Biology Reference
In-Depth Information
Female
Table 8.3
An ESS
model of parental
investment
(Maynard Smith,
1977). Each sex
has the possibility
of caring or
deserting. The
matrix gives the
reproductive
success for males
and females (see
text for details)
Male
Care
Desert
Care
Female
gets
wP
2
WP
1
Male gets
wP
2
WP
1
Desert
Female
gets
wP
1
WP
0
Male gets
wP
1
(1
p
)
WP
0
(1
p
)
+
+
Who should care?
Each parent faces the decision of whether to care or desert. As we have seen, the costs
and benefits of these two options will depend on constraints (e.g. female mammals
lactate, males do not), and ecological factors which will influence both offspring
survival (intensity of predation, availability of food) and the opportunities for further
matings. However, a key influence on these costs and benefits will be the behaviour of
the other parent. If the female cares, it may pay the male to desert; but if the female
deserts, it may pay the male to care. In St Peter's fish, for example, each parent might do
best if the other did the caring and it was then free to desert to seek further matings.
John Maynard Smith (1977) was the first to propose a model which explored the
outcomes of joint decisions by both parents. There is a flaw in his original model, but it
is instructive to explain this, and to explore both the fundamental insights and
limitations of the model.
The model introduced a game theoretic approach to parental conflicts. It assumed
that each parent decides independently whether to care or desert (these 'blind bids' are
a simplifying and often unrealistic assumption - see later). The model looks for a pair of
strategies, say
I
m
for males and
I
f
for females, such that it would not pay a male to diverge
from strategy
I
m
so long as females adopt
I
f
, and it would not pay females to diverge from
I
f
as long as males adopt
I
m
. In other words, we seek the evolutionarily stable strategies
(ESS) for male and female (Chapter 5).
Let
P
0
,
P
1
and
P
2
be the probabilities of survival of eggs which are not cared for, cared
for by one parent and cared for by two parents, respectively;
P
2
The best strategy
for one parent
depends on the
strategy adopted
by the other
parent
An ESS model for
parental
investment
P
0
. A male who
deserts has a chance
p
of mating again. A female who deserts lays
W
eggs and one who
cares lays
w
eggs;
W
>
P
1
>
w
(caring females have fewer resources for eggs).
The pay-off matrix for this game is illustrated in Table 8.3. There are four possible ESSs:
>
ESS 1
:
female deserts and male deserts
. This requires
WP
0
>
wP
1
, or the female will care,
P
1
, or the male will care.
ESS 2
:
female deserts and male cares
. This requires
WP
1
and
P
0
(1
+
p
)
>
>
wP
2
, or the female will care, and
P
1
>
P
0
(1
+
p
), or the male will desert.
