Modelling evolutionary processes in small populations: not as ideal as you think.

Area of Science:

• Population Genetics
• Evolutionary Biology
• Computational Biology

Background:

• Wright-Fisher models are standard for evolutionary simulations, assuming constant population size (N) and binomial variance in reproductive success (V(k)).
• In computational implementations, realized variance (V(k)*) and effective population size (N(e)*) fluctuate randomly, deviating from theoretical binomial expectations.
• The impact of this random variation in N(e)* on evolutionary analyses has been insufficiently explored.

Purpose of the Study:

• To analytically and numerically investigate the consequences of random variation in realized effective population size (N(e)*) in modelled ideal populations.
• To derive expressions for the variance of V(k) and N(e) in computer-simulated ideal populations.
• To quantify the impact of N(e)* variation on genetic metrics and compare it to models assuming constant N(e).

Main Methods:

• Derived analytical expressions for Var(V(k)) and Var(N(e)) in modelled ideal populations.
• Developed a framework to partition the total variance of a genetic metric G = f(N(e)) into components due to gene sampling (Var(Gene)) and demographic variance (Var(Demo)).
• Illustrated findings using empirical examples based on standardized variance of allele frequency (F) and linkage disequilibrium (r(2)).

Main Results:

• Random variation in V(k)* and N(e)* significantly distorts evolutionary analyses that assume a constant N(e).
• Derived Var(V(k)) = 4(2N - 1)(N - 1)/N(3) and Var(N(e)) ≈ N/2.
• The total variance of genetic metrics (Var(G)) is higher than in models with constant N(e), due to the added Var(Demo).
• Effects are pronounced in computer models with small sampling error (large N, loci, alleles) and small populations, relevant for conservation.

Conclusions:

• Random fluctuations in effective population size in computational models are a critical factor affecting the reliability of evolutionary analyses.
• Standard models implicitly assuming constant N(e) may underestimate variance and lead to inaccurate conclusions.
• Researchers must account for N(e)* variation, particularly in simulations for conservation genetics and studies with large numbers of individuals, loci, or alleles.