Risk, resources and state-dependent adaptive behavioural syndromes

Abstract

Many animals exhibit behavioural syndromes-consistent individual differences in behaviour across two or more contexts or situations. Here, we present adaptive, state-dependent mathematical models for analysing issues about behavioural syndromes. We find that asset protection (where individuals with more 'assets' tend be more cautious) and starvation avoidance, two state-dependent mechanisms, can explain short-term behavioural consistency, but not long-term stable behavioural types (BTs). These negative-feedback mechanisms tend to produce convergence in state and behaviour over time. In contrast, a positive-feedback mechanism, state-dependent safety (where individuals with higher energy reserves, size, condition or vigour are better at coping with predators), can explain stable differences in personality over the long term. The relative importance of negative- and positive-feedback mechanisms in governing behavioural consistency depends on environmental conditions (predation risk and resource availability). Behavioural syndromes emerge more readily in conditions of intermediate ecological favourability (e.g. medium risk and medium resources, or high risk and resources, or low risk and resources). Under these conditions, individuals with higher initial state maintain a tendency to be bolder than individuals that start with low initial state; i.e. later BT is determined by state during an early 'developmental window'. In contrast, when conditions are highly favourable (low risk, high resources) or highly unfavourable (high risk, low resources), individuals converge to be all relatively bold or all relatively cautious, respectively. In those circumstances, initial differences in BT are not maintained over the long term, and there is no early developmental window where initial state governs later BT. The exact range of ecological conditions favouring behavioural syndromes depends also on the strength of state-dependent safety.

Figure 1.

Time series of the average boldness (±s.d.) of 1000 individuals that started with low (x₀ = 1, dashed line) versus high (x₀ = 25, solid line) initial state, x with r = 1.3 and θ = 60. (a–c) Asset protection model (which also includes avoidance of starvation) and (d–f) the state-dependent safety model (which also includes asset protection and avoidance of starvation). (a,d) Behaviour during periods of low predation risk (d_l = 0.045) and (b,e) behaviour during periods of high risk (d_t = 0.09). (c,f) Average levels of state, x, across the season.

Figure 2.

From the state-dependent safety model, effects of initial state, x, on the average boldness of 1000 individuals. Shown are averages pooling across periods of low and high predation risk, d_l = 0.045 and d_h = 0.09, during time periods 71–80. r = 1.3 and θ = 60.

Figure 3.

Effects of altering overall average predation risk on the outcome of the state-dependent safety model holding r = 1.3 and θ = 60. The dashed lines show average results for 1000 individuals that started with low initial state (x₀ = 1) while the solid lines show average results for 1000 individuals that started with high initial state (x₀ = 25). With overall average risk reduced, (a) shows average boldness during periods of lower risk (d_l = 0.02) while (b) shows average boldness during periods of higher risk (d_h = 0.04). (c) Resulting levels of x. With overall average risk increased, (d) shows average boldness during periods of lower risk (d_l = 0.07) while (e) shows average boldness during periods of higher risk (d_h = 0.14). (f) Shows the resulting levels of x.

Figure 4.

Effects of altering resource levels on the outcome of the state-dependent safety model with θ = 60. The dashed lines show average results for 1000 individuals that started with low initial state (x₀ = 1) while the solid lines show average results for 1000 individuals that started with high initial state (x₀ = 25). With resource levels reduced to r = 0.8, (a) shows average boldness during periods of low risk (d_l = 0.045), while (b) shows average boldness during high risk (d_h = 0.09). (c) Resulting levels of x. With resource levels increased to r = 1.8, the comparable graphs are in panels (d–f).

Figure 5.

Effects of resource levels (r) and predation risk (average d) on main outcomes in terms of differences in average boldness (from time period 71–80) for individuals that started with x₀ = 1 versus x₀ = 25. Risk is scaled by 0.001; i.e. a value of 50 is d = 0.05. In the black region, individuals diverged in behaviour and state (as in figure 1d–f) and those that started initially with higher state ended up more bold (at least 0.05 higher effort) than individuals that started with low state. Positive feedback dominated under these conditions. In the main grey region (upper left), individuals with different initial states converged in state and behaviour over time, they were generally cautious, and those starting with higher state were even more cautious (at least 0.05 lower effort) than those that started with lower state. This happened when risk was relatively high (as in figure 3d–f) or resources were relatively low (as in figure 4a–c). Negative feedback was the predominant force in this region. White regions are where the difference in average boldness between individuals that started with different initial states was less than 0.05. In highly favourable conditions (the lower right region), when risk was low (as in figure 3a–c) or resources were high, regardless of initial state, all individuals converged on being very bold.