Stability of Population Growth Determined by 2 X 2 Leslie Matrix with Density-Dependent Elements

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Abstract
The matrix considered contains 4 elements, each a function of total number. A special case for which the matrix may be appropriate is when the population may be divided into juveniles and adults, and the survival rates and fecundity are the same for all members of each group. This is true, at least approximately, for many species of birds. The conditions for stability are determined and are illustrated with a model based on the data collected on the Marley Wood, Oxford [England] population of the great tit (Parus major L.). A reformulation of the conditions permits comparison with the conditions for a population with identical survival rates and fecundity for all age groups, i.e., a population without effective age structure. Conditions under which the age structure may be ignored when discussing stability are considered.

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