View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by White Rose E-theses Online End-to-end models of marine ecosystems: exploring the consequences of climate change and fishing using a minimal framework Celina See Wing Wong Doctor of Philosophy University of York Biology March 2014 Abstract Marine ecosystems are vital to human society: as a source of food, for economic growth and for their potential to mitigate climate change. With marine ecosystems threatened by climate change and overfishing, there is a need for sustainable fisheries management, which has been the basis for an ecosystem-based approach to management. This has led to considerable interest in end-to-end ecosystem models, where the physical effects of the environment and the population dynamics of all marine organisms are coupled together into one framework. In this thesis, I studied an end-to-end model which coupled together a box-component model representing phytoplankton and zooplankton, with a size-structured fish community model. I investigated the potential artefacts in model results, caused by numerical methods or by model architecture. I found that care needs to be taken with the choice of numerical method used to simulate size-structured models, as the choice of numerical resolution can yield nu- merically stable results but can also affect large-scale behaviours of the system, such as the slope and mathematical stability of the size-spectra solutions. With regards to model archi- tecture, coupling together two submodels which differ in structure and resolution can lead to large-scale behaviours of the system which appear plausible and consistent with empirical data, but which impose serious discrepancies in the underlying life-histories of the fish. By distinguishing model artefacts from ecosystem-effects, the interactions and feedbacks between the higher and lower trophic level organisms can be investigated. I studied the potential impact of climate change upon the marine ecosystem, and in particular, upon the seasonal dynamics of phytoplankton. I found that under a warming climate, the spring phy- toplankton bloom occurs earlier and for a longer duration, and the model predicts the loss of the autumn phytoplankton bloom. These changes were not solely due to the direct effect of temperature, but also due to the indirect effect of the interactions of the fish population with zooplankton. The effect of fishing upon the marine ecosystem was also explored with this end-to-end model, with two potential fishing strategies applied to the system. Regardless of the choice of fishing strategy, intensive exploitation of fish stocks can lead to a significant shift in the dynamics of phytoplankton. The phytoplankton’s dynamics change from stable annual patterns to unpredictable periodic behaviours. This thesis has developed an end-to-end model which uses a minimal framework to study the interactions of organisms at different trophic levels, and highlights the importance of these interactions and the associated feedbacks under different scenarios. It combines important theoretical insights into the consequences of model architecture and model-derived artefacts upon ecosystem-scale behaviours, at the same time as highlighting the potential for end-to- end models as a practical and flexible management tool. 2 Contents Abstract 2 List of Figures 5 List of Tables 10 Acknowledgements 11 Author’s Declaration 12 1 General Introduction 13 1.1 The modelling of marine ecosystems . 13 1.2 Current developments in end-to-end modelling . 15 1.3 The challenges involved in developing end-to-end models . 17 1.4 The role of end-to-end models . 19 1.5 The importance of body size in marine ecosystems . 20 1.6 Thesis structure . 21 2 Continuous or discrete: consequences of model choice for size-structured ecosystems 22 2.1 Introduction . 23 2.2 Methods and Results . 25 2.2.1 The McKendrick-von Foerster equation . 25 2.2.2 Reliable integration of discretised size-spectrum dynamics . 28 2.2.3 Effects of discretisation on steady-state properties . 29 2.3 Discussion . 33 2.4 Appendix . 38 2.4.1 Deriving the iteration matrix for the discretised size-spectra equation 38 2.4.2 The return times of the steady-state solutions for continuous and dis- crete models . 42 2.4.3 Size-class intervals and number of size-classes . 42 3 Development of an end-to-end model: exploring the importance of the struc- ture of the zooplankton link 45 3.1 Introduction . 46 3.2 Methods . 48 3.2.1 The SR-Fish Model . 48 3.2.2 The PZ-Fish Model . 50 3.2.3 Functional responses . 52 3.2.4 Numerical methods . 54 3 3.3 Results . 58 3.3.1 Stability due to the choice of functional response . 58 3.3.2 Comparing the steady-state solutions . 61 3.4 Discussion . 65 3.5 Appendix . 69 3.5.1 Phase plane analysis of the choice of functional responses . 69 4 The impact of a warming climate upon the seasonal dynamics of phytoplank- ton, and the consequences to the marine ecosystem 71 4.1 Introduction . 72 4.2 Methods . 74 4.2.1 A PZ-Fish model . 74 4.2.2 The phytoplankton and zooplankton dynamics . 74 4.2.3 The size-structured fish community dynamics . 77 4.2.4 Seasonal phytoplankton blooms . 81 4.3 Results . 84 4.3.1 The effect of warming on the timing and duration of the phytoplank- ton bloom . 84 4.3.2 The phytoplankton and zooplankton dynamics . 86 4.4 Discussion . 90 5 The consequences of size-selective fishing and balanced harvesting to the sea- sonal dynamics of phytoplankton 94 5.1 Introduction . 95 5.2 Methods . 96 5.2.1 Fishing strategy . 98 5.3 Results . 101 5.3.1 Euclidean distance . 101 5.3.2 Period of the phytoplankton dynamics . 105 5.3.3 Yield . 109 5.4 Discussion . 112 6 General Discussion 116 6.1 Summary and Synthesis . 116 6.1.1 The discretisation of size-structured models . 117 6.1.2 Model architecture and understanding its impact upon the dynamics of end-to-end models . 118 6.1.3 The importance of the zooplankton dynamics . 120 6.1.4 Climate change and the consequences to marine ecosystems . 121 6.1.5 The impact of fishing on marine ecosystems . 122 6.2 Future perspectives and priorities . 124 Bibliography 127 4 List of Figures 2.1 The numerical stability of the finite-difference approximation is dependent on the step-sizes, Dx and Dt. The size-spectrum solution and its stability con- dition are plotted for different time steps, time = 0.04year, 0.08year, 0.12year and 0.16year. (a) and (c) show the size-spectrum solution over time while (b) and (d) show the eigenvalues of the iteration matrix at different time steps. If each eigenvalue is between the values of -1 and 1, then the finite- differencing method is numerically stable. Otherwise, the finite-differencing method is numerically unstable. (a) and (b) use a small time step (Dt = 0:001) and shows a numerically stable solution. (c) and (d) use a larger time step (Dt = 0:004) and shows a numerically unstable solution. 30 2.2 The gradient of the size-spectrum solution increases as Dx increases from a fine discretisation to a coarse discretisation. (a) The stable size-spectrum solution for varying values of Dx (b) The gradient of the size-spectrum for different values of Dx ............................. 32 2.3 The return time to equilibrium decreases as Dx increases. The shaded grey region shows that if Dx crosses a threshold on the fine scale, the steady-state solution crosses from stable to unstable. 33 2.4 As the log(mass) interval, Dx, increases, the return time to equilibrium after perturbation decreases. Defining return time as − 1 leads to a qualitative lmax similar result to perturbing the system and waiting for the state to return to equilibrium. (Black, filled circle marker, •) return time := − 1 (Blue, cir- lmax cle marker, ◦) the gradient of the phytoplankton size-spectrum was decreased to -1.5 (Green, cross marker, ×) the gradient of the phytoplankton spectrum was increased to -0.5 (Red, star marker, ∗) the abundance of the newborn size-class, u1, was decreased by a factor of 0.5 (Pink, triangle marker,4) the abundance of the newborn size-class, u1, was increased by a factor of 1.5 . 43 2.5 The return time to equilibrium decreases as Dx increases. The shaded grey region shows that if Dx crosses a threshold on the fine scale, the steady-state solution crosses from stable to unstable. 44 3.1 The feeding kernel functions representing the fish community feeding on phytoplankton (fP(x), the solid green line) and zooplankton (fZ(x), the solid −7 −5 red line) where wP = 9:12 × 10 g and wZ = 4:98 × 10 g. 51 5 3.2 The stability of the (P∗;Z∗) steady-state solutions for the three functional responses used to represent the zooplankton’s grazing on the phytoplankton. The marker represents the predation pressures of a size-structured fish com- munity upon the phytoplankton and zooplankton populations (determined using the steady-state solution of the SR-Fish model and calculating Eq.(3.6) at this steady-state). The functional responses used are (a) Holling Type I (b) Holling Type II and (c) Holling Type III. 60 3.3 An illustration of the dynamic behaviours of the (P∗;Z∗) steady-state solu- tion, which are either (a) unstable, where the phytoplankton and zooplankton populations oscillate over time or (b) stable. In this example, a Holling Type III functional response is assumed, but similar behaviour occurs under a Type II response.