Theoretical Ecology

Martínez-Álvarez, Pedro Elías; Toro-Zapata, Hernán Darío; Salcedo-Echeverry, Gladys Elena

doi: 10.1007/s12080-025-00623-wpmid: N/A

Pollinators, particularly honeybees (Apis mellifera), are indispensable for global food security and ecosystem stability. However, pesticide exposure has emerged as a critical stressor threatening colony survival, with complex ecological and population-level consequences that remain poorly quantified. This study introduces a novel mathematical framework to rigorously analyze the nonlinear dynamics of honeybee colonies under pesticide-induced stress. Our dynamical systems model, based on nonlinear ordinary differential equations, integrates multiple ecological mechanisms often overlooked in previous studies, including logistic growth, social inhibition, and the beekeeping principle known as Farrar’s rule. By conducting an extensive equilibrium, stability, and bifurcation analysis, we identify previously unrecognized threshold effects that dictate colony persistence or collapse. A key theoretical finding is that if pesticide-induced mortality inside the hive surpasses the intrinsic population growth rate, extinction is inevitable. Additionally, we reveal a counterintuitive ecological feedback: hive overcrowding, in combination with pesticide exposure, reduces the foraging workforce, exacerbating colony decline in a way not previously described. These insights provide critical quantitative benchmarks for sustainable pesticide regulation and pollinator conservation. Our study not only advances theoretical ecology by elucidating complex stability transitions in pollinator populations but also delivers practical implications for agroecosystem management. By establishing explicit thresholds for intervention, our findings underscore the urgent need to rethink pesticide policies and conservation strategies to safeguard pollinators and global food systems.

Yoshiyama, Kohei; Sawa, Takuma; Yoshiyama, Yoko

doi: 10.1007/s12080-025-00605-ypmid: N/A

In freshwater and marine environments, cyanobacteria can overgrow and accumulate at the water’s surface, forming surface scum. These phenomena disrupt aquatic food webs and degrade water quality. The occurrences are often sporadic and difficult to predict based on environmental factors alone. In this study, we investigate a model of vertical migration for a cyanobacterial colony in a water column. The model reveals a range of steady-state vertical migration patterns, including diurnal, bidiurnal, and chaotic behaviors, depending on colony size and maximum irradiance. Surface scum formation occurs sporadically, either disappearing rapidly or persisting for over a day during chaotic vertical migrations. These findings suggest that the unpredictability of surface scum formation may arise from cyanobacterial physiology itself—particularly under intense light conditions—rather than solely from external environmental factors.

Chen, Renfei; Hopf, Jess K.; White, J. Wilson

doi: 10.1007/s12080-025-00614-xpmid: N/A

Marine protected areas play a growing role in conservation and fisheries management, though they remain controversial. Early theoretical work, based on analyses of population dynamics at stable equilibrium states, suggested that the implementation of marine protected areas could contribute to multiple goals such as maintaining species persistence (conservation goals) and maintaining or increasing fishery yields (fisheries goals), even—under some conditions—exceeding outcomes from conventional (i.e., non-spatial) management strategies. However, more recent work has recognized that when protected areas are first established, the newly protected populations may be far from their eventual equilibrium state, leaving managers to contend with “transient” dynamics as the system moves towards that equilibrium state over years or decades. Here, we review the development of our understanding of those transient dynamics from models, and how that understanding can improve protected area management for both fisheries and conservation goals. The extent to which fish population varies in transient time scales depends on life histories (e.g., reproduction, survival, and fishing mortalities) and the measurement of yield judged by either biomass or number, and the order in which closures are implemented over time for interacting species. Understanding transients also helps set realistic expectations for adaptive management by allowing more accurate predictions of the magnitude of protected area effects on previously fished populations over short time scales. Continuing to consider transient population dynamics will benefit policy-makers in both conservation and economic goals by providing a stronger theoretical foundation for adaptive marine protected area management.

Vandermeer, John

doi: 10.1007/s12080-025-00628-5pmid: N/A

Based on an example of a four dimensional ecological community composed of three ant species and a group of phorid flies, a simplified dynamic model is proposed and analyzed qualitatively. The model contains an intransitive triplet of ant species coupled with a predator/prey pair, where the prey is one of the ants in the intransitive competition, thus coupling a 3D oscillator with a 2D oscillator. Relaxing basic symmetries, a chaotic attractor emerges in which two distinct unstable modalities are recognizable, identifiable with the two biological processes involved. The unstable manifolds of each of the instabilities are of distinct dimensionalities, a characteristic known as hetero-chaos. It is suggested that the qualitative arrangement may be common as a modality within large ecological systems, thus proposing hetero-chaos as possibly common in ecosystems that have chaotic behavior.

Metz, Timo; Drossel, Barbara

doi: 10.1007/s12080-025-00611-0pmid: N/A

When local communities are assembled from a regional species pool, stochastic effects, such as differences in species arrival order and timing, can lead to alternative assembly outcomes. Here, we study the predictability of mutualistic network assembly using a trait-based model with explicit population dynamics. We vary size and composition of the species pool, immigration rates, and the strength of demographic noise. Assembly is more predictable when more species in the pool are only weakly dependent on their mutualistic partners or are interaction generalists. The size of the assembled networks increases with the pool size, with the proportion of species that are only weakly dependent on their mutualistic partner and with the immigration rate. The predominant assembly outcome at low immigration rates is a stable configuration where species composition does not change. At higher immigration rates, we observe also cycles (where a sequence of communities repeats periodically) and more complex temporal patterns. Our results are relevant for ecosystem restoration as they show how the composition of the regional species pool and the immigration rate influence the assembly outcome.

Paul, Ayan; Mukherjee, Tanoy; Saha, Bapi; Chattopadhyay, Joydev

doi: 10.1007/s12080-025-00612-zpmid: N/A

The inevitability of non-consumptive effects (NCE) is evident within the dynamics of prey-predator relationships. These non-lethal effects, notable for their variability, significantly influence the behavioral responses and reproductive patterns of the prey population, leaving a distinct mark on predation numbers. A bulk of existing research has focused on assessing the impact of NCE on the prey population or identifying suitable hunting strategies. But, there exists a noticeable research gap that fails to explore the pervasive influence of NCE on predator hunting strategies, a central point emphasized in this manuscript. Our theoretical investigation effectively bridges that lacuna, where schedule of fear (SOF) is playing a pivotal role. Note that this is the first attempt where the SOF is brought under the umbrella of theoretical framework. In this connection, we evaluate the probability distribution of the predation rate for distinct hunting strategies, which helps to choose the optimal predation scheme under the evoke of NCE. The application of the theoretical result on the movement data of Elk and Mule deer reflects that a predator becomes benefits from employing the “active-search” hunting tactic during the prey-predator interactions.

Mora Van Cauwelaert, Emilio; Li, Kevin; Hajian-Forooshani, Zachary; Vandermeer, John; Benítez, Mariana

doi: 10.1007/s12080-025-00609-8pmid: N/A

The relationship between the spatial structure of hosts and the individual movement of vectors is central to developing a comprehensive representation of pathogen dynamics. Previous studies have proposed that pathogens like coffee leaf rust (CLR; Hemileia vastatrix) can be transported between plants by coffee workers during harvesting. However, the relative influence of harvesting in coffee rust dispersal and plot-level infection is not well understood, and neither is its relation with plantation characteristics. In this study, we developed a 2D plantation model with deterministically moving agents to explore the role of coffee ripening synchronicity in reproducing the different harvesting trajectories reported in the field. We then evaluate how these trajectories modify the potential CLR infection in plots with increasing planting densities. We found that scenarios with interplant asynchronous ripening and scarcity of trees with berries generate trajectories with medium to long steps that are qualitatively similar to those observed in the field. When coupled with a rust dispersal mechanism, these trajectories significantly increased coffee plot infection compared to scenarios with only local dispersal mechanisms (up to 15%). This effect is enhanced for trajectories with medium-sized steps from the asynchronous scenario, and optimized in plantations with medium planting densities (2000–3000 plants/ha). At high planting densities, plants are always highly infected due to local dispersal, making the contribution of harvest negligible. Our results aims to spur discussion on agroecological practices that can reduce the impact of harvesting and specific trajectories, in scenarios where one can benefit from asynchronous maturation of berries and shaded plantations.

Kiss, Lilla Zs.; Klauschies, Toni

doi: 10.1007/s12080-025-00618-7pmid: N/A

Species coexistence relies on ecological trade-offs, such as the gleaner–opportunist trade-off, which enables two consumers to coexist on a single shared resource through temporal resource variation and differences in their resource-dependent growth rates. The shapes of the consumers’ functional responses play a central role in this mechanism as they determine the consumers’ effect on the stability of the consumer–resource dynamics and their response to resource variation. While recent studies suggest that sigmoidal functional responses may be more common in nature than previously assumed, their impact on coexistence in the gleaner–opportunist model has not been systematically analyzed. In this study, we compared population growth models of two consumers with one or both exhibiting a sigmoidal functional response to the original gleaner–opportunist model with one consumer exhibiting a linear and the other a saturating functional response. Comparing the size of the parameter space allowing coexistence, we found that coexistence is most likely when consumers exhibit contrasting effects on and responses to resource variation, such as one consumer exhibiting a stabilizing sigmoidal and the other a saturating functional response, or one exhibiting a destabilizing sigmoidal and the other a linear functional response. Through this stabilizer–destabilizer trade-off, coexistence can also arise between two consumers that exhibit sigmoidal functional responses. Overall, sigmoidal functional responses provided the opportunity for coexistence that was of similar magnitude as in the original gleaner–opportunist model. Critically, sigmoidal functional responses allowed coexistence for less extreme handling times than the original model, emphasizing their importance when fitting models to empirical data.

Terry, J. Christopher D.; Bonsall, Michael B.; Morris, Rebecca J.

doi: 10.1007/s12080-025-00603-0pmid: 41541601

The impact of higher-order interactions, those involving more than two species, is increasingly appreciated as having the potential to strongly influence the dynamics of complex ecological systems. However, although the critical importance of the structure of pairwise interaction networks is well established, studies of higher-order interactions still largely assume random structures. Here, we demonstrate the strong impact of structured higher-order interactions on simulated ecological communities. We focus on effects caused by interaction modifications within food webs, where a consumer resource interaction is modified by a third species, and for which plausible structures can be hypothesised. We show how interaction modifications introduced under a range of non-random distributions may impact the overall network structure. Local stability and the size of the feasibility domain are critically dependent on the inter-relationship between trophic and non-trophic effects. Where interaction modifications are structured into mutual interference motifs (associated with consumers switching between resources) synergistic signs and topological effects have particularly consequential impacts. Furthermore, we show that previous results of the impact of higher-order interactions on diversity-stability relationships can be reversed when higher-order interactions are structured, not random. Empirical data on interaction modifications will be a key part of improving understanding the dynamics of communities, particularly the distribution of interaction modification signs across networks.

Gupta, Prajjwal; Singh, Satyabhan; Priyadarshi, Anupam

doi: 10.1007/s12080-025-00608-9pmid: N/A

Showing prey refuges or hiding from predation in food-web models is quite common and detrimental to maintaining the ecological balance in natural ecosystems. Avoiding higher predation often leads to a significant increase in prey populations. Hence, prey refuges are generally considered a vital factor in preventing species extinction and damp oscillations in food-web models. These theoretical results are based on the analysis of extremely simple food-web models. Hence, there was a need to understand the impact of prey refuges in higher-dimensional food-web systems. The present study investigates the effects of prey refuges on the dynamics of a four-species food-web model, which consists of a bottom prey, two middle predators, and a top predator in which the top predator predates on all three species while middle predators predate only on the bottom prey. In general, studies have shown that refugia have a stabilizing effect on prey-predator dynamics and support prey. From the analysis of the present model, we obtain some results that are remarkably different from the existing results and interesting in the sense that refugia does not always stabilize model dynamics. The prey-refuge below threshold limit dampens chaotic/oscillatory dynamics and brings the system into point stability. Qualitatively, prey-refuge within threshold upper limits prevents species extinction, enhances prey population, and hence supports species coexistence and biodiversity in food-web systems. But, there exists a threshold value of refuge beyond which prey availability for predation becomes too low. This can lead to population oscillations or even chaotic dynamics, disrupting species balance in the ecosystem. Thus, excessive refuge beyond this upper threshold may destabilize the system, causing an imbalance in species populations. These results are structurally stable and hence, qualitatively independent of parameter choices. However, refugia within the limiting range enhances the parameter domain of stable solutions and there is a higher probability for invaders to invade and persist with the species after the invasion. Hence, refugia supports bigger biodiversity in ecosystems and promotes species coexistence. The bigger stability parameter domain through one-parameter bifurcation indicates a higher probability of species coexistence with refugia. Iso-spike diagrams in the bi-parametric space are drawn in which we observe that chaotic solutions become limit cycles or point equilibria for the range of parameter values. The associated Lyapunov exponents diagrams are also drawn to verify the complexity of the model. We hypothesize that prey-refuge within the upper limit range can promote stability, enhance species coexistence, and support bigger biodiversity, which is crucial in maintaining the ecological balance and ecosystem persistence but refugia beyond the upper limit (higher refuges) may destabilize species coexistence and bring ecological imbalance in the ecosystems.