Semelparous organisms breed only once during their lifetime. Examples of this type of reproduction strategy can be found with Pacific salmon and bamboo. The per capita rate of increase, ????, can be thought of as a measure of reproductive fitness. The greater ????, the more offspring an individual produces. The intrinsic rate of increase is typically a function of age, x. Models for age-structured populations of semelparous organisms predict that the intrinsic rate of increase as a function of x is given by r(x)= ln(L(x)M(x))/x where ????(x) is the probability of surviving to age x and ????(x) is the number of female births at age x. Suppose that L(x)= e-0.19x and M(x)= 3x0.7. Find the optimal age of reproduction. xopt=
