Joint evolution of traits for social learning

Abstract

Animals vary in the sophistication of their capacities for social learning, and much research has focused on establishing when learning from others is favourable. However, social learning involves both a receiver (who learns), and a sender (who is learned from). Surprisingly, the joint evolution of traits for social learning has attracted little attention, even though learning by the receiver has consequences for the fitness of the sender. Accordingly, animals are observed to teach and mask, and thereby influence available information. Here, we provide a mathematical model to examine when reliable social learning emerges as a result of investment in traits for social and asocial learning, as well as teaching and masking. Our purpose is to provide a general framework for thinking about how social learning is impacted by sender-receiver joint evolution, so our model is heuristic; its aim is to delineate broad categories of direct and indirect selection on learning traits. Our findings lead us to theorise that social learning exists on a continuum. At one extreme, senders and receivers have strongly opposed interests, selecting for masking to combat informational parasitism; at the other extreme, strongly aligned interests lead to teaching to enhance social learning. Sophisticated, metabolically expensive traits for influencing social learning can evolve under either aligned or opposed interests, although the aim of their design differs. Furthermore, we find that traits for asocial learning should often be more sophisticated than traits for receiving, while receiving traits should often be more sophisticated than sender traits for teaching or masking.

Significance statement

Learning from group members is often crucial for survival, with social learning influencing the development of behaviours in domains as diverse as foraging, mate preference, and predator defence. Formal modelling has provided a good understanding of the conditions that favour social learning, given animals already have the ability to learn asocially. However, the success of social learning also depends on the behaviour of the group member who is learned from. For instance, group members may teach others how to hunt dangerous prey. Alternatively, knowledgeable individuals sometimes take actions to hinder learning, for instance, by disguising the location of a food cache. Here, we provide a unitary mathematical framework to study how behaviours of the group member who is learned from jointly evolve with those of the learner.

Appendices

Appendix 1. Equilibrium and stability

Broadly, we assume changes in the reliability of learning monotonically increase with investment, but can never be perfect (equal 1). Further, we assume that increases in investment lead to diminishing returns. The existence of a single equilibrium, as well as key results about how learning evolves, can be proven making only these weak assumptions (Supplement). However, no closed form solution for this equilibrium can be produced, so we also relied on numerical methods. High-order derivatives were examined by sensitivity analysis that support that this equilibrium is convergent and evolutionarily stable over a broad range of parameter combinations. In particular, we used the following functions for the reliability of asocial and social learning, respectively:

$$\alpha \left(z\right)=1-{\mathrm{e}}^{-z}$$

(3)

$$\beta \left(x,y\right)=\left\{\begin{array}{c} 1-\frac{1}{4}{\mathrm{e}}^{-x}-\frac{1}{4}{\mathrm{e}}^{-y}, \left(b-d\right)r-a>0\\ \frac{1}{2}-\frac{1}{4}{\mathrm{e}}^{-x}+\frac{1}{4}{\mathrm{e}}^{-y}, \left(b-d\right)r-a<0\end{array}\right.$$

(4)

Here, the baseline reliability of social learning is 0.5. Furthermore, to adhere to our assumptions of diminishing returns, we assume metabolic costs escalate with investment according to:

$$\begin{array}{ccc}\kappa \left(i\right)={i}^{2}& \mathrm{where}& i\in \{z,x,y\}\end{array}$$

(5)

Appendix 2. Findings under extreme conditions

Very strong synergy accompanied by high relatedness can lead to a reduction in investment in asocial learning (rather than an increase). In particular, synergy must provide larger benefits than acquiring the behaviour in the first place. This exception occurs because asocial learning avoids synergy between relatives; it becomes better to wait to be helped. By corollary, intense local competition accompanied by high relatedness can lead to investment in asocial learning, as a way of preventing competition between relatives due to social learning.

High benefits of acquiring a novel behaviour can select against teaching when relatedness is negligible (rather than supporting it). This exception occurs when acquired benefits are large, because selection will favour the population to contain many highly effective asocial learners, reducing the need for teaching.