Stabilizing intransitive loops: self‐organized spatial structure and disjoint time frames in the coffee agroecosystem

The population dynamics of clustered consumer-resource spatial patterns: Insights from the demographics of a Turing mechanism

In ecology, Alan Turing's proposed activation-inhibition mechanism has been abstracted as corresponding to several ecological interaction types to explain pattern formation in ecosystems. Consumer-resource interactions have strong theoretical arguments linking them to both the Turing mechanism and pattern formation, but there is little empirical support to demonstrate these claims. Here, we connect several lines of evidence to support the proposition that consumer-resource interactions can create empirically observed spatial patterns through a mechanism similar to Turing's theory. We propose the existence of a fine-scale demographic spatial pattern (DSP), in which the youngest resources are located at the periphery and oldest in the center of clusters. We find evidence of a DSP in the spatially clustered distribution of arboreal ant nests, whose large-scale spatial patterning has previously been hypothesized to be driven by ant parasitoids. Through a combination of field surveys and analysis of demographic trends, we demonstrate how the DSP structures the interactions between the ant and its parasitoid. To explore the implications of DSP for consumer-resource pattern forming systems generally, we use a spatially explicit consumer-resource model to show how relative diffusion rates of the system shape multiscale spatial patterns that structure the demographic trends of the resource population in predictable ways. This work provides both empirical support for consumer-resource spatial patterns as well as a multiscale approach to understand their spatially explicit population dynamics.

Combining intransitive and higher-order effects in a coupled oscillator framework: A case study of an ant community

A growing body of literature recognizes that pairwise species interactions are not necessarily an appropriate metaphorical molecule of community ecology. Two examples are intransitive competition and nonlinear higher-order effects. While these two processes have been discussed extensively, the explicit analysis of how the two of them behave when simultaneously part of the same dynamic system has not yet been explored theoretically. A concrete situation exists on coffee farms in Puerto Rico in which three ant species form an intransitive competitive triplet, and that triplet is strongly influenced, nonlinearly, by a fly parasitoid that modifies the competitive ability of one of the species. Using this arrangement as a template, we explore the dynamical consequences with a simple ordinary differential equation (ODE) model. Results are complicated and include alternative periodic and chaotic attractors. The qualitative structures of those complications, however, may be approximately retrieved from the basic natural history of the system.

Refuge distributions and landscape connectivity affect host-parasitoid dynamics: Motivations for biological control in agroecosystems

Species distributions are affected by landscape structure at different spatial scales. Here we study how the interplay between dispersal at different spatial scales and landscape connectivity and composition affect local species dynamics. Using a host-parasitoid model, we assessed host density and host occupancy on the landscape, under different parasitoid dispersal ranges and three local distributions of non-crop habitats, areas where hosts are unable to grow but parasitoids are provided with alternative hosts and food resources. Our results show distinct responses of host density to increases in non-crop area, measured by differences in slopes for different distributions of non-crop habitats, and that the effect of local landscape composition on species dynamics depends on the landscape connectivity at the regional scale. Moreover, we show how host density and occupancy are affected by increasing parasitoid dispersal ranges depending on landscape structure. Our results demonstrate the role of local and regional scales on species distributions and the importance of the combined effects of species biological parameters and landscape structure on species dynamics. Finally, we highlight the relevance of these aspects for the development of better strategies of biological control.

Theoretical Clues for Agroecological Transitions: The Conuco Legacy and the Monoculture Trap

The multiple ecological crisis that we are facing forces us to ponder the transition toward sustainable agricultural systems. Two key uncertainties need to be unveiled in addressing this problem; first, we need to identify the general features of alternative models that make them sustainable, and second, we need to explore how to build them from the (flawed) existing systems. In this work we explore these two questions using an ethnoecological and theoretical approach. In the exploration of alternative models, we evaluate an ancestral farming system, the conuco, characterized by, (i) the use of the ecological succession to constantly renew its properties, (ii) the increase of its biodiversity over time (in the horizontal and vertical components), and (iii) the self-regulation of the associated populations. Next, we characterize the topology of ecological networks of agroecosystems along the transition from a monoculture to a conuco-like agroecological system. We use topologies obtained from field information of conventional and agroecological systems as starting and arrival points. To model the dynamics of the systems and numerically simulate the transitions, we use a model based on Generalized Lotka-Volterra equations, where all types of population interactions are represented, with outcomes based on a density-dependent conditionality. The results highlight the relevance of increasing the connectance and diminishing the degree centrality of the conventional systems networks to promote their sustainability. Finally, we propose that the transitions between the monoculture and the agroecological systems could be figuratively interpreted as a cusp catastrophe, where the two systems are understood as alternative stable states and the path from one to the other cannot be reverted by just reversing the values of the control parameter. That is, once a system is in either of these states there is a tendency to stay and a resistance to move away from it. This implies that in the process of transition from a monoculture to a multi-diverse system, it is prudent not to despair if there are no immediate improvements in the performance of the system because once a certain point is reached, the system may experience an abrupt improvement.

EcoQBNs: First Application of Ecological Modeling with Quantum Bayesian Networks

A recent advancement in modeling was the development of quantum Bayesian networks (QBNs). QBNs generally differ from BNs by substituting traditional Bayes calculus in probability tables with the quantum amplification wave functions. QBNs can solve a variety of problems which are unsolvable by, or are too complex for, traditional BNs. These include problems with feedback loops and temporal expansions; problems with non-commutative dependencies in which the order of the specification of priors affects the posterior outcomes; problems with intransitive dependencies constituting the circular dominance of the outcomes; problems in which the input variables can affect each other, even if they are not causally linked (entanglement); problems in which there may be >1 dominant probability outcome dependent on small variations in inputs (superpositioning); and problems in which the outcomes are nonintuitive and defy traditional probability calculus (Parrondo’s paradox and the violation of the Sure Thing Principle). I present simple examples of these situations illustrating problems in prediction and diagnosis, and I demonstrate how BN solutions are infeasible, or at best require overly-complex latent variable structures. I then argue that many problems in ecology and evolution can be better depicted with ecological QBN (EcoQBN) modeling. The situations that fit these kinds of problems include noncommutative and intransitive ecosystems responding to suites of disturbance regimes with no specific or single climax condition, or that respond differently depending on the specific sequence of the disturbances (priors). Case examples are presented on the evaluation of habitat conditions for a bat species, representing state-transition models of a boreal forest under disturbance, and the entrainment of auditory signals among organisms. I argue that many current ecological analysis structures—such as state-and-transition models, predator–prey dynamics, the evolution of symbiotic relationships, ecological disturbance models, and much more—could greatly benefit from a QBN approach. I conclude by presenting EcoQBNs as a nascent field needing the further development of the quantum mathematical structures and, eventually, adjuncts to existing BN modeling shells or entirely new software programs to facilitate model development and application.

Endogenous spatial pattern formation from two intersecting ecological mechanisms: the dynamic coexistence of two noxious invasive ant species in Puerto Rico

Endogenous (or autonomous, or emergent) spatial pattern formation is a subject transcending a variety of sciences. In ecology, there is growing interest in how spatial patterns can 'emerge' from internal system processes and simultaneously affect those very processes. A classic situation emerges when a predator's focus on a dominant competitor releases competitive pressure on a subdominant competitor, allowing coexistence of the two. If this idea is formulated spatially, two interesting consequences immediately arise. First, a spatial predator/prey system may take the form of a Turing instability, in which an activator (the dispersing prey population) is contained by a repressor (the more rapidly dispersing predator population) generating a spatial pattern of clusters of prey and predators, and second, an indirect intransitive loop (where A beats B beats C beats A) emerges from the simple fact that the system is spatial. Two common invasive ant species, Wasmannia auropunctata and Solenopsis invicta, and the parasitic phorid flies of S. invicta commonly coexist in Puerto Rico. Emergent spatial patterns generated by the combination of the Turing mechanism and the indirect intransitive loop are likely to be common here. This theoretical framework and the realities of the natural history in the field could explain both the long-term coexistence of these two species, and the highly variable pattern of their occurrence across a large landscape.

The Community Ecology of Herbivore Regulation in an Agroecosystem: Lessons from Complex Systems

Whether an ecological community is controlled from above or below remains a popular framework that continues generating interesting research questions and takes on especially important meaning in agroecosystems. We describe the regulation from above of three coffee herbivores, a leaf herbivore (the green coffee scale, Coccus viridis), a seed predator (the coffee berry borer, Hypothenemus hampei), and a plant pathogen (the coffee rust disease, caused by Hemelia vastatrix) by various natural enemies, emphasizing the remarkable complexity involved. We emphasize the intersection of this classical question of ecology with the burgeoning field of complex systems, including references to chaos, critical transitions, hysteresis, basin or boundary collision, and spatial self-organization, all aimed at the applied question of pest control in the coffee agroecosystem.