Work

Unifying Models of Trophic Exploitation: A Mathematical Framework for Understanding the Paradox of Enrichment

Year: 2026

Type: article

Abstract: The rapid increase in the world’s human population has largely been attributed to efforts aimed at enhancing primary productivity and enriching food resources. However, an intriguing proposition of M. Rosenzweig, known as the paradox of enrichment, challenged the notion that such enrichment schemes always lead to sustained population growth. Instead, they can disrupt the delicate equilibrium of predator–prey systems, potentially driving one or both species to extinction. In this study, we develop a comprehensive mathematical framework that unifies Rosenzweig’s six analytical models of trophic exploitation through the Richards growth model, which can be viewed as a Box–Cox transformation of one species’ abundance relative to carrying capacity. Our analysis not only elucidates the connections and similarities between each model but also presents a generalized framework that unveils the underlying relationships between the proposed functions. Using the generalized logarithm and exponential functions of nonextensive statistical mechanics, we offer a fresh perspective and highlight the importance of a cautious approach when enriching ecosystems. This unification clarifies how the parameters that govern growth dynamics and predator–prey interactions determine system stability in diverse ecological contexts. Through numerical simulations and isoclinic analysis, we demonstrate that our generalized model accurately reproduces the classic paradox of enrichment while providing new insights into the mechanisms driving population fluctuations after environmental enrichment. This mathematical synthesis advances both theoretical ecology and practical conservation efforts by enabling a more accurate assessment of enrichment risks in managed ecosystems.

Source: Mathematical and Computational Applications

DOI: 10.3390/mca31010029

Authors: Lindomar Soares dos Santos, Brenno Caetano Troca Cabella, Alexandre Souto Martinez

Institutions: Universidade de São Paulo, Universidade Estadual Paulista (Unesp)

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

Open Access status: gold

Estimated APC paid: $1,689

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, Conselho Nacional de Desenvolvimento Científico e Tecnológico