Fig 1.
On the left we define all individual evolving variables and constants. Parameters are defined within the relevant life stage.
Fig 2.
The effect of φ on transforming adaptive knowledge.
Here the mean adaptive knowledge of the deme is 1 (Aj = 1).
Fig 3.
Illustration of distributions for how asocial learning and social learning acquire adaptive knowledge.
In (a) an asocial learner has a higher probability of drawing a value closer to their brain size if ζ is higher. In (b) a social learner has a higher probability of drawing a value closer to their model’s adaptive knowledge value if τ is high. Note that in both cases, adaptive knowledge cannot exceed brain size (aij ≤ bij). Curves generated using Magnusson (2016) (rpsychologist.com).
Fig 4.
Reduction in death rate for different values of λ for a given brain size (b = 50 in this example).
Fig 5.
Here we illustrate the causal relationships predicted by the Cultural Brain Hypothesis.
Larger brains allow for the storage and management of more information. More adaptive knowledge supports larger brains and larger groups. Larger groups possess more adaptive knowledge for social learning to exploit. Sufficiently large groups of social learners with sufficient knowledge create a selection pressure for a longer juvenile period for social learners to acquire knowledge selectively via biased oblique learning.
Fig 6.
Here we show the effect of richness of the ecology on brain size and social learning.
These are aggregated over a range of other parameters (a) Mean brain size showing the encephalization slope for different values of λ. Richer ecologies have a steeper slope for brain evolution. (b) Mean social learning showing the slopes over time. Richer ecologies support more social learning when social learning is adaptive. (c) This is made clear in the same plot for a narrower range of other parameters (τ = 1 and ζ = 0.7).
Fig 7.
Bean plots showing the distribution of (a) brain size and (b) social learning means for different values of φ. The dotted horizontal line shows the global mean and the bolded horizontal lines show the group means. Bean plots show the distribution of values. (c) Plot showing the rate of extinction for different values of φ.
Fig 8.
Bean plots showing the distribution of social learning for different values of transmission fidelity (τ) and asocial learning efficacy (ζ).
The dotted horizontal line shows the global mean and the bolded horizontal lines show the group means. Bean plots show the distribution of values. Transmission fidelity interacts with asocial learning efficacy to generate high equilibrium reliance on social learning.
Fig 9.
(a) Histogram of mean social learning probability (s). Under most conditions, selection creates individuals primarily reliant on asocial learning, some of whom maintain a small reliance on social learning. Under a narrow range of conditions, cumulative cultural evolution drives species to an extreme reliance on social over asocial learning. Consistent with previous models [e.g. 24], this range of conditions expands if social learning is assumed to exist in the ancestral species; i.e., if we start the simulation with social learners. (b) Histogram of mean social learning probability (s) when simulations began with all social learners (s = 1.0).
Table 1.
Correlations for each regime across our entire parameter space.
Correlations between log mean brain size, log mean adaptive knowledge, log mean group size, mean social learning, and mean juvenile period with 95% confidence intervals in brackets. The table has been color coded from red (r = −1) to white (r = 0) to blue (r = 1) for ease of comprehension. The upper table has correlations across the entire parameter space. The lower table has primarily asocial learners (s < .5) in the bottom triangle and primarily social learners (s > .5) in the top triangle. Following the empirical literature, social learning is defined as the number of observed incidents of social learning. Thus, we multiplied s by mean group size (N), and then following the empirical work, added 3, and took the natural log [46]. The juvenile period is defined as the probability of socially learning in a second round of learning (sv). Higher sv values should demand a longer juvenile period.
Fig 10.
(A) Our model’s empirical correlations between brain size and group size (r = 0.42 [Asocial], r = 0.72 [Social]). (B) Empirical correlation between brain size and group size from Barton (52) is somewhere between r = 0.48 to r = 0.61.
Fig 11.
Brain size and social learning.
(A) Our model’s empirical correlations between brain size and incidences of social learning (r = −0.23 [Asocial], r = 0.72 [Social]). (B) Empirical correlation between brain size and incidences of social learning among primates from Reader and Laland (46) is r = 0.69 (r = 0.36 controlling for phylogeny). A similar relationship has been shown for birds using indirect measures of opportunities for social learning [e.g. number of caretakers; 23].
Fig 12.
Brain size and the juvenile period.
(A) Our model’s empirical correlations between brain size and the length of the extended juvenile period (r = −0.53 [Asocial], r = 0.17 [Social]). (B) Empirical correlation between brain size and juvenile period among primate species from Joffe (56) is r = 0.61.
Fig 13.
Group size and the juvenile period.
(A) Our model’s empirical correlations between group size and the length of the juvenile period (r = −0.21 [Asocial], r = 0.22 [Social]). (B) Empirical correlation between group size and the length of the juvenile period among primates from Joffe (56) is r = 0.57.
Fig 14.
Cumulative culture and brain size.
Circle size indicates the mean population size. More red indicates high probability of acquiring knowledge through asocial learning and more blue indicates a low probability. The darkest blue circles in the bottom right are the simulations that cross the threshold into the cumulative cultural realm. (a) Log mean brain size against the probability of acquiring the mean adaptive knowledge in the group via asocial learning. (b) Here we show the same data zoomed in-between 0 and 1%.
Fig 15.
Percent of simulations in which cumulative cultural evolution evolves.
Blue simulations are those that began with s = 1.0 and red simulations are those that began with s = 0.0. (a) across different values of reproductive skew (ϕ) and (b) across different values of transmission fidelity (τ).
Fig 16.
Social learning over generations starting with s = 1.0.
Social learning is maladaptive i the absence of adaptive knowledge. Asocial learners quickly invade. It is only when asocial learners have generated sufficient adaptive knowledge that social learners again have an advantage. Since we know that at least two regimes reliably emerge, mean social learning in these plots represents the relative number of conditions in which social and asocial learners emerge rather than a value of social learning characteristic of the world.