Relevance of Community Structure in Assessing Indeterminacy of Ecological Predictions

Abstract

The community matrix is potentially a powerful tool for community ecology. While it details direct interactions between community members, it can also be used to quantify all indirect effects that occur in a community, and thereby to make predictions regarding population response to experimental treatments or natural disturbances. These predictions are essentially hypotheses of system behavior that can be rigorously evaluated. Use of the community matrix, however, has been hindered by indeterminacy and ambiguity in response predictions. In this study, we reveal a theoretical source of the problem that arises as a consequence of community structure. Using a qualitative analysis of the community matrix, we detail the complementary feedback cycles that contribute to the response of a population following a sustained or press perturbation. Complementary feedback is the sum of all direct and indirect effects that can contribute to a response. We develop a “weighted‐predictions matrix” that assigns a probability scale to sign determinacy of predicted responses. This matrix is formed by the quotient of the net sum of complementary feedback cycles and the absolute number of complementary feedback cycles. A qualitative analysis of system structure provides a theoretical benchmark for understanding a spectrum of behavior in biological systems, and for framing and prioritizing management interventions for whole communities. This advance clarifies much of the uncertainty and ambiguity found in predicting the behavior of large and complex systems. We validate these tools by analyzing published studies of community response.

Qualitative analysis of recreational fisher response and the ecosystem impacts of management strategies in a data-limited situation

“…The adjoint of the negative community matrix (adj. -A, Table 1) details the predictions of response (+, -, 0) to press perturbations and accounts for both direct and indirect affects of change (Dambacher et al 2002(Dambacher et al , 2005. Taking indirect affects into account, a perturbation A c c e p t e d M a n u s c r i p t 7 may result in predictions of change in variables that are not directly impacted by the 150 perturbation.…”

Identifying key dynamics and ideal governance structures for successful ecological management

“…Qualitative models are produced using sign directed graphs, or signed digraphs, which 172 are constructed according to the signs (positive or negative) of interactions between variables 173 (e.g., Levins 1974, Puccia and Levins 1985, Dambacher et al 2002. Sign digraphs can be 174 used to represent systems with diverse types of components, including biological, physical, 175 economic and governance.…”

“…Qualitative assessments of stability and perturbation 202 response both rely on examination of system feedback, and proceed either by analysis of 203 signed digraphs (Puccia and Levins 1985) or mathematical operations on the matrix A 204 (Dambacher et al 2002(Dambacher et al , 2003 Stability generally depends on a system being adequately regulated by negative 213 feedback cycles, such that any perturbation to the system results in a return to its previous 214 state or equilibrium. Qualitative model stability is formally assessed according to the Routh-215…”

Interaction sign patterns in biological networks: From qualitative to quantitative criteria

“…The steady-state influence matrix (SSIM), i.e., the sensitivity matrix describing the changes in the equilibrium state vector induced by step-like perturbations of the state variables [15], is related to the inverse of the Jacobian matrix at the equilibrium [9], [10], [17]. Since the dynamics of biological/ecological networks are poorly known, it is useful to approach the problem from a qualitative (parameter-free) perspective and determine the sign pattern of the SSIM, regardless of the numerical values of the Jacobian entries; early attempts to provide qualitative methods in the ecological networks literature rely on the so-called loop analysis, which expands the terms of the Jacobian determinant into products of disjoint elementary circuits [18], [19].…”