×

zbMATH — the first resource for mathematics

A counterintuitive result in Bell’s model of delayed maturity. (English) Zbl 0835.92024
Summary: G. Bell [Am. Nat. 116, 45-76 (1980)] 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 R. Sibly and P. Calow [J. Theor. Biol. 123, 311-319 (1986)] to include the counterintuitive result that an exponential increase in fecudity cannot offset an exponential decline in survival to favor delayed reproduction at any age.
MSC:
92D25 Population dynamics (general)
92D15 Problems related to evolution
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bell, G., The costs of reproduction and their consequences, Amer. nat., 116, 45-76, (1980)
[2] Charlesworth, B., Evolution in age-structured populations, (1980), Cambridge University Press Cambridge, UK · Zbl 0449.92011
[3] Hoogendyk, C.G.; Estabrook, G.F., The consequences of earlier reproduction in declining populations, Math. biosci., 71, 217-235, (1984)
[4] Bell, G., On breeding more than once, Amer. nat., 110, 57-77, (1976)
[5] Stearns, S.C., Life-history tactics: A review of the ideas, Quart. rev. biol., 51, 3-47, (1976)
[6] Harper, J.L., Population biology of plants, (1977), Academic Press London
[7] Stearns, S.C., The evolution of life histories, (1992), Oxford University Press Oxford, UK
[8] Cole, L.C., The population consequences of life history phenomena, Quart. rev. biol., 29, 103-137, (1954)
[9] Mertz, D.B., The mathematical demography of the California condor population, Amer. nat., 105, 437-453, (1971)
[10] Caswell, H., Matrix population models: construction, analysis, and interpretation, (1989), Sinauer Assoc Sunderland, MA
[11] Capildeo, R.; Haldane, J.B.S., The mathematics of bird population growth and decline, J. anim. ecol., 23, 215-223, (1954)
[12] Charnov, E.L.; Schaffer, W.M., Life history consequences of natural selection: Cole’s result revisited, Amer. nat., 107, 791-793, (1973)
[13] Goodman, D., Life history analysis of large mammals, (), 415-436
[14] Ricklefs, R.E., On the evolution of reproductive strategies in birds: reproductive effort, Amer. nat., 111, 453-478, (1977)
[15] Ricklefs, R.E., The optimization of life-history patterns under density dependence, Amer. nat., 117, 403-408, (1981)
[16] Demetrius, L., The sensitivity of population growth rate to perturbations in the life cycle components, Math. biosci., 4, 129-136, (1969) · Zbl 0172.45103
[17] Caswell, H., A general formula for the sensitivity of population growth rate to changes in life history parameters, Theoret. population biol., 14, 215-230, (1978) · Zbl 0398.92024
[18] Sibly, R.; Calow, P., Why breeding earlier is always worthwhile, J. theoret. biol., 123, 311-319, (1986)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.