There are no short-cuts, they say, and it might be impossible to extrapolate from one ecosystem or one experimental plot to other ecosystems. Ives and Carpenter published a review paper on stability and diversity of ecosystems in the journal Science on July 6, Credit and Larger Version.
Investigators Anthony Ives Stephen Carpenter. Contact Help Search search. In , David Tilman and colleagues established experimental plots in the Cedar Creek Ecosystem Science Reserve, each 9 x 9 m in size Figure 3A , and seeded them with 1, 2, 4, 8 or 16 species drawn randomly from a pool of 18 possible perennial plant species Tilman et al. Plots were weeded to prevent new species invasion and ecosystem stability was measured as the stability of primary production over time.
Over the ten years that data were collected, there was significant interannual variation in climate, and the researchers found that more diverse plots had more stable production over time Figure 3B.
In contrast, population stability declined in more diverse plots Figure 3C. These experimental findings are consistent with the theory described in the prior section, predicting that increasing species diversity would be positively correlated with increasing stability at the ecosystem-level and negatively correlated with species-level stability due to declining population sizes of individual species. Figure 3: A biodiversity experiment at the Cedar Creek Ecosystem Science Reserve a demonstrates the relationship between the number of planted species and ecosystem stability b or species stability c.
All rights reserved. Experiments manipulating diversity have been criticized because of their small spatial and short time scales, so what happens in naturally assembled communities at larger spatial scales over longer time scales? In a year study of naturally assembled Inner Mongolia grassland vegetation, Bai et al.
They found that while the abundance of individual species fluctuated, species within particular functional groups tended to respond differently such that a decrease in the abundance of one species was compensated for by an increase in the abundance of another. This compensation stabilized the biomass productivity of the whole community in a fluctuating environment see Figure 1. These findings demonstrate that local species richness — both within and among functional groups — confers stability on ecosystem processes in naturally assembled communities.
Experiments in aquatic ecosystems have also shown that large-scale processes play a significant role in stabilizing ecosystems. A whole-lake acidification experiment in Canada found that although species diversity declined as a result of acidification, species composition changed significantly and ecosystem function was maintained Schindler This suggests that given sufficient time and appropriate dispersal mechanisms, new species can colonize communities from the regional species pool and compensate for those species that are locally lost Fischer et al.
This observation emphasizes the importance of maintaining connectivity among natural habitats as they experience environmental changes. Evidence from multiple ecosystems at a variety of temporal and spatial scales, suggests that biological diversity acts to stabilize ecosystem functioning in the face of environmental fluctuation.
Variation among species in their response to such fluctuation is an essential requirement for ecosystem stability, as is the presence of species that can compensate for the function of species that are lost. While much of the evidence presented here has focused on the consequences of changes in species diversity on primary production in natural ecosystems, recent research has found similar relationships between species diversity and ecosystem productivity in human-managed ecosystems e.
Bai, Y. Ecosystem stability and compensatory effects in the Inner Mongolia grassland. Nature , — Balvanera, P. Quantifying the evidence for biodiversity effects on ecosystem functioning and services. Ecology Letters 9 , — Fischer J. Compensatory dynamics in zooplankton community responses to acidification: Measurement and mechanisms.
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Diversity-dependent production can decrease the stability of ecosystem functioning. Balvanera Pea. Quantifying the evidence for biodiversity effects on ecosystem functioning and services. Ecology letters. View Article Google Scholar 6. Hooper DUea. Effects of biodiversity on ecosystem functioning: A consensus of current knowledge and needs for future research.
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Beehler B. Frugivory and polygamy in birds of paradise. Both the solutions of the linear and nonlinear model are applied to real world ecosystems with positive mutualistic interaction terms between species, so to give a practical example of the two different conditions for stability.
In Section IV we present a discussion of the results. We will first show the solution of the linear model diverges for given values of the interaction species. In general the evolution of species abundances x i t in a ecosystem can be described by dynamical equations of the form:. The dynamics of species densities x i is then described by the following dynamical system of equations:. But when it is close to it i.
Next we will show that this condition for stability can also be found via a local stability analysis of the dynamical system. Negative eigenvalues indicate that the system is stable.
That is, if one of the eigenvalues of the Jacobian is positive, the average may be positive, or zero, and in that case, the system is not stable. Fig 2 shows a plot of the sign of the maximum eigenvalue as a function of the interaction term taken for the real networks numbered 1 to 9 in Table 1. The inset of the figure indicates the number of the real network shown in Table 1.
The networks analyzed are labeled according to the references in Table 1. Notice that networks 4 and 8 are overlapping. If this sign is negative the system is stable. If zero or positive, the system is unstable. Ecological systems are usually only sparsely connected. These results lead to the paradox, since when N increases the system becomes more unstable. Thus, in the stable feasible region of the linear model Eq 3 , the condition:.
We have then shown that all three methods of study of stability for the linear model produce the same stability condition: the so called diversity-stability paradox. We test the stability condition by analyzing 9 real mutualistic networks with positive interactions compiled from available online resources and detailed in Table 1.
We are able to test the stability phase diagram since for these networks the parameters of the model are provided, in particular the strength of interactions which is the parameter that control the stability of the linear ecosystem via Eq 9. Hence the linear model of Eq 3 predicts that these 9 existing ecosystems should indeed collapse i.
We find that the stability condition of the linear model, Eq 9 , is not satisfied by these real ecosystems. Below we will explain in more detail the nonlinear dynamical model, which predicts opposite results for the condition of stability with respect to the linear model and explains the existence of the 9 real mutualistic networks, suggesting the nonlinear model as a more adequate study of ecological systems.
Most of the studies on stability for ecosystems have been done using the linear model explained in Section, mainly because one can find an analytical solution to the fixed point equation and the stability condition is directly related to the eigenvalues of the adjacency or jacobian matrix. This behavior is common for the description of gene regulation, neurons, diffusion of information and ecosystems as presented in their article.
The dynamics of species densities, x i t , interacting via the network A ij , is described by the following set of nonlinear differential equations [ 19 — 22 , 32 ]:. Even if one approximates the interaction term to the Heaviside function, it is possible to compare the solution given by exact numerical simulations to the solution of the approximated method of Eq 11 and show consistency within a After a trimming process of the species in the network, the solution of Eq 11 is shown to be:.
As a consequence, the stability condition is given by:. According to the solution of the nonlinear model, the larger the k -core number k core max i. With the solution Eqs 11 and 13 of the fixed point equations, we can now study the local stability of the type II dynamic equations by analyzing the Jacobian of the stability matrix.
To guarantee the stability of the fixed point one has to verify that the real part of the eigenvalues of 7 are all negative. The maximum eigenvalue, which is obtained when the nodes i. All mutualistic networks lie in the stable feasible region situated below the tipping line, in agreement with the dynamical theory of the nonlinear model, and in contrast to the result of the linear model.
We have then shown that by taking into account the actual fixed point solution in the stability analysis, along with the saturation effect of the interaction term, this resolves the diversity-stability paradox.
We have presented two different approaches for the study of the stability condition in ecosystems and have seen that in the case of a fully connected network, the linear approach [ 1 , 9 , 10 , 33 ] leads to counterintuitive predictions which are in contrast with the exact solution of the full nonlinear model Eq
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