**▎WuXi AppTec Content Team Editor**

From the vast tropical rain forest to the intestinal flora in the human body, various forms and scales of ecological communities play important functions. One of the core challenges of **ecology** is to understand how diverse species coexist, their complex dynamics as communities, and how these behaviors shape the functioning of ecosystems.

**Whether species diversity increases or decreases population stability is a long-standing debate**. By observing natural communities, ecologists have found that many environmental factors can affect both species diversity and community stability, so it is difficult to analyze the causal relationship between the two variables. Scientists lack a unified framework for describing and predicting biodiversity and ecological dynamics.

Recently, the research team of Professor Jeff Gore of the Massachusetts Institute of Technology (MIT) Department of Physics **combined****theory****and****Experiments on bacterial communities****observations prove that****only a small number of community-scale control variables can be used to predict the behavior of complex ecosystems**.

“The thermodynamic description of the behavior of a large number of gas molecules only requires a few emergent state variables such as temperature and pressure, without knowing the coordinates and velocity of each molecule.” Dr. Jiliang Hu, the first author of the paper “We found similar coarse-grained descriptions in ecological networks,” explained the authors. Their experimental and theoretical results suggest that only the **number of species** and the **average interspecies interaction strength need to be known **These two coarse-grained parameters can **predict the dynamic phase behavior and phase transitions that emerge in the ecological community**. An increase in the number of species and average interspecies interactions results in a **community transition between three emerging dynamical phases**, from a stable coexistence phase for all species, to a stable coexistence phase for some species, and finally transition to a phase where species numbers continue to oscillate over time. They also found a positive feedback between high species diversity and continued community oscillations.

**▲****The study’s lead authors, Dr. Hu Jiliang (left) and Prof. Jeff Gore (right) (Image source: Gore’s lab website)**

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**Ecosystem dynamics and species diversity**

**The researchers pointed out that experiments in a controlled environment in the laboratory can effectively avoid the random interference of environmental factors, so as to study the intrinsic properties of the community, such as the effect of interspecific interactions on species diversity and population stability sexual influence. The scientists observed predictable steady-state as well as periodic oscillations in laboratory communities containing a small number of species, and analyzed the function of different interspecies interactions, such as predation, competition, and symbiosis. Given the inability to measure all biological details (interspecies interactions, growth rates, environmental holdings, etc.) for large numbers of species co-existing in laboratory ecological communities, a natural question is whether it is possible for us to predict with the help of a small number of coarse-grained parameters Biodiversity and dynamics of complex communities?**

**Theorists such as the late Professor Robert May, a pioneer of complex systems, have explored predicting complex ecological networks with a small number of coarse-grained parameters, such as the statistical distribution of species numbers and the strength of interactions between species the behavior of. Their work shows that large numbers of species and strong interspecific interactions can lead to destabilization of communities, but there is a lack of understanding of complex behaviors beyond stability, such as how Understand species diversity, chaotic oscillations, and the interplay of community dynamics and diversity.**

**In this work, Dr. Hu Jiliang and Prof. Jeff Gore et al. tried to in theory and experimentcontrol the number of species and the strength of interactions between species, And reveal the relationship between species diversity and community stability.**

**Phase diagrams of community dynamics and biodiversity**

**The study authors used the generalized Lotka-Volterra model to study changes in community dynamics under different parameters. The simulation results show that increasing the number of species and the average interspecific interaction strength, the community will always change from the stable coexistence of all species with the first second-order phase transition to the stable state of some species extinction, and finally the community will have a second-order phase transition. Phase transition, from a steady state to a kinetic phase in which the number of species continues to oscillate.**

**In the simulation, the authors randomly generated the interspecies interaction matrix according to a certain statistical distribution, and proved that the kinetic phase and phase transition did not change with the change of the statistical distribution. With the help of random matrix theory and statistical physics, the author can obtain the analytical solutions of the two phase boundaries, which are in complete agreement with the calculated results. The results of theoretical analysis show that the diversity and stability of complex communities can be predicted only by the number of species and the three coarse-grained parameters of the first and second moments of the distribution of interspecies interactions.**

**The authors further verify that the kinetic phase diagram is robust under different model assumptions (such as considering predator-prey in ecological networks, mutualism, competition, etc.) , and exhibit the same kinetic phase and phase transition order. The authors even obtained qualitatively identical phase diagrams in other types of community dynamics models, such as pH-based interspecies interaction models. These results demonstrate the generality of phase diagrams for community dynamics and biodiversity.**

**▲****Theory predicts that the number of species and the strength of interactions between species shape the phase diagram of the community. As the number of species and the strength of interspecific interactions increase, the community undergoes a phase transition between three emerging dynamical phases, from a phase of stable coexistence of all species, to a phase of stable coexistence of some species, and finally to a phase where species numbers persist over time oscillating phase. (Image source: Reference [1])**

**Dynamic behavior of microbial communities transitioning from steady state to oscillation**

**In order to experimentally verify the kinetic oscillations predicted by the theory, the authors used 48 different bacteria isolated from the soil as experiments, with different combinations of bacteria to form different microbial communities .**

**By varying the concentrations of nutrients (glucose and urea) in the culture medium, the authors found that the strength of bacterial interactions increased significantly with increasing nutrient concentrations. Consistent with theoretical predictions, systematically increasing the number of species and the strength of interspecific interactions in the microbial community in the experiment will cause the species composition within the community to continue to oscillate over time. This kind of continuous fluctuation of the population is reflected not only in the violent fluctuation of the total biomass with time, but also in the violent fluctuation of the proportion of different species with time. The total organisms (Biomass OD) and the proportion of different species in the microbiota pathway showed highly consistent results, that is, the two properties of the same community either reached a steady state or oscillated at the same time.**

**▲****Microbial community experiments confirm theoretical predictions: as species numbers and the strength of interspecies interactions increase, more and more microbial communities exhibit Continue to oscillate over time. ****(Image source: Reference [1])**

**Phase diagram of experimental microbial community dynamics and biodiversity**

**The study authors experimentally verified the emerging phase diagrams and phase transitions in ecosystems by analyzing the biodiversity and stability of microbial communities at different species numbers and interaction strengths. The results are highly consistent with the theory.**

**Specifically, the experimental ecosystem showed the behavior of stable coexistence of all species in the parameter space with a small number of species and weak inter-species interactions, and when the number of species was continuously increased and inter-species interactions were low The first second-order phase transition occurs first, with the loss of some species (species extinction) and the transition to stable coexistence of some species, followed by the second phase transition, where the community loses stability and continues to oscillate.**

**In conclusion, As ecosystem complexity increases, communities always lose species diversity first and then start to lose dynamic stability. It is worth noting that the species survival rate of the ecosystem (the number of surviving species compared to the total number of species) decreased rapidly in Phase II (the stable coexistence phase of some species), but in phase III (oscillation phase), it no longer decreased significantly and reached a relatively stable state.**

**▲****Phase diagram of the experimental microbial community: in the parameter space with the number of species and the interaction strength between species as the coordinates, the microbial community exhibits three different kinetic phases. When the number of species and the strength of interaction between species are gradually increased, the community will undergo two phase transitions, and the community will first lose some species diversity, then lose its dynamic stability and start to oscillate continuously. ****(Image source: Reference [1])**

**Positive feedback exists between population shock and species diversity**

**So, how do dynamic shocks prevent the rapid loss of species diversity? The theory predicts that with the species survival rate of the ecosystem (the number of surviving species is greater than the total number of species), the number of species first declines rapidly, and then enters a gentle interval, that is, the survival rate does not decline rapidly but stabilizes. More interestingly, the calculations showed that under the same conditions, oscillating communities always exhibited higher biodiversity than stable ones. The authors analyzed the experimental data and found results that were highly consistent with theoretical predictions that there was a strong positive feedback between community shock and high species diversity.**

**The protective effect of dynamic shock on species diversity can be understood as the shock of the effective ecological niche over time provides the possibility for the survival of more species. Imagine that a certain group of species has strong competitive inhibition with another group of species and cannot coexist. At this time, if the two groups of species maintain a certain phase difference oscillation over time, they can each grow in different time intervals, and in time “Coexistence” is achieved in the average sense.**

**▲****Theoretical and experimental results consistently show that oscillating communities exhibit higher biodiversity than stable communities. ****(Image source: Reference [1])**

**“Our work proposes an effective framework that integrates two of the most famous achievements in theoretical ecology.” Dr. Jiliang Hu concluded, “One On the one hand, May proposed that the increase in the complexity of the ecological network will inevitably lead to its loss of stability; on the other hand, Chesson proved that the fluctuation of the ecosystem over time can maintain species diversity. The relationship between biodiversity and community stability in the field of ecology has always been controversial , the main reason for this controversy is that the complex dynamics exhibited by natural ecosystems may be caused either by random oscillations of the environment or by the intrinsic properties of ecological networks (complex interspecific interaction networks).Our The experimental system effectively controls the environmental noise and proves the conclusion predicted by the theory that only two coarse-grained parameters, namely the number of species and the strength of the interaction between species, can effectively describe the dynamic behavior of complex ecosystems.”**

**The research team noted that this prediction and theoretical framework is robust to biological details, and similar ecological kinetic phase diagrams can be obtained using either the resource-consumer model or the pH model. Therefore, the phase diagrams of biodiversity and community dynamics proposed in this study may be broadly applicable in more ecosystems. “Future work should try to explore whether our proposed dynamical phase diagram is generally applicable to complex ecological communities composed of various living organisms at various spatiotemporal scales,” the researchers propose.**

**It is worth mentioning that this work may be of interest to scientists in different fields. First, the stability and diversity of microbial communities are critical for the function and health of different microbiomes (eg, gut and soil microbiota). In addition, several types of ecological dynamics models used by researchers are widely used in the study of many other ecosystems, so the ecological dynamics phase diagram proposed here may also be general to other ecological communities. Finally, this study proposes a theoretical framework inspired by statistical physics to extract a small number of coarse-grained control variables from high-dimensional ecological networks, an approach that may be generalized to the study of other complex systems.**

**References:**

**[1] Jiliang Hu et al., (2022) Emergent phases of ecological diversity and dynamics mapped in microcosms. Science Doi: DOI: 10.1126/science.abm7841**