Carrying Capacity of Spatially Distributed Metapopulations

One way or another: Combined effect of dispersal and asymmetry on total realized asymptotic population abundance

Understanding the consequences on population dynamics of the variability in dispersal over a fragmented habitat remains a major focus of ecological and environmental inquiry. Dispersal is often asymmetric: wind, marine currents, rivers, or human activities produce a preferential direction of dispersal between connected patches. Here, we study how this asymmetry affects population dynamics by considering a discrete-time two-patch model with asymmetric dispersal. We conduct a rigorous analysis of the model and describe all the possible response scenarios of the total realized asymptotic population abundance to a change in the dispersal rate for a fixed symmetry level. In addition, we discuss which of these scenarios can be achieved just by restricting mobility in one specific direction. Moreover, we also report that changing the order of events does not alter the population dynamics in our model, contrary to other situations discussed in the literature.

The comparison of dispersal rate between invasive and native species varied by plant life form and functional traits

A long dispersal distance is widely used to indicate high invasiveness, but it ignores the temporal dimensions of plant invasion. Faster dispersal rates (= distance/time) of invasive species than native ones have been widely used in modeling species invasion and planning control management. However, the comparison of dispersal rate between invasive and native plants, particularly for dispersal on a local or landscape scale, has not been tested with a comprehensive dataset. Moreover, both the effects of plant functional traits on the dispersal rate and variation in the functional-trait effects between invasive and native plants remain elusive. Compiling studies from 30 countries globally, we compared seed dispersal rates (km/year) on a local or landscape scale between 64 observations of invasive and 78 observations of native plants given effects of plant life forms, disturbance levels, and measurement methods. Furthermore, we compared the effects of functional traits on dispersal rate between invasive and native species. We found that: (1) Trait values were similar between the invasive and native plants except for the greater height of woody native plants than woody invasive ones; (2) Compared within the same plant life form, the faster dispersal rates of invasive species were found in herbaceous plants, not in woody plants, and disturbance level and measurement methods did not affect the rate comparison; (3) Plant height and seed length had significant effects on dispersal rates of both invasive and native plants, but the effect of leaf dry matter content (LDMC) was only significant on herbaceous invasive plants. The comparison of dispersal rate between invasive and native plants varied by plant life form. The convergent values but divergent dispersal effects of plant traits between invasive and native species suggest that the trait effects on invasiveness could be better understood by trait association with key factors in invasiveness, e.g., dispersal rate, than the direct trait comparison between invasive and native plants.

The effect of dispersal on asymptotic total population size in discrete- and continuous-time two-patch models

Many populations occupy spatially fragmented landscapes. How dispersal affects the asymptotic total population size is a key question for conservation management and the design of ecological corridors. Here, we provide a comprehensive overview of two-patch models with symmetric dispersal and two standard density-dependent population growth functions, one in discrete and one in continuous time. A complete analysis of the discrete-time model reveals four response scenarios of the asymptotic total population size to increasing dispersal rate: (1) monotonically beneficial, (2) unimodally beneficial, (3) beneficial turning detrimental, and (4) monotonically detrimental. The same response scenarios exist for the continuous-time model, and we show that the parameter conditions are analogous between the discrete- and continuous-time setting. A detailed biological interpretation offers insight into the mechanisms underlying the response scenarios that thus improve our general understanding how potential conservation efforts affect population size.

Human mobility and disease prevalence

We examine the effect of human mobility on disease prevalence by studying the dependence of the total infected population at endemic equilibria with respect to population diffusion rates of a diffusive epidemic model. For small diffusion rates, our results indicate that the total infected population size is strictly decreasing with respect to the ratio of the diffusion rate of the infected population over that of the susceptible population. Moreover, when the disease local reproductive function is spatially heterogeneous, we found that: (i) for large diffusion rate of the infected population, the total infected population size is strictly maximized at large diffusion rate of the susceptible population when the recovery rate is spatially homogeneous, while it is strictly maximized at intermediate diffusion rate of the susceptible population when the difference of the transmission and recovery rates are spatially homogeneous; (ii) for large diffusion rate of the susceptible population, the total infected population size is strictly maximized at intermediate diffusion rate of the infected population when the recovery rate is spatially homogeneous, while it is strictly minimized at large diffusion rate of the infected population when the difference of the transmission and recovery rates is spatially homogeneous. Numerical simulations are provided to complement the theoretical results. Our studies may provide some insight into the impact of human mobility on disease outbreaks and the severity of epidemics.

The role of the spatial topology in trophic metacommunities: Species with reduced mobility and total population size

A central question in ecology is understanding the influence of the spatial topology on the dynamics of a metacommunity. This is not an easy task, as most fragmented ecosystems have trophic interactions involving many species and patches. Recent attempts to solve this challenge have introduced certain simplifying assumptions or focused on a limited set of examples. These simplifications make the models mathematically tractable but keep away from real-world problems. In this paper, we provide a novel methodology to describe the influence of the spatial topology on the total population size of the species when the dispersal rates are small. The main conclusion is that the influence of the spatial topology is the result of the influence of each path in isolation. Here, a path refers to a pairwise connection between two patches. Our framework can be readily used with any metacommunity, and therefore represents a unification of biological insights. We also discuss several applications regarding the construction of ecological corridors.

A phenomenological model for COVID-19 data taking into account neighboring-provinces effect and random noise

We model the incidence of the COVID-19 disease during the first wave of the epidemic in Castilla-Leon (Spain). Within-province dynamics may be governed by a generalized logistic map, but this lacks of spatial structure. To couple the provinces, we relate the daily new infections through a density-independent parameter that entails positive spatial correlation. Pointwise values of the input parameters are fitted by an optimization procedure. To accommodate the significant variability in the daily data, with abruptly increasing and decreasing magnitudes, a random noise is incorporated into the model, whose parameters are calibrated by maximum likelihood estimation. The calculated paths of the stochastic response and the probabilistic regions are in good agreement with the data.

Directed movement changes coexistence outcomes in heterogeneous environments

Understanding mechanisms of coexistence is a central topic in ecology. Mathematical analysis of models of competition between two identical species moving at different rates of symmetric diffusion in heterogeneous environments show that the slower mover excludes the faster one. The models have not been tested empirically and lack inclusions of a component of directed movement toward favourable areas. To address these gaps, we extended previous theory by explicitly including exploitable resource dynamics and directed movement. We tested the mathematical results experimentally using laboratory populations of the nematode worm, Caenorhabditis elegans. Our results not only support the previous theory that the species diffusing at a slower rate prevails in heterogeneous environments but also reveal that moderate levels of a directed movement component on top of the diffusive movement allow species to coexist. Our results broaden the theory of species coexistence in heterogeneous space and provide empirical confirmation of the mathematical predictions.

The optimal controlling strategy on a dispersing population in a two-patch system: Experimental and theoretical perspectives

Invasive species, disease vectors, and pathogens are significant threats to biodiversity, ecosystem function and services, and human health. Understanding the optimal management strategy, which maximizes the effectiveness is crucial. Despite an abundance of theoretical work has conducted on projecting the optimal allocation strategy, almost no empirical work has been performed to validate the theory. We first used a consumer-resource model to simulate a series of allocation fractions of controlling treatment to determine the optimal controlling strategy. Further, we conducted rigorous laboratory experiments using spatially diffusing laboratory populations of yeast to verify our mathematical results. We found consistent results that: (1) When population growth is limited by the local resource, the controlling priority should be given to the areas with higher concentration of resource; (2) When population growth is not limited by the resource concentration, the best strategy is to allocate equal amount of controlling efforts among the regions; (3) With restricted budget, it is more efficient to prioritize the controlling effects to the areas with high population abundance, otherwise, it is better to control equally among the regions. The new theory, which was tested by laboratory experiments, will reveal new opportunities for future field interventions, thereby informing subsequent biological decision-making.

Toward a Universal Theoretical Framework to Understand Robustness and Resilience: From Cells to Systems

Research across a range of biological subdisciplines and scales, ranging from molecular to ecosystemic, provides ample evidence that living systems generally exhibit both a degree of resistance to disruption and an ability to recover following disturbance. Not only do mechanisms of robustness and resilience exist across and between systems, but those mechanisms exhibit ubiquitous and scalable commonalities in pattern and function. Mechanisms such as redundancy, plasticity, interconnectivity, and coordination of subunits appear to be crucial internal players in the determination of stability. Similarly, factors external to the system such as the amplitude, frequency, and predictability of disruptors, or the prevalence of key limiting resources, may constrain pathways of response. In the face of a rapidly changing environment, there is a pressing need to develop a common framework for describing, assessing, and predicting robustness and resilience within and across living systems.