Demographic PVA’s Based on vital rates

Basic types of vital rates Fertility rates Survival rates State transition, or growth rates

The estimation of Vital rates Accurate estimation of variance and correlation in the demographic rates We need to know: The mean value for each vital rate The variability in each rate The covariance or correlation between each pair of rates

Limitations of Matrix selection The assumption that the precise combinations of values that we observed the limited duration of a demographic study will always occur is unlikely to be correct.

A more realistic approach Use the means, variances, and correlations between vital rates, and then simulate a broader range of possible values

The problem of negative correlations A hypothetical individual is currently in size class 3 and has mean probability s 3 =0.95 of surviving for one year. If it survives it will either stay the same size, or grow to be in size class 4 with mean probability g 4,3 =0.10 a 33 =s 3 (1-g 43 )=(0.95)(1-0.10) and a 43 =s 3 g 43 =(0.95)(0.10)

The Desert Tortoise

Size classes and definitions of matrix elements for the desert tortoise assuming a prebreeding census Class Yearling 0f5f5 f6f6 f7f7 Juvenile 1 1 s2s2 s 2 (1-g 2 ) Juvenile 2 2 s2g2s2g2 s 2 (1-g 2 ) Immature 3 s2g2s2g2 s 3 (1-g 3 ) Immature 4 s3g3s3g3 s 4 (1-g 4 ) Subadult 5 s4g4s4g4 s 5 (1-g 5 ) Adult 1 6 s5g5s5g5 s 6 (1-g 6 ) Adult 2 7 s6g6s6g6 s7s7

Estimated vital rates GrowthSurvival Class e1980lMeanVar e1980lMeanVar

Pearson Correlations Growth g2g2 g3g3 g4g4 g5g5 g6g6 g2g2 1 g3g g4g g5g g6g

Pearson Correlations Survival s2s2 s3s3 s4s4 s5s5 s6s6 s7s7 s2s2 1 s3s s4s s5s s6s s7s

Pearson Correlations Survival-Growth s2s2 s3s3 s4s4 s5s5 s6s6 s7s7 g2g g3g g4g g5g g6g

0.5, , ,0.2 The beta distribution Key distributions for vital rates

The beta distribution

Lognormal

Stretched Beta

Matrix selection Element selection Vital rate selection