In contemporary ecology and mathematical biology undergraduate courses, textbooks focus on competition and predation models despite it being accepted that most species on Earth are involved in mutualist relationships. Mutualism is usually discussed more briefly in texts, often from an observational perspective, and obligate mutualism mostly not at all. Part of the reason for this is the lack of a simple math model to successfully explain the observations. Traditionally, particular nonlinearities are used, which produce a variety of apparently disparate models.
The failure of the traditional linear model to describe coexisting mutualists has been documented from May (1973) through Murray (2001) to Bronstein (2015). Here we argue that this could be because of the use of carrying capacity, and propose the use of a nutrient pool instead, which implies the need for an autotroph (e.g. a plant) that converts nutrients into living resources for higher trophic levels. We show that such a linear model can successfully explain the major features of obligate mutualism when simple expressions for obligated growth are included.
- Mathematical Geoscience Seminar