Sustaining diversity in trait-based models of phytoplankton communities

Abstract

It is well-established that when equilibrium is attained for two species competing for the same limiting resource in a stable, uniform environment, one species will eliminate the other due to competitive exclusion. While competitive exclusion is observed in laboratory experiments and ecological models, the phenomenon seems less common in nature, where static equilibrium is prevented by the fluctuating physical environment and by other factors that constantly change species abundances and the nature of competitive interactions. Trait-based models of phytoplankton communities appear to be useful tools for describing the evolution of large assemblages of species with aggregate group properties such as total biomass, mean trait, and trait variance, the latter representing the functional diversity of the community. Such an approach, however, is limited by the tendency of the trait variance to unrealistically decline to zero over time. This tendency to lose diversity, and therefore adaptive capacity, is typically "solved" by fixing the variance or by considering exogenous processes such as immigration. Exogenous processes, however, cannot explain the maintenance of adaptive capacity often observed in the closed environment of chemostat experiments. Here we present a new method to sustain diversity in adaptive trait-based models of phytoplankton communities based on a mechanism of trait diffusion through subsequent generations. Our modeling approach can therefore account for endogenous processes such as rapid evolution or transgenerational trait plasticity.

Analyzing the shape of observed trait distributions enables a data‐based moment closure of aggregate models

“…This is in line with the overall tendency of v to decline in aggregate models previously explored in other studies (Merico et al ; Coutinho et al ). To counteract this permanent loss of functional diversity and thus adaptive potential, previous studies had to maintain v by other processes such as immigration or diffusion terms or more complex trade‐offs, all demanding additional assumptions (Wirtz and Eckhardt ; Norberg et al ; Merico et al ; Tirok et al ). It shows that even for weakly non‐linear fitness functions the normal‐based model approach may not be able to reflect changes in biodiversity realistically.…”

“…Equation includes the second central moment, i.e., the trait variance v , which temporal dynamics are not described by an equation. Hence, we have to close this system of differential equations by assuming v either to be constant (Wirtz and Eckhardt ; Merico et al ) or to be well expressed in terms of the lower central moment, (Wirtz and Lemmen ). In general, such moment closure methods are based on assumptions about the shape of the trait distributions.…”

PhytoSFDM version 1.0.0: Phytoplankton Size and Functional Diversity Model

“…Within our modelling tool we also provide two alternative ways of treating the size variance: immigration (following Norberg et al, 2001) and trait diffusion (following Merico et al, 2014). The treatment with immigration considers the introduction of biomass and new trait values from hypothetical adjacent communities into the resident community.…”

Effect of phytoplankton size diversity on primary productivity in the North Pacific: trait distributions under environmental variability

“…The first is to vary the ‘trait diffusion’ (TD) coefficient ( u ), which is the probability that the offspring of individuals from one trait class evolve into other trait classes via genetic mutation or trans‐generational plasticity (Merico et al . ). The second is to vary the zooplankton ‘kill‐the‐winner’ (KTW) grazing coefficient ( a g ), which describes how the zooplankton feeding preference changes with prey abundance (Vallina et al .…”

“…To generate a diversity gradient independent of environmental effects, we employ two approaches to sustain different levels of diversity in the model. The first is to vary the 'trait diffusion' (TD) coefficient (u), which is the probability that the offspring of individuals from one trait class evolve into other trait classes via genetic mutation or trans-generational plasticity (Merico et al 2014). The second is to vary the zooplankton 'kill-the-winner' (KTW) grazing coefficient (a g ), which describes how the zooplankton feeding preference changes with prey abundance (Vallina et al 2014a(Vallina et al , b, 2017Wirtz 2014).…”