Biodiversity and ecosystem productivity in a fluctuating environment: the insurance hypothesis

Abstract

Although the effect of biodiversity on ecosystem functioning has become a major focus in ecology, its significance in a fluctuating environment is still poorly understood. According to the insurance hypothesis, biodiversity insures ecosystems against declines in their functioning because many species provide greater guarantees that some will maintain functioning even if others fail. Here we examine this hypothesis theoretically. We develop a general stochastic dynamic model to assess the effects of species richness on the expected temporal mean and variance of ecosystem processes such as productivity, based on individual species' productivity responses to environmental fluctuations. Our model shows two major insurance effects of species richness on ecosystem productivity: (i) a buffering effect, i.e., a reduction in the temporal variance of productivity, and (ii) a performance-enhancing effect, i.e., an increase in the temporal mean of productivity. The strength of these insurance effects is determined by three factors: (i) the way ecosystem productivity is determined by individual species responses to environmental fluctuations, (ii) the degree of asynchronicity of these responses, and (iii) the detailed form of these responses. In particular, the greater the variance of the species responses, the lower the species richness at which the temporal mean of the ecosystem process saturates and the ecosystem becomes redundant. These results provide a strong theoretical foundation for the insurance hypothesis, which proves to be a fundamental principle for understanding the long-term effects of biodiversity on ecosystem processes.

Figure 1

Determination by dominance: simulations of productivity fluctuations through time in a replicate ecosystem with increasing species richness, n. The horizontal line in each graph shows the temporal mean of ecosystem productivity. Note that the temporal variance decreases while the temporal mean increases as species richness increases. Species responses are independent stochastic processes, and the probability density distribution is a uniform distribution on [0, 1].

Figure 2

Productivity-diversity relationships in the two cases of determination by dominance (A) and determination by equivalence (B): expected values of the temporal mean of productivity, E_e[X_n] (Eq. 2) and temporal variance of productivity, E_e[V_n] (Eq. 3) as a function of species richness, n. r is the correlation coefficient of species responses; r = 0, 1, and ± 1 correspond to the cases of independent responses, perfect positive correlation, and perfect correlation (including negative correlation), respectively. Note that when r = 1, i.e., when there is no asynchronicity at all, no insurance effects occurs. The probability density distribution is a uniform distribution on [0, 1].

Figure 3

(A) Representative shapes of the β-distribution (27) used to describe the species responses in B: For our purpose, we put β = α. Each distribution has the same mean 1/2 and is symmetrical in relation to x = 1/2. Note that as α decreases, the variance of the distribution increases; as a result, the probability that each species takes on maximum productivity (in this case, 1) increases. Thus changing α amounts to changing the variance. (B) Productivity-diversity relationships generated by changing the variance of species responses: expected value of the temporal mean of ecosystem productivity as a function of species richness, in the case where ecosystem productivity is determined by dominance and species responses are independent and follow a β-distribution as in A. Note that, as the variance of species responses increases (i.e., α decreases), the expected value of the temporal mean of ecosystem productivity increases monotonically for a given species richness, and thus attains its maximum value of 1 at a smaller species richness.