Structure, stability and macroecology of populations and ecosystems

Doctoral thesis, 2024

Dispersal and interaction networks underlie many ecological systems, often dictating spatio-temporal dynamics as well as emergent patterns. The mode and time scales of dispersal can vary considerably depending on whether ecosystems exist in contiguous landscapes or in island-like configurations. In particular, island systems have been extensively studied for many ecological processes, in part because of the simplicity in representing processes such as immigration of organisms from outside. This representation has also been used in many other habitats, such as mountain tops which can also be considered island-like because of their isolation and similar properties of immigration.

Immigration could result from species that already exist on the islands or those that are novel. This distinction connects to the concept of species invasions which are driven by new species not present in an ecosystem before. Invasions can be seen as an important part of how ecosystems are assembled. Invasive species can also have disruptive impacts on systems like islands, which for example can introduce novel species like predators. Invasions serve as a useful representation of various means and ends of biological processes, and hence their study has extended way beyond their initial scope.

Dispersal, interactions and invasions have implications ranging from establishment of distinct subpopulations of individual species to large scale spatial patterns that define ecosystems. Such implications and frameworks to explain them are the central themes of this thesis.

One of the systems we study consists of sites along a coastal landscape that harbours the seagrass Halodule uninervis. The task is to partition the entire population into subpopulations that have very little dispersal across them. We use an algorithm to aggregates sites that are more strongly connected in the same subpopulation for a range of dispersal scenarios. These scenarios are useful since the dispersal processes and life-spans of the seagrass are not well-understood.

The other articles focus on ecological communities with a range of interaction types between species. We study how ecological communities on islands are assembled from a large pool of species that can also immigrate from the mainland source, and if it can provide mechanisms to explain the scaling of species richness with island areas -- namely the species-area relationship. A drastically different setting is large contiguous landscapes.

We posit that species interactions vary across space, which helps characterize habitat patches that would be connected by high dispersal of species. This simplified picture provides a range of situations to understand how habitat heterogeneity affects species richness.

We also address the problem of how ecosystems with many interacting species can still be stable. We do this by deriving a very general mathematical bound on stability which is expressed in terms of ecologically realistic constraints.

Species identities are important with respect to biological invasions for the risk of replacement of resident species. We developed a framework to predict the structure of invasion outcomes, i.e., what set of species survive following an invasion event. This method is applicable in a range of cases characterized by high initial abundance of invaders and imperfect knowledge of interactions.

An overarching theme in investigating these complex ecological systems is to first analyze the fully random case without assuming any structure. This null case admits description in terms of a few statistics that greatly simplify the study of system level properties and processes. One can then ask if there are parameter regimes where these properties break down. The difficulty in finding such regimes might indicate universal properties but even the sudden disappearance might unravel phase transitions or unexplored new properties.