Theoretical Ecology

Neutral speciation mechanisms based on isolation by distance and assortative mating, termed topopatric, has recently been shown to describe the observed patterns of abundance distributions and species–area relationships. Previous works have considered this type of process only in the context of hermaphroditic populations. In this work, we extend a hermaphroditic model of topopatric speciation to populations where individuals are explicitly separated into males and females. We show that for a particular carrying capacity, speciation occurs under similar conditions, but the number of species generated is lower than in the hermaphroditic case. As a consequence, the species–area curve has lower exponents, especially at intermediate scales. Evolution results in fewer species having more abundant populations.

This paper compares perfect information and passive–adaptive social learning models of forest harvesting using a simple Markov chain model for land-use dynamics. A perfect information model assumes that landowners know true utility values of forest conservation and harvesting. In contrast, a passive–adaptive social learning model assumes that landowners do not know true utility values and they learn these values by their past experiences and by exchanging information with others in a society. We determine conditions under which the same consequences expected from perfect information and passive–adaptive social learning models. We found that the outcome from a perfect information model resembles that from passive–adaptive social learning model only when the perfect information model incorporates little discounting for future values. The stability analysis of landscape dynamics predicts a cyclic overexploitation of forest resources in a passive–adaptive social learning model with short-term memory, while instability of landscapes is never expected in a perfect information model. We discuss the role of discounting the future and discounting the past in the context of forest management.

Many species of invasive insects establish and spread in regions around the world, causing enormous economical and environmental damage, in particular in forests. Some of these insects are subject to an Allee effect whereby the population must surpass a certain threshold in order to establish. Recent studies have examined the possibility of exploiting an Allee effect to improve existing control strategies. Forests and most other ecosystems show natural spatial variation, and human activities frequently increase the degree of spatial heterogeneity. It is therefore imperative to understand how the interplay between this spatial variation and individual movement behavior affects the overall speed of spread of an invasion. To this end, we study an integrodifference equation model in a patchy landscape and with Allee growth dynamics. Movement behavior of individuals varies according to landscape quality. Our study focuses on how the speed of the resulting traveling periodic wave depends on the interaction between landscape fragmentation, patch-dependent dispersal, and Allee population dynamics.

Local interactions among individual members of a population can generate intricate small-scale spatial structure, which can strongly influence population dynamics. The two-way interplay between local interactions and population dynamics is well understood in the relatively simple case where the population occupies a fixed domain with a uniform average density. However, the situation where the average population density is spatially varying is less well understood. This situation includes ecologically important scenarios such as species invasions, range shifts, and moving population fronts. Here, we investigate the dynamics of the spatial stochastic logistic model in a scenario where an initially confined population subsequently invades new, previously unoccupied territory. This simple model combines density-independent proliferation with dispersal, and density-dependent mortality via competition with other members of the population. We show that, depending on the spatial scales of dispersal and competition, either a clustered or a regular spatial structure develops over time within the invading population. In the short-range dispersal case, the invasion speed is significantly lower than standard predictions of the mean-field model. We conclude that mean-field models, even when they account for non-local processes such as dispersal and competition, can give misleading predictions for the speed of a moving invasion front.

Transients in ecology are extremely important since they determine how equilibria are approached. The debate on the dynamic stability of ecosystems has been largely focused on equilibrium states. However, since ecosystems are constantly changing due to climate conditions or to perturbations driven by  the climate crisis or anthropogenic actions (habitat destruction, deforestation, or defaunation), it is important to study how dynamics can proceed till equilibria. This article investigates the dynamics and transient phenomena in small food chains using mathematical models. We are interested in the impact of habitat loss in ecosystems with vegetation undergoing facilitation. We provide a dynamical study of a small food chain system given by three trophic levels: primary producers, i.e., vegetation, herbivores, and predators. Our models reveal how habitat loss pushes vegetation towards tipping points, how the presence of herbivores in small habitats could promote ecosystem’s extinction (ecological meltdown), or how the loss of predators produce a cascade effect (trophic downgrading). Mathematically, these systems exhibit many of the possible local bifurcations: saddle-node, transcritical, Andronov–Hopf, together with a global bifurcation given by a heteroclinic bifurcation. The associated transients are discussed, from the ghost dynamics to the critical slowing down tied to the local and global bifurcations. Our work highlights how the increase of ecological complexity (trophic levels) can imply more complex transitions. This article shows how the pernicious effects of perturbations (i.e., habitat loss or hunting pressure) on ecosystems could not be immediate, producing extinction delays. These theoretical results suggest the possibility that some ecosystems could be currently trapped into the (extinction) ghost of their stable past.

Seed dispersal is a critical mechanism for escaping specialist natural enemies. Despite this, mean dispersal distances can vary by an order of magnitude among plant species in the same community. Here, we develop a theoretical model to explore how interspecific differences in seed dispersal alter the impact of specialist natural enemies, both on their own and though a trade-off between seed dispersal and enemy susceptibility. Our model suggests that species are more able to recover from rarity if they have high dispersal because (1) seedlings are more likely to escape their parent’s natural enemies, (2) adults are more spread out, reducing the chance that a seed will disperse near conspecifics, and (3) seedlings compete less with kin for open gaps. Differences in dispersal do not produce stabilizing mechanisms—species with low dispersal are purely at a disadvantage and do not gain a novel niche opportunity. However, dispersal-susceptibility trade-offs will be equalizing, as species disadvantaged by low dispersal will benefit from being less susceptible to specialist natural enemies. This mechanism, unlike most mechanisms of dispersal-mediated coexistence, does not require that there is an abundance of empty space: high-dispersers gain an advantage by escaping from their enemies, not by colonizing empty habitat. Our study therefore suggests that differences in dispersal are unlikely to promote diversity on their own, but may strengthen other coexistence mechanisms.

Studies of time-invariant matrix metapopulation models indicate that metapopulation growth rate is usually more sensitive to the vital rates of individuals in high-quality (i.e., good) patches than in low-quality (i.e., bad) patches. This suggests that, given a choice, management efforts should focus on good rather than bad patches. Here, we examine the sensitivity of metapopulation growth rate for a two-patch matrix metapopulation model with and without stochastic disturbance and found cases where managers can more efficiently increase metapopulation growth rate by focusing efforts on the bad patch. In our model, net reproductive rate differs between the two patches so that in the absence of dispersal, one patch is high quality and the other low quality. Disturbance, when present, reduces net reproductive rate with equal frequency and intensity in both patches. The stochastic disturbance model gives qualitatively similar results to the deterministic model. In most cases, metapopulation growth rate was elastic to changes in net reproductive rate of individuals in the good patch than the bad patch. However, when the majority of individuals are located in the bad patch, metapopulation growth rate can be most elastic to net reproductive rate in the bad patch. We expand the model to include two stages and parameterize the patches using data for the softshell clam, Mya arenaria. With a two-stage demographic model, the elasticities of metapopulation growth rate to parameters in the bad patch increase, while elasticities to the same parameters in the good patch decrease. Metapopulation growth rate is most elastic to adult survival in the population of the good patch for all scenarios we examine. If the majority of the metapopulation is located in the bad patch, the elasticity to parameters of that population increase but do not surpass elasticity to parameters in the good patch. This model can be expanded to include additional patches, multiple stages, stochastic dispersal, and complex demography.

The Santa Monica Mountains are home to many species of chaparral shrubs that provide vegetative cover and whose deep roots contribute to the stability of the steep slopes. Recently, native chaparral have been threatened by an unprecedented drought and frequent wildfires in Southern California. Besides the damage from the wildfires themselves, there is the potential for subsequent structural losses due to erosion and landslides. In this paper, we develop a mathematical model that predicts the impact of drought and frequent wildfires on chaparral plant community structure. We begin by classifying chaparral into two life history types based on their response to wildfires. Nonsprouters are completely killed by a fire, but their seeds germinate in response to fire cues. Facultative sprouters survive by resprouting but also rely on seed germination for post-fire recovery. The individual-based model presented here simulates the growth, seed dispersal, and resprouting behavior of individual shrubs across two life history types as they compete for space and resources in a rectangular domain. The model also incorporates varying annual rainfall and fire frequency as well as the competition between plants for scarce resources. The parameters were fit using seedling and resprout survivorship data as well as point quarter sampling data from 1986 to 2014 at a biological preserve within the natural landscape of the Malibu campus of Pepperdine University. The simulations from our model reproduce the change in plant community structure at our study site which includes the local extinction of the nonsprouter Ceanothus megacarpus due to shortened fire return intervals. Our simulations predict that a combination of extreme drought and frequent wildfires will drastically reduce the overall density of chaparral, increasing the likelihood of invasion by highly flammable exotic grasses. The simulations further predict that the majority of surviving shrubs will be facultative sprouting species such as Malosma laurina.