Summary

Gi

F2

F3

■ Fm - i

Fm

P1

G2

0

... 0

0

0

P2

G3

... 0

0

0

0

P3

... 0

0

0

0

0

■.. Gm- 1

0

0

0

0

. Pm - i

Figure 2 Population projection matrices. (a) An age-structured Leslie matrix (Ma). (b) A stage-based Lefkovitch matrix MB. Subscripts represent the age or size class with m being the oldest or largest class, respectively.

number of offspring born to each stage class that survive a given time period as well as the proportion of individuals in each stage class that survive and remain in that stage as compared with those that survive and enter a new stage (i.e., the transition probability). The elements of the matrix are Fx (stage-specific fecundity), Gx (probability of surviving and remaining in the same stage), and Px (probability of surviving and growing to the next stage). Within the Lefkovitch matrix Mx Fx is put along the top row, Px along the subdiagonal, and Gx along the diagonal while all other elements in the matrix are assigned a value of zero (Figure 2). The primary differences between the Lefkovitch stage-class matrix and the Leslie age-class matrix are that the stages may incorporate several ages (i.e., they may differ in their duration and that individuals may remain in a stage from one time to the next).

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