Introduction

Nearly all species that have existed on Earth are now extinct; an unmistakable signature of competition1. Understanding the nature of this competition is vital for interpreting observed biodiversity. Competition based on the acquisition of limiting resources is a concept pervasive in the aquatic science literature, as well as other ecological disciplines. An example with respect to phytoplankton is found in Evelyn Hutchinson’s2 famous paradox: “The problem that is presented…is essentially how it is possible for a number of species to coexist in a…unstructured environment all competing for the same sorts of materials. … According to the principle of competitive exclusion, we should expect that one species alone would outcompete all the others…”. Beginning in the 1970’s, laboratory phytoplankton competition experiments clearly demonstrated resource-based species exclusion by showing that the outcome of a competition can be predicted based on a priori knowledge of relationships between nutrient concentration and uptake for two competing species3,4,5,6,7,8,9. From this emerged the ‘R* rule’ stating that, for a common limiting resource, the species that can achieve a steady-state population at the lowest resource level (denoted R*) will outcompete all other species4,10. This view prevails in textbooks on marine ecology (e.g.11,12).

The long-standing focus on resource competition in phytoplankton ecology is woven into how we construct and interpret ecosystem models and in our predictions of change under a warming climate. It is also at odds with one of the most basic phytoplankton observations in nature. Spanning from the most nutrient-depleted ‘oligotrophic’ waters to nutrient-rich ‘eutrophic’ waters, measurements consistently demonstrate continuous size distributions of diverse coexisting phytoplankton species with dramatically different resource acquisition potentials13,14,15 (Fig. 1a). A provocative proposal to explain this inconsistency is that phytoplankton in nature are too distantly spaced to allow the type of resourced-based competitive exclusion exhibited in laboratory experiments16,17,18,19. However, spatial distancing, when considered in isolation, is not sufficient to prevent competition in microbial communities reliant on the diffusion of limiting resources20. Here, we explain why resource-based competitive exclusion is unlikely in natural open-ocean phytoplankton communities and why the ‘R* rule’ does not hold in these systems. We then advocate for a more holistic consideration of factors defining division-loss balances among coexisting species and propose that adopting such a view will improve understanding of biodiversity and predictions of change in phytoplankton communities, and likely other ecological systems.

Fig. 1
figure 1

Properties of natural phytoplankton populations. (a) Across all open ocean nutrient conditions, phytoplankton populations exhibit continuous size distributions with slopes typically ranging from − 3.5 to − 4.5 between the logarithm of cell number concentration per unit length and the logarithm of equivalent spherical cell diameter, with steeper slopes observed in more nutrient impoverished waters13,25. Division rates are progressively more diffusion-limited as cell size increases (red arrow), implying that competitive potential for resources increases with decreasing cell size (green arrow). Data shown here were collected in the north Atlantic subtropical gyre (from91). (b) Conceptual illustration of the nutrient field experienced by phytoplankton (a 2-dimensional slice through a 3-dimensional field), showing reductions in nutrient concentration through the boundary layers of four, variably-spaced phytoplankton cells being supplied by diffusion of nutrients from the far-field. In nature, cell-to-cell spacing is typically greater than depicted in this figure and far-field nutrient concentrations (S∞) are not necessarily uniform as in this illustration, but can exhibit short-lived, high-concentration patches resulting from discrete sources of recycled nutrients (e.g., zooplankton excretion).

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Building intuition on resource sharing among phytoplankton

From oligotrophic to eutrophic waters, neighboring phytoplankton cells in the open ocean are separated on average by ~ 100–400 body lengths21. Nutrient uptake by these cells results in a depletion zone referred to as the ‘diffusive boundary layer’ that extends for up to nine times a cell’s diameter22, beyond which nutrient concentrations are essentially equivalent to that of the bulk media (S∞) (Fig. 1b). For natural communities of nutrient-limited phytoplankton, the vast intercellular spacing noted above implies that boundary layers rarely overlap between cells, a conclusion that persists even when the relative movement of cells caused by small scale turbulence is considered17,21. Nevertheless, these boundary layers are mechanistically interlinked.

To build intuition on the resource environment experienced by phytoplankton, we expand here upon an analogy introduced by20 regarding water level regulation in Lake Berryessa, California. In this analogy, the ‘Glory Hole’ spillway represents a phytoplankton cell and the depression of water around this spillway is the boundary layer (Fig. 2a). Despite its meager cross-sectional area, the ‘Glory Hole’ can maintain a constant water level across the entire 80 km2 lake surface (Fig. 2b) because a strong force (i.e., gravity) rapidly eliminates gradients in water elevation. Indeed, if the lake’s surface is two meters above the spillway when it is opened, the time required for the ‘Glory Hole’ (maximum flow rate ~ 1400 m3 s−1) to drop the lake level to 1 m above the spillway (t1/2) is a mere 16 h20. For phytoplankton, the ‘strong force’ tending to homogenize resource concentrations between cells is obviously not gravity, but rather diffusion. Because of diffusion, nutrient uptake by a cell has the potential to deplete resources far beyond its own boundary layer, thereby promoting competition with distant phytoplankton. What are the timescales of this interaction in nature?

Fig. 2
figure 2

Lake analogy for nutrient competition concepts in steady-state plankton systems. (a) The ‘Glory Hole’ spillway of (b) Lake Berryessa, California. The small spillway can maintain lake levels across its ~ 80 km2 surface area because the strong force of gravity rapidly eliminates elevation differences across the lake and the spillway has a high flow capacity. Similarly, phytoplankton cells have the ability to rapidly take up nutrients at their cell surface, creating a strong concentration gradient in their boundary layers. Because diffusion acts to rapidly eliminate concentration differences, the discrete uptake by cells has the potential to rapidly deplete far-field concentrations in the absence of a resupply source. (c) A lake analogy of the R* rule, where the two spillways (A, B) represent populations of phytoplankton with different uptake capacities. In this panel, the lake level is initially above both spillways (dashed surface), water drained by the spillways is removed from the system, and there is no new source of water to the lake. Under these conditions, the B spillway is ‘outcompeted’ by the A spillway because of the latter’s greater drainage ability. In laboratory competition experiments, a superior resource competitor can exclude an inferior competitor, irrespective of distancing between cells, because the former can continue increasing its biomass until the concentration of limiting resource is sufficiently low that division rate of the inferior competitor is less than the experimentally imposed predation rate. (d) Lake analogy of steady-state plankton systems where water passing through the spillways (blue arrows) is redeposited on the lake’s surface. In this case, the drawdown potential of the different spillways does not alter the steady-state lake level and, consequently, spatial distancing of spillways A and B impedes the former from preventing flow through the latter. In phytoplankton communities, nutrient recycling and spatial distancing similarly allow coexistence of species with vastly different resource uptake potentials. These analogies are intended to provide intuition regarding plankton systems, rather than a robust depiction of the three-dimensional space defining growth conditions of phytoplankton cells. Image credit: (a) “Monticello Dam spillway, Lake Berryessa” by Jeremy Brooks; (b) “Aerial view of Lake Berryessa” by Dick Lyon. Both images can be found on commons.wikimedia.org, and are licensed under CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/).

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In the oligotrophic central ocean gyres, nitrogen is often a limiting resource for phytoplankton growth23,24, with total concentrations of biologically available forms (e.g., NO3, NO2, NH4) typically ranging from S∞ = 3 to 17 nM21. Phytoplankton communities in these waters exhibit steep size distributions with slopes of − 4 to − 4.5 between the logarithm of cell number concentration per unit length and the logarithm of cell diameter (d)13,14,15,25 (e.g., Fig. 1a). The most abundant taxon in ocean subtropical gyres is Prochlorococcus (d = 0.6 µm) and, at cell concentrations ranging from 2 × 104 to 2 × 105 cell ml−121,26, these populations can potentially decrease the forestated S∞ values by 50% in t1/2 = 4.5 to 5.8 h (Fig. 3). Values of t1/2 for the second most abundant taxon, Synechococcus (d = 1.5 µm), and larger cells range from ~ 1 day to many months, respectively (Fig. 3). These depletion potentials are comparable to (or much longer than) nutrient recycling rates in quasi-steady-state plankton systems27, where loss and growth processes operating on similar time scales prevent long-period predator–prey oscillations of the Lotka-Voltera type.

Fig. 3
figure 3

Nutrient depletion potentials as a function of cell size and far-field nutrient concentration (S∞). Time required (t1/2) for a 50% reduction in S∞ for phytoplankton with cell diameters (spherical equivalents) ranging from 0.6 to 130 µm (coloring defined in box), assuming no new input of limiting resource. Green shading = typical dissolved nitrogen concentrations in oligotrophic subtropical ocean gyres. See methods for details on calculations and discussion of features in the graph.

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The size-dependent nutrient depletion times (t1/2) given above apply to spatial scales far greater than those separating neighboring phytoplankton in nature. Returning to our analogy, consider now the hypothetical scenario of a Lake Berryessa with two spillways (A, B) representing populations of phytoplankton of two species (A, B), where spillway width sets potential drawdown rate (i.e., product of nutrient affinity and cell number for each species) and height sets the lake level at which flow through a spillway stops (Fig. 2c). With a high initial lake level (dashed surface in Fig. 2c), both spillways contribute to lake drainage but, in time, spillway A (e.g., Prochlorococcus) ‘competitively excludes’ spillway B (e.g., larger diatoms) because the former can drain the entire lake below the intake levels of the latter (Fig. 2c). This is the essence of the ‘R* rule’ and it is independent of the spacing between spillways (i.e., cells).

What happens to the above lake analogy of resource-based competitive exclusion if it is raining? Rainfall to the Lake Berryessa drainage basin causes the lake level drop-rate to decrease and, if this water inflow is > 1400 m3 s−1, then the ‘Glory Hole’ t1/2 → ∞ and it can no longer control the level of the lake. This scenario is depicted in Fig. 2d where all the water passing through the spillways is redeposited on the lake’s surface. Consequently, the lake level is not determined by the drawdown potential of a given spillway, but rather by the summed flow cycling through the spillways and the total amount of water in the system. This condition is essentially analogous to nutrient-limited quasi-steady-state phytoplankton communities. Spatial separation causes water flow (i.e., resource uptake) through the two spillways (i.e., cell populations) to be independent, albeit with more flow passing through the higher potential A spillway (Prochlorococcus) than spillway B (the diatoms) (Fig. 2d).

One final modification is needed to complete our analogy. The outcome depicted in Fig. 2d reverts to that in Fig. 2c if we allow the diameter of each spillway (i.e., population size of species A and B) to increase over time in proportion to its flow rate. In such a case, spillway A will increase in diameter faster than spillway B, the lake level will drop below the top of spillway B (i.e., ‘extinction’), and, eventually, the diameter of A will reach a steady state where drainage rate equals recycling rate. In other words, the amount of water (i.e., resource) in the system no longer determines the lake height (i.e., S∞) but, rather, the total flow rate through the more competitive A spillway (Prochlorococcus). This is what happens in laboratory phytoplankton competition experiments. When initial nutrient levels are high, biomass of the competing species increases at a rate proportional to their uptake capacities. If unrestricted, the more competitive species achieves a biomass where its nutrient uptake reduces S∞ to a level where the less competitive species goes extinct. In natural phytoplankton communities, this is not the case because losses constrain biomass in a manner proportional to resource acquisition potential (i.e., division rate). In other words, the diameter of spillway A is restricted such that the lake level remains above the B spillway (as in Fig. 2d). A shortcoming in our analogy is that ‘coexistence’ of the two spillways requires maximum flow through spillway A (in Fig. 2d there is no ‘boundary layer above spillway A). In natural phytoplankton populations, coexistence of all size classes occurs even when the smallest, most competitive species are nutrient limited (i.e., nutrient flow through this population of cells is below maximum potential and boundary layer gradients remain)21.

Clearly, the dynamics of plankton ecosystems are not literally equivalent to lake level regulation, so the foregoing analogies are simply intended to provide a more tangible (and equation-less) understanding of resource constraints at the microscale of phytoplankton and not a literal equivalence. The key take-home message here is that resource-based competitive exclusion should not be anticipated in systems where individuals are distantly spaced and unrestricted proliferation of size classes with greatly enhanced resource acquisition potentials is prevented. This is the case for natural phytoplankton populations and the reason they do not obey the R* rule. As explained in more detail below, the concentration of limiting nutrient in the far-field between cells (S∞) is not determined by the species that can maintain steady-state biomass at the lowest resource level (i.e., as in laboratory competition experiments), but rather by the total amount of limiting resource in the system (i.e., balance between sources and sinks) and ecological constraints on biomass.

Cultures versus nature: key distinctions

To better understand the above vital conclusions, it is instructive to consider differences between laboratory competition experiments and natural plankton communities. In classic competition experiments (e.g.,3,4,5), culture media is inoculated with two phytoplankton species at concentrations below steady-state carrying capacity and then changes in each species’ biomass (P) are monitored over time. As the experiment progresses, a fraction of the culture is removed and replaced by fresh media at a predefined cadence (l; per unit time). The significance of this practice is that the removal of culture simulates perfectly neutral (i.e., species-independent) and linear (i.e., lP) predation. The winner of the competition is the species that can achieve a division rate (µ) equal to the predation rate at the highest steady-state biomass, which is equivalent to saying the species that can achieve µ = l at the lowest S∞. As the superior competitor decreases S∞, predation on the inferior competitor exceeds its division rate and it is washed out of the culture at the specific rate, \({e}^{-\left(l-\mu \right)t}\), where t = time28. This outcome is the same whether steady-state biomass is so high that diffusive boundary layers continuously overlap between cells (i.e., concentration of limiting resource in fresh media is very high) or so low that they rarely overlap (i.e., concentration of limiting resource in fresh media is very low) because diffusion rates are fast and simple linear predation allows the superior competitor to reach a final steady state where its µP (in units of limiting resource per time) equals the limiting resource resupply rate.

In nature, predation on phytoplankton is neither neutral nor linear. Rather, most zooplankton predators are size-specific in their prey selection29,30,31,32,33,34 and their grazing rate is dependent on both phytoplankton concentration and their own abundance, which generally increases in parallel with prey abundance35,36,37. At quasi-steady state (e.g., ocean subtropical gyres), the balance between division and loss is such that no single predator–prey size class can reach a µP equal to the total limiting resource resupply rate. Instead, this resource is distributed across all predator–prey size classes in a manner proportional to the µ of each class, as dictated in part by boundary layer diffusion. Thus, the total supply rate of limiting resource is equal to the sum of µP for all size classes (as in the water recycling loop of Fig. 2d). This is the fundamental difference between laboratory competition experiments and natural plankton populations, and it implies that no phytoplankton size class can exclude another size class based on resource competition (contrary to the R* rule). It also implies that the smallest cells will dominate the phytoplankton community biomass when the total inventory of limiting resource is particularly low (due to their faster diffusion-limited division rates) and that larger cells will increase in prominence as the resource inventory increases (due to their often-higher maximum division rate potentials paralleled by resource saturation of division in the smallest cells)21. Thus, phytoplankton size distributions become less steep as the total amount of limiting resource in the system increases.

Demonstration with a simple ecosystem model

The potential for all phytoplankton size classes to coexist across the full range of open ocean nutrient concentrations was recently explored in21. Their model was essentially identical to38 and the earlier model of39 except that the non-grazing constant phytoplankton mortality rate in38,39 was either excluded or allowed to vary between size classes (Methods). The model of21 (Eqs. 1a, b) was executed here assuming nitrogen-limited growth of all phytoplankton species (thus maximizing the potential for resource-based competitive exclusion) and it included 25 size classes of both phytoplankton (d = 0.6 to 134 µm) and zooplankton, with phytoplankton and zooplankton dynamics described by:

$$\frac{{dP_{i}^{N} }}{dt} = \mu_{i} P_{i}^{N} - m_{i} P_{i}^{N} - g_{1} Z_{i}^{N} f_{i} P_{i}^{N}$$
(1a)

and

$$\frac{{dZ_{i}^{N} }}{dt} = g_{1} g_{2} Z_{i}^{N} f_{i} P_{i}^{N} - g_{3} Z_{i}^{N} - g_{4} j_{i} \left( {Z_{i}^{N} } \right)^{2}$$
(1b)

where \({P}_{i}^{N}\) is the nitrogen content (µmol L−1) of the ith phytoplankton size class, \({Z}_{i}^{N}\) is the nitrogen content (µmol L−1) of the ith zooplankton size class grazing upon a constrained range of phytoplankton size classes (Methods), µi is the diffusion-supported nitrogen-limited division rate (d−1), mi is the non-grazing mortality rate, fi defines the phytoplankton size range preyed upon by the ith zooplankton size class, ji defines the phytoplankton grazer size range preyed upon by the ith zooplankton predator size class, and g1 through g4 are zooplankton grazing rate, ingestion efficiency, non-predator mortality rate, and density-dependent mortality rate, respectively (Methods). At steady state, the nutrient supply rate is equal to the sum of non-grazing phytoplankton mortality, zooplankton egestion/sloppy feeding and mortality [i.e., \(\sum_{1}^{i}{m}_{i}{P}_{i}^{N}+ {g}_{1}\left({1-g}_{2}\right) {Z}_{i}^{N}{f}_{i} {P}_{i}^{N}+{g}_{3}{Z}_{i}^{N}+{g}_{4} {j}_{i}{\left({Z}_{i}^{N}\right)}^{2}\)] (Fig. 4a, right axis). As detailed in21, this model is equally valid whether phytoplankton are treated as discrete and distantly spaced cells or simply as a continuous field of an elemental stock. It may be noted that Eq. 1a could be expanded to include other losses (e.g., viruses, parasites) by including additional biomass terms and density-dependent loss terms similar as those for grazing, but for the current purpose the simplified expression in Eq. 1a suffices.

Fig. 4
figure 4

Predictions of phytoplankton community properties and resource distributions from a one-dimensional ecosystem model. (a) Relationship between nitrogen inventory (ΣN), far-field nitrogen concentration (S∞; blue line), and steady-state nitrogen supply rate (orange line). Dashed green lines bracket typical nitrogen S∞ values for oligotrophic subtropical ocean gyres. (b) Phytoplankton size distributions (blue line) (logarithm of cell number concentration per unit length versus logarithm of cell diameter) become increasingly steep as ΣN decrease from 20 to 4 µM, but all 25 phytoplankton size classes included in model initiations are retained at steady state (orange line) for all values of ΣN. (c) Steady-state partitioning of nitrogen inventories between phytoplankton (blue line), zooplankton (orange line), and dissolved (green line) pools. For ΣN < 10 µM, nearly all of the resource is sequestered in phytoplankton and zooplankton biomass (gray line). See methods for details.

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For nitrogen inventories (ΣN) ranging from 4 to 20 µM, our minimal equation set consistently predicts the stable coexistence of all 25 phytoplankton size classes (Fig. 4b, right axis). In other words, there is no evidence of resource based competitive exclusion between size classes. The model also yields phytoplankton communities with size distribution slopes that steepen with decreasing ΣN (consistent with field observations)13,14,15 (Fig. 4b, left axis), it predicts ocean gyre-type S∞ values (3–17 nM) for ΣN of ~ 5 to 8 µM (Fig. 4a, left axis), and, for all ΣN < 10 µM, results in more than 97% of the total nitrogen inventory being sequestered in biomass (~ 60% in phytoplankton, ~ 40% in zooplankton) (Fig. 4c).

The take-home message from these model results is that, using an equation set minimally altered from earlier studies, resource-based competitive exclusion is not observed of any phytoplankton size class at any nitrogen level. Instead, size-dependent predation permits the coexistence of phytoplankton with vastly different resource acquisition potentials and determines the partitioning of limiting resource across size classes that ultimately defines S∞. This finding is very different than previous models such as39 and38 that report minimal size-class coexistence at low nutrient levels and then increasing size diversity as the best resource competitors become nutrient saturated and associated increases in S∞ allow weaker competitors to be successively added (in a size-dependent manner) to the community. Such nutrient-dependent changes in modelled diversity are typically interpreted as a consequence of resource-based competitive exclusion following the R* rule38, but instead are a consequence of earlier models including a constant non-grazing mortality term for all phytoplankton size classes that unrealistically eliminates slow growing sizes at low nutrient levels (Methods). Unlike the sustained size diversity of the model described above, these earlier models are forced to artificially ‘re-seed’ background phytoplankton size classes to avoid complete extinction of slower growing species, a clear indicator of a problem in the model formulation. The sustained size diversity across nutrient levels shown in Fig. 4b is achieved by allowing the non-grazing mortality rate in Eq. (1a) to realistically vary in proportion to size-dependent division rates (Methods).

Appeal for a change

We began our narrative with a statement that competitive exclusion is likely responsible for most extinctions on Earth. What we are advocating for here is a change in how we conceive of and teach the underlying mechanisms of this competitive exclusion, at least for the phytoplankton and perhaps other ecological systems. As demonstrated in laboratory experiments, resource-based exclusion can occur when species with different acquisition potentials compete for a common limiting resource, the species share common and non-selective predators, and negative inter-species interactions (e.g., allelopathy) do not counter resource acquisition advantages. Under such conditions, the baseline prediction is that the number of stably coexisting species will equal the number of different limiting resources3,4,40,41,42, although some additional nuances can be added to these predictions to modestly enhance diversity e.g.,43,44,45,46. Field observations routinely evidence the stable coexistence of phytoplankton communities with a continuum of size classes having strongly contrasting resource acquisition potentials and we argue that the reason for this is that the aforenoted requirements for resource-based competitive exclusion are not valid in these natural systems.

In our portrayal of plankton communities, different phytoplankton size classes are associated with different sets of predators, with each predator–prey set defining a unique ‘ecological niche’19,47. Within these ecological niches, the expectation is that competition is severe and that even minor differences in fitness will, over time, result in exclusion1. This concept of predator–prey dynamics influencing biodiversity is not new and is the topic of a vast (largely terrestrial-oriented) literature e.g.,8,48,49,50,51,52. Our appeal is that a holistic and ecological framework be widely adopted as an explanation for competition and phytoplankton community structuring, as opposed to the simplistic bottom-up view of resource competition that dominates the phytoplankton literature today. The importance of viewing competition in this expanded framework of ecological interactions and dynamics is that ‘fitness’ is no longer determined solely by a species’ ability to acquire a limiting resource but rather by the combination of adaptations defining its division-loss balance relative to that of other species within its ecological niche (Fig. 5)53.

Fig. 5
figure 5

Depiction of the multi-dimensional trade-space available to phytoplankton for achieving equivalent fitness within predator–prey created ecological niches. In this schematic, phytoplankton species have twelve investment options indicated by nodes (black labeled squares) that are evenly distributed across the surface of the trade-space volume. Any location within this volume (infinite options) is a valid solution for achieving equal fitness in an ecological niche, but the actual positions of extent coexisting species are defined by evolved investment strategies. For example, species A (red sphere) is positioned within the trade-space volume closer to defense-related investment options [e.g., vectors (red dotted lines) connecting to armory, predator avoidance, chemical defense], implying a competition solution focused on reducing the loss term (l) in the predator–prey balance (i.e., µ—l). Species B (green sphere), on the other hand, is positioned closer to resource relevant nodes [e.g., vectors (green dotted lines) connecting to resource affinity, cell quota, opportunistic physiology], implying investments focused more on the division element (µ) of the predator–prey balance. As described in the text, each investment option identified in this figure may have multiple forms [e.g., ‘opportunistic physiology’ could include chemotaxis, excess photosynthetic capacity, luxury nutrient uptake, enhanced division rate maxima, among others], and the full suite of options available to phytoplankton likely exceeds the twelve shown here. A phytoplankton species might also invest in only a subset of these options, such as a ‘defense specialist’ investing in armor and predator avoidance (e.g., swimming) and neglecting investment in chemical defenses. Figure created with Matlab R2018b Version 9.5.0 (https://www.mathworks.com/).

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Competition within an ecological niche is an issue of investment strategy, where resources dedicated to one advantage are not available to invest in others. While the model employed herein focuses on phytoplankton-grazer relationships, the full investment landscape is much broader. An incomplete list of phytoplankton options includes reduction in cell quotas for limiting resources (e.g., metabolic networking54,55), development of symbiotic relationships (e.g., nitrogen fixing bacteria)56, opportunistic adaptions to exploit resource patchiness (e.g., chemotaxis57, retention of excess photosynthetic capacity58,59, luxury uptake60,61,62, elevated maximum division rate63), enhanced resource affinity3,4, allelopathy64, mixotrophy65, production of chemical grazing deterrents, armored cell walls (e.g., coccoliths, thecal plates, frustules), and grazer avoidance (swimming)66, and adaptations reducing losses to pathogens (e.g., low maximum division rate potential preventing explosive increases in abundance63) (Fig. 5). In regions with strong temporal environmental variability, physiological adaptations enabling seasonal blooming63 or resting spore formation67,68 can also contribute to a species’ retention in the community. The requirement for stable coexistence within an ecological niche is that each phytoplankton species has identical fitness when averaged over the timescale of exclusion69, which can span years to decades for closely matched species18,19. Breaking free of the R* restriction of diversity equaling the number of different limiting resources, the multi-dimensional landscape of investment options illustrated in Fig. 5 implies that diverse (infinite?) options may exist for achieving fitness equality within an ecological niche, even if growth of all species is limited by the same nutrient resource.

In the depiction of phytoplankton community structuring promoted here, competitive exclusion is decided by all factors influencing the relative division-loss balance of species within an ecological niche (Fig. 5)18,19,70,71,72, while differences in resource acquisition potentials are expressed through the relative cell abundances between size-structured ecological niches (Fig. 4b, left axis). We expect the same mechanisms to structure quasi-steady-state light-limited phytoplankton communities (e.g., populations living at the bottom of the sunlit layer of ocean gyres). The requirement for time-averaged equal fitness in ecological niches implies elevated potentiality for stable biodiversity in variable environments (e.g., high latitudes), as temporal changes in growth conditions will continually shift the relative fitness of different species2,25,63,73,74. Fitness equivalence in ecological niches should also be a defining element in phytoplankton biogeography75,76, where unique adaptions to a specific environment (e.g., physiological temperature optima, photosynthetic light harvesting structures optimized for perpetually low-light growth) drive competitive exclusion of less fit species adapted for other environments.

The ability of predator–prey relationships to override the inevitable resource-based outcome of a two species competition experiment has been demonstrated in plankton cultures77,78,79,80,81. Here we explain why growth, loss, and recycling processes in nature prevent species exclusions based on resource acquisition alone. Similar rules of community structuring should equally apply to other ecological systems where unchecked proliferation of superior resource competitors is prevented by tightly coupled losses51,52,82,83 or other competitive strategies (Fig. 5). For all such systems, abandoning a bottom-up view in favor of an ecosystem-based view will nurture a more thorough understanding and effective modeling of natural communities52.

Methods

Calculation of far-field nutrient depletion time scales

The time required for a population of like-sized phytoplankton to reduce far-field nutrient concentrations (S∞) by one half (t1/2) in the absence of any new source of that nutrient is dependent of cell properties (size, motility, etc.), cell abundance, maximum division rate (i.e., the degree to which division is saturated by the diffusion of limiting resource), and the concentration gradient between the cell surface and the far-field. To estimate size-dependent t1/2 values for specific size classes within representative natural phytoplankton populations, we assumed a phytoplankton size distribution with a − 4.4 slope between the logarithm of cell number concentration per unit length and the logarithm of cell diameter. t1/2 values were estimated for cell diameters of 0.6, 1.5, 2.5, 4, 8, 16, 30, 50, 70, 100, and 130 µm and a range in S∞ of 1 nM to 10 µM (in steps of 1 nM from 1 to 21 nM, ~ 8 nM from 21 to 500 nM, and ~ 1 µM from 1 to 10 µM). The smallest size class represents Prochlorococcus, which typically exhibits cell concentrations ranging from 2 × 104 to 2 × 105 cell ml−1 in natural oligotrophic waters21. Inorganic nitrogen concentrations (S∞) in these waters typically range from 3 to 17 nM. Since the predator–prey determined steady-state in phytoplankton concentration increases with increasing division rate84,85, we assumed Prochlorococcus concentrations to increase linearly from 2 × 104 to 2 × 105 cell ml−1 as S∞ increases from 1 to 17 nM. Division rate (µ) for each phytoplankton size class was calculated as a size-dependent saturating function of S∞ defined by diffusion rate (D) and maximum potential µ, as described in detail in21. Depletion half times were calculated for each size class following20 as t1/2 = ln(2) (DA)−1, where D is from21 and A is the numerical abundance of cells as defined above. For these calculations, we assumed that all phytoplankton were motile and non-vacuolated (i.e., non-diatoms)21.

Figure 3 shows the resultant relationships between t1/2 and S∞ from the calculations described above. We call attention to a variety of aspects regarding these results. First, t1/2 for oligotrophic gyre conditions (green shading in Fig. 3) ranges from ~ 1 day to > 1 year for all size classes ≥ 1.5 µm [i.e., Synechococcus (d = 1.5 µm) and larger]. Only Prochlorococcus has a t1/2 < 1 day in these waters. Second, for S∞ < 17 nM, t1/2 decreases with increasing S∞ for all size classes ≥ 1.5 µm, which is a consequence of both the assumed increase in cell abundance as S∞ increases from 1 to 17 nM and the increasing concentration gradient from the cell surface (S0) to the far-field (S∞). In contrast, t1/2 for Prochlorococcus increases over essentially the full range of S∞, despite increases in cell numbers from S∞ of 1 to 17 nM. The reason for this increase is that division rates for Prochlorococcus are nearly saturated by diffusion at even the lowest S∞21 and the assumed increase in cell abundance over the oligotrophic range in S∞ is not sufficient to overcome the longer time requirement for an essentially constant uptake rate to deplete far-field nutrients by 50% (note that this saturation of division by diffusion is also apparent in the shouldering of t1/2 for Synechococcus as S∞ approaches 17 nM and the shouldering of t1/2 for larger cells at S∞ > 17 nM). Third, diffusion rates described in21 assume that each cell in each size class can achieve the theoretical maximum µ. Because measured maximum µ values for many phytoplankton species fall below these theoretical limits, our calculated t1/2 values (Fig. 3) will tend to be underestimated. On the other hand, concentrations of larger cells tend to increase in nature as S∞ increases, causing the slope of the size distribution to be greater than -4.4, implying somewhat smaller t1/2 for these larger cells at high S∞. Finally,20 reported a t1/2 value for Prochlorococcus of 22 min, which is much faster than our values. The reason for this discrepancy is that the former study assumed a fixed concentration of Prochlorococcus at 105 cells ml−1 and unrestricted uptake by diffusion. If we adopt these same assumptions in our calculations, we get the very comparable estimate of t1/2 = 23 min for S∞ = 3 nM, illustrating the significance of our more realistic assessments of cell abundance and saturation of division by diffusive flux.

Ecosystem modeling

Results presented in Fig. 4 are based on the one-dimensional “idealized food-chain model” originally developed by38 and later modified by21. The model includes 25 phytoplankton size-classes with diameters ranging from 0.6 µm to 135 µm, where cells in a given size class are 1.25 times larger than those in the class one size smaller. Each size class is initiated with a representative diatom and non-diatom, which are distinguished by the former being non-motile and vacuolated and the latter being motile and non-vacuolated (these properties impact diffusion as vacuolation increases the cell surface area per unit cytoplasmic volume, while motility distorts the diffusive boundary layer around a cell; see21 for full details). We note here that, in nature, there are many factors at play in the multidimensional competition landscape of the phytoplankton (Fig. 5), but our model assumes all species are limited by a common resource and are competitively distinguished only by factors influencing diffusion (i.e., size, vacuolation, swimming). By doing so, we maximize the potential for resource-based competitive exclusion yet still do not observe it in the model results. If additional factors influencing competition (e.g., diatom susceptibility to Si limitation or different investment options identified in Fig. 5) are included, the potential for stable coexistence only increases.

The model includes 25 zooplankton size classes. Predators of phytoplankton and predators of zooplankton are assumed to consume prey over feeding size ranges (fi and ji in Eq. 1a,b) that are proportional to the geometric mean prey size (ps). This proportionality factor is defined as fi, ji =  ± (0.5 × ps) + ps. For example, a predator with a mean prey size of 80 µm will have a feeding range of 40–120 µm, while a predator with a mean prey size of 2 µm will have a feeding range of 1–3 µm21,38,86. The model is intended to characterize phytoplankton community composition under steady-state nitrogen-limited growth conditions and, thus, temporal environmental variability (which would increase the potential for stable coexistence) is not included. Division rate for each phytoplankton size class and phytoplankton type (µi in Eq. 1a) follows a size-dependent saturating function defined by diffusion rate and maximum potential division rate, as described in detail in21. Predation is dependent on prey abundance and is described by a zooplankton grazing rate (g1) of 3.24 m3 mmol−1 d−1, an ingestion efficiency (g2) of 0.5 (unitless), a non-grazing zooplankton mortality rate (g3) of 0.06 d−1, and a density-dependent zooplankton mortality rate (g4) of 1.6 m3 mmol−1 d−184,87. Model runs correspond to steady-state nitrogen inventories (ΣN) of 4 to 20 µM and S∞ values of 1 nM to 10 µM, with increments in S∞ of 1 nM from 1 to 21 nM, ~ 8 nM from 21 to 500 nM, and ~ 1 µM from 1 to 10 µM. For all model runs, light levels are assumed constant and saturating for growth. Each model run is initiated with \({P}_{i}^{N}\) = 0.18 mmol N m−3 for both the diatom and non-diatom phytoplankton and \({Z}_{i}^{N}\) = 0.04 mmol N m−3 for all size classes and then executed until steady state is reached21. Size diversity for the steady-state populations was assessed as the number of size-classes remaining that contributed at least 0.0001% to total phytoplankton biomass21.

The model employed here is simplistic and does not include the many factors influencing phytoplankton population dynamics and competition (Fig. 5). A benefit of using such a model is that it fosters a clearer interpretation of results. The key difference between our model and that of38 is the description of the ‘non-grazing’ phytoplankton mortality rate (mi). In38, mi = 0.02 d−1 at all times and for all phytoplankton groups. In other words, 2% of the population in each group is simply assumed to ‘die’ each day from non-predatory losses. We are unaware of any empirical observations in the field to justify this approach. Part of the problem is that it is unclear precisely what processes are encompassed in this ‘non-grazing’ mortality. Potential mechanisms for phytoplankton losses include grazing (final term in the right-hand side of Eq. 1a), pathogenic losses (e.g., viruses, parasites), physical transport out of the volume in question, and physiological malfunctions leading to cell death, among other processes. Viral infection is expected to be dependent on host density. In addition, recent work suggests that marine phytoplankton viruses may primarily follow a temperate (i.e., non-lytic) lifestyle and only switch to virulent dynamics during host stress88. Accordingly, phytoplankton losses attributable to viruses cannot be described by a constant mi applied to all size classes. Much less is known about the rate of phytoplankton mortality attributable to other types of pathogens. Phytoplankton losses due to physical processes, such as sinking, are also complex and dependent on factors such as physiological stress (e.g., diatoms of all sizes can remain neutrally buoyant when physiologically healthy and then sink rapidly during stress)63, cell abundances, and turbulent motion. Again, these dynamics will differ between cell sizes and are not expected to be captured in a constant daily mi.

Given the above considerations, it may be concluded that mi primarily represents phytoplankton losses due to physiological processes. Recently, it has been suggested that some bloom-forming diatoms may chemically trigger mass physiologically-based sinking events of their own species following sexual reproduction63, but such phenomena are rare and irrelevant to parameterizations of mi. A more continuous physiological source of cell death may be associated with genetic mutations during replication. Under normal growth conditions, genome mutations occur O(1 per > 1000 cell divisions)89. In diploid cells, the fraction of recessive lethal mutations is thought to be < 10%90. Recognizing that vegetative cells for a majority of phytoplankton species are haploid63, we might constrain this rate to < 30% of mutations being lethal or competitively detrimental. While there are considerable uncertainties in these rates, two conclusions can be drawn: (1) mutation-based cell deaths under normal growing conditions are very rare (likely < 0.03% probability of mortality per division), which is far lower than the 2% per day non-grazing mortality rate assumed in38, and (2) if genetic mutations are the dominate basis for non-grazing mortality then mi should be described as a function of cell division rate rather than a constant rate applied to all phytoplankton size classes and species irrespective of division rate. The model-based analysis of community composition and competition in21 primarily employed a version of the current Eq. (1a) where the \({m}_{i}{P}_{i}^{N}\) term was simply removed, consistent with this term being negligible compared to other loss process [conclusion (1) above]. However,21 also considered a model implementation where mi was described as a constant fraction of size-dependent division rate [conclusion (2) above]. This latter model run yielded the same key outcome as the former: all 25 phytoplankton size classes coexisted across all limiting nutrient conditions. Model results in the current study (Fig. 4) are based on the assumption that mi = 0.01 µi. In other words, 1% of cells in each size class die from non-predator mortality per cell division. Given the above considerations regarding lethal mutation rates (i.e., < 0.03% per division), this 1% loss rate is almost certainly an extreme overestimate for mi, implying that our results are robust to uncertainties in ‘non-predator mortality’ in nature.