Currently, there are 100 plants in age class 0, 50 plants in age class 1, 25 plants in age class 2, and 10 plants in age class 3. Based on previous work, you know that the expected survival rates are S0=0.4, S1=0.6, S2=0.8, and S3=0. Fecundities are F0=0, F1=0, F2=10, F3=5. What is the expected total population size two generations later? [medium]

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batolisis batolisis · Answer 1 · 2021-09-29T12:00:39+02:00

The expected total population size two generations later is = 568

Using the given data :

Age classes and number in each

0 = 100

1 = 50

2 = 25

3 = 10

Represent age class with ( Xi ) where i = class number

Xo = 100 , So = 0.4 , Fo = 0

X1 = 50 , S1 = 0.6 , F1 = 0 -------------- , X3 = 10

First step ; determine the size of the 1st Generation

For class 0 ; ( Xo * Fo ) + ( X1 * F1 ) + ( X2 * F2 ) + ( X3 * F3 )

= 0 + 0 + ( 25 * 10 ) + ( 10 * 5 ) = 300

For class 1 ; Xo * So ) = 100 * 0.4 = 40

For class 2 ; X1 * S1 = 50 * 0.6 = 30

For class 3 ; X2 * S2 = 25 * 0.8 = 20

Finally determine the population of 2nd Generation

For age class 0 ; 0 + 0 + ( 30 * 10 ) + ( 20 * 5 ) = 400

For age class 1 ; Yo * So = 300 * 0.4 = 120

For age class 2 ; 40 * 0.6 = 24

for age class 3 ; 30 * 0.8 = 24

∴ Total expected population size for two generations later

= 400 + 120 + 24 + 24 + 0 = 568

Hence we conclude that the expected total population size two generations later = 568

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