Maternal effects on offspring consumption can stabilize fluctuating predator-prey systems

Abstract

Maternal effects, where the conditions experienced by mothers affect the phenotype of their offspring, are widespread in nature and have the potential to influence population dynamics. However, they are very rarely included in models of population dynamics. Here, we investigate a recently discovered maternal effect, where maternal food availability affects the feeding rate of offspring so that well-fed mothers produce fast-feeding offspring. To understand how this maternal effect influences population dynamics, we explore novel predator-prey models where the consumption rate of predators is modified by changes in maternal prey availability. We address the 'paradox of enrichment', a theoretical prediction that nutrient enrichment destabilizes populations, leading to cycling behaviour and an increased risk of extinction, which has proved difficult to confirm in the wild. Our models show that enriched populations can be stabilized by maternal effects on feeding rate, thus presenting an intriguing potential explanation for the general absence of 'paradox of enrichment' behaviour in natural populations. This stabilizing influence should also reduce a population's risk of extinction and vulnerability to harvesting.

Keywords: consumer resource; consumption rate; dynamics; maternal effect; mathematical model; predator–prey.

Figure 1.

Maternal effects model. (a) Model schematic. Predators give birth to high-feeding (P_H) and low-feeding (P_L) predators with proportions q and 1 − q. A sigmoidal curve describes how q changes with the density of the resource (x), as shown in (b,c). (b) Increasing a increases the slope of the curve and (c) increasing increases the mid-point of the curve. In (b) and in (c) a = 5.

Figure 2.

Population dynamics of predators and prey with and without the maternal effect: (a) K = 3 with no maternal effect, (b) K = 10 with no maternal effect, (c) K = 10 with a moderate (B = 0.3) maternal effect and (d) K = 10 with a large (B = 0.5) maternal effect. Plots are the last 500 days of a 1000-day simulation except for (d) in which the entire 1000-day simulation is shown. In (a–d), C = 0.67, e = 0.6, h = 1.67 and μ = 0.15. In (c,d), a = 2 and

Figure 3.

Maternal effect and population stability. Combined effect of three maternal effect parameters ( a and B) on population dynamics. Graphs show the parameter space in which cyclical dynamics occur (‘cycling’), or where populations reach a stable equilibrium (‘stable’).

Figure 4.

Thresholds for where the predator population cannot survive (‘no predator’), survive stably (‘stable’) and cycle (‘cycling’), and the average predation rate required for each to occur, plotted against varying capacity K. The dashed line is the predation rate without any maternal effect.

Figure 5.

Maternal effect and stable equilibrium population sizes. Combined effect of three maternal effect parameters ( a and B) on the population sizes of predators and prey and the proportion of low-feeding predators (P_L) in the population.