LeslieMatrix

Lesliematrix is a term used in theoretical discussions to denote an extension of the classical Leslie matrix, a population projection model for age-structured populations. The term is not widely standardized and may refer to various generalized forms that incorporate additional structure, such as spatial distribution, multiple life stages, or nonlinear transitions. In many descriptions, a Lesliematrix is still a square matrix that projects a population vector from one time step to the next, but with richer dynamics than the standard model.

Construction: In a standard Leslie matrix L for n age classes, the first row contains age-specific fecundities and the subdiagonal contains survival probabilities. A Lesliematrix L' extends this by allowing entries to vary with time or state, or by embedding age structure in a larger block matrix that includes spatial compartments or additional stages. For example, L' may be written in a block form that couples births, survival, and movement between subpopulations, or entries may depend on density or environmental factors.

Analysis and interpretation: As with Leslie matrices, the dominant eigenvalue of a constant Lesliematrix governs asymptotic growth under fixed structure. When the matrix changes over time, one analyzes products of matrices over intervals rather than a single eigenvalue, yielding a growth rate per period or a stochastic growth rate in random environments. Applications include wildlife management, conservation planning, and ecological studies requiring joint age and spatial or stage structure.

Notes: The term is not a standard in formal literature; several authors use it informally to describe generalized age-structured models. See also Leslie matrix, population projection matrix, stage-structured models. For the original concept, see P. H. Leslie (1945).