Dyar's Rule and the Investment Principle: optimal moulting strategies if feeding rate is size–dependent and growth is discontinuous

Abstract

We consider animals whose feeding rate depends on the size of structures that grow only by moulting (e.g. spiders' legs). Our Investment Principle predicts optimum size increases at each moult; under simplifying assumptions these are a function of the scaling of feeding rate with size, the efficiency of moulting and the optimum size increase at the preceding moult. We show how to test this quantitatively, and make the qualitative prediction that size increases and instar durations change monotonically through development. Thus, this version of the model does not predict that proportional size increases necessarily remain constant, which is the pattern described by Dyar's Rule. A literature survey shows that in nature size increases tend to decline and instar durations to increase, but exceptions to monotonicity occur frequently: we consider how relaxing certain assumptions of the model could explain this. Having specified various functions relating fitness to adult size and time of emergence, we calculate (using dynamic programming) the effect of manipulating food availability, time of hatching and size of the initial (or some intermediate) instar. The associated norms of reaction depend on the fitness function and differ from those when growth follows Dyar's Rule or is continuous. We go on to consider optimization of the number of instars. The Investment Principle then predicts upper and lower limits to observed size increases and explains why increases usually change little or decline through development. This is thus a new adaptive explanation for Dyar's Rule and for the most common deviation from the Rule.

Proximate sources of sexual size dimorphism in insects: locating constraints on larval growth schedules

“…The proximate mechanisms determining this limit are not clear, however. A relatively old idea that larvae moult primarily to increase the size of their mouthparts (Nijhout 1981;Hutchinson et al 1997) was not supported by a recent study (Esperk and Tammaru 2004). A promising suggestion is that of Harrison (2004, 2005) who see the primary purpose of larval moult in renewing the respiratory system, thereby avoiding the oxygen limitation.…”

Post-Embryonic Development inZaprionus indianus(Diptera: Drosophilidae)

“…By analyzing the results of these measurements, a more pronounced growth was observed between the Þrst and second instar compared with the period between the second and third instar. Generally, arthropods have an uneven growth rate, even when the food supply is constant; this difference could be because of structural limitations, such as mouthpart sizes, or because of differences in their ability to accumulate and assimilate food in the different stages (Hutchinson et al 1997). According to Hutchinson et al (1997), the conßict between delaying or anticipating ecdysis results in an optimal interval for each instar stage to maximize size and reserve gain.…”

Preliminary assessment of cephalopharyngeal skeleton length and body length of Hemipyrellia ligurriens (Wiedemann) (Diptera: Calliphoridae) larvae as potential parameters to estimate minimum post mortem interval

“…Furthermore, information gathered from this analysis could provide baseline for allometric study or multivariate measurement of size of forensic blow fly larvae as explained in Dyar's rule on the growth of immature arthropods (Klingenberg and Zimmermann 1992;Hutchinson et al 1997). In forensic practice, cephalopharyngeal skeleton growth data could be so useful if the larval body length could not be obtained due to improper handling of specimens intended for PMI min analysis.…”