Towards a resolution of ‘the paradox of the plankton’: a brief overview of the proposed mechanisms

In plankton ecology, it is a fundamental question as to how a large number of competing phytoplankton species coexist in marine ecosystems under a seemingly-limited variety of resources. This ever-green question was first proposed by Hutchinson [Hutchinson, G.E., 1961. The paradox of the plankton. Am. Nat. 95, 137–145] as ‘the paradox of the plankton’. Starting from Hutchinson [Hutchinson, G.E., 1961. The paradox of the plankton. Am. Nat. 95, 137–145], over more than four decades several investigators have put forward varieties of mechanisms for the extreme diversity of phytoplankton species. In this article, within the boundary of our knowledge, we review the literature of the proposed solutions and give a brief overview of the mechanisms proposed so far. The proposed mechanisms that we discuss mainly include spatial and temporal heterogeneity in physical and biological environment, externally imposed or self-generated spatial segregation, horizontal mesoscale turbulence of ocean characterized by coherent vortices, oscillation and chaos generated by several internal and external causes, stable coexistence and compensatory dynamics under fluctuating temperature in resource competition, and finally the role of toxin-producing phytoplankton in maintaining the coexistence and biodiversity of the overall plankton population that we have proposed recently. We find that, although the different mechanisms proposed so far is potentially applicable to specific ecosystems, a universally accepted theory for explaining plankton diversity in natural waters is still an unachieved goal.

Competing effects of toxin-producing phytoplankton on overall plankton populations in the Bay of Bengal

The coexistence of a large number of phytoplankton species on a seemingly limited variety of resources is a classical problem in ecology, known as ‘the paradox of the plankton’. Strong fluctuations in species abundance due to the external factors or competitive interactions leading to oscillations, chaos and short-term equilibria have been cited so far to explain multi-species coexistence and biodiversity of phytoplankton. However, none of the explanations has been universally accepted. The qualitative view and statistical analysis of our field data establish two distinct roles of toxin-producing phytoplankton (TPP): toxin allelopathy weakens the interspecific competition among phytoplankton groups and the inhibition due to ingestion of toxic substances reduces the abundance of the grazer zooplankton. Structuring the overall plankton population as a combination of nontoxic phytoplankton (NTP), toxic phytoplankton, and zooplankton, here we offer a novel solution to the plankton paradox governed by the activity of TPP. We demonstrate our findings through qualitative analysis of our sample data followed by analysis of a mathematical model.

Do phytoplankton communities evolve through a self-regulatory abundance-diversity relationship?

A small group of phytoplankton species that produce toxic or allelopathic chemicals has a significant effect on plankton dynamics in marine ecosystems. The species of non-toxic phytoplankton, which are large in number, are affected by the toxin-allelopathy of those species. By analysis of the abundance data of marine phytoplankton collected from the North-West coast of the Bay of Bengal, an empirical relationship between the abundance of the potential toxin-producing species and the species diversity of the non-toxic phytoplankton is formulated. A change-point analysis demonstrates that the diversity of non-toxic phytoplankton increases with the increase of toxic species up to a certain level. However, for a massive increase of the toxin-producing species the diversity of phytoplankton at species level reduces gradually. Following the results, a deterministic relationship between the abundance of toxic phytoplankton and the diversity of non-toxic phytoplankton is developed. The abundance–diversity relationship develops a unimodal pathway through which the abundance of toxic species regulates the diversity of phytoplankton. These results contribute to the current understanding of the coexistence and biodiversity of phytoplankton, the top-down vs. bottom-up debate, and to that of abundance–diversity relationship in marine ecosystems.

Spatial interaction among nontoxic phytoplankton, toxic phytoplankton and zooplankton: emergence in space and time

In homogeneous environments, by overturning the possibility of competitive exclusion among phytoplankton species, and by regulating the dynamics of overall plankton population, toxin-producing phytoplankton (TPP) potentially help in maintaining plankton diversity—a result shown recently. Here, I explore the competitive effects of TPP on phytoplankton and zooplankton species undergoing spatial movements in the subsurface water. The spatial interactions among the species are represented in the form of reaction-diffusion equations. Suitable parametric conditions under which Turing patterns may or may not evolve are investigated. Spatiotemporal distributions of species biomass are simulated using the diffusivity assumptions realistic for natural planktonic systems. The study demonstrates that spatial movements of planktonic systems in the presence of TPP generate and maintain inhomogeneous biomass distribution of competing phytoplankton, as well as grazer zooplankton, thereby ensuring the persistence of multiple species in space and time. The overall results may potentially explain the sustainability of biodiversity and the spatiotemporal emergence of phytoplankton and zooplankton species under the influence of TPP combined with their physical movement in the subsurface water.

Nutrient-limited toxin production and the dynamics of two phytoplankton in culture media: a mathematical model

In this paper we have proposed and analyzed a simple mathematical model consisting of four variables, viz., nutrient concentration, toxin producing phytoplankton (TPP), non-toxic phytoplankton (NTP), and toxin concentration. Limitation in the concentration of the extracellular nutrient has been incorporated as an environmental stress condition for the plankton population, and the liberation of toxic chemicals has been described by a monotonic function of extracellular nutrient. The model is analyzed and simulated to reproduce the experimental findings of Graneli and Johansson [Graneli, E., Johansson, N., 2003. Increase in the production of allelopathic Prymnesium parvum cells grown under N- or P-deficient conditions. Harmful Algae 2, 135–145]. The robustness of the numerical experiments are tested by a formal parameter sensitivity analysis. As the first theoretical model consistent with the experiment of Graneli and Johansson (2003), our results demonstrate that, when nutrient-deficient conditions are favorable for the TPP population to release toxic chemicals, the TPP species control the bloom of other phytoplankton species which are non-toxic. Consistent with the observations made by Graneli and Johansson (2003), our model overcomes the limitation of not incorporating the effect of nutrient-limited toxic production in several other models developed on plankton dynamics.

Role of marine biology in glacial-interglacial CO2 cycles

It has been hypothesized that changes in the marine biological pump caused a major portion of the glacial reduction of atmospheric carbon dioxide by 80 to 100 parts per million through increased iron fertilization of marine plankton, increased ocean nutrient content or utilization, or shifts in dominant plankton types. We analyze sedimentary records of marine productivity at the peak and the middle of the last glacial cycle and show that neither changes in nutrient utilization in the Southern Ocean nor shifts in plankton dominance explain the CO2 drawdown. Iron fertilization and associated mechanisms can be responsible for no more than half the observed drawdown.

Phytoplankton–zooplankton dynamics in the ‘presence’ or ‘absence’ of toxic phytoplankton

The inhibitory effects of toxin-producing phytoplankton (TPP) on zooplankton modulate the dynamics of marine plankton. In this article, we employ simple mathematical models to compare theoretically the dynamics of phytoplankton–zooplankton interaction in situations where the TPP are present with those where TPP are absent. We consider two sets of three-component interaction models: one that does not include the effect of TPP and the other that does. The negative effects of TPP on zooplankton is described by a non-linear interaction term. Extensive theoretical analyses of the models have been performed to understand the qualitative behaviour of the model systems around every possible equilibria. The results of local-stability analysis and numerical simulations demonstrate that the two model-systems differ qualitatively with regard to oscillations and stability. The model system that does not include TPP is asymptotically stable around the coexisting equilibria, whereas, the system that includes TPP oscillates for a range of parametric values associated with toxin-inhibition rate and competition coefficients. Our analysis suggests that the qualitative dynamics of the plankton–zooplankton interactions are very likely to alter due to the presence of TPP species, and therefore the effects of TPP should be considered carefully while modelling plankton dynamics.

Toxin-allelopathy among phytoplankton species prevents competitive exclusion

Toxic or allelopathic compounds liberated by toxin-producing phytoplankton (TPP) acts as a strong mediator in plankton dynamics. On an analysis of a set of phytoplankton biomass data that have been collected by our group in the northwest part of the Bay of Bengal, and by analysis of a three-component mathematical model under a constant as well as a stochastic environment, we explore the role of toxin-allelopathy in determining the dynamic behavior of the competing phytoplankton species. The overall results, based on analytical and numerical wings, demonstrate that toxin-allelopathy due to the TPP promotes a stable co-existence of those competitive phytoplankton that would otherwise exhibit competitive exclusion of the weak species. Our study suggests that TPP might be a potential candidate for maintaining the co-existence and diversity of competing phytoplankton species.

Interaction among non-toxic phytoplankton, toxic phytoplankton and zooplankton: inferences from field observations

We explore the mutual dependencies and interactions among different groups of species of the plankton population, based on an analysis of the long-term field observations carried out by our group in the North–West coast of the Bay of Bengal. The plankton community is structured into three groups of species, namely, non-toxic phytoplankton (NTP), toxic phytoplankton (TPP) and zooplankton. To find the pair-wise dependencies among the three groups of plankton, Pearson and partial correlation coefficients are calculated. To explore the simultaneous interaction among all the three groups, a time series analysis is performed. Following an Expectation Maximization (E-M) algorithm, those data points which are missing due to irregularities in sampling are estimated, and with the completed data set a Vector Auto-Regressive (VAR) model is analyzed. The overall analysis demonstrates that toxin-producing phytoplankton play two distinct roles: the inhibition on consumption of toxic substances reduces the abundance of zooplankton, and the toxic materials released by TPP significantly compensate for the competitive disadvantages among phytoplankton species. Our study suggests that the presence of TPP might be a possible cause for the generation of a complex interaction among the large number of phytoplankton and zooplankton species that might be responsible for the prolonged coexistence of the plankton species in a fluctuating biomass.