Some nonlinear problems in plankton ecology

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Biology, 1995.Includes bibliographical references.by Maria Mercedes Pascual-Dunlap.Ph.D

Detecting and distinguishing transitions in ecological systems: model and data-driven approaches

There exists a plethora of systems that have the capacity to undergo sudden transitions that result in a significantly different state or dynamic. Consider the collapse of fisheries, outbreak of disease or transition to a 'Hothouse Earth' to name a few. The common factor among these transitions is mathematical - they are the result of crossing a bifurcation point. This thesis is concerned with the detection and description of these bifurcations from time series data, and the mechanisms that lead to these transitions. We begin in the domain of climate change, where models of the climate system are extremely sophisticated, but those that incorporate social dynamics and its two-way coupling with climate dynamics are lacking. In developing a simple socio-climate model, we show how mechanisms such as social learning, social norms, and perceived mitigation costs play a major role in climate change trajectories. These social effects can strongly determine the predicted peak global temperature anomaly, how quickly human populations respond to a changing climate, and how we can chart optimal pathways to climate change mitigation. However, we also show that if the climate model is subject to a tipping point, the climate can transition to a new state before mitigating behaviour becomes sufficiently widespread to prevent the transition. This motivates a need for early warning signals (EWS) of tipping points. Hence, in the next chapter we focus on the development of EWS in time series data that can be used to detect an upcoming bifurcation. This thesis develops two 'spectral EWS', which are derived from the power spectrum. We show that the peak in the power spectrum provides a more sensitive and conservative EWS when compared to conventional metrics, and the shape of the power spectrum, quantified using AIC weights, provides clues as to the type of approaching bifurcation. We validate these spectral EWS with empirical data from a predator-prey system. Finally we focus on EWS for population extinction, where we study the efficacy of EWS in seasonal environments. We find that conventional EWS prevail under seasonal environments, however asymmetries exist in higher-order metrics such as skewness and kurtosis that could be used to distinguish the driver of extinction. To conclude, nonlinear behaviour arising from social learning and social norms yield bifurcations that have profound impacts on future trajectories of climate change, and bifurcations can be anticipated across a wide range of systems using spectral EWS, that also provide information on the type of bifurcation. The further development of generic and system-specific EWS will play an important role in preserving healthy ecosystem functioning in the Anthropocene

Tipping points in natural systems. An inventory of types, early warnings, and consequences

Hoe creatief om te gaan met de toenemende druk door de menselijke populatie en de mogelijke belangenverstrengelingen van verschillende belangenhouders die dat met zich meebrengt, bv. door systemen meerdere functies tegelijk te laten vervullen. Het KB IV-programma “groenblauwe ruimte” beoogt te onderzoeken hoe, door goed gebruik te maken van de half-natuurlijke terrestrische (‘groene’) en aquatische (‘blauwe’) ruimte, hier oplossingen kunnen worden geboden. Onderzoek heeft uitgewezen dat er in meerdere natuurlijke en menselijke systemen mogelijke ‘kantelpunten’ (Eng. ‘tipping points’) bestaan: Kleine veranderingen in factoren die van belang voor het systeem zijn, kunnen onverwacht leiden tot plotselinge grote veranderingen

Dynamical Models of Biology and Medicine

Mathematical and computational modeling approaches in biological and medical research are experiencing rapid growth globally. This Special Issue Book intends to scratch the surface of this exciting phenomenon. The subject areas covered involve general mathematical methods and their applications in biology and medicine, with an emphasis on work related to mathematical and computational modeling of the complex dynamics observed in biological and medical research. Fourteen rigorously reviewed papers were included in this Special Issue. These papers cover several timely topics relating to classical population biology, fundamental biology, and modern medicine. While the authors of these papers dealt with very different modeling questions, they were all motivated by specific applications in biology and medicine and employed innovative mathematical and computational methods to study the complex dynamics of their models. We hope that these papers detail case studies that will inspire many additional mathematical modeling efforts in biology and medicin

Principles for Designing Robust and Stable Synthetic Microbial Consortia

Engineering stable microbial consortia with robust functions are useful in many areas, including bioproduction and human health. Robust and stable properties depend on proper control of dynamics ranging from single cell-level to population-environment interactions. In this thesis, I discuss principles of building microbial consortia with synthetic circuits in two design scenarios. First, for one microbial population, strong disturbances in environments often severely perturb cell states and lead to heterogeneous responses. Single cell-level design of control circuits may fail to induce a uniform response as needed. I demonstrate that cell-cell signaling systems can facilitate coordination among cells and achieve robust population-level behaviors. Moreover, I show that heterogeneity can be harnessed for robust adaptation at population-level via a bistable state switch. Second, multi-pecies consortia are intrinsically unstable due to competitive exclusion. Previous theoretical investigations based on models of pairwise interactions mainly explored what interaction network topology ensures stable coexistence. Yet neglecting detailed interaction mechanisms and spatial context results in contradictory predictions. Focusing on chemical-mediated interaction, I show that detailed mechanisms of chemical consumption/accumulation and chemical-induced growth/death, interaction network topology and spatial structures of environments all are critical factors to maintain stable coexistence. With a two population-system, I demonstrate that the same interaction network topology can exhibit qualitatively different or even opposite behaviors due to interaction mechanisms and spatial conditions.</p

The paradox of the plankton: Investigating the effect of inter-species competition of phytoplankton and its sensitivity to nutrient supply and external forcing

Hutchinson (1961) first posed the paradox of the plankton: Why do so many phytoplankton species coexist while competing for a limited number of resources? High biodiversity has been explained in terms of the phytoplankton system not reaching an equilibrium state. Spatial and temporal variability can be achieved through externally imposed physical variability or internally-induced behaviour including periodic oscillations or irregular, chaotic behaviour. The research presented in this thesis investigates whether the non-equilibrium, chaotic response of the phytoplankton community is a likely outcome within the aquatic ecosystems. The thesis addresses the extent that chaotic behaviour remains a robust response with externally-imposed environmental variability. The sparsity of long-term time-series data and infrequent sampling inhibits the ability to verify whether marine ecosystems exhibit complex behaviour. The analysis of the time-series records of phytoplankton taxa in the English Channel suggests that chaos might occur within diatom and dinoflagellates abundance time series. However, simulations using a chemostat model for phytoplankton and nutrients suggests that time series sampled every 1-2 days for more than 5 years are required to confidently distinguish deterministic chaos from noise. The model simulations suggest that the community response depends on the phytoplankton requirement for nutrients and attributed physiological traits allowing each species to be a stronger competitor for a different resource. A wider inter-species specialization increases the likelihood of oscillatory and chaotic responses, with competitive exclusion decreasing from 50% to 20% of the cases. Higher departures from the Redfield ratio in the elemental composition of species favour complex community behaviour and act to increase biodiversity. Whether chaotic response can be sustained is sensitive to the strength of the diffusive feedback between nutrient supply and ambient nutrient concentration that acts to sustain steady-state nutrient concentrations. Including seasonal and stochastic variability in the nutrient supply reveals that the frequency of chaotic dynamics increases by 20% and 45% respectively. In addition, seasonal forcing leads to temporal variability in the strength of the chaotic response, with chaos becoming more prevalent in the summer. In contrast to a well-mixed, homogeneous environment, physical dispersal can stir different phytoplankton communities together, which might act to inhibit chaos, but at the same time enhance phytoplankton diversity. Idealised model simulations are conducted to mimic the small and large scale transport processes by including 2 or 3 well-mixed boxes. Locally generated chaotic response is sustained if: 1) there is a low rate of exchange with a strong nutrient competitor that maintains the contrasts in the community structure; 2) a strong competitor is inhibited by a high mortality rate. In addition, if the local community is outcompeted, chaos can be exported through the advection of stronger competitors that exhibit chaotic fluctuations. This study highlights the importance of understanding the interactions between ambient nutrients and phytoplankton community. The variability in the nutrient supply and connectivity between ecosystems shape the community response to inter-species competition. Complex behaviour arising from inter-species competition is suggested to have a significant contribution in driving biodiversity. Future research on assessing the extent of chaos requires extending and analysing the available time-series data obtained from stable or isolated marine provinces

Cellular decision-making models in yeast

Decision-making is ubiquitous throughout all levels of biological complexity, from social insect colonies to individual cells and multi-cellular organisms. The study of decision-making by different fields has suggested that there are shared underlying principles and decision-making mechanisms that can be used to describe the behaviour of any given biological system, regardless of its specific nature. The relatively recent application of decision theory to the study of cellular systems has provided great insights into the nature of different cellular processes. In this thesis, I aim to explore and describe the sugar consumption dynamics observed in a yeast culture growing in a binary-sugar mixture. In order to study this cellular process, I develop several mathematical models to describe the sugar consumption behaviour of yeast. The models are influenced by the work of Pais et al. (2013) on house-hunting honeybee swarms. I use experimental data gathered from yeast cultures grown in maltose, galactose, and a mixture of both sugars to validate and parameterise the models. I show that with a single parameterisation, the models are capable of replicating the metabolic and biomass experimental data of yeast growing in single sugar, as well as binary-sugar mixtures. Additionally, the models are studied by means of bifurcation and dynamical systems analysis. As pointed out by Aidelberg et al. (2014), microorganisms growing in a media with two different sugars present one of three different consumption strategies: 1) simultaneous consumption of both sugars present in the media, 2) exclusive consumption of one of the two sugars available, and 3) no consumption. I show that the models developed present features such as decision-deadlock, deadlock-breaking bifurcations, and deadlock-restoring bifurcations, which give rise to these consumption strategies. We also show that the transition between these regimes depends on the value of key parameters of our models

Mathematical analysis, modelling and simulation of microbial population dynamics

The physiology of unicellular organisms results from a central metabolism which input-output balance accounts for both the cells’ state and their culture medium’s abundance. When bacteria are cultivated in a locally fed fermenter and transported in a turbulent flow, they have to deal with concentration gradients throughout their trajectory in the reactor. Simulating this physics in a multiscale modelling approach requires taking into account not only the well-known laws of hydrodynamics, but also the cells’ biochemistry which is still ill-understood to date. Moreover, the prohibitive cost of the numerics forces to reduce the models to constrain the duration of the experiments to a few weeks. In this context, special consideration has been given to the biological phase. The bacteria population dynamics is given by an integro-differential transport-rupture equation in the space of the particles’ inner coordinates. Picking the most appropriate variables is of paramount importance to best report the time evolution of the cells’ state throughout their history in the fermenter, the latter being comparable to a markovian process. The microorganisms’ length testifies to their morphology and their progress in the cell cycle, whereas the uptake rate of the surrounding resources leads to an evaluation of the material transfer between the liquid and biotic phases. The result is the estimation of the source term in the organisms’ central metabolism which outputs are the apparent rate of anabolism and, if over-uptake, activation of peripheral reactions to combust the surplus in organic compounds. Beyond their own history, the individuals’ metabolic yields can be impacted by the substrate availability at their neighbourhood, which stems from the feeding and the level of mixing in the reactor. The state variables have a compact support, what raises the question of the mathematical problem’s wellposedness, similarly as solving a PDE over a bounded set is traditionally more difficult than over $\mathbb{R}^{n}$, $n \in \mathbb{N}$. It is shown that the Malthus eigenfunction associated with the transport-rupture equation is $\mathcal{C}^{1}$ as soon as fragmentation trumps cell growth near the right-hand edge of the size-distribution’s support. All in all, the solution is continuous at each time in the state space. These results allow the implementation of numerical codes to solve (in this work, by Monte-Carlo, Finite Volume, or Quadrature of MOMents methods) the well-posed problem, the algorithms being exploited to simulate five biochemical engineering experiments which conclusions are detailed in the literature