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**Session: Species Interactions 3**
# COS 59-3 - What constrains food webs? A maximum entropy model for predicting their structure with minimal biases

**Background/Question/Methods**

The scarcity of data on species interactions impedes our ability to study the functioning and dynamics of food webs and other ecological networks. However, because these networks have a structure that is both ecologically and statistically constrained, we can use these constraints to make better predictions of important food-web properties using a method specifically designed for this purpose. In this presentation, we show how the principle of maximum entropy, a rigorous mathematical method of finding constrained probability distributions, can predict many aspects of food-web structure, including the joint degree distribution and the adjacency matrix. The joint degree distribution is a joint probability distribution of the numbers of prey and predators for each species in the network, whereas the adjacency matrix is a representation of the food web in a matrix format. Specifically, we show how least-biased predictions of the joint degree distribution can be obtained from the numbers of species and interactions. We also show how the joint degree distribution can be used to predict the adjacency matrix by finding constrained networks of maximum entropy. We then compare our predictions with null models and empirical networks (N = 257) principally archived on the ecological interactions database Mangal.

**Results/Conclusions**

Our results show that the joint degree distribution, constrained by the number of species and the number of interactions, is well predicted by our maximum entropy model. Moreover, we found that empirical food webs (SVD entropy = 0.888 +/- 0.041) are close to maximum entropy (SVD entropy = 0.939 +/- 0.029) given a fixed joint degree distribution. Overall, our model offered a better or similar fit to empirical data than null models for 5 out of 7 measures of the adjacency matrix considered. In particular, two important food-web properties, namely the nestedness and the motifs distribution (e.g., the proportion of apparent competition in the network), were very well predicted by our maximum entropy model. This suggests that the joint degree distribution has a fundamental role in shaping food-web structure. These results also have practical applications since our predictions can be used as informative priors in Bayesian analyses for making better predictions of species interactions networks and as first-order approximations of food-web structure given a known joint degree distribution.

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Contributed Talk

Tuesday, August 16, 2022

8:30 AM – 8:45 AM EDT

Location: 518B

Francis Banville, n/a

PhD candidate

Université de Montréal

Montréal, Quebec, Canada- DG
Dominique Gravel

Université de Sherbrooke, Quebec, Canada

- TP
Timothée Poisot, PhD

Associate Professor

Université de Montréal, Quebec, Canada

The scarcity of data on species interactions impedes our ability to study the functioning and dynamics of food webs and other ecological networks. However, because these networks have a structure that is both ecologically and statistically constrained, we can use these constraints to make better predictions of important food-web properties using a method specifically designed for this purpose. In this presentation, we show how the principle of maximum entropy, a rigorous mathematical method of finding constrained probability distributions, can predict many aspects of food-web structure, including the joint degree distribution and the adjacency matrix. The joint degree distribution is a joint probability distribution of the numbers of prey and predators for each species in the network, whereas the adjacency matrix is a representation of the food web in a matrix format. Specifically, we show how least-biased predictions of the joint degree distribution can be obtained from the numbers of species and interactions. We also show how the joint degree distribution can be used to predict the adjacency matrix by finding constrained networks of maximum entropy. We then compare our predictions with null models and empirical networks (N = 257) principally archived on the ecological interactions database Mangal.

Our results show that the joint degree distribution, constrained by the number of species and the number of interactions, is well predicted by our maximum entropy model. Moreover, we found that empirical food webs (SVD entropy = 0.888 +/- 0.041) are close to maximum entropy (SVD entropy = 0.939 +/- 0.029) given a fixed joint degree distribution. Overall, our model offered a better or similar fit to empirical data than null models for 5 out of 7 measures of the adjacency matrix considered. In particular, two important food-web properties, namely the nestedness and the motifs distribution (e.g., the proportion of apparent competition in the network), were very well predicted by our maximum entropy model. This suggests that the joint degree distribution has a fundamental role in shaping food-web structure. These results also have practical applications since our predictions can be used as informative priors in Bayesian analyses for making better predictions of species interactions networks and as first-order approximations of food-web structure given a known joint degree distribution.