(a) Positive niche construction, independent renewal, and no external selection (R_t = λ₁R_t−1 + λ₂p_t + λ₃, γ = 0, α₁ = β₁ = α₂ = β₂ = 1, r = 1/2, n = 1). Here, the only selection is that generated by the resource. The arrows represent the trajectories of a population, the heavy line represents stable equilibria, and the dashed line represents unstable equilibria. The direction of selection generated by the resource switches at R = 1/2. In b–d, with independent renewal and external selection favouring allele A, niche construction generates selection that may oppose the external selection, taking populations to alternative equilibria and generating polymorphisms. b and c show positive niche construction (R_t = λ₁R_t−1 + λ₂p_t + λ₃, γ = 0), with weak selection (α₁ = β₁ = 1, α₂ = 1.01, β₂ = 0.99, r = 1/2) (b), and strong selection (α₁ = β₁ = 1, α₂ = 1.1, β₂ = 0.9, r = 1/2) (c). d shows negative niche construction, independent renewal, and external selection favoring allele A (R_t = λ₁R_t−1(1 − γp_t) + λ₃, λ₂ = 0, α₁ = β₁ = 1, α₂ = 1.1, β₂ = 0.9, r = 1/2). When selection favors allele A and ɛ is negative, positive niche construction (γ = 0) (e) and negative niche construction (λ₂ = 0) (f) generate polymorphisms (α₁ = β₁ = 1, α₂ = 1.1, β₂ = 0.9, r = 1/2).

Positive niche construction, independent renewal, and heterozygote advantage (R_t = λ₁R_t−1 + λ₂p_t + λ₃, γ = 0, α₁ = α₂ = 0.99, β₁ = β₂ = 0.9, r = 1/2, n = 1). Provided r is not very small, populations converge to a single equilibrium in linkage equilibrium, the position of which may be strongly affected by niche construction. The + represents the equilibrium in the absence of niche construction. By increasing R, niche construction changes the frequency-dependent component of genotype fitnesses, affecting the equilibrium frequency of allele A. In both a and b, without niche construction, allele a would be fixed, whereas in a, niche construction allows A and a to coexist, and in b, niche construction drives A to fixation.