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Keywords:

  • amphibians and reptiles;
  • birds;
  • life history evolution;
  • mammals;
  • quantitative genetics;
  • simulation;
  • theory;
  • trade-offs.

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

We present a model for the advantage of sexual reproduction in multicellular long-lived species in a world of structured resources in short supply. The model combines features of the Tangled Bank and the Red Queen hypothesis of sexual reproduction and is of broad applicability. The model is ecologically explicit with the dynamics of resources and consumers being modelled by differential equations. The life history of consumers is shaped by body mass-dependent rates as implemented in the metabolic theory of ecology. We find that over a broad range of parameters, sexual reproduction wins despite the two-fold cost of producing males, due to the advantage of producing offspring that can exploit underutilized resources. The advantage is largest when maturation and production of offspring set in before the resources of the parents become depleted, but not too early, due to the cost of producing males. The model thus leads to the dominance of sexual reproduction in multicellular animals living in complex environments, with resource availability being the most important factor affecting survival and reproduction.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

The importance of ecology for evolutionary processes is being increasingly acknowledged. Whereas traditional population genetics models of evolution assign fitness values directly to genotypes, models based on ecological interactions calculate the survival and reproduction of species by considering their interactions with resources and other species. Both types of approaches have also been employed in models on the evolution and maintenance of sex. The disadvantage of sex is that females have to produce males which do not themselves produce offspring, thereby encountering a two-fold disadvantage in the number of offspring produced per generation (Williams, 1975; Maynard Smith, 1978). Yet, in spite of this two-fold cost, most species are sexual. As proposed early by Weismann (1889), the advantage of sexual reproduction must be associated with the mixis of genotypes.

Among population genetic models of sex, Muller’s ratchet (1964) has been most prominent (Felsenstein, 1974; Manning, 1976). It assumes that the advantage of sex lies in eliminating deleterious mutations, thereby preventing mutational meltdown. However, this advantage is only experienced in the long term, and models drawing on long-term advantages have been assumed to be insufficient to explain the predominance of sexual reproduction (Williams, 1975; Maynard Smith, 1978; Bell, 1982). Rather, there must be short-term advantages balancing the large costs associated with the production of males.

Population genetics models that yield short-term advantages of sexual reproduction are usually lottery models (Williams, 1975), which assume that the environment is unpredictable and therefore the fitness of offspring genotypes varies at random and is independent of the fitness of parent genotypes in the previous generations. However, as pointed out by Bell (1982), lottery models are in conflict with the observation that harsh and unstable environments favour asexual rather than sexual reproduction.

The two most important ecological hypotheses for the maintenance of sexual reproduction have been the Red Queen hypothesis and the Tangled Bank hypothesis, both of which stress the importance of interactions with other species. The Red Queen hypothesis is most vividly illustrated by the arms race between host and parasite (Jaenike, 1978; Hamilton, 1980) or predator and prey, but it is also applied more generally to the temporal change in the interaction between a species and its biotic environment (Bell, 1987; Salathe et al., 2008). In contrast, the Tangled Bank is based on the spatial heterogeneity of the biotic environment (Maynard Smith, 1978; Bell, 1982), emphasizing that genetically diverse offspring can exploit a broader spectrum of resources. The advantage of sexual reproduction according to the Tangled Bank hypothesis is therefore often viewed as lying in the reduction of sib competition. Currently, the Red Queen hypothesis has become the most popular explanation for the short-term advantage of sexual reproduction (Lively & Dybdahl, 2000; Lively, 2009), although it is doubted that Red Queen processes are sufficient for explaining the dominance of sexual reproduction (West et al., 1999; Salathe et al., 2008).

Some authors have argued that a theory that combines Red Queen and Tangled Bank processes is most promising (Doebeli, 1996; Song et al., 2011b). Offspring are likely to be confronted with resources depleted by their parents, leading to a negative correlation between the fitness of a given genotype in the parent and offspring generations. This is the essence of the Red Queen model but has been overlooked as a part of sib-competition models. A theory that combines Tangled Bank and Red Queen features can enable offspring with a different genotype than their parents to exploit resources that have not been depleted by their parents. This results in an ongoing change with time in the usage of a broad set of resources in heterogeneous space by consumers with continuously changing genotypes (Song et al., 2010).

Recently, Scheu & Drossel (2007) introduced such a model that combines features of both the Tangled Bank theory and the Red Queen theory. In contrast to an earlier model by Doebeli (1996), it implements explicitly the dynamics of resources and consumers. The model is tailored to seasonal species with intermittent mixis, such as aphids or cladocerans. It successfully predicts the predominance of sexual reproduction over a large parameter range when resource diversity is high and resources regrow slowly and are in limited supply. When a spatial dimension is included, the model also successfully predicts the geographic distribution of sexual and parthenogenetic reproduction that is, the dominance of sexual reproduction in favourable environments and the dominance of asexual reproduction in harsh environments, a phenomenon termed geographic parthenogenesis (Vandel, 1928; Song et al., 2011a).

Until now, no model exists targeting the maintenance of sex of multicellular long-lived species that explicitly includes the dynamics of the resources used by such species. Such a model requires the implementation of life-history traits such as growth until maturity and size- or age-dependent mortality. A suitable life-history model that is based on metabolic theory (Brown et al., 2004) and on explicit consumer-resource dynamics was recently introduced by us (Y. Song, S. Scheu & B. Drossel, under review). In the following, we will combine this life-history model with features of our structured resource model (Scheu & Drossel, 2007) by including resource diversity in space and time and the associated fitness benefits of sexual versus asexual reproduction. The resulting model provides a general theory on the maintenance of sexual reproduction in multicellular long-lived species, such as virtually all metazoan animals. Similarly to the model for seasonal species, the model for long-lived species leads to an advantage of sexual reproduction over a large parameter range and to an ongoing change in resource usage and in the genotypic composition of the sexual population. These findings demonstrate that the advantage of sexual reproduction derived from a combination of the Tangled Bank and the Red Queen hypotheses holds not only for seasonal species, but also for long-lived species with overlapping generations, where sexual reproduction is even more prevalent than in seasonal species.

Model

  1. Top of page
  2. Abstract
  3. Introduction
  4. Model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Resources and their consumption

Just as in the model for seasonal species with intermittent mixis (Scheu & Drossel, 2007), we consider a patch that contains × L different resources, with = 20 in most of our simulations. This patch represents a limited part of space with its various resources, such as different types of plants that could in principle be used by herbivore species. The patch contains only a limited number of consumers, which means that only a few genotypes can be locally present at the same time. In order to take the larger extension of space into account, we will later also consider several such patches that will be connected by migration of the consumers.

Resources are numbered by = 1,…, L2 with the niche coordinates of resource j being inline image. Consumer genotypes are labelled in the same way and numbered using the index i. A consumer with genotype (xi, yi) is best adapted to the resource with niche value (xi, yi), but can also feed on resources with neighbouring niche values. This means that individuals use a small subset of the population’s resource base, and that this resource usage is to a large extent determined genetically. These assumptions seem reasonable in the light of what is known about individual specialization (Araujo et al., 2011), and we will discuss them in more depth in the concluding section of this paper.

An important feature of our model is that resources grow at a limited rate, which means that consumption reduces their biomass to a level considerably below the carrying capacity. Resources grow continuously according to the logistic equation with a maximum growth rate G and carrying capacity Kr, and loose biomass due to being consumed,

  • image(1)

Here, Bi is the body mass of consumer i, and inline image is its maximum ingestion rate, the level of which can be tuned by changing the parameter ε, and with inline image being proportional to inline image in agreement with metabolic theory (see below). The consumption term is basically the widely used Holling type II functional response (Holling, 1959), with the attractiveness of resource j to consumer i being given by

  • image(2)

Ω is a normalization factor chosen such that for a consumer, the sum of all α’s equals 1. As αij is very small when (xj − xi)2 + (yj − yi)2 > 8, we set it to zero in this case. Each individual thus feeds strongly on nine resources, and weakly on 16 additional resources. These 25 resources represent sixteenth (i.e., 25/400) of all resources, and up to 1/4 of the resources used by the sexual population (see below).

Consumer growth, metabolism and death

The life cycle of consumer individuals is tailored to iteroparous species (Y. Song, S. Scheu & B. Drossel, under review), that is multicellular long-lived organisms that reproduce more than once per lifetime, which is typical for large metazoan animals in particular vertebrates such as lizards (Ballinger, 1977) and deer (Gaillard & Yoccoz, 2003).

After birth, the body mass Bi of an individual i increases from the initial value Bjuvenile = 1 due to resource consumption resulting in somatic growth, and it decreases due to respiration according to the equation

  • image(3)

According to metabolic theory, we assume

  • image(4)

that is, the rate of energy loss due to respiration is proportional to inline image The allometric constant α is chosen to be 0.314, which is a typical value for consumers of resources with unit body mass (Rall et al., 2008). Larger individuals need less energy per unit body mass for metabolism. When the body mass gained by resource consumption does not outweigh the cost of metabolism, the individual loses weight. Once the body mass drops below the offspring weight Bjuvanile, the individual is considered dead and removed from the system. The ecological efficiency λ was chosen to be 0.4 (Turner, 1970).

The death of individuals due to causes other than starvation was included with the probability of dying depending on body mass and population density, controlled by a variable n, which is a measure of how many individuals the considered area can tolerate. Larger values of n imply lower mortality, and vice versa. We therefore denote the parameter 1/n as ‘mortality strength’. As an individual dies as a whole not partially, mortality is implemented as a probability for occasional death in our individual-based model. A year has the duration τ = 1. At the end of every time interval inline image each individual dies with a probability inline image depending on its body mass and the total consumer biomass,

  • image(5)

This is the time-discrete version of density-dependent mortality, as implemented, e.g., by Kartascheff et al. (2010). Larger individuals have a smaller probability of dying. Mortality is scaled with body mass in the same way as metabolism, in agreement with empirical data (Brown et al., 2004). This means that juveniles have a higher mortality than adults. All adults in our model have a similar body mass; therefore, they also have a similar mortality. As we assume that mortality is most often due to density-dependent effects such as parasites, predators or diseases, we did not consider the effect of age on mortality. Dead individuals are removed from the system.

Consumer reproduction

Once per year, reproduction takes place, just before the first death events of that year. An individual, sexual or asexual, is considered mature once it has reached the minimum adult body mass Badult, which will be set to 15 in most of our simulations. An asexual female with a body mass Bmother, prev larger than Badult by at least twice the offspring weight Bjuvenile = 1 produces

  • image(6)

offspring (rounded to an integer) with body mass Bjuvenile = 1. Taking into account parental care such as nursing and feeding, we estimate the cost of each offspring to be twice Bjuvenile, therefore the body mass of the mother due to offspring production is decreased by twice the offspring body mass 2Bjuvenile = 2 for each child.

The precise value of the cost of producing offspring is not important for our results. Offspring body mass Bjuvenile is interpreted as the minimum juvenile body mass after parents have stopped investing into their offspring, that is, when juveniles begin to independently feed on resources.

The genotype of an asexual offspring (xi, yi), is identical with that of its mother. For a mature sexual female to reproduce, there must be mature males in the same patch. Sexual females mate with a randomly chosen partner, with the probability of a male to be chosen being proportional to its body mass, assuming that female mate choice is largely based on male body size (Andersson, 1994; Clutton-Brock & McAuliffe, 2009). However, as the body mass of males in our simulations never went above 25.6, the mating chances of males varied by at most 25%, and choosing all males with equal probability would yield very similar results. The number of offspring produced by a sexual female and its decline in body mass due to reproduction are calculated the same way as for asexual females.

The genotype of a sexual offspring is chosen randomly from a Gaussian distribution around the midparent value of each of the two genotype trait values, rounded to the nearest integer that still lies within the allowed range [1, L]. The variance of the Gaussian distribution was chosen to be Vg = 2.52, as in the original paper (Scheu & Drossel, 2007). The value of Vg determines together with the mortality strength 1/n the total niche width of the sexual population, which is approximately 17 with our standard parameter set, and it decreases to 10, i.e., to twice the individual niche width, when the mortality strength 1/n is increased to the largest values where the sexual mode of reproduction still prevails. However, Vg can be chosen as small as 1 for our simulations to yield similar results, and in this case, the total niche width of the sexual population is just below 10, which means that the sexual population covers approximately 1/4 of the total niche space.

This type of quantitative genetics approach is often used when modelling individual specialization, due to the lack of knowledge of the precise way in which many genes contribute to the relevant trait values. Nevertheless, in our previous work, we have also used a genetically explicit approach with several diallelic loci (Song et al., 2011a), demonstrating that the main results of the model are independent of the precise genetic implementation.

With a small probability = 0.001, a sexual offspring becomes asexual, based on the fact that asexual lineages can arise in sexual populations, in agreement with the ‘frozen niche variation hypothesis’ of Vrijenhoek (1979). The remaining sexual offspring have a probability of 1/2 to be female or male. After reproduction, the body mass of males decreases to Badult + 2·Bjuvenile if they are larger than this value. This prevents males from becoming ever larger and is justified by the cost of competing for mates (Andersson, 1994). It should be noted that we have not included investment of the father into rearing offspring, which would result in a larger offspring body mass or a smaller mortality of sexual offspring compared to asexual offspring (Clutton-Brock, 1991). By omitting this benefit for the sexual offspring, we implement the full two-fold cost of having males in the sexual populations. Only if this cost is more than compensated for by the advantage of being able to use additional resources, the sexual populations do have a chance to win. The symbols used in our model are summarized in Table 1.

Table 1.   Meaning of symbols used in the model.
SymbolMeaning
τA year’s time
BadultMinimum adult body mass
BjuvenileMinimum juvenile body mass
εMaximum consumption rate, relative to metabolic rate
LResource diversity, i.e., width of the total niche space
GIntrinsic growth rate of resources
1/nMortality strength
KrResource carrying capacity
αijAttractiveness of resource j to consumer i
λEcological efficiency
VgGenetic variance
uProbability for a sexual offspring becoming asexual
ηMigration probability for an offspring to a neighbouring patch

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Simulation set-ups

We performed computer simulations of the model to determine the more successful mode of reproduction. The model was initiated with a maximum resource biomass Rj = Kr = 100 in each niche, and with 20 asexual individuals and 20 sexual individuals with randomly chosen genotypes. Half of the sexual individuals were male and half were female.

We run the processes of growth, feeding, death and reproduction for 1000 years before evaluating the proportion of sexual individuals. The simulations were performed for different values of the three ecological parameters, resource diversity L, intrinsic resource growth rate G (Kr has an effect similar to that of G) and the mortality strength 1/n, which is a measure of the extent to which population density is regulated by factors other than resource availability. We also investigated the influence of the maximum consumption rate ε and the minimum adult body mass Badult on the dominance of sexual reproduction. All results were averaged over 1000 simulations.

Advantage of sexual reproduction as a function of the parameters

Figure 1 shows the average percentage of sexual females among all females in each patch after 1000τ, which corresponds to between 7 and 146 generations, depending on the parameters. The typical generation time, that is, the average age of the mother of a newly born offspring, is 12τ for the standard parameter set of Badult = 15, ε = 20, = 20, = 0.1, and = 20 000. In general, the mean generation time of sexual females is shorter than that of asexual females. As sexual offspring can exploit resources different from those of their parents and siblings, a sexual individual obtains on average more resources than an asexual individual and grows faster. Mostly, it took < 700τ either for the sexual population or for the asexual population to drive the other to extinction. Usually, the sexual population cannot win during the first few generations, when resources are still abundant and asexuals have higher productivity. Even when none of the two reproduction modes has won after 1000τ, this time period is sufficient to obtain an equilibrium composition of sexual and asexual individuals. Actually, 600τ is long enough, and a comparison of results after 600τ and 1000τ showed no difference.

image

Figure 1.  Average equilibrium percentage of sexual females in dependence of (a) maximum consumption rate ε, (b) intrinsic growth rate of resources G, (c) mortality strength 1/n, (d) resource diversity L, and (e) minimum adult body mass Badult. The parameters that are not varied are Badult = 15, ε = 20, = 20, = 0.1, and = 20 000. Sexual-to-asexual mutation rate and the genetic variance of sexual offspring genotypes are kept constant at = 0.001 and Vg = 2.52, respectively. Each data point is the average over 1000 simulation runs, and at the end of most simulations, either the sexual or the asexual population had died out.

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Figure 1a shows the average percentage of sexual females after 1000τ as a function of the maximum consumption rate ε. When the consumption rate is small, resource exploitation is low, and there is no advantage to sexual reproduction, rather the disadvantage of producing males prevails. The larger ε, the heavier is the exploitation of resources and the larger is the advantage of sexual reproduction, as manifested by the close to 100% success of the sexual lineages. The ability of sexual offspring to exploit resources in other underutilized niches is of great advantage.

Similar mechanisms underlie the results shown in Fig. 1b,c. Slow growth of resources (i.e., small values of G) or low mortality (i.e., large values of n) results in heavy exploitation of resources, and sexual reproduction dominates as sexual offspring can exploit unused resources, outweighing again the cost of producing males. In the opposite situation, when fast resource growth or high mortality prevents strong resource exploitation, the level of all resources is close to carrying capacity. In this situation, there is no advantage of being sexual, and asexuals win.

In contrast to the original model for seasonal species (Scheu & Drossel, 2007), sexual reproduction still dominates for values of n that are so large that a considerable fraction of the niches are occupied in the patch. This is because asexual individuals coexist with their offspring in the same niche, which means that they compete for resources and grow slower than individuals that are distributed over several niches. Therefore, the asexual individuals are soon outnumbered by sexual individuals exploiting a broader niche spectrum and acquiring more resources, due to parents using different resources than their offspring and siblings also differing in resource exploitation from each other.

By varying maximum consumption rate, intrinsic growth rate of resources and the mortality strength (Fig. 1a–c), we found that asexual reproduction wins when the level of exploitation of all resources is low. However, asexual reproduction also wins when all resources are exploited to a large extent. This happens in Fig. 1d, where the average percentage of sexual females decreases with decreasing resource diversity, L. When, for instance, = 8, there are 64 niches, but as each individual feeds strongly on nine resources, a large part of resources are covered when there are seven genotypes in the population. Producing offspring with a different genotype is only of modest advantage, and the proportion of sexual females has sunk to 20% in our simulations for = 8.

In Fig. 1e, we show the results of an investigation that is typical for large long-lived species with varying minimum adult body mass, Badult. Here sexual lineages performed best for intermediate values of Badult. If Badult is small, the generation time is short and the two-fold cost of producing males is incurred so often that the asexual population wins more easily due to its higher production of offspring. On the contrary, if Badult becomes too large, the generation time is so long that also the sexual individuals suffer heavily from the exploitation of their resources. These findings confirm the hypothesis that sexual reproduction is most advantageous when it sets in at the moment when resources become scarce. When it sets in earlier (i.e., when the generation time is too short), resources are not yet consumed, and there is no advantage of producing offspring that exploits different resources, but the disadvantage of producing males. When it sets in later, sexual individuals suffer from resource scarceness almost as severely as asexual individuals, resulting once again in a loss of the advantage of sexual reproduction.

To summarize this subsection, the sexual population fares better than the asexual population whenever parameters are such that their offspring can exploit underutilized resources. When most resources are exploited to the same large or small extent, this advantage vanishes. Using underutilized resources leads to a faster growth and to a faster production of offspring, which amounts to a larger rate of reproduction.

Influence of space, and geographic parthenogenesis

The results shown in Fig. 1 were obtained by averaging over 1000 simulations of a single patch. At the end of most simulations, either the sexual or the asexual model of reproduction had won. This result does, however, not take spatial extension into account. In a spatially extended system, a mode of reproduction that has locally died out can immigrate from surrounding patches, if it still is present there. This possibility restrains stochastic local extinctions and always leads to the victory of the same mode of reproduction, if this mode has a considerably higher probability to win in a patch. As was shown by Ament et al. (2008) for the model with seasonal species, a system of many patches coupled by weak migration thus leads to a much steeper transition from sexual to asexual reproduction when the control parameters investigated in Fig. 1 are varied. Furthermore, the parameter range over which sexual reproduction wins is extended, because sexual individual immigrating from neighbouring patches can increase the genetic variance of a local population. However, the asexual population cannot be driven to extinction when patch numbers are high and the migration rate is large.

We performed this type of spatial simulation also with our present model and obtained similar results (not shown). We furthermore investigated the phenomenon of geographic parthenogenesis in our model. To this purpose, we arranged again 20 patches along a one-dimensional chain and coupled them by migration. By assigning to the patches different values of the ecological parameters, we investigated now the influence of a gradually changing environment in space.

After birth, each individual was allowed to migrate to each neighbouring patch with a migration probability η. Figure 2 shows the results obtained for different migration rates. When the migration rate is zero, the curves are identical to those of Fig. 1. With increasing migration rate, the parameter range for which sexual reproduction dominates increases first, because sexual migrants increase the genetic variance, as just explained. For not too large values of the migration rate, the pattern of geographic parthenogenesis emerges: when the conditions are harsh, as manifest at high mortality or low resource diversity at the right end of the graphs in Fig. 2, asexual reproduction dominates; otherwise, sexual reproduction dominates.

image

Figure 2.  Influence of the migration rate η on the equilibrium percentage of sexual females in the 20 patches for varying (a) resource diversity L and (b) mortality strength 1/n. The parameters are identical to those in Fig. 1d,c, respectively, with an added migration rate η.

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To ensure that these results are not due to the initial conditions chosen by us (which are to some extent arbitrary), we also run simulations where we started with 20 sexual females and 20 sexual males in each patch, with no asexual individuals. To accelerate the production of asexual mutants, we set the sexual-to-asexual mutation rate u = 0.01, which is unrealistically high. In spite of this high value, we still found a large range of parameters where the proportion of sexual females is above 90%, demonstrating the advantage of sexual reproduction in a world of diverse resources in short supply.

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Based on earlier ideas that the prevalence of sexual reproduction is due to genetically different offspring being able to consume different resources (Maynard Smith, 1971; Williams, 1975; Bell, 1982), we developed a model for the evolution of sex in large and long-lived organisms, thus complementing our earlier results obtained for seasonal species. The model includes the two fundamental processes of virtually any living multicellular organisms, that is, the consumption of resources for somatic growth and the investment of resources into offspring production. In unitary organisms, which grow to maturity by multiplying cells based on mitosis, resources are invested into somatic growth until reaching a certain body size, after which sexual reproduction is initiated by the activation of cells in the germline (Stearns, 1992; Hughes, 1989). Remarkably, resources are then invested into the production of offspring genetically different from the parents, by the processes of meiosis and fusion with genetically different gametes (outcrossing). This change in resource investment from clonal growth during ontogenesis to offspring produced sexually after reaching maturity characterizes the life cycle of unitary organisms, that is, most metazoan animals (Stearns, 1992; Begon et al., 2005), but why this switching occurs remains unclear and presents the essence of the enigma of the maintenance of sexual reproduction. Our model for the first time includes both of these fundamental processes of virtually all living multicellular organisms. It focuses on large and long-lived metazoan animals, such as vertebrates, which reproduce several times per lifetime, that is, are iteroparous. The model therefore combines theories on life-history evolution with theories on the maintenance of sexual reproduction. Combining these two bodies of theories and basing both of them on the consumption of resources as the main driving force was possible by building on our previous work. In 2007, we presented a model on the maintenance of sexual reproduction in organisms characterized by intermittent mixis, that is, organisms that reproduce asexually except once per season when resources become limiting (Scheu & Drossel, 2007). This model ignored that allocating resources to somatic growth fundamentally changes life-history characteristics and the fitness of organisms. Focusing on these changes, we presented a model on the evolution of life histories based on metabolic theory and explicit resource-consumer dynamics (Y. Song, S. Scheu & B. Drossel, under review). The unifying approach taken in the present model is based on the assumption that both somatic growth during ontogenesis and the production of offspring by sexual reproduction are driven by resource availability as the most important factor determining growth, survival and the mode of reproduction (Ghiselin, 1974; Williams, 1975; Bell, 1982, 1988).

Our model explicitly takes into account the dynamics of resources and the negative feedback between resource use in the current generation and the resource availability to offspring in the next generation. Similar to the model for seasonal species with intermittent mixis (Scheu & Drossel, 2007), we found that asexual reproduction predominates when mortality is high, resource diversity is low or resources regrow so fast that resource scarceness never occurs. As in these situations, there is no advantage to producing genetically different offspring, asexual reproduction performs better due to its higher productivity. By extending the model to include a spatial dimension (Ament et al., 2008) and by applying a mortality gradient in space (Song et al., 2010, 2011a), we gained a distribution pattern of sexual reproduction resembling geographic parthenogenesis (Vandel, 1928; Kearney, 2006), with sexual reproduction dominating in favourable and asexual reproduction dominating in harsh environments. With the current and previous work (Song et al., 2010, 2011a), we have thus shown that the concept of a world of structured resources in short supply results in the predominance of sexual reproduction for both modular short-lived organisms experiencing sex only once per season and long-lived unitary organisms reproducing several times during their life cycle. The structured resource model therefore offers a general theory for the maintenance of sexual reproduction. It combines processes and assumptions of two of the main theories on the evolution of sex, that is, the Tangled Bank and the Red Queen, as it explicitly considers the dynamics of resource exploitation in space, and feedback between resources and consumers in time.

We found that asexual individuals that mature at the same body mass as sexual individuals have a longer generation time, because they obtain less resource. This demonstrates the superiority of sexual offspring at exploiting resources. For long-lived species, the advantage of producing genetically different offspring is in fact larger than for seasonal species, because long-lived species are iteroparous and coexist with their offspring, possibly over several generations. Together, the coexisting individuals produced sexually exploit resources more efficiently than individuals produced asexually. The phenomenon that resources are exploited more efficiently in more diverse communities recently received considerable attention in experiments on functional consequences of the diversity of species (Tilman, 2004; Balvanera et al., 2006; Schmid et al., 2009), but also of the diversity of genetically different lineages within species (Cadotte et al., 2009; Devictor et al., 2010; Ellers et al., 2011; Jousset et al., 2011; Tack & Roslin, 2011).

A central assumption of our model is that an individual uses only a small part of the resources present in a patch, and that this resource usage is to a large extent determined genetically. Our model functions as long as the niche width of an individual is not larger than half the niche width of the population, and as long as the niche width of the population is such that there are a sufficient number of unexploited resources. The specialization of individuals within a population to different resources has good empirical foundation (Araujo et al., 2011; Schreiber et al., 2011). With the recent advances in genetic analyses of populations, it is increasingly realized that the spectrum of consumers of plants varies markedly with the genetic constitution of plant individuals (Bangert et al., 2006; Bailey et al., 2009; Schädler et al., 2010). For terrestrial systems, it has long been disputed why only little of the plant resources present are actually consumed by herbivores, that is, why the world is green (Hairston et al., 1960; Oksanen & Oksanen, 2000). Despite no consensus has been reached on the relative importance of top-down versus bottom-up factors in regulating herbivores (Walker & Jones, 2001; Gruner et al., 2008), the fundamental role of resource limitation is appreciated (Cornelissen et al., 2008; White, 2008). Further, it is widely accepted that the defence of plants most efficiently works against generalist consumers but usually there are at least some specialists undermining their defence system (Speight et al., 2008). However, by genetically manipulating plant defence, it has only been shown recently that plants in fact are attacked by an increasing number of generalists with knocking out defence genes (Wu & Baldwin, 2010). These findings largely support our assumptions that consumers only feed on a fraction of resources available and that the consumption of resources varies with resource quality. Importantly, they also support the fundamental assumption of our model that resource usage to a large extent is determined genetically and that populations use a considerably larger fraction of resources than individuals.

Asexual individuals in our model have the same narrow niche width as sexual individuals, an assumption that is justified if we assume that asexuals originate from sexuals. The results of our simulations are essentially the same when asexual offspring are allowed to mutate to another niche chosen from a Gaussian distribution with variance Vg with a small probability of up to 1% per individual.

The body mass at which an individual reaches maturity is an important feature of the model. Individuals that mature at a larger body mass have the advantage that they can produce more offspring per year once they are mature, at the expense of having to wait longer before starting to produce offspring. Also, larger individuals experience lower mortality. However, all these advantages vanish when resources are depleted. Therefore, there is in fact an optimal range for the body mass of sexual populations. From the view of metabolic theory, somatic growth, which represents asexual propagation of cell lineages, should continue until resource exploitation has progressed to an extent that the advantage of producing genetically different offspring outweighs the cost of producing males. Of course, other factors not considered in this model, such as predation or the correlation between resource accessibility and consumer body mass, can favour smaller body mass in sexual organisms.

Given the fact that large long-lived organisms can adjust the relation between sexual reproduction and asexual (somatic) growth by adjusting their body mass, it might be well that in the evolutionary past of metazoan animals such as vertebrates, the need to produce offspring asexually has vanished almost completely. Eventually, sexual reproduction became so hard-wired that today in mammals and birds, no switching to asexual reproduction is possible any more, due to genomic imprinting (Swales & Spears, 2005).

Acknowledgments

  1. Top of page
  2. Abstract
  3. Introduction
  4. Model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

This study was funded by the Deutsche Forschungsgemeinschaft (DFG) under contract number Dr300/6.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Data deposited at Dryad: doi: 10.5061/dryad.4dp71437