A NEW EQUATION FOR CALCULATING REPRODUCTIVE SUCCESS OF CLUTCHES AS A FUNCTION OF THE DAY ON WHICH INCUBATION STARTS: SOME IMPLICATIONS

Auk, The, Jul 2006 by Murray, Bertram G Jr

A problem arises in measuring the lengths of the incubation and fledging periods, because first-hatched nestlings may not leave the nest when they are ready. In the Least Flycatcher, for example, the older nestlings usually do not leave the nest until a day or two after they are capable of leaving successfully (Briskie and Sealy 1989). In the Snow Bunting (Plectrophenax nivalis), nestlings are "capable of leaving the nest at about 9 d of age, but they usually remain in the nest until about 13 d old" (Hussell 1985:207). Even in the precocial, nidifugous Spur-winged Plover (Vanellus spinosus), chicks may remain in the nest up to two days after hatching (Yogev et al. 1996). Selection may favor early incubation, but it does not necessarily favor early fledging, because early fledging may reduce survival probabilities of the remaining nestmates. Thus, the probability of nest success (s) may be underestimated. In testing hypotheses, these data will have to be determined with care.

In all these examples, I have considered only the effect of fledging of earlier-hatched nestlings on the later-hatched nestlings remaining in the nest. I have not considered the reverse: the effect of parental care for the nestlings remaining in the nest on fledging survival. If survival were worse for fledglings than for nestlings, then, seemingly, selection should favor the early-hatched young to stay in the nest. This is apparently what they may do (as recounted above). I believe, however, by invoking Occam's razor (see below), that the "staying-in-the-nest" behavior is an adaptation that increases the probability of fledging of the later-hatched nestlings. Thus, the start of incubation before all eggs are laid is an adaptation that increases the probability of rearing at least some young that are capable of leaving should a predator attack, not an adaptation that assures early fledging of early-hatched nestlings.

ADDITIONAL COMPLEXITIES

(1) The basic equations of Clark and Wilson (1981; their equation 1) and Hussell (1985; his equation 2), as well as equation 1, do not consider the effect of within-brood loss. Clark and Wilson (1981), however, proposed that not all of the chicks have an equal probability of surviving. They suggested that, as a result of starvation, one of the chicks-in particular the last hatched, and especially if hatching were asynchronous-had a lower probability of surviving (q). Hussell (1985) broadened q to mean the reduced probability of survival from any cause, including predation, and added q', the reduced probability that a second chick has of surviving. Both q and q' will affect k, but will they affect k*?

Suppose that predators cause some mortality of the brood without taking the whole brood. Let us say that we have 1,000 successful nests and observe that 150 of them have lost a single chick from predation (but it could be from any cause). Thus, the probability of losing a single chick from a successful nest is z = 0.15. This number, z, should be subtracted from k. It should be readily apparent that partial brood loss results in lower k and k*, but it does not affect the relative values of k*; thus, the incubation pattern with the greatest k* without partial brood loss is the same as that with the greatest k* with partial brood loss. Partial brood loss, then, has no effect on the start of incubation. The same can be said for the loss of a second egg or nestling from a nest (when clutch size is greater than two).