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The Leslie matrix is a discrete, age-structured model of population growth that is very popular in population ecology named after Patrick H. Leslie. [1] [2] The Leslie matrix (also called the Leslie model) is one of the most well-known ways to describe the growth of populations (and their projected age distribution), in which a population is closed to migration, growing in an unlimited ...
Patrick Holt Leslie (1900 – June 1972) nickname "George" [1] was a Scottish physiologist best known for his contributions to population dynamics, including the development of the Leslie matrix, a mathematical tool widely used in ecological and demographic studies.
The matrix L is referred to as the Leslie matrix for age-structured models, and as the Lefkovitch matrix for stage-structured models. [ 17 ] If parameter values in L are estimated from demographic data on a specific population, a structured model can then be used to predict whether this population is expected to grow or decline in the long-term ...
Since any 0–1 matrix is the biadjacency matrix of some bipartite graph, Valiant's theorem implies [9] that the problem of counting the number of perfect matchings in a bipartite graph is #P-complete, and in conjunction with Toda's theorem this implies that it is hard for the entire polynomial hierarchy. [10] [11]
In the study of age-structured population growth, probably one of the most important equations is the Euler–Lotka equation.Based on the age demographic of females in the population and female births (since in many cases it is the females that are more limited in the ability to reproduce), this equation allows for an estimation of how a population is growing.
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In some cases parsimonious reductions, a more specific type of reduction that preserves the exact number of solutions, are used. #P-complete problems are at least as hard as NP-complete problems. [1] A polynomial-time algorithm for solving a #P-complete problem, if it existed, would solve the P versus NP problem by implying that P and NP are ...
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