Measuring the Response Diversity of Ecological Communities Experiencing Multifarious Environmental Change

Abstract

The diversity in organismal responses to environmental changes (i.e., response diversity) plays a crucial role in shaping community and ecosystem stability. However, existing measures of response diversity only consider a single environmental variable, whereas natural communities are commonly exposed to changes in multiple environmental variables simultaneously. Thus far, no approach exists to integrate multifarious environmental change and the measurement of response diversity. Here, we show how to consider and quantify response diversity in the context of multifarious environmental change, and in doing so introduce a distinction between response diversity to a defined or anticipated environmental change, and the response capacity to any possible set of (defined or undefined) future environmental changes. First, we describe and illustrate the concepts with empirical data. We reveal the role of the trajectory of environmental change in shaping response diversity when multiple environmental variables fluctuate over time. We show that, when the trajectory of the environmental change is undefined (i.e., there is no information or a priori expectation about how an environmental condition will change in future), we can quantify the response capacity of a community to any possible environmental change scenario. That is, we can estimate the capacity of a system to respond under a range of realistic or extreme environmental changes, with utility for predicting future responses to even multifarious environmental change. Finally, we investigate determinants of response diversity within a multifarious environmental change context. We identify factors such as the diversity of species responses to each environmental variable, the relative influence of different environmental variables and temporal means of environmental variable values as important determinants of response diversity. In doing so, we take an important step towards measuring and understanding the insurance capacity of ecological communities exposed to multifarious environmental change.

Keywords: directional derivatives; ecological stability; generalised additive models (GAMs); multiple stressors; response capacity; response diversity; response surface.

FIGURE 1

Calculation of directional derivatives of the growth rate of one species for a time series of environmental change. (a) Time series of temperature change. (b) Time series of phosphate concertation change. (c) Time series of temperature and phosphate concertation change overlayed on the performance surface of the phytoplankton species Ankistrodesmus nannoselene based on the species' growth rate. Sequential numbers in white boxes represent positions on the performance surface at time points corresponding to (a) for temperature and (b) for the phosphate concentration. Colours indicate the growth rate. (d) The time series of directional derivatives corresponding to the time series of environmental change in (a–c) and the species performance surface in (c). Note that in (d), the offset on the x‐axis is meant to show that the directional derivatives are calculated as we go from t = 1 to t = 2.

FIGURE 2

Illustration of the principle underlying the calculation of response capacity. (a) and (b) show the response surfaces of Ankistrodesmus nannoselene and Monoraphidium minutum with one point on them from which directional derivatives extend in many possible directions. (c) and (d) The same species' response surfaces shown in (a) and (b), but in this case, there is a grid of points covering the whole surfaces. Response surfaces are shown in greyscale to better visualise directional derivatives. From each point, directional derivatives extend in many possible directions. In (e) and (f), considering the difficulties related to displaying multiple 3D performance surfaces, each having multiple points with directional derivatives extending in all possible directions, we focus here on representing only two species and nine points on each surface. For those points, we only display three directional derivatives to help visualise the calculation process, but note that computationally this is done for every possible combination of locations and directional derivatives.

FIGURE 3

Response capacity calculated for two hypothetical communities. In each of (a) and (b) the predicted surfaces of response capacity of a community are shown. Regions with higher response capacity represent the environmental conditions under which the communities may be expected to maintain constant levels of aggregate community and ecosystem properties.

FIGURE 4

Determinants of response diversity. In (a), the response of growth rate of one species to environmental variables E ₁ and E ₂ is shown. The panels on the left show the growth rate (y‐axis) of the species as a function of environmental variable E ₁ (x‐axis) with lines representing different levels of E ₂, colour‐coded accordingly. The variation in growth rate reflects the interaction between E ₁ and E ₂. Panels on the right side of (a) show the growth rate (y‐axis) as a function of environmental variable E ₂ (x‐axis), with lines colour‐coded based on the values of E ₁. (a) Highlights the dependence of growth rate on E2 while illustrating the impact of varying E ₁ levels. (a) A case where one environmental variable (E ₁) is dominant (upper panels), and for a case where the two variables have an equal effect (lower panels). (b) The concept of diversity in species responses together with the one of different means of one environmental variable. The three panels display three levels of response diversity with respect to E ₁ for a community of four species, that is, low response diversity (top panel), intermediate response diversity (middle panel) and high response diversity (bottom panel). The three different background colours in the panels show different means around which the environment fluctuates. (c) The amount of and correlation between diversity of species' responses to E ₁ and E ₂. The different panels illustrate different patterns of correlation in interspecific variation in E ₁ optima. Each coloured circle represents a species; the colour of the circle shows which community the species belongs to; the x‐ and y‐coordinate shows the E ₁ and E ₂ optima of that species. The top panel illustrates the no correlation treatment. All three communities have a fixed and rather low amount of variation in the position of the E2 optimum (y‐axis), whereas the variation in the position of the E ₁ optimum increases from low in community 1 (purple), to medium in community 2 (green), to high in community 3 (yellow). The intermediate panel illustrates the positive correlation treatment. Community 1 (purple) has low variation in the position of the optima for both E ₁ and E ₂, Community 2 (green) has intermediate variation in the position of optima for both E ₁ and E ₂. Community 3 (yellow) has high variation in the position of the optima for E ₁ and E ₂. Since the variation in the position of the optima gradually increases across the communities for both E ₁ and E ₂, this is the positive correlation treatment. The lower panel illustrates the negative correlation treatment. Community 1 has high variation in the position of the optima for E ₂, but low for E ₁. Community 2 has intermediate variation in the position of the optima for both E ₁ and E ₂, and Community 3 has high variation in the position of the optima for E ₁, but low for E ₂. Since, in this scenario, when variation in optima position for E ₂ is high, variation in optima position for E ₁ is low and vice versa, we call this the negative correlation treatment.

FIGURE 5

Effects of diversity in species' responses on response diversity measured as divergence. (a–c) How divergence changes in the different scenarios of correlation between E ₁ and E ₂ optimum diversity depending on the mean value of the environment in the case where E1 is the dominant variable. (d–f) How divergence changes in the different scenarios of correlation between E ₁ and E ₂ optimum diversity depending on the mean value of the environment in the case where E ₁ and E ₂ have an equal effect on species' growth rate. For all panels, small dots represent the divergence values measured for each community in our simulations, whereas the big dots are the mean values for each of the factor's levels.