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Mathematical models of species dispersal and the resilience of metapopulations against habitat loss
(2021)

Habitat loss and fragmentation due to climate and land-use change are among the biggest threats to biodiversity, as the survival of species relies on suitable habitat area and the possibility to disperse between different patches of habitat. To predict and mitigate the effects of habitat loss, a better understanding of species dispersal is needed. Graph theory provides powerful tools to model metapopulations in changing landscapes with the help of habitat networks, where nodes represent habitat patches and links indicate the possible dispersal pathways between patches.
This thesis adapts tools from graph theory and optimisation to study species dispersal on habitat networks as well as the structure of habitat networks and the effects of habitat loss. In chapter 1, I will give an introduction to the thesis and the different topics presented in this thesis. Chapter 2 will then give a brief summary of tools used in the thesis.
In chapter 3, I present our model on possible range shifts for a generic species. Based on a graph-based dispersal model for a generic aquatic invertebrate with a terrestrial life stage, we developed an optimisation model that models dispersal directed to predefined habitat patches and yields a minimum time until these patches are colonised with respect to the given landscape structure and species dispersal capabilities. We created a time-expanded network based on the original habitat network and solved a mixed integer program to obtain the minimum colonisation time. The results provide maximum possible range shifts, and can be used to estimate how fast newly formed habitat patches can be colonised. Although being specific for this simulation model, the general idea of deriving a surrogate can in principle be adapted to other simulation models.
Next, in chapter 4, I present our model to evaluate the robustness of metapopulations. Based on a variety of habitat networks and different generic species characterised by their dispersal traits and habitat demands, we modeled the permanent loss of habitat patches and subsequent metapopulation dynamics. The results show that species with short dispersal ranges and high local-extinction risks are particularly vulnerable to the loss of habitat across all types of networks. On this basis, we then investigated how well different graph-theoretic metrics of habitat networks can serve as indicators of metapopulation robustness against habitat loss. We identified the clustering coefficient of a network as the only good proxy for metapopulation robustness across all types of species, networks, and habitat loss scenarios.
Finally, in chapter 5, I utilise the results obtained in chapter 4 to identify the areas in a network that should be improved in terms of restoration to maximise the metapopulation robustness under limited resources. More specifically, we exploit our findings that a networkâ€™s clustering coefficient is a good indicator for metapopulation robustness and develop two heuristics, a Greedy algorithm and a deducted Lazy Greedy algorithm, that aim at maximising the clustering coefficient of a network. Both algorithms can be applied to any network and are not specific to habitat networks only.
In chapter 6, I will summarize the main findings of this thesis, discuss their limitations and give an outlook of future research topics.
Overall this thesis develops frameworks to study the behaviour of habitat networks and introduces mathematical tools to ecology and thus narrows the gap between mathematics and ecology. While all models in this thesis were developed with a focus on aquatic invertebrates, they can easily be adapted to other metapopulations.