(Note to prospective students: As our students are from a diverse background of expertise, we will tailor and fine tune your project along the following these research focuses. Our postgraduates are from different departments: mathematics [pure/applied/computer science/epidemiology], botany and zoology, conservation ecology and entomology, environmental sciences [geography] and operations research [logistics]. Recommended reads are links to published articles. You could also check the short titles of current and previous postgraduate projects at the Team page)
1. SPATIAL BIODIVERSITY
Species distributions are neither uniform across space nor independent from each other, reflecting the interplay between habitat heterogeneity and the underlying nonlinear biotic regulation. Due to the non-random nature, most, if not all, ecological patterns change with spatial scales and exhibit distinct scaling properties. The aim here is to depict how species occupancy and its aggregation level, as well as the partitions of biodiversity (e.g. alpha, beta and zeta components) change when scaling up and down, and therefore provide a universal basis for ensuring cross-scale consistency. Models of spatial biodiversity are therefore often developed to ensure the consistency of measurements across different scales. To ensure the consistency, patterns across scales are normally bridged using combinatorics and probability theories. Specifically, we investigate how aggregated structures of populations and biodiversity change with spatial scales, which biological patterns resonate with underlying processes structured at the same spatial scales, and why.
2. SPATIAL DYNAMICS
Self-organised patterns; invasion dynamics;..Humans have moved organisms around the world for centuries but it is only relatively recently that invasion ecology has grown into a mainstream research field. This book examines both the spread and impact dynamics of invasive species, placing the science of invasion biology on a new, more rigorous, theoretical footing, and proposing a concept of adaptive networks as the foundation for future research. Biological invasions are considered not as simple actions of invaders and reactions of invaded ecosystems, but as co-evolving complex adaptive systems with emergent features of network complexity and invasibility. Invasion Dynamics focuses on the ecology of invasive species and their impacts in recipient social-ecological systems. It discusses not only key advances and challenges within the traditional domain of invasion ecology, but introduces approaches, concepts, and insights from many other disciplines such as complexity science, systems science, and ecology more broadly. It will be of great value to invasion biologists analyzing spread and/or impact dynamics as well as other ecologists interested in spread processes or habitat management.
3. ECOLOGICAL NETWORKS & COMMUNITIES
In particular, this section examines self-organized pattern emergence in bottom-up models of ecological networks. The function and architecture of ecological networks emerge from the life-history, physiological constraints and optimization of each population in the network. Specifically, the scaling pattern of hierarchy depicts how the structure and function of asymmetrical ecological systems emerge and change with the system complexity. Using ecological networks as a proxy, this section aims to investigate how cascade interactions affects the robustness and resilience of networks, how network architectures, especially nestedness and compartmentalization, emerge and function, and the role of network complexity on the stability of ecological networks. Forty years ago, Robert May published his iconic book, Stability and Complexity in Model Ecosystems. Using a mathematical model of differential equations, May derived an opposite conclusion to the common belief in ecology: complexity leads to instability. The endeavour to resolve May’s complexity and stability dilemma by scientists using networks as a proxy is classical ongoing example of how characteristics of the parts affect the function of the whole in ecology. Mutualistic interactions are crucial processes to sustain ecosystem function and services, foster biodiversity and affect community stability. Mutualistic networks often exhibit a distinctive nested structure, with the observed level of nestedness significantly higher than that of random network generated from a variety of null models, yet still much lower than that of perfectly nested networks. It is evident that species often switch their interactive partners in real-world mutualistic networks such as pollination and seed-dispersal networks, and this adaptive behaviour can be important to the structure and stability of networks. Antagonistic interactions, such as herbivory, parasitism and predation, are important to the provision of ecosystem function and service. It represents the process of resource exploitation in ecological networks and can divide species into clusters where consumers within a cluster are likely to share the same function and exploit similar resources. Such a clustering architecture (i.e. compartmentalization) can have profound effects on the stability of ecological communities. Specifically, compartmentalization tends to stabilize ecological networks by containing the effect of perturbations within modules. Despite their important role in securing ecosystem functions and services during perturbations, mechanisms that can account for the level of compartmentalization close to those observed in real ecological networks remain poorly understood. The two dominant theories on the development and structure of communities are niche and neutral theory. Niche theory explains the structure of communities using the relationship between species traits and habitat characteristics. Meanwhile, neutral theory assumes a fixed species pool in the absence of speciation and invasion, and considers all species to be ecologically equivalent, with stochastic dispersal and ecological drift being the only processes determining community structure. Despite contrasting opinions on the value of neutral theory, it is now generally accepted that neutral and niche processes interact in natural communities and both contribute towards the structure of species assemblages. The relative roles of neutral and niche processes have been shown to differ across spatio-temporal scales and modelling these processes in combination better represents biological patterns than neutral or niche models alone.
4. TRAIT EVOLUTION
Evolutionary dynamics concern a few key variables: genotypes and traits of interest, the relative abundance (frequency) of specific traits, the fitness of the genotype which is defined as its replication rate and dependent on both its trait value and frequency, and finally the mutation rate. Several models are available that depict the interplay of these variables: the quasi-species equation of molecular evolution, evolutionary game theory, the replicator-mutation equation, the Price equation, adaptive dynamics, and a few unified models that synthesize all these specific models into one. A standard procedure for analyzing these models is known as the evolutionary invasion analysis, where the evolutionary singularity and selection gradient are examined with the faster ecological dynamics set at its equilibrium. Together, these models and their unified forms provide a complete description of evolutionary dynamics and behaviour under natural selection. The impact of evolution at contemporary scales, also known as the rapid eco-evolutionary feedback, has gained momentum in literature, especially when dealing with adaptive response to global changes. This kind of rapid evolution challenges the standard approach of setting the fast ecological dynamics at equilibrium in the analysis and calls for further considering the impact in the dynamic behaviours of both traits and populations. Games