A general solution for optimal egg size during external fertilization, extended scope for intermediate optimal egg size and the introduction of Don Ottavio ‘tango’

Egg sizes of marine invertebrates vary greatly, both within and between species. Among the proposed causes of this are a trade-off between egg size, egg number and survival probability of offspring, and a selection pressure exerted by sperm limitation during external fertilization. Although larger eggs are indeed a larger target for sperm, producing larger eggs also implies making fewer of them. There has been discussion about whether sperm limitation can (theoretically) and does (in nature) select for larger egg size than under ad libitum sperm. In one specific model, based on a particular fertilization kinetics model and an empirically derived mortality function, the theoretical possibility of a negative shift in optimal egg size with sperm concentration was demonstrated. Here we present a generalized analytical model to explore the effects of survival and fertilization probabilities on optimal egg size. It is demonstrated that incorporating fertilization kinetics greatly increases the scope for intermediate optimal egg size, as opposed to eggs of minimal or maximal size. Second, we present a general analytical qualitative solution to the question whether optimal egg size depends on sperm concentration. It is shown that, under the condition that an intermediate optimal egg size exists, this qualitative outcome of the model (positive, negative or no relation between optimal egg size and sperm limitation) depends on the structure of the fertilization kinetics part of the model. Finally, we evaluate fertilization kinetics models with respect to the general solution, using two previously published kinetics models ('Don Giovanni' and 'Don Ottavio') and a novel alteration of one of them in which sperm concentration covaries with egg concentration (Don Ottavio 'tango'). For all three models the relationship between optimal egg size and sperm concentration is shown to be always negative. This paper thus shows how biologically realistic relationships between egg size on the one hand and survival and fertilization probability on the other hand predict optimal egg size to be intermediate, and that this optimum is in general expected to increase when sperm become more limiting.

Spatially structured genetic variation in a broadcast spawning bivalve: quantitative vs. molecular traits

Understanding the origin, maintenance and significance of phenotypic variation is one of the central issues in evolutionary biology. An ongoing discussion focuses on the relative roles of isolation and selection as being at the heart of genetically based spatial variation. We address this issue in a representative of a taxon group in which isolation is unlikely: a marine broadcast spawning invertebrate. During the free-swimming larval phase, dispersal is potentially very large. For such taxa, small-scale population genetic structuring in neutral molecular markers tends to be limited, conform expectations. Small-scale differentiation of selective traits is expected to be hindered by the putatively high gene flow. We determined the geographical distribution of molecular markers and of variation in a shell shape measure, globosity, for the bivalve Macoma balthica (L.) in the western Dutch Wadden Sea and adjacent North Sea in three subsequent years, and found that shells of this clam are more globose in the Wadden Sea. By rearing clams in a common garden in the laboratory starting from the gamete phase, we show that the ecotypes are genetically different; heritability is estimated at 23%. The proportion of total genetic variation that is between sites is much larger for the morphological additive genetic variation (QST = 0.416) than for allozyme (FST = 0.000-0.022) and mitochondrial DNA cytochrome-c-oxidase-1 sequence variation (phiST = 0.017). Divergent selection must be involved and intraspecific spatial genetic differentiation in marine broadcast spawners is apparently not constrained by low levels of isolation.

Disjunct distribution of highly diverged mitochondrial lineage clade and population subdivision in a marine bivalve with pelagic larval dispersal

Mitochondrial DNA sequence data for 295 individuals of the marine bivalve Macoma balthica (L.) were collected from 10 sites across the European distribution, and from Alaska. The data were used to infer population subdivision history and estimate current levels of gene flow. Inferred historical biogeography was expected to be congruent with colonization of the Atlantic Ocean from the Pacific Ocean after the opening of the Bering Strait 3.5 Ma. In addition, the last glacial maximum, about 18000 years ago, was expected to have been responsible for most of the present-day distribution of molecular variation within Europe, because the area must have been recolonized after confinement to France and the south of the British Isles during the last glacial maximum. Current gene flow was hypothesized to be high, because the larvae of M. balthica spend 2-5 weeks drifting in the water column. The geographical distribution of one highly diverged haplotype clade was found to be disjunct and was encountered exclusively in samples from the Baltic Sea and Alaska. A molecular clock calibration for marine bivalve cytochrome-c-oxidase I dates this clade as having split off from the other haplotypes 9.8-39 Ma. Multiple colonizations of the Atlantic Ocean from the Pacific by M. balthica may explain the strong differences found between Baltic Sea and other European populations of this species. The sympatric occurrence of the highly diverged mitochondrial lineages in western parts of the Baltic Sea points to secondary admixture. With the use of coalescent analysis, population divergence times for French vs. other non-Baltic European populations ('Atlantic population assemblage') were estimated at a minimum of about 110000 years ago, well before the last glacial maximum 18000 years ago. Signatures of population divergence of M. balthica that appear to have originated during the Pleistocene have thus survived the last glacial maximum. Some of the populations within the Atlantic assemblage are currently isolated, while others appear to be connected by gene flow. Apparently, populations of this species can remain highly subdivided in spite of the potential for high gene flow, implying that their population and evolutionary dynamics can be independent.

Sexual selection at the protein level drives the extraordinary divergence of sex-related genes during sympatric speciation

An increasing number of molecular studies are indicating that, in a wide variety of species, genes directly related to fertilization evolve at extraordinarily high rates. We try to gain insight into the dynamics of this rapid evolution and its underlying mechanisms by means of a simple theoretical model. In the model, sexual selection and sympatric speciation act together in order to drive rapid divergence of gamete recognition proteins. In this process, intraspecific competition for fertilizations enlarges male gamete protein variation by means of evolutionary branching, which initiates sympatric speciation. In addition, avoidance of competition for fertilizations between the incipient species drives the rapid evolution of gamete recognition proteins. This mechanism can account for both strong stabilizing selection on gamete recognition proteins within species and rapid divergence between species. Moreover, it can explain the empirical finding that the rate of divergence of fertilization genes is not constant, but highest between closely related species.