Figure 1.
Schematic of cultural niche construction.
Cultural niche construction results in environmental variation, which may produce two distinct forms of feedback. Route 1: a cultural trait modifies selection pressures, which can induce further cultural change. Route 2: gene-culture coevolution, where a cultural trait changes selection pressures, causes population level genetic changes in response. Evolutionary outcomes from both route 1 and route 2 depend on the frequency of T (cultural or genetic) and N (cultural) traits in the population and the selection pressures they generate, here represented by σi. Modified from Odling-Smee, Laland, and Feldman (2003).
Table 1.
Relative fitnesses of the four phenotypes.
Table 2.
Mating frequencies for all possible matings.
Table 3.
Probabilities of offspring outcomes from cultural trait pairings.
Figure 2.
Cultural transmission in different subsets of the parameter space.
In this and subsequent figures, a filled square at a vertex indicates a stable fixation at that vertex. A filled circle indicates an equilibrium that is unstable except in a specific hyperplane. Inside the tetrahedron, arrows originate at the population's initial phenotype frequencies and point toward the equilibrium. Arrows are color-coded by the equilibrium approached (TN: red, Tn: blue, tN: green, tn: cyan, tN-tn edge: black, internal polymorphism: pink). A. No selection, no assortative mating, no cultural mutation: when b1+b2>1 and c1+c2>1, the TN vertex is stable. When 0<α1, α2<1, the same vertex is stable. B. No selection, no assortative mating, no cultural mutation: when b1+b2<1, the t state approaches fixation, and if c1+c2 = 1, N and n persist in their initial proportions. Any point along the edge connecting the tn and tN vertices can represent an equilibrium. C. Selection but no assortative mating, no cultural mutation. For certain parameters, cultural transmission favors fixation of one phenotype but selection favors another. In some of these cases, two fixations are stable and which is approached depends on the initial frequencies. In the case shown here, α1 = α2 = 0, b0 = c0 = 0, b3 = c3 = 1, b1 = 0.8, b2 = 0.5, c1 = 0.5, c2 = 0.2, σ1 = −0.2, and σ2 = −0.6. The transmission favors T and n, but Tn is selected against, so the population approaches fixation of either TN or tn depending on initial frequencies. D. Assortative mating, selection, and cultural mutation. From all initial phenotype frequencies, the population will approach a single stable polymorphism. In this case, α1 = 0.1, α2 = 0.1, b0 = 0.05, b1 = 0.49, b2 = 0.52, b3 = 0.95, c0 = 0.05, c1 = 0.51, c2 = 0.53, c3 = 0.95, σ1 = −0.2, and σ2 = −0.1. At equilibrium, x1≈0.1438, x2≈0.0492, x3≈0.6262, and x4≈0.1808.
Figure 3.
Cultural transmission with assortative mating and selection but no cultural mutation.
For most parameter sets, the population approaches a single vertex; in rare cases a stable polymorphism is also present. Panels A–C show the parameter values α1 = 0.8, α2 = 0.3, b0 = 0, b1 = 0.7, b2 = 0.7, b3 = 1, c0 = 0, c1 = 0.5, c2 = 0.2, c3 = 1, σ1 = −0.2, σ2 = −0.7, and A–B shows varied pairs of transmission parameters. A. The effect of transmission of T on the presence of a polymorphism. The x-axis represents the value of b1, the y-axis represents the value of b2, and the color scale shows the value of x1. B. The effect of transmission of N on the presence of a polymorphism. The x-axis represents the value of c1, the y-axis represents the value of c2, and the color scale represents the value of x1. C. The pink square represents a stable polymorphism (x1≈0.814, x2≈0.0162, x3≈0.0937, x4≈0.0763). Pink arrows illustrate the domain of attraction of this equilibrium. The yellow circle represents an unstable equilibrium between the domains of attraction of the polymorphism and the tn vertex. D. A polymorphism where c1+c2 = 1. For some initial frequencies, the population approaches a single fixed point at the blue square. The pink square represents a stable polymorphic internal equilibrium, pink arrows illustrate the domain of attraction of this equilibrium. Red, green, cyan, and black circles represent unstable equilibria. Black arrows begin at initial conditions that result in an equilibrium on the tN-tn edge of the tetrahedron. Black circles represent unstable equilibria on the n and t fixation edges. In this case, α1 = 0.8, α2 = 0.3, b0 = 0, b1 = 0.2, b2 = 0.3, b3 = 1, c0 = 0, c1 = 0.3, c2 = 0.7, c3 = 1, σ1 = 0.2, and σ2 = 0.4.
Figure 4.
A cultural trait modifying the evolution of a genetic trait.
When the T trait is transmitted by Mendelian inheritance and the N trait is transmitted culturally, assorting and selection may lead to gene-culture polymorphisms. We took the parameter set α1 = 0.83, α2 = 0.24, b0 = 0, b1 = b2 = 0.5, b3 = 1, c0 = 0, c3 = 1, σ1 = −0.01, and σ2 = −0.82 and varied pairs of parameters as indicated. A. Cultural transmission affects equilibria: c1 and c2 varied between 0 and 1, and the equilibrium approached from initial frequencies near the x1−x2 edge is indicated by color. Polymorphisms exist in the orange region. In B and D, we considered the transmission parameters indicated by the black star in A: c1 = 0.4 and c2 = 0.31. In C and E, we used the Mendelian transmission parameters indicated by the white star in A: c1 = 0.5 and c2 = 0.5. B. Selection parameters that produce a polymorphism are shown in orange. C. When both traits show Mendelian transmission, no stable polymorphisms exist for any combination of selection levels. D. The assorting parameter combinations that produce a gene-culture polymorphism are shown in orange. E. When both traits show Mendelian transmission, polymorphisms do not exist for any combination of assorting parameters.
Figure 5.
Model for the evolution of religious beliefs.
Small fitness differences can alter the evolutionary dynamics of cultural traits. N represents the genetically transmitted religious predisposition trait and T represents the culturally transmitted belief trait. For both panels, α1 = 0.73, α2 = 0.94, b0 = 0.02, b1 = 0.3, b2 = 0.31, b3 = 0.98, c0 = 0, c1 = c2 = 0.5, and c3 = 1. A. When σ1 = σ2 = 0.12, a stable equilibrium exists on the Tn-tn edge (black square), i.e. fixation of the non-religiosity allele (n) and a polymorphism between religious belief (T) and non-belief (t), which is approached from all starting points except those on the TN-tN edge, which approach the equilibrium illustrated by the black circle. B. When σ1 = 0.12 and σ2 = 0.11, a stable polymorphism (pink square) exists such that both religious and non-religious predispositions, as well as religious belief and non-belief, coexist in the population (x1≈0.521, x2≈0.127, x3≈0.295, x4≈0.057). This polymorphism is approached from all starting points except those on the TN-tN or Tn-tn edges, which approach the equilibrium illustrated by the black circles.