was chosen at random
from the host population. In the case of assortative
mating, a fixed sized set of randomly selected potential mates was screened
(usually 20 individuals), and the genotypically most
similar individual was chosen for mating. Dissortative
mating was similar to assortative mating, but the
preference was for mates with the most dissimilar alleles. Mated individuals
transmitted their genes to the offspring according to the rules of bisexual
diploid reproduction (i.e. meiosis), so that they received a mix of genes from
both parents. The operator used for recombination is similar to the uniform crossover (Syswerda, 1989) employed in
conventional Genetic Algorithms (Goldberg, 1989).
Infection. The infection model used was
inspired by Hamilton et. al (1990), however, no artificial fitness scores were
used. The Red Queen effect was simulated in the sense that hosts could not
evolve an optimal genotype that conferred them resistance to parasites. Host
resistance against parasites was simulated as multiple loci, each possibly resistant
to one parasite type. When a random encounter between a host and a parasite was
simulated, the allelic value of the resistance locus of a host, and the
virulence allele of parasite type had to be the same in order for infection to
occur. As in Hamilton’s model, two
alleles (0 and 1) were considered for each host resistance locus and parasite
virulence locus. For diploid organisms
the convention was that the first allele of the double chain was always expressed,
although in the crossover process, there was a shuffle of the alleles of both
chains. In this model of virulence-resistance, we had a ‘Red Queen Effect’
arising from the co-evolutionary arms race. In this co-evolution of hosts and
parasites, the host’s resistance evolved against the parasite virulence, which
also evolved, so that each lineage’s fitness landscape changed perpetually.
Under this co-evolution scenario, adaptive advantage is continually undermined.
Selection. The model did not assume any simplified expression of
fitness. Parasite survival depended only on their fixed life span outside hosts
and the rate of reproduction (clutch size) inside hosts. Given that parasites
reproduced only inside hosts, their ability to reproduce and survive was
related to their ability to invade the hosts, which in turn depended on the
parasites type and virulence alleles in relation to the respective host’s
resistance allele. Hosts survival depended on their life span and clutch size,
with parasites imposing a strong selective pressure upon them. When born, hosts
had a pre-determined quantity of biomass. Each individual parasite, once inside
a host, consumed a fixed quantity of this biomass at each simulation step. When
the first parasite invaded a host, there was a period of latency of one time
step, after which the host was "killed”, that is, it was unable to
reproduce. Parasites inside a “dead” host
were able to live on and reproduce, consuming the dead body until
exhausting the available biomass. At a fixed rate of 30 %, newborn parasites dispersed from
the hosts at each simulation step. When the biomass of the host was exhausted,
the host was eliminated from the simulated population and the remaining
internal parasites larvae were liberated as free living larvae. In addition
organisms (parasites and hosts) were randomly excluded from their populations
each simulation step, with a probability determined by the formula :
0 if r1
* Nt
³ ops * r2
Survival of individual i at time
step t = {
1 if r1
* Nt
< ops * r2
where ops is the optimal population
size (determined by the experimenter) , Nt
the population size at time-step t and r1 and r 2 are
random numbers between 0 and 1.
Results
Several thousand
simulations were performed, and thus, only the most relevant results are discussed.
Simulations where asexual and sexual hosts coexisted and where the gene coding
for reproductive strategy was subject to mutation and recombination, showed
that the population rapidly eliminated the allele for sex. The allele for
asexual reproduction almost always got fixed in the population. That is, sex
proved to be evolutionary unstable in our simulations. Only for very few and
extreme parameter settings could alleles coding for sex invade a population of
asexual organisms.
Another set of
experiments simulated co-evolution on host populations in which all individuals
had the same reproductive strategy, and no mutation in the reproductive
strategy gene was allowed. The four reproductive strategies modeled (asexual,
sexual with random mating, sexual with assortative mating and sexual with dissortative
mating) were tested considering distinct number of loci for host
resistance. Also simulations with
haploid and diploid genotypes were run. Each simulation lasted 150 time steps,
which corresponds to approximately 50 host generations. In order to cope with
the considerable stochastic noise of our model, 200 replicas for each
experiment were computed. The fitness measure used was the percentage of host
populations which survived after a given number of simulation steps (% survival
= survival rate). Simulation results obtained for these experiments are as
follows.
Fig. 1, shows the
percentage of survival for the same 200 simulations after 50, 100 and 150 time
steps. Results show that the simulations were robust in time, as the same
qualitative differences between the strategies were observed, although the
relative differences among the various strategies increased with time. Thus,
for future comparisons, we present the results of simulations after 150 time steps.
Increasing the number of time steps further slowed the simulations considerably
and did not improved the results (not shown).
In all the
simulations (Fig. 1, to 3) we observe that sexual reproduction with dissortative mating produced the highest survival rates.
This difference was large and consistent. In almost all cases, an increase in
the number of parasite types produces a reduction in the survival rate for all
reproductive strategies. Fig. 2 shows that the mutation rate did not critically
affect the relative performance of the distinct strategies. However, the
survival rates in all the strategies diminished considerably with the reduction
of the mutation rate. Fig. 3 shows that when diploid hosts are simulated,
curiously, sexual reproduction with random mating outperforms asexual
reproduction, but even here, the criterion of choosing dissimilar mates proved
to be the most successful mate selection criterion.
Discussion
The simulation model
explored adaptation in populations of variable densities in time, using more
elaborate selection mechanisms than those used by Hamilton et al (1990). Under
these more realistic conditions, we could not replicate the findings from the
model by Hamilton et al. (1990), which found that sexual reproduction with random
mating in haploid host, accelerates the evolution of defensive alleles against multiple parasite
species. In Hamilton’s model the success of sex against asexuals
increased with the number of loci involved in defense against parasites. Our
simulations did not show this tendency, although we worked in the same range of
number of parasite types. We suggest that this contradictory result is due to
differences in the following assumptions : Hamilton’s model used ‘soft
selection’ in which the host population is truncated artificially and in which
infected hosts could survive. The selection criteria for the truncation were
determined by the experimenter, selecting each time step the fittest individuals
for further reproduction. In our model infections were always lethal and
selection and reproduction had important random components which were not
controlled by the experimenter. That is, ‘soft selection’ as used in Hamilton´s models, in practice, works as a mate selection
mechanisms based on criteria defined externally by the experimenter. In fact,
the results of Hamilton´s models are actually more
comparable with results of simulations using strong mate selection of ‘good
genes’ (Jaffe 1996, 1999), and thus, it is not appropriate to consider these
simulations as driven by random mating.
Hamilton’s model was
very susceptible to mutation rates but not ours, although we tested
approximately the same range of mutation rates. We suggest that this difference
is due to the following : Our model included rudiments of a life history
of organisms, coded by 4 loci, which were absent in Hamilton’s model. The
susceptibility of simulations to mutations is very dependent on the number of
loci simulated and on the mate selection strategy used (Fig 2). Thus, in our
model there where 4 more loci than in Hamilton´s
model, and in Hamilton´s model no true random mating
was simulated (see above), making exact comparisons not possible. In addition,
although in both, Hamilton´s and our model, parasites
had shorter generation times than their host, Hamilton´s
model assumed larger differences in the generation time between hosts and
parasites than the present simulations.
When studying
diploid hosts, sexual population with random mating and with dissortative mating largely outperformed asexual ones,
suggesting that the adaptive value of
sex is higher in diploid organisms. Also, only among diploids did random
mating sexual organisms outperform asexual ones. That is, the effect of diploidy in simulation models could be significant and
thus, results obtained modeling haploid
organisms should not be extended to diploid organisms. This may support the
importance of ploidy
cycles or meiosis in the evolutionary dynamics of sex (Kondrashov,
1994; Jaffe 1996). Simulations comparing the likelihood of the emergence of sex
and its maintenance (Jaffe submitted) confirmed that sex may become
evolutionary stable only among diploids, with several loci subject to
adaptation, and with some kind of non random mating (Jaffe 1999).
The present study shows that simplifications assumed for modeling purposes in the case of Hamilton’s model did affect the results obtained. A more realistic life history, genetic complexity, ploidy and mating system as attempted here showed that the Red Queen hypothesis is not sufficient to explain the maintenance nor the emergence of sex. We propose that any comprehensive explanation for the existence of sex should include in addition to variable adaptive landscapes also non-random mating strategies and diploidy. Our results, although based on an independently developed computer model, are consistent with simulations of organisms evolving in worlds which can eventually have absolute optimal genetic configurations (Jaffé, 1996, 1998, 1999, Jaffé et al. 1997), confirming the importance of mate selection as an evolutionary catalyst, favouring the maintenance of sex. Here we showed that selection by females of genetically different males increase allelic variability. For example, some organisms select their mates so as to increase the variability of the immune systems (Weedekind et al. 1995), by preferring mates with a different Mayor Histocompatibility Complex. In simulations where large genetic variability is not so important, assortative mating showed to be the most successful strategy (Jaffe 1999). These results, thus, allow for a falsifiable prediction. Organisms in nature should select their mates so as to achieve an optimal degree of allelic variability in their offspring. Excess genetic variability is not optimal (Jaffe 1999), nor is pure assortative mating (this work). Thus, organisms should not maximize outbreeding nor inbreeding but should strive for intermediate levels of genetic mixing. Studies of mate choice related to the genetic distance of the breeding pair in natural populations could provide data to settle this point. Although controversial, some indirect evidence for this is available for humans (Thiessen and Gregg 1980, Rushton 1989, Jaffe and Chacon 1995, but see the open peer commentaries in Rushton 1989 for example). Such evidence for plant pollination for example would be a very strong support for our hypothesis, as no data on mate selection in plants could be found in the literature. Another way of looking at this hypothesis is that mating in sexual organisms should aim at achieving optimal genetic mixes (not maximal mixes),. The optimal genetic mix should vary in accordance to environmental pressures. That is, populations (or species) colonising new ecosystems for example should aim at larger genetic mixing compared to populations adapted to stable niches, and thus, both group of populations should differ in their mate selection criteria. An alternative way to achieve improved genetic mixing in anisogamous species (Kodric-Brown and Brown 1987) when environmental challenges call for it would be an increased production of males or of sperm.
Acknowledgements: We thank A. Meier, H. Buxton and anonymous
referees for useful comments and corrections of the manuscript.
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Fig. 1:
Average rate of survival for
haploid host populations calculated from the results of the same 200 simulations after 50, 100 and
150 time steps. Results are for simulations with 2, 5, 10 and 15 loci for resistance
(parasite types). Mutation rate for both parasites and host was 0.04 mutations
per loci. Reproductive strategies tested were: Asex: parthenogenetic; SexRnd: sexual
with random mating; SexSim: sexual with assortative mating, SexDif:
sexual with dissortative mating.
Fig. 2: Average rate of haploid host
population survival for 200 simulations after 150 time steps, for simulations
using mutation rates 0.04 and 0.016 for both, hosts and parasites. Results are
for simulations with 2, 5, 10 and 15 loci for resistance (parasite types). Else
as in Fig 1.
Fig. 3: Average rate of population
survival for 200 simulations after 150 time steps, for haploid and diploid
hosts. Results are from simulations with 2, 5, 10 and 15 loci for resistance
(parasite types). Mutation rate for all organisms was 0.04. Else as in Fig. 1.
Fig. 1
Fig. 2
Fig. 3
