Sib competition and sperm competitiveness: an answer to ‘Why so many sperms?’ and the recombination/sperm number correlation

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Abstract
Sperm, or inter-ejaculate, competition leads to the evolution of many sperm per ejaculate. However, sperm competition theory does not predict the correlation between sperm number and chiasma, or that between sperm number and haploid chromosome number. Firstly, we show that phylogenetic inertia cannot account for at least the latter relation, and secondly, a model is presented which incorporates sib competition (intra-ejaculate competition) and sperm competitiveness to explain the relation between sperm numbers and recombination and the question 'Why so many sperms?'. It is argued that if there are deleterious mutations which affect sperm competitiveness this will lead to sib or intra-ejaculate competition. If inter-ejaculate competition also exists, then there will be selection for increased recombination. A chiasmate male heterozygous for n mutations which reduce sperm competitiveness can produce gametes with 0...n mutations. The proportion of gametes with 0 mutations per ejaculate is s = 0.5n, which is a small fraction. This means that to ensure on average one sperm with 0 mutations per ejaculate, a chiasmate male must produce 1/s sperm. We may therefore expect that 1/s will be positively correlated with sperm numbers. If inter-ejaculate competition leads to an optimum sperm number of x, then the optimum number of sperm per ejaculate is x/s. Sperm numbers will be increased by: (i) the number of loci which affect sperm competitiveness in the haploid state; (ii) the mutation rate; and (iii) the recombination rate. A correlation between recombination rates and sperm numbers is therefore to be expected.