Regime shifts in bistable biological systems

Abstract

The key objective of this thesis is to study regime shift in various bistable biological systems. Many natural systems can undergo sudden, large and often irreversible changes under the influence of small stochastic perturbations. Such qualitative sudden changes in the structure and function of a system are known as regime shift. Well known examples of regime shifts in complex systems include: collapse of ecosystems (ecology), crash of markets in global finance (finance), systemic failures such as epileptic seizures (biology) and Arctic sea ice melting (climate). Each of these shifts has the potential to invoke serious and harmful consequences for environment as well as human well-being. Therefore, understanding the mechanisms of regime shifts and predicting them using early warning signals (EWS) are important issues due to the potential application in management and prevention of catastrophes in complex systems. There are mainly two types of regime shifts that can occur in systems with alternative stable states. One is critical transition which is associated with the bifurcation points (so called tipping points) and another is noise induced transition (also known as stochastic switching). Purely noise driven regime shift and its prediction using EWS are very less studied in comparison with the studies on regime shifts associated with tipping points. In this thesis, we explore the effect of noise on regime shifts and robustness of EWS, for both cases, the critical transition and noise induced transition. An important example of regime shift in molecular biology is genetic regulatory system which includes sudden transition in protein production level in individual cells resulting disease onset. Here, we study regime shift in a bistable gene regulatory positive feedback loop model. We investigate the effect of additive and multiplicative white/colored noise intensities, cross correlation intensity between two white/colored noises, and correlation time of colored noise on the model by calculating the probability density and potential function. We find that both the noises (white/colored) have the potential to invoke regime shifts in gene expression. We also identify that using EWS indicators, prediction of an impending bifurcation induced regime shift is relatively easier than that of a noise induced regime shift in the considered system. Moreover, the success of EWS indicators also strongly depends upon the nature of noise. We also study a bistable insect outbreak model to reveal the role of stochasticity in generating outbreak dynamics. Our calculations reveal that stochasticity with higher intensity generally weakens bistability, causing the trajectory to spend more time at a single state rather than jumping between alternative stable states. Which state the population tends toward depends on the noise color. High-intensity white noise causes the insect population to spend more time at low density, potentially reducing the severity or frequency of outbreaks. However, red noise can make the population spend more time near the high density state, intensifying outbreaks. We find that under neither type of noise do EWS reliably predict impending outbreaks nor population crashes. xiii Development of EWS has given ecologists hope of predicting rapid regime shifts before they occur. Accurate predictions, however, rely on the signals being appropriate to the particular system under consideration. Here, we study a range of models with different types of dynamical transitions and several perturbation schemes, and test the ability of EWS to warn of an upcoming transition. We also test the sensitivity of our results to the amount of available pre-transition data and various decisions that must be made in the analysis (i.e., the rolling window size and smoothing bandwidth used to compute the EWS). We conclude that the EWS developed for saddle-node bifurcations perform well in a range of noise environments, but different methods should be used to predict other types of regime shifts. Finally, we show the use of multifractal properties and recurrence parameters of time series in order to anticipate a regime shift beforehand. We consider different sets of simulated ecological time series data pertaining to dynamically two different cases of regime shifts: bifurcation induced and purely noise induced regime shifts. We observe concurrent rise in the chosen multifractal properties and recurrence parameters upon approaching a regime shift, and we can very well then use these parameters as EWS for predicting catastrophic regime shifts. Keywords:- regime shifts, tipping points, critical slowing down, stochastic switching, early warning signals, alternative stable states, white noise, colored noise.