EVOLUTION OF SPERM SHORTAGE IN A SELFING HERMAPHRODITE.

In this note I examine the theoretical consequences of a negative correlation between the production of sperm and eggs in a protandrous, selfing hermaphrodite. This trade-off may explain the unusual condition of sperm-limited fecundity that has been described in the nematode Caenorhabditis elegans (Maupas). An enormous amount of work has been done in recent decades on the genetics, development, and neuroanatomy of C. elegans (Wood, 1988). Populations in the lab and in nature consist of self-fertilizing hermaphrodites and rare males. Hermaphrodites are little more than females able to mature sperm in a portion of their ovaries; they are not able to exchange sperm with other hermaphrodites, but they can be inseminated by a male. The physical basis of the trade-off between sperm and egg production is clear. Meiosis begins in the hermaphrodite gonad at the end of the third larval stage (Kimble and Ward, 1988). Gametes begin to mature as sperm in the proximal end (nearest the genital opening) of each gonad arm, and as maturation proceeds distally the type of gamete matured switches from sperm to oocyte. Temporally, almost all sperm are matured before the first oocytes mature (Kimble and Ward, 1988; Hirsh et al., 1976). During the lifetime of an individual there is only one bout of sperm production; once egg maturation begins the animal possesses its full complement of sperm. In laboratory and freshly isolated wild cultures the hermaphrodite exhibits a sperm shortage (Maupas, 1900; Ward and Carrel, 1979). On maturity, an unmated hermaphrodite releases a continuous series of self-fertilized eggs. As the sperm supply of the hermaphrodite dwindles she begins to release unfertilized oocytes mixed with fertile eggs. The frequency of fertile eggs declines until only oocytes are released. About as many oocytes are released as are fertilized eggs, at which point egg release of any kind ceases for the remainder of the individual's life (Ward and Carrel, 1979). The sperm shortage is a puzzling character. Because sperm seem relatively cheap to produce and the likelihood of a mating in the wild may be low due to the rarity of males, it seems the hermaphrodite should produce enough sperm to fertilize all of her eggs in the event that she never mates. To explain why C. elegans runs out of sperm before it runs out of eggs, I will provide an analysis of an explanation suggested by Jonathan Hodgkin and John Sulston (pers. comm.). The hypothesis is this: given that sperm production must occur before egg production, the production of more sperm, in order to increase overall fecundity, delays egg production and may therefore be selected against. This explanation attributes to sperm a hidden cost not reflected by the resources (cell contents) invested in them. This cost is due to the delay in reproduction that producing sperm causes and arises because of the discounting in the value of offspring produced later in life due to positive population growth and mortality. Hodgkin and Bames (1991) have provided empirical evidence that a mutant which produces more sperm (i.e., has a higher fecundity) has a lower intrinsic rate of increase than the wild type. I begin with a description of a simplified nematode life history, which is used to determine the evolutionary equilibrium for the age at which gamete production switches from sperm to eggs. This result is used to calculate the fraction of a cohort alive when the sperm are depleted. While not a direct measure of the number of sperm produced, this quantity reflects how the shortage has actually been described and what is seen in a population of worms growing in the laboratory. I argue that if most of a cohort survives past the point where sperm are exhausted, then we have found support for the model as an explanation for sperm shortage. Assume individuals undergo a preliminary growth period, g, after which they mature sperm during a period, s, and then switch to production of oocytes at age g + s. Without delay the oocytes are fertilized and released as zygotes. Individuals are assumed to be able to mature oocytes until they die. The organism's mortality schedule is a function of age; fecundity, once initiated, is independent of age. Individuals produce only fertile eggs until they deplete the sperm produced early in life (i.e., fertile and infertile eggs do not overlap as in real individuals). The age at which sperm will run out, d, is equal to the age at switching, g + s, plus an age increment, f(s). We would like to know what value for s would maximize the rate of increase of a genotype possessing it. I assume that, other than the value of s, the genotype's life history cannot evolve, and that s is evolving under conditions of unlimited growth. Thus natural selection will act to maximize the intrinsic rate of increase (Charlesworth, 1980). The intrinsic rate of increase, r, is defined as the solution to the Euler equation: