Phytoplankton size diversity and ecosystem function relationships across oceanic regions

Trait diversity, a key component of biodiversity, mediates many essential ecosystem functions and services. However, the mechanisms behind such relationships at large spatial scales are not fully understood. Here we adopt the functional biogeography approach to investigate how the size composition of phytoplankton communities relates to primary production and export production along a broad latitudinal gradient. Using in situ phytoplankton size distribution data and a trait-based model, we find an increase in the average phytoplankton size, size diversity, primary production and export when moving from low to high latitudes. Our analysis indicates that the interplay between spatio-temporal heterogeneities in environmental conditions and a trade-off between the high affinity for nutrients of smaller cells and the ability to avoid predation by larger cells are the main mechanisms driving the observed patterns. Our results also suggest that variations in size diversity alone do not directly lead to changes in primary production and export. The trade-off thus introduces a feedback that influences the relationship between size diversity and ecosystem functions. These findings support the importance of environmentally mediated trade-offs as crucial mechanisms shaping biodiversity and ecosystem function relationships at large spatial scales.

Fitness function. The phytoplankton fitness function f(S,E) represents the net growth of phytoplankton and is a function of mean cell size S and the relevant environmental variables E, as follows: where Is is the light level at which photosynthesis saturates, I(z) is the irradiance at depth z, I0 is the light at surface, i.e. PAR (considered as external forcing to the model), and kw is the generic light extinction coefficient.
Nutrient limitation is simulated with a Monod function [7] with an size--scaled half--saturation constant (KN) based on observed allometric relationships [8]: where βU and αU are respectively the intercept and slope of the KN allometric function. This size--dependent process tends to favour smaller over larger organisms, especially, under nutrient limited conditions (Supplementary Figure   1).
The loss term G(S,P) is the size--selective grazing, inspired by meta--analyses of laboratory data [9,10] and encoded as a Holling Type--II or Monod functional response [11]. This formulation considers the zooplankton as a generic group with a specific feeding preference that depends on the slope αG of a power law function with an intercept of 1 [1,12], and half saturation constant of KP: In line with previous work [8] our grazing formulation represents a generic grazer with a preference towards smaller phytoplankton cells (Supplementary Figure 1B).
The size--dependent process ν(S,M) describes sinking as a function of size S and depth of the mixed layer M, using the allometric relationship reported by [13], which depends on the intercept βν and slope of the αν: This sinking formulation favors smaller over larger organisms, making larger cells to sink faster even under weak vertical mixing (See figure 1C).
Last, the term K quantifies the losses due to mixing and the term mP accounts for phytoplankton losses other than grazing and mixing.
Derivatives of the fitness function and higher order correction terms. The phytoplankton community described here follows the adaptive dynamics approach in which changes of a characteristic trait (phytoplankton cell size in our case) are approximated with a Taylor series expansion and a moment closure technique [14][15][16]. The respective first and second order derivate of the fitness function f with respect to the trait S are solved in PhytoSFDM using the python library for symbolic algebra sympy. The higher corrections terms ε, εN, εZ εD accounts for higher order moments resulting from the moment closure technique and have little impact on the model dynamics [14][15][16]. • ) and Z (i.e.: ℎ • ) due to mixing.

Supplementary Text 4. Size diversity and export relationship across the latitudinal gradient.
The figure below shows the annual averaged size diversity and the export produced by the model. Export accounts for all outfluxes, i.e. mixing and sinking terms. As described in the article, not only primary production but also export shows a positive correlation with size diversity along the Atlantic Meridional Transect.

Supplementary Text 5. Sensitivity Analyses
Here we summarized the results of three sensitivity tests. The first sensitive test is aimed at assessing the impact that the parameters δI and VI have on size diversity, gross primary production, and export (Supplementary Figure 5). For this a categorization of the 25 possible combinations into nine categories was implemented to simplify the analysis of the results (Supplementary Table 2).
The second sensitivity test evaluates how the size--based trade--off operates to produce the predicted latitudinal patterns in our model. We did this by fixing the mean cell size to three values first for nutrient uptake (Supplementary Figure  6 and 7) and then for grazing (Supplementary Figure 8 and 9), while letting all the other size dependent process to vary dynamically. In the third sensitivity test we evaluate the role that nutrient supply and its variability has in producing the δI --50% δI --25% δI δI +25% δI +50% δI --VI δI VI δI + VI VI +25% δI --VI + δI VI + δI + VI + VI +50% Supplementary Figure 5. Sensitivity test to changes in the parameters δI and VI. has on phytoplankton size diversity, gross primary production (GPP) and export at each location along the Atlantic Meridional Transect. For simplicity, we reduced the 25 possible combinations of changes in ±25% and ±50% into 9 combinations, considering only increase (superscripted plus sign), decrease (superscripted minus sign) or no change (no superscripted sign) of the parameters with respect to their reference values. For guidance see Supplementary Table 1. Notice that latitude is represented in absolute values, therefore, each box--plot includes the results for two ten degree location one in the northern and another in the southern hemisphere, e.g. 40 to 50 °N and --40 to --50 °S.