Biology Reference
In-Depth Information
BOX 3.1 THE MARGINAL VALUE THEOREM AND REPRODUCTIVE
DECISIONS
The model of load carrying for starlings is applicable to many other situations in
which animals experience diminishing returns within a patch and is known as
the 'marginal value theorem' (Charnov, 1976a). It has been used to predict how
much time an animal foraging for itself (as opposed to carrying loads) will spend
in each site before moving on (Cowie, 1977). Diminishing returns in each patch
(generally referred to as 'resource depression') might arise, for example, simply
because of depletion, or because prey in the patch take evasive action and
become harder to catch, or because the predator becomes less likely to search
new areas in the patch (it crosses its own path more) as time goes by, or because
the predator starts with the easy prey and then goes on to hunt for those that
are more difficult to catch or are less rewarding. An example of the last of these
is when bumblebees or other nectar feeders visit the biggest and most rewarding
flowers on an inflorescence first, and then go on to the smaller flowers which
hold less nectar (Hodges & Wolf, 1981).
Reproductive decisions can be analysed with the same model. An example is
Geoff Parker's (1970a) analysis of how male dung flies search for mates (see also
Parker & Stuart, 1976). Males compete with one another for the chance to mate
with females arriving at cowpats to lay their eggs. Often one male will succeed in
kicking another male off a female during copulation and take her over. When two
males mate with the same female the second one is the individual whose sperm
fertilizes most of the eggs. Parker (1970a) showed this by the clever technique
of irradiating males with a synthetic isotope of cobalt ( 60 Co). The sperm of
irradiated males can still fertilize an egg but the egg does not develop. If a normal
male is allowed to mate after a sterile one about 80% of the eggs hatch, whereas
if the sterile male mates second only 20% of them hatch. The conclusion from
these 'sperm competition' experiments is clear: the second male's sperm fertilizes
about 80% of the eggs. It is not surprising, therefore, that after a male has
copulated he sits on top of the female and guards her until the eggs are laid, only
relinquishing his position to a rival male after a severe struggle.
When a second male takes over (or when a male encounters a virgin) how long
should he spend copulating? Parker carried out sperm competition experiments
in which he interrupted the second male's copulation after different times; this
showed that the longer the second male mates the more eggs he fertilizes, but the
returns for extra copulation time diminish rapidly (see Fig.B3.1.1). There is a cost
associated with a long copulation: the male misses the chance to go and search
for a new female. After the male has copulated for long enough to fertilize about
80% of the eggs, the returns for further copulating are rather small and the male
might do better by searching elsewhere for a new mate.
The analogue of travel time in the starling model is the time the male dung fly
must spend guarding the present female until she has laid her eggs plus the time
he spends searching for a new female. This total is 156 minutes on average. As
shown below, this estimate of travel time can be used to predict with reasonable
accuracy how long the male spends copulating with a female.
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