The Chinese Alligator Alligator sinensis above is a critical

The Chinese Alligator (Alligator sinensis; above) is a critically endangered species living in a restricted reserve area in the Yangtze River in China\'s Anhui province. (Captive populations are doing much better; where individuals may live up to 70 years). a. If, during four consecutive years the population was sampled and its population size was 200, 100, 50 and 10, what is the effective population size (N_e) of this population? Show your work.

Solution

Effective population size is the number of individuals in a population who contribute offspring to the next generation.

Effective population size that accounts for fluctuating population size is calculated a the harmonic mean of the census size. The harmonic mean is the reciprocal of the {average of reciprocals}.

N_e= 1 / ( 1/ P₁ + 1 / P₂ + 1 /P₃ + 1/ P₄)

In this question, P₁= 200, P₂= 100, P₃ = 50 and P₄= 10. Put all these values in the formula to get your answer.

N_e = 1 / ( 1/200 + 1/100 + 1/50 + 1/10)

= 1 / (27/200)

= 200/27 = 7.40 is the effective population.