Brood Reduction and Optimal Parental Investment when Offspring Differ in Quality

Any parent has finite amounts of resources available for reproduction. The more resources supplied to an offspring, the greater should be the offspring's chances of survival and future reproduction, but the fewer resources should remain for the parent to produce other offspring. Thus, a parent could invest a small amount in each of a large number of inexpensive offspring ora large amount in each of a smaller number of offspring. Smith and Fretwell (1974) developed a simple graphic model of the selective consequences of different resource allocations among offspring. They assumed that parental investment could be represented as a single quantity and that an offspring's fitness could be expressed as a function of the investment received. Parental fitness, for a given allocation, was defined as the return in offspring fitness per unit of investment. This corresponds to the slope of a line from the origin to the appropriate point on the function. The tangent o the curve through the origin had the steepest gradient and gave the allocation to individual offspring that maximized parental fitness. Their model has been widely used and was recently formalized by Lloyd (1987). Smith and Fretwell's model predicts that an optimal parent should invest the same amount in each offspring. However, the model assumes that the function relating offspring fitness to parental investment isthe same for all offspring; more precisely, the model assumes that a parent cannot detect differences inoffspring quality before resources are committed. Temme (1986) argued that equal investment does not maximize parental fitness if offspring differ in quality. Rather, the parent should invest different amounts in offspring of different quality, such that the marginal return from additional investment would be the same for all offspring. In this note, I extend Temme's argument by deriving the optimal parental investment for different relative frequencies of offspring types. I also consider when it is in a parent's interests to abort rather than provision offspring oflower quality. My model addresses a basic question: how should a parent allocate resources among offspring when the offspring have different expectations of fitness given the same parental investment? The answer is simple. Parental resources are optimally distributed when (1) the marginal return from each provisioned offspring equals the average return from all offspring, and (2) offspring whose quality falls below some threshold are aborted and yield no return on their cost.