Fractal measures of spatial pattern as a heuristic for return rate in vegetative systems

Reactive persistence, spatial management, and conservation of metapopulations: An application to seagrass restoration

Assessing the conditions for persistence of spatially structured populations, especially those that are exploited by humans or threatened by global change, is of critical importance to inform management and conservation efforts. Observations for entire metapopulations are usually incomplete and rarely, if ever, sufficiently long to deduce population persistence from spatial patterns of abundance. Instead, insights based on metapopulation theory are often used for interpreting the demographic trajectories of real populations and for informing management decisions. The classical theoretical tool used to assess conditions for metapopulation persistence is the "invasibility criterion," which characterizes the asymptotic, or long-term, stability of a small colonizing population. Essentially, when the linear operator governing the metapopulation dynamics of an invasion event has a positive eigenvalue, recovery and resistance to extinction (resilience) are implied. The converse, however, is not necessarily the case-an invasion may grow over multiple generations, even when the eigenvalues indicate that extinction will eventually occur, a situation referred to here as "reactive persistence." For the management, restoration, and conservation of real metapopulations subject to continual disturbance, this transient behavior is often more relevant than the asymptotic behavior over long time scales. We develop the theoretical tools for assessing reactive persistence, demonstrating how the conditions for asymptotic and reactive persistence differ in both the patch-occupancy models suited to many terrestrial populations and those where local patch extinctions can be disregarded in the dynamics, often suited to marine species. After presenting the mathematical basis for generalizing the invasibility criterion to include reactive persistence, we illustrate how these concepts and tools can be applied in practice, using as a case study the population ecology and restoration of the seagrass Zostera muelleri (Irmisch ex Ascherson, 1867) in the Port of Gladstone in the Great Barrier Reef World Heritage Area Australia. It is shown how the analysis of the transient dynamics of the Z. muelleri metapopulation can be used to guide restoration efforts. Moreover, it is demonstrated that these reactive persistence concepts provide a more appropriate basis for site prioritization for restoration interventions than traditional stability analysis.

Low genotypic diversity and long-term ecological decline in a spatially structured seagrass population

In isolated or declining populations, viability may be compromised further by loss of genetic diversity. Therefore, it is important to understand the relationship between long-term ecological trajectories and population genetic structure. However, opportunities to combine these types of data are rare, especially in natural systems. Using an existing panel of 15 microsatellites, we estimated allelic diversity in seagrass, Zostera marina, at five sites around the Isles of Scilly Special Area of Conservation, UK, in 2010 and compared this to 23 years of annual ecological monitoring (1996–2018). We found low diversity and long-term declines in abundance in this relatively pristine but isolated location. Inclusion of the snapshot of genotypic, but less-so genetic, diversity improved prediction of abundance trajectories; however, this was spatial scale-dependent. Selection of the appropriate level of genetic organization and spatial scale for monitoring is, therefore, important to identify drivers of eco-evolutionary dynamics. This has implications for the use of population genetic information in conservation, management, and spatial planning.

Universal scaling of the distribution of land in urban areas

In this work, we explore the spatial structure of built zones and green areas in diverse western cities by analyzing the probability distribution of areas and a coefficient that characterize their respective shapes. From the analysis of diverse datasets describing land lots in urban areas, we found that the distribution of built-up areas and natural zones in cities obey inverse power laws with a similar scaling for the cities explored. On the other hand, by studying the distribution of shapes of lots in urban regions, we are able to detect global differences in the spatial structure of the distribution of land. Our findings introduce information about spatial patterns that emerge in the structure of urban settlements; this knowledge is useful for the understanding of urban growth, to improve existing models of cities, in the context of sustainability, in studies about human mobility in urban areas, among other applications.

Conservation of pattern as a tool for inference on spatial snapshots in ecological data

As climate change and other anthropogenic factors increase the uncertainty of vegetation ecosystem persistence, the ability to rapidly assess their dynamics is paramount. Vegetation and sessile communities form a variety of striking regular spatial patterns such as stripes, spots and labyrinths, that have been used as indicators of ecosystem current state, through qualitative analysis of simple models. Here we describe a new method for rigorous quantitative estimation of biological parameters from a single spatial snapshot. We formulate a synthetic likelihood through consideration of the expected change in the correlation structure of the spatial pattern. This then allows Bayesian inference to be performed on the model parameters, which includes providing parameter uncertainty. The method was validated against simulated data and then applied to real data in the form of aerial photographs of seagrass banding. The inferred parameters were found to be able to reproduce similar patterns to those observed and able to detect strength of spatial competition, competition-induced mortality and the local range of reproduction. This technique points to a way of performing rapid inference of spatial competition and ecological stability from a single spatial snapshots of sessile communities.

Disease transmission promotes evolution of host spatial patterns

Ecological dynamics can produce a variety of striking patterns. On ecological time scales, pattern formation has been hypothesized to be due to the interaction between a species and its local environment. On longer time scales, evolutionary factors must be taken into account. To examine the evolutionary robustness of spatial pattern formation, we construct a spatially explicit model of vegetation in the presence of a pathogen. Initially, we compare the dynamics for vegetation parameters that lead to competition induced spatial patterns and those that do not. Over ecological time scales, banded spatial patterns dramatically reduced the ability of the pathogen to spread, lowered its endemic density and hence increased the persistence of the vegetation. To gain an evolutionary understanding, each plant was given a heritable trait defining its resilience to competition; greater competition leads to lower vegetation density but stronger spatial patterns. When a disease is introduced, the selective pressure on the plant's resilience to the competition parameter is determined by the transmission of the disease. For high transmission, vegetation that has low resilience to competition and hence strong spatial patterning is an evolutionarily stable strategy. This demonstrates a novel mechanism by which striking spatial patterns can be maintained by disease-driven selection.