The effect of energy reserves and food availability on optimal immune defence

Abstract

In order to avoid both starvation and disease, animals must allocate resources between energy reserves and immune defence. We investigate the optimal allocation. We find that animals with low reserves choose to allocate less to defence than animals with higher reserves because when reserves are low it is more important to increase reserves to reduce the risk of starvation in the future. In general, investment in immune defence increases monotonically with energy reserves. An exception is when the animal can reduce its probability of death from disease by reducing its foraging rate. In this case, allocation to immune defence can peak at intermediate reserves. When food changes over time, the optimal response depends on the frequency of changes. If the environment is relatively stable, animals forage most intensively when the food is scarce and invest more in immune defence when the food is abundant than when it is scarce. If the environment changes quickly, animals forage at low intensity when the food is scarce, but at high intensity when the food is abundant. As the rate of environmental change increases, immune defence becomes less dependent on food availability. We show that the strength of selection on reserve-dependent immune defence depends on how foraging intensity and immune defence determine the probability of death from disease.

Figure 1

The optimal strategy, mortality from disease and the reproductive value as a function of reserves. (a) The rate of energy expenditure on immune defence (as a multiple of BMR) as a function of energy reserves for different rates of challenge, d₀. (b) The optimal foraging intensity as a function of reserves for the same values of d₀ (line types mark the same d₀ values as in (a)). (c) The rate of mortality from disease as a function of energy reserves for the previous values of d₀. (d) The reproductive value as a function of reserves for d₀=0.5. The thick grey lines show the case when d₁=0.3, i.e. foraging intensity has a strong effect on the probability of death from disease (see equation (3.1)). Other parameters are the same as given in the electronic supplementary material, table 1. The probability of death from disease, D(u, z), is given by equation (3.1).

Figure 2

The comparison between fixed and reserve-dependent immune investments. (a) The baseline case: curve, the survival probability as a function of fixed (not changing with reserves) immune investment; triangle, the optimal fixed investment; circle, the mean investment and survival probability under the optimal reserve-dependent strategy. (b) The relation between the survival probability and the relative survival under fixed investment to that under reserve-dependent investment for different parameters. Relative survival was calculated as S_fixed/S_reserve, where S_i is the appropriate survival value for the given investment scheme (fixed or reserve-dependent). The symbols show the parameter that was varied to obtain the survival values. All other parameters are the same as given in the electronic supplementary material, table 1. The probability of death from disease, D(u, z), is given by equation (3.1).

Figure 3

The effects of the mean amount, p_fa_f, and variance, $p_{\text{f}}(1-p_{\text{f}})a_{\text{f}}^2$, of food. The mean is varied by changing both p_f and a_f in such a way that the variance, $p_{\text{f}}(1-p_{\text{f}})a_{\text{f}}^2$, remains constant at its baseline value. Variance is varied by changing both a_f and p_f in such a way that their product, the mean, remains constant at its baseline value. (a,d) Mean energy expended on immune defence as a multiple of BMR. (b,e) The proportion of animals dying from predation, disease or starvation over 100 days and the proportion surviving 100 days. (c,f) The mean reserves of individuals who are alive and the mean reserves at death of animals that die from predation and disease. The probability of death from disease, D(u,z), is given by equation (3.2). Parameters other than a_f and p_f are the same as given in the electronic supplementary material, table 1.

Figure 4

The case in which food availability changes between three different levels: low (a_f=0.3), medium (0.35) and high (0.4) food availability. (a) The optimal rate of energy expenditure on immune defence (as a multiple of BMR) as a function of energy reserves (p_c=0.001). (b) The mean energy (as multiple of BMR) expended on the immune defence as a function of environmental stability, p_c, for low, medium and high food availability. (c) The mean optimal foraging intensity as a function of environmental stability, p_c, for low, medium and high food availability. The probability of death from disease, D(u, z), is given by equation (3.2). Parameters other than a_f and p_c are the same as given in the electronic supplementary material, table 1.