Stabilities and instabilities in population dynamics

Stability in population size is illusory: populations left to themselves either grow beyond all bounds or die out. But if they do not die out their composition stabilizes. These problems are discussed in terms of general abstract, multitype branching processes. The life and descent of a typical individual is described.

[1]  Esa Nummelin,et al.  On non-singular renewal kernels with an application to a semigroup of transition kernels , 1986 .

[2]  O. Nerman,et al.  The growth and composition of branching populations , 1984, Advances in Applied Probability.

[3]  P. Holgate,et al.  Branching Processes with Biological Applications , 1977 .

[4]  E. Nummelin.  General irreducible Markov chains and non-negative operators: Preface , 1984 .

[5]  Joel E. Cohen,et al.  Ergodicity of age structure in populations with Markovian vital rates, III: Finite-state moments and growth rate; an illustration , 1977, Advances in Applied Probability.

[6]  V. M. Shurenkov.  On the Theory of Markov Renewal , 1985 .

[7]  J. Hajnal,et al.  On products of non-negative matrices , 1976, Mathematical Proceedings of the Cambridge Philosophical Society.

[8]  Valerie Isham,et al.  Non‐Negative Matrices and Markov Chains , 1983 .

[9]  J. Cohen.  Ergodicity of age structure in populations with Markovian vital rates. II. General states , 1977, Advances in Applied Probability.

[10]  P. Jagers.  General branching processes as Markov fields , 1989 .

[11]  Olle Nerman,et al.  The stable doubly infinite pedigree process of supercritical branching populations , 1984 .

[12]  E. Nummelin.  General irreducible Markov chains and non-negative operators: List of symbols and notation , 1984 .

[13]  J. Cohen.  Ergodicity of Age Structure in Populations with Markovian Vital Rates, I: Countable States , 1976 .

[14]  Olle Nerman,et al.  On Products of Nonnegative Matrices , 1990 .

[15]  Nathan Keyfitz,et al.  Applied Mathematical Demography , 1978 .