Malthusian Relativityι**=7/3ψ
Life history evolution - traits & transitions

Sexual reproduction

Interactive competition outbalances the two-fold cost of meiosis and selects for sexual reproduction

When natural selection forms reproducing units with reproducing and interacting individuals it will either select for asexual reproduction with offspring workers as interactors, or for sexual reproduction between a reproducing female and an interacting male.

A reproducing individual can use sexual reproduction to enhance the competitive quality of the interacting unit relative to units with asexual reproduction. This is because a female can attract the competitively superior individuals by allowing them to allocate some fraction of their genome to her offspring. Frequency dependent interactions are thus expected to select sexual interacting units over asexual units.

Sexual reproduction may thus be selected by an interactive competition where females compete for the interactively superior males in the population. And the more attractive females, that can attract the competitively superior males, are those that allow the largest fraction of the male genome in the offspring. But this enhanced competitive quality of sexual reproduction comes at a cost; the cost of meiosis (Williams, 1975, 1988) which is the cost of genomic dilution where the probability that a gene in the female is copied to an offspring is declining with the fraction of the offspring genome that comes from the male.

Due to the cost of meiosis we do not expect sexual reproduction to evolve in the absence of interactive competition. But more generally we may expect that the degree of sexual reproduction will evolve to be proportional to the level of interference competition in the population. To analyse this we can allow for a sexual reproduction continuum where the fraction f of the male genome that is allocated to the offspring is representing also the competitive quality of the females interacting unit. Then, by letting the interactive competition select on the replication rate of the female genome, we find the following selection attractor

f** = ψ ι** / ( 1 + ψ ι** )

on the fraction of the male genome that is allocated to the offspring (Witting, 1997, 2002). Hence we find that the transition from the interaction fix-points of self-replicating cells [ι* << 1 / ψ] to the equilibrium fix-point of the multicellular animal [ι** = 1 / ψ] is selecting for a transition from asexual reproduction to the well-known form of sexual reproduction, where a female and a male individual share the genome of the offspring equally among them.

By extending the argument, we find also that additional transitions to the evolutionary steady state [ι** = (4d - 1) / (2d - 1) ψ] or the upward constrained mass [ι** → ∞] are selecting for unknown forms of sexual reproduction, where females mate with several males and each parent provides only a small fraction of the genome in the offspring. The latter result, however, is dependent upon the assumption that offspring workers are produced asexually by the female. When they are allowed also to be produced sexually we predict that the well-known form of sexual reproduction applies also to co-operatively and eusocially reproducing organisms (see section on offspring workers).


  • Williams, G.C. 1975. Sex and evolution. Princeton University Press, Princeton.
  • Williams, G.C. 1988. Retrospect on sex and kindred topics. pp. 287--298, In: R. E. Michod and B. R. Levin (eds.) The Evolution of Sex. Sinauer, Sunderland.
  • Witting, L. 1997. A general theory of evolution. By means of selection by density dependent competitive interactions. Peregrine Publisher, Århus, 330 pp, URL
  • Witting, L. 2002. From asexual to eusocial reproduction by multilevel selection by density dependent competitive interactions. Theoretical Population Biology 61:171--195.