SPEAD 1.0 – A model for Simulating Plankton Evolution with Adaptive Dynamics in a two-trait continuous fitness landscape applied to the Sargasso Sea

Abstract

Abstract. Diversity plays a key role in the adaptive capacities of marine ecosystems to environmental changes. However, modeling phytoplankton trait diversity remains challenging due to the strength of the competitive exclusion of sub-optimal phenotypes. Trait diffusion (TD) is a recently developed approach to sustain diversity in plankton models by allowing the evolution of functional traits at ecological timescales. In this study, we present a model for Simulating Plankton Evolution with Adaptive Dynamics (SPEAD), where phytoplankton phenotypes characterized by two traits, nitrogen half-saturation constant and optimal temperature, can mutate at each generation using the TD mechanism. SPEAD does not resolve the different phenotypes as discrete entities, computing instead six aggregate properties: total phytoplankton biomass, mean value of each trait, trait variances, and inter-trait covariance of a single population in a continuous trait space. Therefore SPEAD resolves the dynamics of the population's continuous trait distribution by solving its statistical moments, where the variances of trait values represent the diversity of ecotypes. The ecological model is coupled to a vertically-resolved (1D) physical environment, and therefore the adaptive dynamics of the simulated phytoplankton population are driven by seasonal variations in vertical mixing, nutrient concentration, water temperature, and solar irradiance. The simulated bulk properties are validated by observations from BATS in the Sargasso Sea. We find that moderate mutation rates sustain trait diversity at decadal timescales and soften the almost total inter-trait correlation induced by the environment alone, without reducing the annual primary production or promoting permanently maladapted phenotypes, as occur with high mutation rates. As a way to evaluate the performance of the continuous-trait approximation, we also compare the solutions of SPEAD to the solutions of a classical discrete entities approach, both approaches including TD as a mechanism to sustain trait variance. We only find minor discrepancies between the continuous model SPEAD and the discrete model, the computational cost of SPEAD being lower by two orders of magnitude. Therefore SPEAD should be an ideal eco-evolutionary plankton model to be coupled to a general circulation model (GCM) at the global ocean.

A Theoretical Framework for Trait-Based Eco-Evolutionary Dynamics: Population Structure, Intraspecific Variation, and Community Assembly

“…This, however, comes at the cost that diversification into multiple peaks cannot be easily incorporated as opposed to our approach here. Finally, our moment equations closely resemble those derived in trait-diffusion approaches (Merico et al, 2014;Le gland et al, 2020), where mutations are generated by a diffusion process in trait space. Merico et al (2014) derived the moment equations for well-mixed, single-species, single-trait populations and Le gland et al ( 2020) extended this to multiple traits and spatial structure by way of reaction-diffusion equations in continuous space.…”

“…We shall refer to these types of equations as trait-space equations. As in adaptive dynamics and trait-diffusion approaches (Merico et al, 2014;Le gland et al, 2020;Nordbotten et al, 2020), we are not here concerned with any specific genetic makeup that would result in these dynamics for phenotypic traits, but simply assume that new heritable variation is generated in some ecological process such as births and mutations. For a single class, our setup is however very similar to the one-locus continuum-of-alleles class of models (Kimura, 1965;Bürger, 1986).…”

A general theoretical framework for trait-based eco-evolutionary dynamics: population structure, intraspecific variation, and community assembly

“…Finally, our moment equations closely resemble those derived in trait-diffusion approaches (Merico et al, 2014; Le gland et al, 2020), where mutations are generated by a diffusion process in trait space. Merico et al (2014) derived the moment equations for well-mixed, single-species, single-trait populations and Le gland et al (2020) extended this to multiple traits and spatial structure by way of reaction-diffusion equations in continuous space. For mutation kernels with small variance-covariance matrices without covariances, our mutation convolution integral is well approximated by such trait-diffusion processes (Kimura, 1965; Débarre et al, 2013), and our assembly framework is easily adapted to this setting, equipping the trait-diffusion approaches with a way of assembling eco-evolutionarily stable communities of several species.…”

“…In a phytoplankton model Peeters and Straile (2018) compared trait-space equations without mutations to single-species moment equations, and concluded that single-species moment equations failed to provide any useful information when considering parts of parameter space where the trait-space equations diverged into multiple species. In a similar model using the trait-diffusion approach Le gland et al (2020) noted that their trait-space equations sometimes exhibited multi-modality and speculated on the utility of modeling multiple modes, making the selection of how many modes to include based on functional groups. While multi-species moment models are not new (Sasaki and Dieckmann, 2011; Norberg et al, 2012; Barabás and D’Andrea, 2016), our assembly approach obviates the need for a-priori decisions on how many modes or species to include by assembling the correct number of species, at least as long as the number of species is not ambiguous.…”