Age-Structured Models: The Leslie Matrix by Mike Martin

This page generates plots, information, and data for a Leslie-Matrix Model:

The model helps to describe the dynamics between the different, age-based population classes within the population of a given species. Usually, the populations in the model are those of the females within a larger population. The vector x has components that represent the populations of each of the age-based classes of the females. The Leslie matrix (or projection matrix) has fertilities or fecundities on the first row of the matrix. That is, the parameters, b_{i}, represent the average number of newborn females produced by one female in the i^{th} age group that survive through the time interval in which they were born. The b_{i}'s are all greater than or equal to zero. The other parameters, s_{i}'s, represent the survival probabilities from one class to the next. More specifically, s_{i} is the fraction of the i^{th} age group that live to the (i+1)^{st} age group. Each s_{i} is positive and less than or equal to one. A new population distribution, x_{t+1}, is obtained by multiplying the Leslie matrix, L, by the old population distribution, x_{t}. On this page we have arbitrarily set the number of population classes to four (say, juveniles, young adults, adults, and old adults).

Enter in the values of the parameters (described above), the initial distribution, and the number of steps, then press the "Evaluate" button.

b_{1} =

b_{2} =

b_{3} =

b_{4} =

s_{1} =

s_{2} =

s_{3} =

x_{1} =

x_{2} =

x_{3} =

x_{4} =

N =

PERCENTAGE POPULATIONS PLOT Class 1 (Juveniles) in BLUE // Class II (Young Adults) in PURPLE // Class III (Adults) in BROWN // Class IV (Old Adults) in Gray

References:

Perron-Frobenius Theory The Leslie Matrix

The Leslie Matrix