Impact of domain size, shape and other human interventions
Most mathematical studies of patterns in spatially extended systems take place assuming an idealised domain: a sufficiently large open space in which environmental conditions do not change. In real systems, however, such idealized domains do not exist and it is a priori not evident if, and how, results carry over to more realistic domains. For instance, if the area in which an ecosystem can evolve freely is too small, we expect that the mechanisms by which a spatially extended system may evade tipping do not work. This implies a minimum domain size for system resilience, which is typical an order of magnitude larger than the length scales associated to the spatial patterns, or the width of a coexistence front. However, not only the spatial extent of the domain is an important factor, also the shape of the spatial domain is crucial for the potentiality of a domain to form patterns and thus to generate multi-stability. Either by natural causes or by human activities, the character of a domain will have a strong impact on the nature and multiplicity of the patterns that may be exhibited and thus on the resilience of the system. Similarly, localized effects will impact pattern formation. For instance, we expect that strong localized effects by human interventions, think of local logging, or ‘slash and burn’ agricultural land use, will have a strong impact on the appearance, stability and dynamics of patterns (Gowda et al 2018, Wuyts et al 2018). Albeit localized, such a human perturbation may significantly reduce the flexibility and thus resilience of a patterned system as a whole. On the other hand, localized perturbations can also increase the resilience of the system to droughts by directing it to stable patterns rather than to bare soil (Zelnik et al 2021). Also, global homogenizing disturbance by humans may affect the resilience of the system, because the mechanisms of pattern formation cannot work anymore. Think of large-scale agriculture, homogeneous restoration measures combatting desertification, or large scale logging or tree planting. Therefore, we will embed the study of spatial patterns in complex systems and ecosystems and their impact on its resilience in a careful analysis of the impact of spatial restrictions of the domain and the effects of local and global, human induced effects. Our approach will be a combination of computational and analytical studies to determine the effects of such spatial inhomogeneities and spatial homogenization on pattern dynamics and resilience (cf. Gowda et al 2014, Doelman et al 2018, Zelnik et al 2021). This will include measures directed towards ecosystem restoration, evading and even reversing critical transitions, such as (in)homogeneous water and nutrient harvesting measures, vegetation restoration and (spatial) grazing schemes (Berghuis et al 2020, Zelnik et al 2021). This is of relevance for ecosystem restoration and mitigating the effects of land use and climate change.