A counterintuitive result in Bell's model of delayed maturity

Bell formulated a model with constant parameters in which he applied the commonsense argument that delayed maturity would be favored in iteroparous species if fecundity at first episode increased with age at a rate greater than the rate of decline in survival. However, analysis of his model reveals a flaw leading to the counterintuitive result that a geometric increase in fecundity with age cannot be made large enough to offset even a small geometric decline in survival so that population growth rate could increase with age of maturity. Thus, favorable selection of delayed maturity is unlikely in Bell's model. Some age-dependent models are described that avoid this flaw. This analysis extends the models of Sibly and Calow to include the counterintuitive result that an exponential increase in fecundity cannot offset an exponential decline in survival to favor delayed reproduction at any age.