Zooplankton Foraging induces Chaos in Dynamic Green Ocean Models
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The exchange of important greenhouse gases between the ocean and atmosphere is influenced by the dynamics of near-surface plankton ecosystems. Marine plankton ecosystems are modified by climate change creating a feedback mechanism that could have significant implications for predicting future climates, for example, the collapse or extinction of a plankton population may push the climate system across a tipping point. Dynamic green ocean models (DGOMs) are currently being developed for inclusion in climate models to predict the future state of the climate. These models are often complicated, commonly with 5-10 competing phytoplankton and several omnivorous zooplankton (Le Quéré et al., 2005). Complicated dynamics including chaos are readily found even in unforced forms of the relatively simple nonlinear plankton ecosystem ordinary differential equation models that underpin DGOMs (Cropp et al., 2014). The appropriate complexity of the DGOMs is an ongoing issue, with models tending to become more complex, and perhaps an increasing propensity for chaos (Fussmann and Heber, 2002). The complexity of DGOMs means that most attempts to confer them with “desirable” properties proceed by numerical experimentation and/or model inter-comparison projects such as the MARine Ecosystem Model Inter-comparison Project (MAREMIP, Sailley et al., 2013). Some recent investigations into DGOMs have considered the role of zooplankton predation functional forms in determining model properties (for example, Anderson et al., 2010; Visser and Fiksen, 2013; Vallina et al., 2014). The functional forms considered in these experiments are generally based on the classic Holling Type II or III forms (Holling, 1959) with modifications to represent zooplankton strategies such as the specialised or generalised feeding strategies described by Koen-Alonso (2007) and prey switching (Gentleman et al., 2003). However, little consensus has been reached on the most useful form of grazing function for plankton systems that underpin both green ocean models and fisheries ecologies (Le Quéré et al., 2005). We consider a relatively simple (three-population) DGOM of two phytoplankton and a zooplankton where the interacting plankton populations compete for a single limiting nutrient. We find chaotic dynamics are possible in this low trophic order ecological model with a specialist foraging strategy as we vary the zooplankton mortality. This suggests that chaotic dynamics might be ubiquitous in the more complex models, but this is rarely observed in DGOM simulations. The physical equations of DGOMs are well understood and are constrained by conservation principles, but the ecological equations are not as well understood, and are often constructed without explicit consideration of conserved quantities as closed model domains are considered unrealistic by some ecologists (Loreau, 2010, p 16). The work we present here utilizes a theoretical framework constructed on the fundamental principles of conservation of mass, finite resources and explicit resource limitations to growth. Our results, when considered in the context of the paucity of the empirical and theoretical bases upon which DGOMs are constructed, raises the interesting question of whether DGOMs would represent reality better if they include or exclude chaotic dynamics. Our analysis of this simple, but representative, plankton system suggests that apparently innocuous choices of grazing terms, varying from indiscriminate to discriminate types which do not appear significantly different, and which may be equivalent up to observational/experimental accuracy, can predetermine the emergent properties of the systems. We observe that the indiscriminate grazer appears to have more reliable and steadier shares of the ecosystem biomass in contrast to the discriminate grazer’s very strongly fluctuating biomass share. Indiscriminate grazing functions for zooplankton are commonly used in the current generation of GCMs, where the emphasis is to maintain biodiversity and to represent the dynamics of large groups of plankton functional types (PFTs). However, future generations of GCMs may wish to resolve more detailed dynamics, such as bloom succession, and we suggest that for these models introducing discriminate grazing functions for the marginal populations may be more appropriate.
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Dynamical Systems in Applications