The role of spatial self-organization in the design of agroforestry systems

Abstract

The development of sustainable agricultural systems in drylands is currently a crucial issue in the context of mitigating the outcomes of population growth under the conditions of climatic changes. The need to meet the growing demand for food, fodder, and fuel, together with the hazards due to climate change, requires cross-disciplinary studies of ways to increase livelihood while minimizing the impact on the environment. Practices of agroforestry systems, in which herbaceous species are intercropped between rows of woody species plantations, have been shown to mitigate several of the predicaments of climatic changes. Focusing on agroforestry in drylands, we address the question of how we can improve the performance of agroforestry systems in those areas. As vegetation in drylands tends to self-organize in various patterns, it seems essential to explore the various patterns that agroforestry systems tend to form and their impact on the performance of these systems in terms of biomass production, resilience to droughts, and water use efficiency. We use a two-soil-layers vegetation model to study the relationship between deep-rooted woody vegetation and shallow herbaceous vegetation, and explore how self-organization in different spatial patterns influences the performance of agroforestry systems. We focus on three generic classes of patterns, spots, gaps, and stripes, assess these patterns using common metrics for agroforestry systems, and examine their resilience to droughts. We show that in contrast to the widespread practice of planting the woody and herbaceous species in alternating rows, that is, in a stripe pattern, planting the woody species in hexagonal spot patterns may increase the system's resilience to droughts. Furthermore, hexagonal spot patterns reduce the suppression of herbs growth by the woody vegetation, therefore maintaining higher crop yields. We conclude by discussing some limitations of this study and their significance.

Evasion of tipping in complex systems through spatial pattern formation

“…This, together with the flammability and fire resistance of grasses that can easily regrow after fires, is the key of the positive feedback mentioned earlier, generating alternative stable states between open savanna and tropical forests. Second, both types of spatial pattern formation as we outlined, namely Turing patterns and coexistence states, have been observed in real and model systems (12,25,68,(70)(71)(72)(73)(74)(75)(76) (Fig. 2).…”

“…To the best of our knowledge, no unified savanna model exists that explains all of the possible ecosystem states including spatial Turing patterns and coexistence states. To develop a unified spatially explicit savanna model, existing savanna models (71,76,77) could be combined in such a way that the new model consists of (at least) the state variables water, grass biomass, savanna tree biomass, and forest tree biomass. Savanna and forest trees should be distinguished by their different fire responses and shade tolerance (78,79).…”

“…Preliminary analyses of spatially extended ecosystems, such as dry savannas, modeled by activator-inhibitor-type reaction-diffusion equations (27,75,76), show that tipping may or may not be preceded by a pattern-forming Turing bifurcation (Box 1 and Fig. 1).…”

Stationary peaks in a multivariable reaction--diffusion system: Foliated snaking due to subcritical Turing instability

“…Evidently, the conjectured universal organization of peaks in the foliated snaking structure generated by a subcritical Turing instability provides a distinct mathematical description of homoclinic snaking in multi-variable reaction-diffusion media. The results suggest that the nonlinear mechanisms behind both peak generation and wavenumber selection that appear to be involved in the side-branching model studied here lead to a robust phenomenon that is essential, among other examples, to studies of ecological systems, ranging from the initiation of root hairs [8] to the generation of vegetation patches [52] and the design of agroforestry systems [71].…”

Dynamics of a mountain grassland: Environment predicts long‐term trends, while species’ traits predict short‐term fluctuations

“…As a result, dynamics of any community follows a complex trajectory due to superimposed fluctuations of different lengths, which are often asynchronous among species (Valencia et al 2020a). Short‐term fluctuations (year‐to‐year or slightly longer) have been documented in many plant populations and communities (Dunnett & Grime, 1999; Lawson et al, 2015; Tzuk et al, 2020). They may be of cyclic character, namely when they involve a feedback process, such as in dynamics of legume–grass systems (Thornley et al, 1995; Schwinning & Parsons, 1996; Herben et al, 2017, but see also Gonzalez‐Andujar et al, 2006 or Lima et al, 2012 for other examples), but in the majority of cases are less regular as they result from species‐specific processes affecting their demographies, often in a highly unpredictable manner (Valencia et al, 2020a, 2020b).…”