Question

Demographic data are collected for a threatened population of African cheetahs over a period of 10 years allowing nine year-to-year estimates of the population growth rate (λ) to be calculated λ₁=1.20, λ₂=1.10, λ₃=0.8, λ₄=0.5, λ₅=1.0, λ₆=1.29, λ₇=1.13, λ₈ =0.76, λ₉=1.07. Over the long term, do you expect this population to grow, remain the same size, or shrink? Provide a quantitative answer and explain your answer. What mechanism might be at play here?

Answer 1

λ₁=1.20; λ₂=1.10; λ₃=0.8; λ₄=0.5; λ₅=1.0; λ₆=1.29; λ₇=1.13; λ₈ =0.76; λ₉=1.07

i) Geometric mean λ = (λ₁*λ₂*λ₃*λ₄*λ₅*λ₆*λ₇*λ₈*λ₉)^1/9 = (1.20*1.10*0.8*0.5*1.0*1.29*1.13*0.76*1.07)^1/9 = (0.6259)1/9= 0.9493 <1.

Since Geometric mean λ is less than 1, the population should shrink.

ii) Number of individuals in the population at the end of 10 years(N₁₀) = N₀ * λ₁*λ₂*λ₃*λ₄*λ₅*λ₆*λ₇*λ₈*λ₉ = 0.6259N₀

N₁₀ = 0.6259N_0.

0.6259< 1; So N₁₀ < N_0. This indicates that the population should shrink.

From the λ values, the population growth rate does not reduce at a constant rate. This indicates that the reduction in population is due to some catastrophic impacts on population. So this is due to density-independent factors.