Sexual conflict over parental investment by the female in a species with uniparental maternal care when there are (

*a*) no current costs of investment, and no future costs for the male, (

*b*) current costs of investment, but no future costs for the male and (

*c*) no current costs of investment, but future costs for the male. Filled male and female symbols indicate the optimal investment by females for the male and female, respectively. Curves shown are the expected fitness from the current brood (dotted line; which in (

*a*) and (

*b*) is also the male's expected remaining-lifetime fitness with the female), the expected future fitness of the female (thin solid line) or male (thin dashed line), and the expected total remaining-lifetime fitness of the female (thick solid line) or male (thick dashed line in (

*c*)). Values and functions assumed in the figures are:

,

and

*p*=0.7.

*Model*: the curves shown are based on a model in which a female produces one brood per year and invests

*x* in the brood. As a consequence of this investment, the female survives with a probability of

*s*(

*x*) to the start of the following breeding season, and, provided that she survives until the young are independent,

*b*(

*x*) young from the brood survive to maturity. Females are assumed not to senesce, so that the same functions

*b*(

*x*) and

*s*(

*x*) govern the female's productivity and survival throughout her lifespan. This also means that her optimal investment

is independent of her age. If she invests the same each year throughout her life, at the start of each season the expected further number of seasons in which she attempts to breed (including the current one) is 1/(1−

*s*(

*x*)). (

*a*) If the survival costs of reproduction are paid after the current brood is independent, the fitness that she accrues from the current brood is

*b*(

*x*) and her expected fitness from future broods is

, summing to a total fitness over her remaining lifespan of

. Her optimal investment,

, is found by setting the partial derivative of her total remaining-lifetime fitness equal to zero and solving for

, and is given by

, where primes denote the partial derivate with respect to

*x*. If pairs breed together in only one year, a male's expected lifetime fitness with the current female is

*b*(

*x*), and his optimal investment by the female,

, then occurs at the maximum of this function. If

*b*(

*x*) increases monotonically with

*x*, then his optimum is the maximum value of

*x* of which the female is capable. (

*b*) If the survival costs of reproduction are paid entirely before the current brood is independent, the fitness from the current brood is

*b*(

*x*)

*s*(

*x*), the female's expected fitness from future broods is

, and her total expected remaining-lifetime fitness

. Her optimal investment,

, is then given by

. If pairs breed together in only 1 year, the male's optimal investment by the female,

, is that which gives maximum fitness from the current brood, and is given by

. (

*c*) If the survival costs of reproduction are paid (as in (

*a*)) after the current brood is independent, but either of the pair benefit from the survival of the mate, the optimal investment of that sex may change. Here, I assume somewhat implausibly, but for the purposes of illustration, that pairs breed together provided that they are still alive, that the female can remate costlessly if her mate dies, and that males are polygynous and the rate at which they acquire additional mates and the breeding success of all their mates is unaffected by their harem size. Under these conditions the fitness and optimal investment for the female is unchanged. However, the expected remaining-lifetime fitness of a male with a female is now

, where

*p* is his annual survival and is independent of the female's investment, and the female's investment is the same each year. His optimal investment by the female,

is now given by

.

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