Mathematical and Computational Modelling Investigations of the Role of Trait Variation in Savanna-Woodland Bistable systems

Abstract

Over the last decade, several studies have shown the importance of individual variation in natural populations. Theoretical ecological studies are beginning to incorporate trait variations in models, but they continue to be largely ignored in the context of ecosystems that exhibit alternative stable states. We study the role of trait variation in the context of a bistable ecological system, specifically a savanna-woodland system. In the first chapter, we begin with a mean-field model of bistable savanna-woodland system and then introduce trait variation in functional and demographic traits of savanna trees and saplings in the model. Our study reveals that higher trait variation reduces the extent of bistability in the system, such that the woodland state is favored; i.e. woodland occurs over a wider range of driver values in comparison to the grassland state. We also find that the shift from one state to another can become less or more drastic, depending on the trait which exhibits variation. Interestingly, we find that even if the overall tree and grass cover remain insensitive to different initial conditions, the steady-state population trait distribution can be sensitive to these conditions. Studies have shown that spatial interactions can alter system dynamics, and therefore have important consequences for ecosystem resilience. Savannas are important ecosystems that are frequently disturbed by fires and experience strong seasonality. These spatiotemporal processes are important to include in theoretical studies of these complex systems to analyse how ecosystem-level properties change with changes in the driver (rainfall in our case). In the second chapter, we formulate a spatially explicit model of the savanna-woodland bistable systems to include these realistic features of fire and seasonality, along with two different demographic stages of savanna species. When comparing the spatial model to the mean-field approximation of the spatial model, we find that grassland state exists for a larger range of driver values, as short-range dispersal limits the spread of savanna species in the system. We find that fire leads to bistability in the system with grassland and woodlands as alternative stable states, while savanna state occurs as a transient state. We also find that irrespective of the initial flammable cover, the proportion burnt area depends on the flammable cover before the dry season, which depends on the wet season processes. We also observe periodicity in spatial patterns which might be important for understanding the resilience of these systems. In the third chapter, we introduce trait variation in the spatial model to understand its role. We find that among all savanna species types, the fittest individual survives, while other types get eliminated from the population. The dynamics followed by the system with variation is same as the dynamics of a system with only the fittest individual. These insights into the dynamics of these systems can help us better understand such complex systems and can be important for their management and restoration strategies.