A population dynamics model with strong maternal care
A two-sex age-structured nondispersing population dynamics deterministic model is presented taking into account strong maternal and weak paternal care of offspring. The model includes a weighted harmonic-mean type pair formation function and neglects the spatial dispersal and separation of pairs. It is assumed that each sex has pre-reproductive and reproductive age intervals. All adult individuals are divided into single males, single females, permanent pairs, and female-widows taking care of their offsprings after the death of their partners. All pairs are of two types: pairs without offspring under parental care at the given time and pairs taking child care. All individuals of pre-reproductive age are divided into young and juvenile groups. The young offspring are assumed to be under parental or maternal (after the death of their father) care. Juveniles can live without parental or maternal care but they cannot reproduce offsprings. It is assumed that births can only occur from couples. The model consists of nine integro-PDEs subject to the conditions of integral type. A class of separable solutions is studied, and a system for macro-moments evolving in time is derived in the case of age-independent vital ones.
Keywordspair formation child care paternal care maternal care
Unable to display preview. Download preview PDF.
- 4.F. C. Hoppensteadt, Mathematical theories of populations, genetics, and epidemics, in: CBMS Appl. Math. SIAM, vol. 20, Philadelphia (1975).Google Scholar
- 5.M. Iannelli, Mathematical theory of age-structured population dynamics, Comitato Nazionale per le Scienze Mathematiche, C. N.R., 7, Gardini Editori e Stampatori in Pisa (1995).Google Scholar
- 8.S. Moss de Oliveira, Consequences of parental care on population dynamics, Physica, A 273, 140–144 (1999).Google Scholar
- 11.V. Skakauskas, A density-dependent population dynamics model with offspring production at fixed ages and child care, in: Mathematical Modelling and Computing in Biology and Medicine 1 (5th ESMTB conference 2002), V. Capasso (Ed.), pp. 368–373.Google Scholar
- 12.V. Skakauskas, Large time behavior in a density-dependent population dynamics problem with age structure and child care, in: Mathematical Modelling of Population Dynamics, vol. 63, R. Rudnicki (Ed.), Banach center publications, Inst. of Math., Polish Acad. Sci., Warszawa (2004), pp. 243–258.Google Scholar
- 17.G. F. Webb, Theory of Non-Linear Age-Dependent Population Dynamics, New York, Marcel Dekker (1985).Google Scholar