In Malthusian Relativity the evolution of sexual reproduction is given by the evolution of the interacting, reproducing, and sexual units. Here the interacting unit is the number of individuals that join in their interactions with other interacting units, while the reproducing and sexual units are defined by the compositions of the individuals in the interacting unit.

The reproducing unit is given by a single replicating individual and from zero to infinite non-replicating individuals. The replicating individual is the individual that produces offspring and/or macrogametes and it is usually an asexually reproducing individual or a sexually reproducing female or hermaphrodite. The non-replicating individuals can be males that produce microgametes copying their heritable code to the offspring through the sexual reproduction of the female or the hermaphrodite. The non-replicating individuals may also be offspring workers that get their heritable code copied indirectly through the relatedness with the replicating and/or male individuals.

The sexual unit is not present in asexual organisms. In sexual organisms the number of individuals in the sexual unit is usually one - a self-fertilising hermaphrodite - or two - a female and a male. But more generally there may be higher levels of sexual reproduction where females allocate heritable codes from more than a single male to the offspring. And sexually produced offspring need not necessarily obtain half of their genome from the mother and the other half from a single farther. To allow for the evolution of larger sexual units Malthusian Relativity applies a model where the sexual unit with three individuals is a unit with a single female and two males with each of the three individuals allocating one third of their heritable code to the offspring. And at the upper limit of sexuality the model allows for infinitely large sexual units composed of a single female and an infinite number of males with all individuals allocating an infinitely small fraction of their heritable code to the offspring.

For organisms beyond the lowest level of reproduction there is a cost related to each of the three units. For the interacting unit the cost is the cost of sharing local resources, with the cost being proportional to the number of individuals in the unit. For the reproducing unit the cost is the cost of non-replicating individuals with the cost being proportional to the number of non-replicating individuals in the unit. This cost resembles the well-known two-fold cost of the male when the reproducing unit is composed of a single female and a single male. For the sexual unit the cost is the cost of dilution of the replicating individuals heritable code in the offspring. This cost is zero if the heritable code is provided entirely by the replicating individual. It is the two-fold cost of meiosis for the usual form of sexual reproduction. And it is close to infinity at the limit where the sexual unit contains a single female and an infinite number of males and all individuals transmit an infinitely small fraction of their genome to the offspring.

For natural organisms beyond the lowest level of reproduction we expect that the costs of the interacting, reproducing, and sexual units be balanced by advantages provided by those units. It is thus essential to explain why the apparent benefit in mobile organisms of both the interacting and the reproducing unit is zero for asexual self-replicators, two-fold for pair-wise reproduction, three-fold for co-operative reproduction among three individuals, and close to infinity for eusocial reproduction. Likewise it is essential to explain why the apparent benefit of the sexual unit is zero for the asexual self-replicator, and why it is two-fold and only two-fold for dioecious sexual organisms no matter whether the organism reproduces pairwisely, co-operatively, or eusocially.

For Malthusian Relativity it has been shown (Witting, 2002) that selection by the density dependent competitive interactions among the interacting units may outbalance the cost of interacting, reproducing, and sexual units given that the three units evolve as traits that enhance the interactive quality of the interacting unit. And this might actually be the case. It is evident that the interacting unit may evolve as an interactive trait because, other things being equal, units with more individuals should be able to evolve a higher interactive quality. And the reproducing unit may also evolve as an interactive trait because the energy and time that the non-replicating individuals save on replication may be invested in interactive quality and competitive interactions. And even the sexual unit may evolve as an interactive trait because the replicating individual may use the father/s fraction of the offspring's genome to attract interactively superior sexually reproducing males to the reproducing unit.

But sexual reproduction can evolve by this mechanism only if the level of interactive competition is sufficiently high. Interestingly it follows that it is exactly the predicted increase in interactive competition associated with the transition from low-energy organisms with negligible body masses to high-energy organisms with large body masses that will explain the evolutionary transition from asexual reproduction to the usual form of sexual reproduction with a single male per female and a two-fold cost of meiosis.

However, if offspring workers can be produced only asexually, selection by density dependent competitive interactions predicts unknown forms of sexual reproduction where n-1 males mate with a single female and the sexually produced offspring receive genes from n>3 parents. But with the possibility of sexually produced offspring workers it follows that the sexual unit in pair-wise, co-operative, and eusocially reproducing organisms is a single male per female with a two-fold cost of meiosis, instead of any other number of males per female and any other level of cost. Sexual units with more than two individuals are not expected to evolve for the case of sexually produced offspring workers because the interactive quality of the male is transferred to the sexually produced offspring workers. This generates a diminishing return where the interactive quality that can be gained by exchanging an offspring worker with a sexual male is a declining function of the number of males per female. And it is only for the initial transition from asexual to pair-wise sexual reproduction that the interactive quality of the male can outbalance the cost of sexual reproduction.

This model is the first to explain the balance between fitness and the cost of the interacting, reproducing, and sexual units in organisms ranging from simple self-replicators to eusocial colonies. The model is also quite different from the models traditionally considered in relation to the evolution of sexual reproduction. Nearly all traditional models are reflections over the hypothesis that genetic diversity is beneficial to the organism per se. The various versions of the Fisher-Muller hypothesis suggest that sex and recombination protect against a genetic deterioration caused by the accumulation of deleterious mutations (e.g., Fisher, 1930; Muller, 1932, 1964; Manning and Thompson, 1984; Wagner and Gabriel, 1990; Charlesworth et al., 1993; Lynch et al., 1993, 1995; Peck, 1994; Peck et al., 1997). Most of these studies provide only a long-term advantage to sexual populations, while they lack a short-term advantage that will explain the evolution of sexual reproduction as well as the maintenance for cases where asexual variants can arise in sexual populations. Kondrashov's (1982) synergetic-fitness theory, however, can provide a short-term advantage given a special type of deleterious mutations that act together so that each gene becomes increasingly deleterious as the number of deleterious mutations increases. And Peck et al. (1999) show that the Fisher-Muller hypothesis may provide a short-term advantage if the population is subdivided into demes with sufficiently low migration among demes.

Another class of models is based on the idea that sexual reproduction may evolve because recombination produces genetically variable offspring (Weismann, 1889), which may increase the speed and efficiency of natural selection (Kondrashov, 1993; Barton, 1995; Feldman et al., 1997). Genetically variable offspring may provide an advantage in biotic interactions (Bell, 1982; Bell and Maynard Smith, 1987), for example, in host-parasite interactions where sexual reproduction can stores genes that currently are bad but can protect against future mutant parasites (Hamilton, 1980; Hamilton et al., 1990; Ebert and Hamilton, 1996). Another example is the sib competition models of Williams (1975) and Young (1981) that assume that competition is more severe between asexual sibs, which are genetically identical, than between sexual sibs, which are genetically diverse. More recently it has been suggested that sexual reproduction may evolve or be evolutionarily maintained by non-random mating that accelerates the evolution of beneficial traits (Kodric-Brown and Brown, 1987; Davis, 1995; Jaffe, 1996, 1999), or because of interactions among the different genetic models (West et al., 1999).

It has been said that none of the genetic hypotheses for the evolution of sexual reproduction are very convincing (Green and Noakes, 1995). The models will generally not explain why asexual reproduction in mobile organisms is more common in negligible sized organisms than in larger organisms. And nor will they explain why the sexual unit is a single male per female with the average offspring receiving half of the genes from the father and the other half from the mother. The genetical models tend to predict that only a small degree of sex is fine (Green and Noakes, 1995; Hurst and Peck, 1996; but see Peck and Waxman, 2000), suggesting that the degree of gene exchange that occurs among haploid and asexually reproducing prokaryotes may be sufficient to account for most of the genetic diversity hypotheses. The pluralist approach of West et al. (1999) may provide a more efficient framework for generating an advantage that may outbalance the two-fold cost of meiosis. But it might be more likely that the beautiful and simple phenomenon of sexual reproduction in higher organisms has evolved by a simple and clear-cut mechanism, instead of being explained by messy interactions among very different processes (Kondrashov, 1999).

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