The emergence and maintenance of mutualism, defined as mutually beneficial interspecies interactions, remain challenging topics in evolutionary ecology. Partner choice is considered one of the key mechanisms for preventing spread of cheaters that receive benefits from partners while providing no or less return. However, partner choice can eventually destabilize mutualistic systems. Here, a mathematical model was developed to examine whether adaptive partner recruitment by hosts, defined as the optimal control of the number of associating symbionts, can help stabilize the coevolutionary dynamics of mutualistic systems with partner choice. The host population was assumed to consist of two types of strains, those with symbiont choice (discriminator) and those without (indiscriminator). The symbiont population was likewise assumed to consist of two types of strains, those that contributed to their associated host (cooperator) and those that did not (non-cooperator). Comparison of Case I, wherein the hosts are associated with a fixed number of symbionts, with Case II, wherein they can optimize the number of associating symbionts to maximize their fitness, revealed that the equilibrium where mutualism persists was neutrally stable in Case I, while it was asymptotically stable in Case II because adaptive partner recruitment induces a negative frequency dependence in the fitness difference between cooperator and non-cooperator symbionts. Moreover, the parameter area where the equilibrium exists expanded with increasing environmental nutrient availability to the host in Case I, but contracted in Case II.
Vertical transmission of an infectious disease from parent to offspring is a common transmission route in many systems. However, the majority of vertical transmission modelling has assumed a well-mixed population, and we do not know how the spatial structure present in most real-world populations will impact the dynamics of these systems. Here we investigate how spatial structure affects the dynamics of a pathogen with both horizontal and vertical transmission. We introduce a lattice model with a pair approximation that includes both local and global transmission and reproduction. We find that vertical transmission’s ability to determine pathogen invasion is dependant on spatial structure. When the majority of transmission and reproduction is local, vertical transmission can destabilise a host population to cause limit cycles. Given the advantages of a pathogen having both horizontal and vertical transmission routes, we extend the model to investigate the likelihood of a mutant strain with both transmission modes outcompeting a resident strain with only horizontal transmission. In the absence of cost the mutant always invades. When there is a trade-off between vertical and horizontal transmission, the mutant emerges when the cost to the horizontal transmission rate is not too large. Depending on how the mutant appears within the host population, it may have an initial advantage over the resident strain even if it cannot outcompete in the long-term. Our work demonstrates that the importance of vertical transmission within host-parasite dynamics is preserved when spatial structure is included.
Elm woodlands provide important ecological functions in sandy dryland ecosystems, but their regeneration and population dynamics are affected by environmental stress and biotic interactions. Understanding how symmetric and asymmetric forms of intraspecific competition and facilitation influence elm populations can improve theoretical understanding of woodland dynamics under stress. In this study, we developed a hybrid agent-based and system-dynamics model to examine how interaction symmetry and environmental stress affect final population abundance, age structure, and spatial organization of elm populations. The results showed that completely asymmetric competition produced a significantly larger final population than completely symmetric competition (P < 0.01). This outcome reflected size-biased resource capture by larger individuals in the model, but it was also accompanied by a more seedling-dominated age structure, indicating that higher final abundance did not necessarily correspond to greater demographic balance. Facilitation had stress-dependent effects. Under low stress, differences between symmetric and asymmetric facilitation were small, whereas under moderate and high stress, completely symmetric facilitation produced significantly larger final populations than completely asymmetric facilitation (P < 0.05 and P < 0.01, respectively). Symmetric facilitation was also associated with a less strongly truncated age structure under higher stress, suggesting that broadly distributed stress buffering helped maintain juvenile and mature-stage representation in the simulated population. Spatial point-pattern analysis showed that elm populations were generally clustered, but the effects of facilitation on clustering depended on competition mode and stress level. Overall, the results indicate that competition and facilitation jointly shape simulated elm population outcomes through size-biased resource capture, stress buffering, and local spatial interactions. The ABM-SD framework provides a theoretical tool for comparing alternative interaction mechanisms in sparse elm woodlands, although the results should be interpreted as scenario comparisons rather than site-specific predictions.
Species dispersal plays a critical role in shaping the spatial structure of communities and ultimately determines species distributions. In this study, we incorporated spatial factors and constructed a mathematical model of spatial community dynamics using a three-species food web to explore how different dispersal patterns influence species coexistence in a landscape of habitat loss and habitat fragmentation. We further examined how variation in colonization rates under different dispersal strategies affects species within the food web. The results show that: (1) In landscapes experiencing habitat fragmentation and habitat loss, increasing dispersal range enlarges the coexistence region of species; (2) Coexistence is maximized at intermediate dispersal rates and declines when dispersal is either too weak or too strong; (3) Changes in dispersal patterns can either promote or inhibit coexistence, depending on the direction and magnitude of the changes; (4) when all species adopt global dispersal, habitat loss exerts a progressively negative effect on each species, whereas habitat fragmentation has no impact. This study provides theoretical insights into the role of dispersal in shaping species distributions and offers a foundation for future research on species dispersal dynamics.
Climate change has created new and evolving environmental conditions, impacting all species, including hosts and parasitoids. In that context, we present integrodifference equation (IDE) models of host–parasitoid systems to model population dynamics in the context of climate-driven shifts in habitats. In this paper, we describe and analyze two IDE models of host–parasitoid systems to determine criteria for coexistence of the host and parasitoid. Specifically, we determine the critical habitat speed, beyond which the parasitoid cannot survive. By comparing the results from two IDE models, we investigate the impacts of assumptions that reduce the system to a single-species model. We also compare critical speeds predicted by a spatially-implicit difference-equation model with critical speeds determined from numerical simulations of the IDE system. The spatially-implicit model uses approximations for the dominant eigenvalue of an integral operator. The classic methods to approximate the dominant eigenvalue for IDE systems do not perform well for asymmetric kernels, including those that are present in shifting-habitat IDE models. Therefore, we compare several methods for approximating dominant eigenvalues that have not previously been compared in two-species IDE moving-habitat models. Ultimately, geometric symmetrization and iterated geometric symmetrization approximations give the best estimates of the parasitoid critical speed, which extends the superiority of these approximations into the two-species context.
