Higher-order species interactions cause time-dependent niche and fitness differences: Experimental evidence in plant-feeding arthropods

Species interact in different ways, including competition, facilitation and predation. These interactions can be non-linear or higher order and may depend on time or species densities. Although these higher-order interactions are virtually ubiquitous, they remain poorly understood, as they are challenging both theoretically and empirically. We propose to adapt niche and fitness differences from modern coexistence theory and apply them to species interactions over time. As such, they may not merely inform about coexistence, but provide a deeper understanding of how species interactions change. Here, we investigated how the exploitation of a biotic resource (plant) by phytophagous arthropods affects their interactions. We performed monoculture and competition experiments to fit a generalized additive mixed model to the empirical data, which allowed us to calculate niche and fitness differences. We found that species switch between different types of interactions over time, including intra- and interspecific facilitation, and strong and weak competition.

Epidemic highs and lows: a stochastic diffusion model for active cases

We derive a stochastic epidemic model for the evolving density of infective individuals in a large population. Data shows main features of a typical epidemic consist of low periods interspersed with outbreaks of various intensities and duration. In our stochastic differential model, a novel reproductive term combines a factor expressing the recent notion of 'attenuated Allee effect' and a capacity factor is controlling the size of the process. Simulation of this model produces sample paths of the stochastic density of infectives, which behave much like long-time Covid-19 case data of recent years. Writing the process as a stochastic diffusion allows us to derive its stationary distribution, showing the relative time spent in low levels and in outbursts. Much of the behaviour of the density of infectives can be understood in terms of the interacting drift and diffusion coefficient processes, or, alternatively, in terms of the balance between noise level and the attenuation parameter of the Allee effect. Unexpected results involve the effect of increasing overall noise variance on the density of infectives, in particular on its level-crossing function.

Block-pulse integrodifference equations

We present a hybrid method for calculating the equilibrium population-distributions of integrodifference equations (IDEs) with strictly increasing growth, for populations that are confined to a finite habitat-patch. This method is based on approximating the growth function of the IDE with a piecewise-constant function, and we call the resulting model a block-pulse IDE. We explicitly write out analytic expressions for the iterates and equilibria of the block-pulse IDEs as sums of cumulative distribution functions. We characterize the dynamics of one-, two-, and three-step block-pulse IDEs, including formal stability analyses, and we explore the bifurcation structure of these models. These simple models display rich dynamics, with numerous fold bifurcations. We then use three-, five-, and ten-step block-pulse IDEs, with a numerical root finder, to approximate models with compensatory Beverton-Holt growth and depensatory, or Allee-effect, growth. Our method provides a good approximation for the equilibrium distributions for compensatory and depensatory growth and offers numerical and analytical advantages over the original growth models.

Could non-native species boost their chances of invasion success by socializing with natives?

Most invasions start with the introduction of a few individuals and the majority fail to establish and become invasive populations. A possible explanation for this is that some species are subject to Allee effects-disadvantages of low densities-and fail to perform vital activities due to the low availability of conspecifics. We propose that 'facilitation' from native individuals to non-natives through heterospecific sociability could enhance chances of the latter establishing in novel environments by helping them avoid Allee effects and even reducing the minimum number of non-native individuals necessary to achieve the density for a viable population (the Allee effect threshold). There is evidence from experiments carried out with freshwater fish, snails, lizards, mussels and bird that supports the idea of heterospecific sociability between native and non-native species as a process to promote invasion success. We propose that to understand invasion success in social non-native species we need to investigate how they integrate into the recipient community. Furthermore, to manage them, it may be necessary to reduce population density not just below the Allee effect threshold but also to understand how natives could help them shift the conspecific Allee effect threshold to their benefit. This article is part of the theme issue 'Mixed-species groups and aggregations: shaping ecological and behavioural patterns and processes'.

Sex-biased infections scale to population impacts for an emerging wildlife disease

Demographic factors are fundamental in shaping infectious disease dynamics. Aspects of populations that create structure, like age and sex, can affect patterns of transmission, infection intensity and population outcomes. However, studies rarely link these processes from individual to population-scale effects. Moreover, the mechanisms underlying demographic differences in disease are frequently unclear. Here, we explore sex-biased infections for a multi-host fungal disease of bats, white-nose syndrome, and link disease-associated mortality between sexes, the distortion of sex ratios and the potential mechanisms underlying sex differences in infection. We collected data on host traits, infection intensity and survival of five bat species at 42 sites across seven years. We found females were more infected than males for all five species. Females also had lower apparent survival over winter and accounted for a smaller proportion of populations over time. Notably, female-biased infections were evident by early hibernation and likely driven by sex-based differences in autumn mating behaviour. Male bats were more active during autumn which likely reduced replication of the cool-growing fungus. Higher disease impacts in female bats may have cascading effects on bat populations beyond the hibernation season by limiting recruitment and increasing the risk of Allee effects.

Tipping Cascades in a Multi-patch System with Noise and Spatial Coupling

Forecasting tipping points in spatially extended systems is a key area of interest to ecologists. A slowly declining spatially distributed population is an important example of an ecological system that could exhibit a cascade of tipping points. Here, we develop a spatial two-patch model with environmental stochasticity that is slowly forced through population collapse, in the presence of changing environmental conditions. We begin with a basic spatial model, then introduce a fast-slow version of the model using geometric singular perturbation theory, followed by the inclusion of stochasticity. Using the spectral density of the fluctuating subpopulation in each patch, we derive analytic expressions for candidate indicators of population extinction and evaluate their performance through a simulation study. We find that coupling and spatial heterogeneity decrease the magnitude of the proposed indicators in coupled populations relative to isolated populations. Moreover, the degree of coupling dictates the trends in summary statistics. We conclude that this theory may be applied to other contexts, including the control of invasive species.

The Effect of the Recombination Rate between Adaptive Loci on the Capacity of a Population to Expand Its Range

AbstractPrevious theoretical work on range expansions over heterogeneous environments showed that there is a critical environmental gradient where range expansion stops. For populations with freely recombining loci underlying the trait under selection (hereafter, "adaptive loci"), the critical gradient in one-dimensional habitats depends on the fitness cost of dispersal and the strength of selection relative to genetic drift. Here, we extend the previous work in two directions and ask, What is the role of the recombination rate between the adaptive loci during range expansions? And what effect does the ability of selfing as opposed to obligate outcrossing have on range expansions? To answer these questions, we use computer simulations. We demonstrate that while reduced recombination rates between adaptive loci slow down range expansions as a result of poor purging of locally deleterious alleles at the expansion front, they may also allow a species to occupy a greater range. In addition, we find that the allowance of selfing may improve the ability of populations to expand their ranges, for example, because selfing among potentially rare high-fitness individuals facilitates the establishment and maintenance of locally well-adapted genotypes. We conclude that during range expansions there is a trade-off between positive and negative effects of recombination within and between individuals.

The Role of Stochasticity in Noise-Induced Tipping Point Cascades: A Master Equation Approach

Tipping points have been shown to be ubiquitous, both in models and empirically in a range of physical and biological systems. The question of how tipping points cascade through systems has been less explored and is an important one. A study of noise-induced tipping, in particular, could provide key insights into tipping cascades. Here, we consider a specific example of a simple model system that could have cascading tipping points. This model consists of two interacting populations with underlying Allee effects and stochastic dynamics, in separate patches connected by dispersal, which can generate bistability. From an ecological standpoint, we look for rescue effects whereby one population can prevent the collapse of a second population. As a way to investigate the stochastic dynamics, we use an individual-based modeling approach rooted in chemical reaction network theory. Then, using continuous-time Markov chains and the theory of first passage times, we essentially approximate, or emulate, the original high-dimensional model by a Markov chain with just three states, where each state corresponds to a combination of population thresholds. Analysis of this reduced model shows when the system is likely to recover, as well as when tipping cascades through the whole system.

Predicting the Outbreak Risks and Inflection Points of COVID-19 Pandemic with Classic Ecological Theories

Predicting the outbreak risks and/or the inflection (turning or tipping) points of COVID-19 can be rather challenging. Here, it is addressed by modeling and simulation approaches guided by classic ecological theories and by treating the COVID-19 pandemic as a metapopulation dynamics problem. Three classic ecological theories are harnessed, including TPL (Taylor's power-law) and Ma's population aggregation critical density (PACD) for spatiotemporal aggregation/stability scaling, approximating virus metapopulation dynamics with Hubbell's neutral theory, and Ma's diversity-time relationship adapted for the infection-time relationship. Fisher-Information for detecting critical transitions and tipping points are also attempted. It is discovered that: (i) TPL aggregation/stability scaling parameter (b > 2), being significantly higher than the b-values of most macrobial and microbial species including SARS, may interpret the chaotic pandemic of COVID-19. (ii) The infection aggregation critical threshold (M 0) adapted from PACD varies with time (outbreak-stage), space (region) and public-health interventions. Exceeding M 0, local contagions may become aggregated and connected regionally, leading to epidemic/pandemic. (iii) The ratio of fundamental dispersal to contagion numbers can gauge the relative importance between local contagions vs. regional migrations in spreading infections. (iv) The inflection (turning) points, pair of maximal infection number and corresponding time, are successfully predicted in more than 80% of Chinese provinces and 68 countries worldwide, with a precision >80% generally.

Mazes to Study the Effects of Spatial Complexity, Predation and Population Density on Mate Finding

The difficulty to locate mates and overcome predation can hamper species establishment and population maintenance. The effects of sparseness between individuals or the effect of predators on the probability of population growth can be difficult to measure experimentally. For testing hypotheses about population density and predation, we contend that habitat complexity can be simulated using insect mazes of varying mathematical difficulty. To demonstrate the concept, we investigated whether the use of 3D printed mazes of varying complexity could be used to increase spatial separation between sexes of Drosophila simulans, and whether the presence of a generalist predator hampered mate-finding. We then examined how increasing D. simulans population density might overcome the artificially created effects of increasing the distance between mates and having a predator present. As expected, there was an increase in time taken to find a mate and a lower incidence of mating as habitat complexity increased. Increasing the density of flies reduced the searching time and increased mating success, and overcame the effect of the predator in the maze. Printable 3D mazes offer the opportunity to quickly assess the effects of spatial separation on insect population growth in the laboratory, without the need for large enclosed spaces. Mazes could be scaled up for larger insects and can be used for other applications such as learning.

Pollination outcomes reveal negative density-dependence coupled with interspecific facilitation among plants

Pollination is thought to be under positive density-dependence, destabilising plant coexistence by conferring fitness disadvantages to rare species. Such disadvantage is exacerbated by interspecific competition but can be mitigated by facilitation and intraspecific competition. However, pollinator scarcity should enhance intraspecific plant competition and impose disadvantage on common over rare species (negative density-dependence, NDD). We assessed pollination proxies (visitation rate, pollen receipt, pollen tubes) in a generalised plant community and related them to conspecific and heterospecific density, expecting NDD and interspecific facilitation due to the natural pollinator scarcity. Contrary to usual expectations, all proxies indicated strong intraspecific competition for common plants. Moreover interspecific facilitation prevailed and was stronger for rare than for common plants. Both NDD and interspecific facilitation were modulated by specialisation, floral display and pollinator group. The combination of intraspecific competition and interspecific facilitation fosters plant coexistence, suggesting that pollination can be a niche axis maintaining plant diversity.

Asexual Reproduction Can Account for the High Diversity and Prevalence of Rare Taxa Observed in Microbial Communities

There have been numerous recent efforts to integrate microbes into broad-scale ecological theories. Microbial communities are often structurally distinct from macrobial communities, but it is unclear whether these differences are real or whether they are due to the different methodologies used to study communities at these two scales. One major difference between macroorganisms and microorganisms is that microbes are much more likely to reproduce asexually. Sexually reproducing taxa have diminished growth rates at low population size, because they must encounter another member of their species before reproducing. This study shows that communities of asexually reproducing taxa are expected to be more diverse, because taxa persist longer. Furthermore, asexually reproducing taxa can exist at much lower densities than sexually reproducing taxa. Thus, asexual reproduction by microbes can account for two major differences between microbial and macrobial communities, namely, greater diversity and greater prevalence of rare taxa for microbes.

Recent studies evaluating the community structures of microorganisms and macroorganisms have found greater diversity and rarity within micro-scale communities, compared to macro-scale communities. However, reproductive method has been a confounding factor in these comparisons; the microbes considered generally reproduce asexually, while the macroorganisms considered generally reproduce sexually. Sexual reproduction imposes the constraint of mate finding, which can have significant demographic consequences by depressing birth rates at low population sizes. First, I construct an island biogeography model to study the organization of ecological communities under neutral stochastic processes. Then, I examine theoretically how the effects of mate finding in sexual populations translate to the emergent community properties of diversity, rarity, and dominance (size of the largest population). In mate-limited sexual populations, the decreased growth rates at low population densities translate to a higher extinction rate; this increased extinction rate had a disproportionately strong effect on taxa with low population densities. Thus, mate limitation decreased diversity, primarily by excluding small populations from communities. However, the most abundant taxa were minimally affected by mate limitation. Therefore, mate limitation affected the diversity and rarity of taxa in communities but did not alter the dominance of the largest population. The observed shifts in community structure mirror recent empirical studies of micro-scale versus macro-scale communities, which have shown that microbial communities have greater diversity and rarity than macrobial communities but are not different in dominance. Thus, reproductive method may contribute to observed differences in emergent properties between communities at these two scales.

IMPORTANCE There have been numerous recent efforts to integrate microbes into broad-scale ecological theories. Microbial communities are often structurally distinct from macrobial communities, but it is unclear whether these differences are real or whether they are due to the different methodologies used to study communities at these two scales. One major difference between macroorganisms and microorganisms is that microbes are much more likely to reproduce asexually. Sexually reproducing taxa have diminished growth rates at low population size, because they must encounter another member of their species before reproducing. This study shows that communities of asexually reproducing taxa are expected to be more diverse, because taxa persist longer. Furthermore, asexually reproducing taxa can exist at much lower densities than sexually reproducing taxa. Thus, asexual reproduction by microbes can account for two major differences between microbial and macrobial communities, namely, greater diversity and greater prevalence of rare taxa for microbes.

Evaluating the effects of landscape structure on the recovery of an invasive vertebrate after population control

CONTEXT

Effective landscape control of invasive species is context-dependent due to the interplay between the landscape structure, local population dynamics, and metapopulation processes. We use a modelling approach incorporating these three elements to explore the drivers of recovery of populations of invasive species after control.

OBJECTIVES

We aim to improve our understanding of the factors influencing the landscape-level control of invasive species.

METHODS

We focus on the case study of invasive brushtail possum (Trichosurus vulpecula) control in New Zealand. We assess how 13 covariates describing the landscape, patch, and population features influence the time of population recovery to a management density threshold of two possums/ha. We demonstrate the effects of those covariates on population recovery under three scenarios of population growth: logistic growth, strong Allee effects, and weak Allee effects.

RESULTS

Recovery times were rapid regardless of the simulated population dynamics (average recovery time < 2 years), although populations experiencing Allee effects took longer to recover than those growing logistically. Our results indicate that habitat availability and patch area play a key role in reducing times to recovery after control, and this relationship is consistent across the three simulated scenarios.

CONCLUSIONS

The control of invasive possum populations in patchy landscapes would benefit from a patch-level management approach (considering each patch as an independent management unit), whereas simple landscapes would be better controlled by taking a landscape-level view (the landscape as the management unit). Future research should test the predictions of our models with empirical data to refine control operations.

Size-based ecological interactions drive food web responses to climate warming

Predicting climate change impacts on animal communities requires knowledge of how physiological effects are mediated by ecological interactions. Food-dependent growth and within-species size variation depend on temperature and affect community dynamics through feedbacks between individual performance and population size structure. Still, we know little about how warming affects these feedbacks. Using a dynamic stage-structured biomass model with food-, size- and temperature-dependent life history processes, we analyse how temperature affects coexistence, stability and size structure in a tri-trophic food chain, and find that warming effects on community stability depend on ecological interactions. Predator biomass densities generally decline with warming - gradually or through collapses - depending on which consumer life stage predators feed on. Collapses occur when warming induces alternative stable states via Allee effects. This suggests that predator persistence in warmer climates may be lower than previously acknowledged and that effects of warming on food web stability largely depend on species interactions.

Fertilization limitation of Diadema antillarum on coral reefs in the Florida Keys

Mass mortality of the sea urchin Diadema antillarum due to disease outbreaks in 1983 and 1991 decimated populations in the Florida Keys, and they have yet to recover. Here, we use a coupled advection-diffusion and fertilization-kinetics model to test the hypothesis that these populations are fertilization limited. We found that fertilization success was ≥ 96% prior to the first disease outbreak, decreased substantially following recurrent disease to 3%, and has since remained low. By investigating the combined effects of physical factors (population spatial extent and current velocity) and sea urchin behavior (aggregation) on density-dependent fertilization success, we show that fertilization success at a given density increases with increasing population spatial extent and decreasing current velocity, and is greater under simulated aggregation behavior of D. antillarum. However, at present population densities, the increase in fertilization success due to aggregation is < 1%, even under the most favorable physical conditions. These results indicate that populations are severely fertilization limited, and that Allee effects at low population density will continue to limit recovery. Our results can serve as a practical guide to managers in the development of coral reef restoration strategies, including the design of a D. antillarum restocking program to obtain reproductively viable populations.

Heterogeneity in local density allows a positive evolutionary relationship between self-fertilisation and dispersal

Despite empirical evidence for a positive relationship between dispersal and self-fertilization (selfing), theoretical work predicts that these traits should always be negatively correlated, and the Good Coloniser Syndrome of high dispersal and selfing (Cf. Baker's Law) should not evolve. Critically, previous work assumes that adult density is spatiotemporally homogeneous, so selfing results in identical offspring production for all patches, eliminating the benefit of dispersal for escaping from local resource competition. We investigate the joint evolution of dispersal and selfing in a demographically structured metapopulation model where local density is spatiotemporally heterogeneous due to extinction-recolonization dynamics. Selfing alleviates outcrossing failure due to low local density (an Allee effect) while dispersal alleviates competition through dispersal of propagules from high- to low-density patches. Because local density is spatiotemporally heterogeneous in our model, selfing does not eliminate heterogeneity in competition, so dispersal remains beneficial even under full selfing. Hence the Good Coloniser Syndrome is evolutionarily stable under a broad range of conditions, and both negative and positive relationships between dispersal and selfing are possible, depending on the environment. Our model thus accommodates positive empirical relationships between dispersal and selfing not predicted by previous theoretical work and provides additional explanations for negative relationships.

Best in the company of nearby males: female success in the threatened cycad, Zamia portoricensis

Variation in plant reproductive success is affected by ecological conditions including the proximity of potential mates. We address the hypothesis that spatial distribution of sexes affects female reproductive success (RS) in the dioecious cycad, Zamia portoricensis. Are the frequencies of males, operational sex ratios, and distances to the nearest mate associated with RS in females? We studied the spatial distribution of sexes in two populations in Puerto Rico and compared RS of target females with the number of males and operational sex ratios. Population structure suggests regular successful recruitment. Adults, males, and females were randomly distributed with respect to one another. Reproductive success of females was highly variable, but was higher in neighborhoods with more males than females and generally decreased with increasing distance to the nearest male, becoming statistically significant beyond 190 cm. This possible mate-finding Allee effect indicates that pollinator movement among plants may be limited for this mutually dependent plant-pollinator interaction. Yet being close to male plants is a matter of chance, perhaps a factor generating the high intra-population genetic diversity in Z. portoricensis.

On the intrinsic dynamics of bacteria in waterborne infections

The intrinsic dynamics of bacteria often play an important role in the transmission and spread of waterborne infectious diseases. In this paper, we construct mathematical models for waterborne infections and analyze two types of nontrivial bacterial dynamics: logistic growth, and growth with Allee effects. For the model with logistic growth, we find that regular threshold dynamics take place, and the basic reproduction number can be used to characterize disease extinction and persistence. In contrast, the model with Allee effects exhibits much more complex dynamics, including the existence of multiple endemic equilibria and the presence of backward bifurcation and forward hysteresis.

Novel insights on population and range edge dynamics using an unparalleled spatiotemporal record of species invasion

Quantifying the complex spatial dynamics taking place at range edges is critical for understanding future distributions of species, yet very few systems have sufficient data or the spatial resolution to empirically test these dynamics. This paper reviews how data from a large-scale pest management programme have provided important contributions to the fields of population dynamics and invasion biology. The invasion of gypsy moth (Lymantria dispar) is well-documented from its introduction near Boston, Massachusetts USA in 1869 to its current extent of over 900,000 km² in Eastern North America. Over the past two decades, the USDA Forest Service Slow the Spread (STS) programme for managing the future spread of gypsy moth has produced unrivalled spatiotemporal data across the invasion front. The STS programme annually deploys a grid of 60,000-100,000 pheromone-baited traps, currently extending from Minnesota to North Carolina. The data from this programme have provided the foundation for investigations of complex population dynamics and the ability to examine ecological hypotheses previously untestable outside of theoretical venues, particularly regarding invasive spread and Allee effects. This system provides empirical data on the importance of long-distance dispersal and time-lags on population establishment and spatial spread. Studies showing high rates of spatiotemporal variation of the range edge, from rapid spread to border stasis and even retraction, highlight future opportunities to test mechanisms that influence both invasive and native species ranges. The STS trap data have also created a unique opportunity to study low-density population dynamics and quantify Allee effects with empirical data. Notable contributions include evidence for spatiotemporal variation in Allee effects, demonstrating empirical links between Allee effects and spatial spread, and testing mechanisms of population persistence and growth rates at range edges. There remain several outstanding questions in spatial ecology and population biology that can be tested within this system, such as the scaling of local ecological processes to large-scale dynamics across landscapes. The gypsy moth is an ideal model of how important ecological questions can be answered by thinking more broadly about monitoring data.

New revised simple models for interactive wild and sterile mosquito populations and their dynamics

Based on previous research, we formulate revised, new, simple models for interactive wild and sterile mosquitoes which are better approximations to real biological situations but mathematically more tractable. We give basic investigations of the dynamical features of these simple models such as the existence of equilibria and their stability. Numerical examples to demonstrate our findings and brief discussions are also provided.

Density dependence in demography and dispersal generates fluctuating invasion speeds

Density dependence plays an important role in population regulation and is known to generate temporal fluctuations in population density. However, the ways in which density dependence affects spatial population processes, such as species invasions, are less understood. Although classical ecological theory suggests that invasions should advance at a constant speed, empirical work is illuminating the highly variable nature of biological invasions, which often exhibit nonconstant spreading speeds, even in simple, controlled settings. Here, we explore endogenous density dependence as a mechanism for inducing variability in biological invasions with a set of population models that incorporate density dependence in demographic and dispersal parameters. We show that density dependence in demography at low population densities-i.e., an Allee effect-combined with spatiotemporal variability in population density behind the invasion front can produce fluctuations in spreading speed. The density fluctuations behind the front can arise from either overcompensatory population growth or density-dependent dispersal, both of which are common in nature. Our results show that simple rules can generate complex spread dynamics and highlight a source of variability in biological invasions that may aid in ecological forecasting.

Stage-structured wild and sterile mosquito population models and their dynamics

To study the impact of the sterile insect technique and effects of the mosquitoes' metamorphic stage structure on the transmission dynamics of mosquito-borne diseases, we formulate stage-structured continuous-time mathematical models, based on systems of differential equations, for the interactive dynamics of the wild and sterile mosquitoes. We incorporate different strategies for the releases of sterile mosquitoes in the models and investigate the model dynamics, including the existence of positive equilibria and their stability. Numerical examples are provided to demonstrate the dynamical features of the models.

Canopy interactions and physical stress gradients in subtidal communities

Species interactions are integral drivers of community structure and can change from competitive to facilitative with increasing environmental stress. In subtidal marine ecosystems, however, interactions along physical stress gradients have seldom been tested. We observed seaweed canopy interactions across depth and latitudinal gradients to test whether light and temperature stress structured interaction patterns. We also quantified interspecific and intraspecific interactions among nine subtidal canopy seaweed species across three continents to examine the general nature of interactions in subtidal systems under low consumer pressure. We reveal that positive and neutral interactions are widespread throughout global seaweed communities and the nature of interactions can change from competitive to facilitative with increasing light stress in shallow marine systems. These findings provide support for the stress gradient hypothesis within subtidal seaweed communities and highlight the importance of canopy interactions for the maintenance of subtidal marine habitats experiencing environmental stress.

Allee effects, adaptive evolution, and invasion success

The mechanisms that facilitate success of an invasive species include both ecological and evolutionary processes. Investigating the evolutionary dynamics of founder populations can enhance our understanding of patterns of invasiveness and provide insight into management strategies for controlling further establishment of introduced populations. Our aim is to analyze the evolutionary consequences of ecological processes (i.e., propagule pressure and threshold density effects) that impact successful colonization. We address our questions using a spatially-explicit modeling approach that incorporates dispersal, density dependent population growth, and selection. Our results show that adaptive evolution may occur in small or sparse populations, providing a means of mitigating or avoiding inverse density dependent effects (i.e., Allee effects). The rate at which this adaptation occurs is proportional to the amount of genetic variance and is a crucial component in assessing whether natural selection can rescue a population from extinction. We provide theoretical evidence for the importance of recognizing evolution in predicting and explaining successful biological invasions.

Allee effects and population spread in patchy landscapes

Invasion of alien species is one of the major threats for natural community structures, potentially leading to high economic and environmental costs. In this work, we study through a reaction-diffusion model the dynamics of an invasion in a heterogeneous environment and in the presence of a strong Allee effect. We model space as an infinite landscape consisting of periodically alternating favourable and unfavourable patches. In addition, we consider that at the interface between patch types individuals may show preference for more favourable regions. Using homogenization techniques and a classical result for spread with Allee effect in homogeneous landscapes, we derive approximate expressions for the spread speed. When compared with numerical simulations, these expressions prove to be very accurate even beyond the expected small-scale heterogeneity limit of homogenization. We demonstrate how rates of spatial spread depend on demographic and movement parameters as well as on the landscape properties.

Modelling releases of sterile mosquitoes with different strategies

To prevent the transmissions of malaria, dengue fever, or other mosquito-borne diseases, one effective weapon is the sterile insect technique in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population. To study the impact of the sterile insect technique on disease transmission, we formulate discrete-time mathematical models, based on difference equations, for the interactive dynamics of the wild and sterile mosquitoes, incorporating different strategies in releasing sterile mosquitoes. We investigate the model dynamics and compare the impact of the different release strategies. Numerical examples are given to demonstrate rich dynamical features of the models.

Overcoming Allee effects through evolutionary, genetic, and demographic rescue

Despite the amplified threats of extinction facing small founder populations, successful colonization sometimes occurs, bringing devastating ecological and economic consequences. One explanation may be rapid evolution, which can increase mean fitness in populations declining towards extinction, permitting persistence and subsequent expansion. Such evolutionary rescue may be particularly important, given Allee effects. When a population is introduced at low density, individuals often experience a reduction in one or more components of fitness due to novel selection pressures that arise from diminished intraspecific interactions and positive density dependence (i.e. component Allee effects). A population can avoid extinction if it can adapt and recover on its own (i.e. evolutionary rescue), or if additional immigration sustains the population (i.e. demographic rescue) or boosts its genetic variation that facilitates adaptation (i.e. genetic rescue). These various forms of rescue have often been invoked as possible mechanisms for specific invasions, but their relative importance to invasion is not generally understood. Within a spatially explicit modelling framework, we consider the relative impact of each type of rescue on the probability of successful colonization, when there is evolution of a multi-locus quantitative trait that influences the strength of component Allee effects. We demonstrate that when Allee effects are important, the effect of demographic rescue via recurrent immigration overall provides the greatest opportunity for success. While highlighting the role of evolution in the invasion process, we underscore the importance of the ecological context influencing the persistence of small founder populations.

Exotic invaders gain foraging benefits by shoaling with native fish

Freshwater habitats are under increasing threat due to invasions of exotic fish. These invasions typically begin with the introduction of small numbers of individuals unfamiliar with the new habitat. One way in which the invaders might overcome this disadvantage is by associating with native taxa occupying a similar ecological niche. Here we used guppies (Poecilia reticulata) from a feral population in Mexico to test the prediction that exotic shoaling fish can associate with heterospecifics, and that they improve their foraging efficiency by doing so. Guppies have invaded the Mexican High Plateau and are implicated in the declines of many native topminnow (Goodeinae) species. We show that heterospecific associations between guppies and topminnows can deliver the same foraging benefits as conspecific shoals, and that variation in foraging gains is linked to differences in association tendency. These results uncover a mechanism enabling founding individuals to survive during the most vulnerable phase of an invasion and help explain why guppies have established viable populations in many parts of Mexico as well in every continent except Antarctica.

Dynamics of SI models with both horizontal and vertical transmissions as well as Allee effects

A general SI (Susceptible-Infected) epidemic system of host-parasite interactions operating under Allee effects, horizontal and/or vertical transmission, and where infected individuals experience pathogen-induced reductions in reproductive ability, is introduced. The initial focus of this study is on the analyses of the dynamics of density-dependent and frequency-dependent effects on SI models (SI-DD and SI-FD). The analyses identify conditions involving horizontal and vertical transmitted reproductive numbers, namely those used to characterize and contrast SI-FD and SI-DD dynamics. Conditions that lead to disease-driven extinction, or disease-free dynamics, or susceptible-free dynamics, or endemic disease patterns are identified. The SI-DD system supports richer dynamics including limit cycles while the SI-FD model only supports equilibrium dynamics. SI models under "small" horizontal transmission rates may result in disease-free dynamics. SI models under with and inefficient reproductive infectious class may lead to disease-driven extinction scenarios. The SI-DD model supports stable periodic solutions that emerge from an unstable equilibrium provided that either the Allee threshold and/or the disease transmission rate is large; or when the disease has limited influence on the infectives growth rate; and/or when disease-induced mortality is low. Host-parasite systems where diffusion or migration of local populations manage to destabilize them are examples of what is known as diffusive instability. The exploration of SI-dynamics in the presence of dispersal brings up the question of whether or not diffusive instability is a possible outcome. Here, we briefly look at such possibility within two-patch coupled SI-DD and SI-FD systems. It is shown that relative high levels of asymmetry, two modes of transmission, frequency dependence, and Allee effects are capable of supporting diffusive instability.

Backward bifurcations and strong Allee effects in matrix models for the dynamics of structured populations

In nonlinear matrix models, strong Allee effects typically arise when the fundamental bifurcation of positive equilibria from the extinction equilibrium at r=1 (or R0=1) is backward. This occurs when positive feedback (component Allee) effects are dominant at low densities and negative feedback effects are dominant at high densities. This scenario allows population survival when r (or equivalently R0) is less than 1, provided population densities are sufficiently high. For r>1 (or equivalently R0>1) the extinction equilibrium is unstable and a strong Allee effect cannot occur. We give criteria sufficient for a strong Allee effect to occur in a general nonlinear matrix model. A juvenile-adult example model illustrates the criteria as well as some other possible phenomena concerning strong Allee effects (such as positive cycles instead of equilibria).

A simple epidemiological model for populations in the wild with Allee effects and disease-modified fitness

The study of the dynamics of human infectious disease using deterministic models is typically carried out under the assumption that a critical mass of individuals is available and involved in the transmission process. However, in the study of animal disease dynamics where demographic considerations often play a significant role, this assumption must be weakened. Models of the dynamics of animal populations often naturally assume that the presence of a minimal number of individuals is essential to avoid extinction. In the ecological literature, this a priori requirement is commonly incorporated as an Allee effect. The focus here is on the study disease dynamics under the assumption that a critical mass of susceptible individuals is required to guarantee the population's survival. Specifically, the emphasis is on the study of the role of an Allee effect on a Susceptible-Infectious (SI) model where the possibility that susceptible and infected individuals reproduce, with the S-class the best fit. It is further assumed that infected individuals loose some of their ability to compete for resources, the cost imposed by the disease. These features are set in motion in as simple model as possible. They turn out to lead to a rich set of dynamical outcomes. This toy model supports the possibility of multi-stability (hysteresis), saddle node and Hopf bifurcations, and catastrophic events (disease-induced extinction). The analyses provide a full picture of the system under disease-free dynamics including disease-induced extinction and proceed to identify required conditions for disease persistence. We conclude that increases in (i) the maximum birth rate of a species, or (ii) in the relative reproductive ability of infected individuals, or (iii) in the competitive ability of a infected individuals at low density levels, or in (iv) the per-capita death rate (including disease-induced) of infected individuals, can stabilize the system (resulting in disease persistence). We further conclude that increases in (a) the Allee effect threshold, or (b) in disease transmission rates, or in (c) the competitive ability of infected individuals at high density levels, can destabilize the system, possibly leading to the eventual collapse of the population. The results obtained from the analyses of this toy model highlight the significant role that factors like an Allee effect may play on the survival and persistence of animal populations. Scientists involved in biological conservation and pest management or interested in finding sustainability solutions, may find these results of this study compelling enough to suggest additional focused research on the role of disease in the regulation and persistence of animal populations. The risk faced by endangered species may turn out to be a lot higher than initially thought.