The evidence for Allee effects

Immunological feedback loops generate parasite persistence thresholds that explain variation in infection duration

Infection duration affects individual host fitness and between-host transmission. Whether an infection is cleared or becomes chronic depends on the complex interaction between host immune responses and parasite growth. Empirical and theoretical studies have suggested that there are critical thresholds of parasite dose that can determine clearance versus chronicity, driven by the ability of the parasite to manipulate host immunity. However, the mammalian immune response is characterized by strong positive and negative feedback loops that could generate duration thresholds even in the absence of direct immunomodulation. Here, we derive and analyse a simple model for the interaction between T-cell subpopulations and parasite growth. We show that whether an infection is cleared or not is very sensitive to the initial immune state, parasite dose and strength of immunological feedbacks. In particular, chronic infections are possible even when parasites provoke a strong and effective immune response and lack any ability to immunomodulate. Our findings indicate that the initial immune state, which often goes unmeasured in empirical studies, is a critical determinant of infection duration. This work also has implications for epidemiological models, as it implies that infection duration will be highly variable among individuals, and dependent on each individual's infection history.

Bottom-up effects drive the dynamic of an Antarctic seabird predator-prey system

Understanding how populations respond to variability in environmental conditions and interspecific interactions is one of the biggest challenges of population ecology, particularly in the context of global change. Although many studies have investigated population responses to climate change, very few have explicitly integrated interspecific relationships when studying these responses. In this study, we aimed to understand the combined effects of interspecific interactions and environmental conditions on the demographic parameters of a prey-predator system of three sympatric seabird populations breeding in Antarctica: the south polar skua (Catharacta maccormicki) and its two main preys during the breeding season, the Adélie penguin (Pygoscelis adeliae) and the emperor penguin (Aptenodytes forsteri). We built a two-species integrated population model (IPM) with 31 years of capture-recapture and count data and provided a framework that made it possible to estimate the demographic parameters and abundance of a predator-prey system in a context where capture-recapture data were not available for one species. Our results showed that predator-prey interactions and local environmental conditions differentially affected south polar skuas depending on their breeding state of the previous year. Concerning prey-predator relationships, the number of Adélie penguin breeding pairs showed a positive effect on south polar skua survival and breeding probability, and the number of emperor penguin dead chicks showed a positive effect on the breeding success of south polar skuas. In contrast, there was no evidence for an effect of the number of south polar skuas on the demography of Adélie penguins. We also found an important impact of sea ice conditions on both the dynamics of south polar skuas and Adélie penguins. Our results suggest that this prey-predator system is mostly driven by bottom-up processes and local environmental conditions.

Allee effects introduced by density dependent phenology

We consider a hybrid model of an annual species with the timing of a stage transition governed by density dependent phenology. We show that the model can produce a strong Allee effect as well as overcompensation. The density dependent probability distribution that describes how population emergence is spread over time plays an important role in determining population dynamics. Our extensive numerical simulations with a density dependent gamma distribution indicate very rich population dynamics, from stable/unstable equilibria, limit cycles, to chaos.

The role of Allee effects for Gaussian and Lévy dispersals in an environmental niche

In the study of biological populations, the Allee effect detects a critical density below which the population is severely endangered and at risk of extinction. This effect supersedes the classical logistic model, in which low densities are favorable due to lack of competition, and includes situations related to deficit of genetic pools, inbreeding depression, mate limitations, unavailability of collaborative strategies due to lack of conspecifics, etc. The goal of this paper is to provide a detailed mathematical analysis of the Allee effect. After recalling the ordinary differential equation related to the Allee effect, we will consider the situation of a diffusive population. The dispersal of this population is quite general and can include the classical Brownian motion, as well as a Lévy flight pattern, and also a "mixed" situation in which some individuals perform classical random walks and others adopt Lévy flights (which is also a case observed in nature). We study the existence and nonexistence of stationary solutions, which are an indication of the survival chance of a population at the equilibrium. We also analyze the associated evolution problem, in view of monotonicity in time of the total population, energy consideration, and long-time asymptotics. Furthermore, we also consider the case of an "inverse" Allee effect, in which low density populations may access additional benefits.

Demographic effects of aggregation in the presence of a component Allee effect

The component Allee effect (AE) is the positive correlation between an organism's fitness component and population density. Depending on the population spatial structure, which determines the interactions between organisms, a component AE might lead to positive density dependence in the population per-capita growth rate and establish a demographic AE. However, existing spatial models impose a fixed population spatial structure, which limits the understanding of how a component AE and spatial dynamics jointly determine the existence of demographic AEs. We introduce a spatially explicit theoretical framework where spatial structure and population dynamics are emergent properties of the individual-level demographic and movement rates. This framework predicts various spatial patterns depending on its specific parametrization, including evenly spaced aggregates of organisms, which determine the demographic-level by-products of the component AE. We find that aggregation increases population abundance and allows population survival in harsher environments and at lower global population densities when compared with uniformly distributed organisms. Moreover, aggregation can prevent the component AE from manifesting at the population level or restrict it to the level of each independent aggregate. These results provide a mechanistic understanding of how component AEs might operate for different spatial structures and manifest at larger scales.

Population genomics of the invasive Northern Giant Hornet Vespa mandarinia in North America and across its native range

The northern giant hornet Vespa mandarinia (NGH) is a voracious predator of other insect species, including honey bees. NGH's native range spans subtropical and temperate regions across much of east and southeast Asia and, in 2019, exotic populations of the species were discovered in North America. Despite this broad range and invasive potential, investigation of the population genomic structure of NGH across its native and introduced ranges has thus far been limited to a small number of mitochondrial samples. Here, we present analyses of genomic data from NGH individuals collected across the species' native range and from exotic individuals collected in North America. We provide the first survey of whole-genome population variation for any hornet species, covering this species' native and invasive ranges, and in doing so confirm likely origins in Japan and South Korea for the two introductions. We additionally show that, while this introduced population exhibited strongly elevated levels of inbreeding, these signatures of inbreeding are also present in some long-standing native populations, which may indicate that inbreeding depression alone is insufficient to prevent the persistence of NGH populations. As well as highlighting the importance of ongoing monitoring and eradication efforts to limit the spread of this species outside of its natural range, our data will serve as a foundational database for future genomic studies into introduced hornet populations.

Predicting the dispersal and invasion dynamics of ambrosia beetles through demographic reconstruction and process-explicit modeling

Evaluating potential routes of invasion of pathogens and vectors of sanitary importance is essential for planning and decision-making at multiple scales. An effective tool are process-explicit models that allow coupling environmental, demographic and dispersal information to evaluate population growth and range dynamics as a function of the abiotic conditions in a region. In this work we simulate multiple dispersal/invasion routes in Mexico that could be taken by ambrosia beetles and a specific symbiont, Harringtonia lauricola, responsible for a severe epiphytic of Lauraceae in North America. We used Xyleborus bispinatus Eichhoff 1868 as a study subject and estimated its demography in the laboratory in a temperature gradient (17, 20, 26, 29, 35 °C), which we then used to parameterize a process-based model to estimate its metapopulation dynamics. The maximum intrinsic growth rate of X. bispinatus is 0.13 with a thermal optimum of 26.2 °C. The models suggest important regions for the establishment and dispersal the states of Veracruz, Chiapas and Oaxaca (high host and secondary vectors diversity), the Isthmus of Tehuantepec (connectivity region), and Michoacán and Jalisco (important avocado plantations). The use of hybrid process-based models is a promising tool to refine the predictions applied to the study of biological invasions and species distributions.

Insect population dynamics under Wolbachia-induced cytoplasmic incompatibility: Puzzle more than buzz in Drosophila suzukii

In theory, the introduction of individuals infected with an incompatible strain of Wolbachia pipientis into a recipient host population should result in the symbiont invasion and reproductive failures caused by cytoplasmic incompatibility (CI). Modelling studies combining Wolbachia invasion and host population dynamics show that these two processes could interact to cause a transient population decline and, in some conditions, extinction. However, these effects could be sensitive to density dependence, with the Allee effect increasing the probability of extinction, and competition reducing the demographic impact of CI. We tested these predictions with laboratory experiments in the fruit fly Drosophila suzukii and the transinfected Wolbachia strain wTei. Surprisingly, the introduction of wTei into D. suzukii populations at carrying capacity did not result in the expected wTei invasion and transient population decline. In parallel, we found no Allee effect but strong negative density dependence. From these results, we propose that competition interacts in an antagonistic way with Wolbachia-induced cytoplasmic incompatibility on insect population dynamics. If future models and data support this hypothesis, pest management strategies using Wolbachia-induced CI should target populations with negligible competition but a potential Allee effect, for instance at the beginning of the reproductive season.

Turing-Hopf Bifurcation Analysis in a Diffusive Ratio-Dependent Predator-Prey Model with Allee Effect and Predator Harvesting

This paper investigates the complex dynamics of a ratio-dependent predator-prey model incorporating the Allee effect in prey and predator harvesting. To explore the joint effect of the harvesting effort and diffusion on the dynamics of the system, we perform the following analyses: (a) The stability of non-negative constant steady states; (b) The sufficient conditions for the occurrence of a Hopf bifurcation, Turing bifurcation, and Turing-Hopf bifurcation; (c) The derivation of the normal form near the Turing-Hopf singularity. Moreover, we provide numerical simulations to illustrate the theoretical results. The results demonstrate that the small change in harvesting effort and the ratio of the diffusion coefficients will destabilize the constant steady states and lead to the complex spatiotemporal behaviors, including homogeneous and inhomogeneous periodic solutions and nonconstant steady states. Moreover, the numerical simulations coincide with our theoretical results.

Lotka-Volterra model with Allee effect: equilibria, coexistence and size scaling of maximum and minimum abundance

The Lotka-Volterra competition model (LVCM) is a fundamental tool for ecology, widely used to represent complex communities. The Allee effect (AE) is a phenomenon in which there is a positive correlation between population density and fitness, at low population densities. However, the interplay between the LVCM and AE has been seldom analyzed in multispecies models. Here, we analyze the mathematical properties of the LVCM [Formula: see text] AE, investigating the coexistence of species interacting through neutral diffuse competition, their equilibria and stable points. Minimum viable population density arises as the threshold below which species go extinct, characteristic of strong Allee effects. Then, by imposing relationships of main parameters to body size, i.e. allometric scaling, we derive a general solution to the size-scaling maximum and minimum expected density under plausible scenarios. The scaling of maximum population density is consistent with the literature, but we also provide novel predictions on the scaling of the lower limit to population density, a critical value for conservation science. The resulting framework is general and yields results that increase our current understanding of how complex demographic processes can be linked to ubiquitous ecological patterns.

Variation in environmental stochasticity dramatically affects viability and extinction time in a predator-prey system with high prey group cohesion

Understanding how tipping points arise is critical for population protection and ecosystem robustness. This work evaluates the impact of environmental stochasticity on the emergence of tipping points in a predator-prey system subject to the Allee effect and Holling type IV functional response, modeling an environment in which the prey has high group cohesion. We analyze the relationship between stochasticity and the probability and time that predator and prey populations in our model tip between different steady states. We evaluate the safety from extinction of different population values for each species, and accordingly assign extinction warning levels to these population values. Our analysis suggests that the effects of environmental stochasticity on tipping phenomena are scenario-dependent but follow a few interpretable trends. The probability of tipping towards a steady state in which one or both species go extinct generally monotonically increased with noise intensity, while the probability of tipping towards a more favorable steady state (in which more species were viable) usually peaked at intermediate noise intensity. For tipping between two equilibria where a given species was at risk of extinction in one equilibrium but not the other, noise affecting that species had greater impact on tipping probability than noise affecting the other species. Noise in the predator population facilitated quicker tipping to extinction equilibria, whereas prey noise instead often slowed down extinction. Changes in warning level for initial population values due to noise were most apparent near attraction basin boundaries, but noise of sufficient magnitude (especially in the predator population) could alter risk even far away from these boundaries. Our model provides critical theoretical insights for the conservation of population diversity: management criteria and early warning signals can be developed based on our results to keep populations away from destructive critical thresholds.

Impact of Allee and fear effects in a fractional order prey-predator system with group defense and prey refuge

This paper presents a novel fractional-order model of a prey-predator system that incorporates group defense and prey refuge mechanisms, along with Allee and fear effects. First, we examine the existence, uniqueness, non-negativity, and boundedness of the solution of the system. Second, a comprehensive analysis is conducted on the existence, stability, and coexistence of equilibrium states in the system, which are crucial for comprehending prey-predator system behavior. Our investigation reveals that the coexistence equilibrium undergoes a Hopf bifurcation under five key parameters. Specifically, an increased threshold for the transition between group and individual behavior, influenced by different strengths of the Allee effect, enhances the stability of both populations. This discovery sheds light on the role of group effects in shaping prey-predator interactions and ecosystem stability. Third, system discretization is employed to explore the impact of step size on stimulating stability and to investigate the Neimark-Sacker bifurcation, providing a more comprehensive understanding of system behavior. The role of step size as a constraint on stability is examined, revealing the system's progression from stability to chaos. Consequently, our results offer a more flexible mechanism for adjusting the stability and dynamics of the two species. Finally, numerical simulations are utilized to validate the reasonableness of the research findings.

Allee effects in an invasive social wasp: an experimental study in colonies of Vespula germanica

Allee effects rely on the existence of mutually beneficial intraspecific interactions that increase individual fitness and per capita growth rate, as the number of individuals in a population or group increases. When the number of individuals falls below a given number, the success of a group or population drops. Social insects heavily rely on cooperation between individuals for various tasks such as foraging and breeding. In this study, we experimentally explored component Allee effects and the underlying mechanisms in colonies of the social wasp Vespula germanica. After the removal of workers, we counted the number of gynes produced, estimated the body mass index as a proxy of their quality, and registered the protein-food collected by foragers in colonies. Our research revealed a correlation between the decrease in worker population and a subsequent decrease in the production of gynes. However, the removal of workers did not impact the quality of the produced gynes or the quantity of protein-food collected by the colonies. These findings highlight the crucial role of the worker caste in the success of eusocial species and suggested an ability of workers to perform multiple tasks that enable colonies to respond to disturbances. Additionally, our study provides the first evidence of Allee effects at the colony level of V. germanica, with potential practical implications for managing this invasive species.

Noise-induced dynamics in a single species model with Allee effect driven by correlated colored noises

In this paper, a single species model with Allee effect driven by correlated colored noises is proposed and investigated. The stationary probability density of the model is obtained using the approximative Fokker-Planck equation, and its shape is discussed in detail. P-bifurcation and noise-induced bistability are explored, followed by the observation of noise-enhanced stability through mean first passage time analysis. Our findings demonstrate that: (i) noise can induce P-bifurcation, causing the structure of a stationary probability distribution to shift from unimodal to monotonic under positive correlation and switch from unimodal to bimodal under negative correlation; (ii) correlation time promotes population growth, leading to a higher probability of large population size and delaying the extinction process; (iii) noise-enhanced stability induced by multiplicative noise depends on both additive noise and correlation time, while it always exists for additive noise.

Short-term particulate matter contamination severely compromises insect antennal olfactory perception

The consequences of sub-lethal levels of ambient air pollution are underestimated for insects, for example, the accumulation of particulate matter on sensory receptors located on their antennae may have detrimental effects to their function. Here we show that the density of particulate matter on the antennae of houseflies (Musca domestica) collected from an urban environment increases with the severity of air pollution. A combination of behavioural assays, electroantennograms and transcriptomic analysis provide consistent evidence that a brief exposure to particulate matter pollution compromises olfactory perception of reproductive and food odours in both male and female houseflies. Since particulate matter can be transported thousands of kilometres from its origin, these effects may represent an additional factor responsible for global declines in insect numbers, even in pristine and remote areas.

Analytical detection of stationary and dynamic patterns in a prey-predator model with reproductive Allee effect in prey growth

Allee effect in population dynamics has a major impact in suppressing the paradox of enrichment through global bifurcation, and it can generate highly complex dynamics. The influence of the reproductive Allee effect, incorporated in the prey's growth rate of a prey-predator model with Beddington-DeAngelis functional response, is investigated here. Preliminary local and global bifurcations are identified of the temporal model. Existence and non-existence of heterogeneous steady-state solutions of the spatio-temporal system are established for suitable ranges of parameter values. The spatio-temporal model satisfies Turing instability conditions, but numerical investigation reveals that the heterogeneous patterns corresponding to unstable Turing eigenmodes act as a transitory pattern. Inclusion of the reproductive Allee effect in the prey population has a destabilising effect on the coexistence equilibrium. For a range of parameter values, various branches of stationary solutions including mode-dependent Turing solutions and localized pattern solutions are identified using numerical bifurcation technique. The model is also capable to produce some complex dynamic patterns such as travelling wave, moving pulse solution, and spatio-temporal chaos for certain range of parameters and diffusivity along with appropriate choice of initial conditions. Judicious choices of parametrization for the Beddington-DeAngelis functional response help us to infer about the resulting patterns for similar prey-predator models with Holling type-II functional response and ratio-dependent functional response.

Morphological instability of solid tumors in a nutrient-deficient environment

A phenomenological reaction-diffusion model that includes a nutrient-regulated growth rate of tumor cells is proposed to investigate the morphological instability of solid tumors during the avascular growth. We find that the surface instability could be induced more easily when tumor cells are placed in a harsher nutrient-deficient environment, while the instability is suppressed for tumor cells in a nutrient-rich environment due to the nutrient-regulated proliferation. In addition, the surface instability is shown to be influenced by the growth moving speed of tumor rims. Our analysis reveals that a larger growth movement of the tumor front results in a closer proximity of tumor cells to a nutrient-rich region, which tends to inhibit the surface instability. A nourished length that represents the proximity is defined to illustrate its close relation to the surface instability.

Mechanisms of collective learning: how can animal groups improve collective performance when repeating a task?

Learning is ubiquitous in animals: individuals can use their experience to fine-tune behaviour and thus to better adapt to the environment during their lifetime. Observations have accumulated that, at the collective level, groups can also use their experience to improve collective performance. Yet, despite apparent simplicity, the links between individual learning capacities and a collective's performance can be extremely complex. Here we propose a centralized and broadly applicable framework to begin classifying this complexity. Focusing principally on groups with stable composition, we first identify three distinct ways through which groups can improve their collective performance when repeating a task: each member learning to better solve the task on its own, members learning about each other to better respond to one another and members learning to improve their complementarity. We show through selected empirical examples, simulations and theoretical treatments that these three categories identify distinct mechanisms with distinct consequences and predictions. These mechanisms extend well beyond current social learning and collective decision-making theories in explaining collective learning. Finally, our approach, definitions and categories help generate new empirical and theoretical research avenues, including charting the expected distribution of collective learning capacities across taxa and its links to social stability and evolution. This article is part of a discussion meeting issue 'Collective behaviour through time'.

Aggregation pheromones have a non-linear effect on oviposition behavior in Drosophila melanogaster

Female fruit flies (Drosophila melanogaster) oviposit at communal sites where the larvae may cooperate or compete for resources depending on group size. This offers a model system to determine how females assess quantitative social information. We show that the concentration of pheromones found on a substrate increases linearly with the number of adult flies that have visited that site. Females prefer oviposition sites with pheromone concentrations corresponding to an intermediate number of previous visitors, whereas sites with low or high concentrations are unattractive. This dose-dependent decision is based on a blend of 11-cis-Vaccenyl Acetate (cVA) indicating the number of previous visitors and heptanal (a novel pheromone deriving from the oxidation of 7-Tricosene), which acts as a dose-independent co-factor. This response is mediated by detection of cVA by odorant receptor neurons Or67d and Or65a, and at least five different odorant receptor neurons for heptanal. Our results identify a mechanism allowing individuals to transform a linear increase of pheromones into a non-linear behavioral response.

Exploring Old Data with New Tricks: Long-Term Monitoring Indicates Spatial and Temporal Changes in Populations of Sympatric Prairie Grouse in the Nebraska Sandhills

The contiguous grasslands of the Sandhills region in Nebraska, USA, provide habitat for two sympatric, grassland-obligate species of grouse, the greater prairie-chicken (Tympanuchus cupido pinnatus) and the plains sharp-tailed grouse (Tympanuchus phasianellus jamesi). Collectively referred to as prairie grouse, these birds are monitored and managed jointly by wildlife practitioners who face the novel challenge of conserving historically allopatric species in shared range. We reconstructed region-wide and route-specific prairie grouse population trends in the Sandhills, using a 63-year timeseries of breeding ground counts aggregated from old reports and paper archives. Our objective was to repurpose historical data collected for harvest management to address questions pertinent to the conservation of prairie grouse, species whose populations have declined precipitously throughout their respective ranges. Because we cannot change the sampling protocol of historical data to answer new questions, we applied 3 different methods of data analysis—traditional regional mean counts used to adjust harvest regulations, spatially implicit, site-specific counts, and spatially explicit trends. Prairie-chicken populations have increased since the 1950s, whereas sharp-tailed grouse populations have remained stable or slightly declined. However, each species exhibited unique shifts in abundance and distribution over time, and regional indices masked important aspects of population change. Our findings indicate that legacy data have the capacity to tell new stories apart from the questions they were collected to answer. By integrating concepts from landscape ecology—a discipline that emerged decades after the collection of our count data began—we demonstrate the potential of historical data to address questions of modern-day conservation concern, using prairie grouse as a case study.

Density regulation amplifies environmentally induced population fluctuations

Background

Density-dependent regulation is ubiquitous in population dynamics, and its potential interaction with environmental stochasticity complicates the characterization of the random component of population dynamics. Yet, this issue has not received attention commensurate with its relevance for descriptive and predictive modeling of population dynamics. Here we use a Bayesian modeling approach to investigate the contribution of density regulation to population variability in stochastic environments.

Methods

We analytically derive a formula linking the stationary variance of population abundance/density under Gompertz regulation in a stochastic environment with constant variance to the environmental variance and the strength of density feedback, to investigate whether and how density regulation affects the stationary variance. We examine through simulations whether the relationship between stationary variance and density regulation inferred analytically under the Gompertz model carries over to the Ricker model, widely used in population dynamics modeling.

Results

The analytical decomposition of the stationary variance under stochastic Gompertz dynamics implies higher variability for strongly regulated populations. Simulation results demonstrate that the pattern of increasing population variability with increasing density feedback found under the Gompertz model holds for the Ricker model as well, and is expected to be a general phenomenon with stochastic population models. We also analytically established and empirically validated that the square of the autoregressive parameter of the Gompertz model in AR(1) form represents the proportion of stationary variance due to density dependence.

Discussion

Our results suggest that neither environmental stochasticity nor density regulation can alone explain the patterns of population variability in stochastic environments, as these two components of temporal variation interact, with a tendency for density regulation to amplify the magnitude of environmentally induced population fluctuations. This finding has far-reaching implications for population viability. It implies that intense intra-specific resource competition increases the risk of environment-driven population collapse at high density, making opportune harvesting a sensible practice for improving the resistance of managed populations such as fish stocks to environmental perturbations. The separation of density-dependent and density-independent processes will help improve population dynamics modeling, while providing a basis for evaluating the relative importance of these two categories of processes that remains a topic of long-standing controversy among ecologists.

Impacts of demographic and environmental stochasticity on population dynamics with cooperative effects

Different types of stochasticity play essential roles in shaping complex population dynamics. This paper presents a novel approach to model demographic and environmental stochasticity in a single-species model with cooperative components that are measured by component Allee effects. Our work provides rigorous mathematical proof on stochastic persistence and extinction, ergodicity (i.e., the existence of a unique stationary distribution) and the existence of a nontrivial periodic solution to study the impacts of demographic and environmental stochasticity on population dynamics. The theoretical and numerical results suggest that stochasticity may affect the population system in a variety of ways, specifically: (i) In the weak Allee effects case (e.g., strong cooperative efforts), the demographic stochasticity from the attack rate contributes to the expansion of the population size, while the demographic stochasticity from the handling rate and the environmental stochasticity have the opposite role, and may even lead to population extinction; (ii) In the strong Allee effects case (cooperative efforts not strong enough), both demographic and environmental stochasticity play a similar role in the survival of population, and are related to the initial population level: if the initial population level is large enough, demographic stochasticity and environmental stochasticity may be detrimental to the survival of population, otherwise if the initial population level is small enough, demographic stochasticity and environmental stochasticity may bring survival opportunities for the population that deterministically would extinct indefinitely; (iii) In the extinction case, demographic and environmental stochasticity can not change the trend of population extinction, but they can delay or promote population extinction.

Invasion impacts and dynamics of a European-wide introduced species

Globalization has led to the introduction of thousands of alien species worldwide. With growing impacts by invasive species, understanding the invasion process remains critical for predicting adverse effects and informing efficient management. Theoretically, invasion dynamics have been assumed to follow an "invasion curve" (S-shaped curve of available area invaded over time), but this dynamic has lacked empirical testing using large-scale data and neglects to consider invader abundances. We propose an "impact curve" describing the impacts generated by invasive species over time based on cumulative abundances. To test this curve's large-scale applicability, we used the data-rich New Zealand mud snail Potamopyrgus antipodarum, one of the most damaging freshwater invaders that has invaded almost all of Europe. Using long-term (1979-2020) abundance and environmental data collected across 306 European sites, we observed that P. antipodarum abundance generally increased through time, with slower population growth at higher latitudes and with lower runoff depth. Fifty-nine percent of these populations followed the impact curve, characterized by first occurrence, exponential growth, then long-term saturation. This behaviour is consistent with boom-bust dynamics, as saturation occurs due to a rapid decline in abundance over time. Across sites, we estimated that impact peaked approximately two decades after first detection, but the rate of progression along the invasion process was influenced by local abiotic conditions. The S-shaped impact curve may be common among many invasive species that undergo complex invasion dynamics. This provides a potentially unifying approach to advance understanding of large-scale invasion dynamics and could inform timely management actions to mitigate impacts on ecosystems and economies.

Annual adult survival rates for four sympatric breeding swallow species: effects of environmental factors and density-dependence

Swallow (Family: Hirundinidae) populations in the Canadian Maritimes have declined since the 1980s. Using mark-recapture data from 2012–2019, we determined apparent annual adult survival rates for Barn Hirundo rustica Linnaeus, 1758, Tree Tachycineta bicolor Vieillot, 1808, Bank Riparia riparia Linnaeus, 1758, and Cliff swallows Petrochelidon pyrrhonota Vieillot, 1817. For two data-rich species (Barn and Tree swallows), we modelled the relationships between survival and weather (cold snaps, precipitation, temperature, and wind speed); climate (El Niño-Southern Oscillation (ENSO) and North Atlantic Oscillation (NAO)); Enhanced Vegetation Index (EVI) as a measure of primary productivity during the winter; number of active nests as a measure of site quality; and the Breeding Bird Survey (BBS) annual population index as density dependent processes. Survival rates for all four species were typically higher (Barn and Tree) or similar to (Cliff and Bank) of estimates from populations that have not undergone severe, long-term declines. Across weather and climate variables, conditions that are typically favourable for high insect availability (e.g., higher precipitation, warmer temperatures and lower wind speeds) resulted in higher survival. For female Barn and Tree Swallows, survival was higher when EVI was lower, and for Barn Swallows, survival was also higher when the BBS index was higher. Collectively our results demonstrate that conditions throughout the annual cycle affect survival, and the relationships with weather and climate variables support the importance of high insect availability

On Large and Small Data Blow-Up Solutions in the Trojan Y Chromosome Model

The Trojan Y Chromosome Strategy (TYC) is the only genetic biological control method in practice in North America for controlling invasive populations with an XX–XY sex determinism. Herein a modified organism, that is a supermale or feminised supermale, is introduced into an invasive population to skew the sex ratio over time, causing local extinction. We consider the three species TYC reaction diffusion model, and show that introduction of supermales above certain thresholds, and for certain initial data, solutions can blow-up in finite time. Thus, in order to have biologically meaningful solutions, one needs to restrict parameter and initial data regimes, in TYC type models.

Autocrine signaling can explain the emergence of Allee effects in cancer cell populations

In many human cancers, the rate of cell growth depends crucially on the size of the tumor cell population. Low, zero, or negative growth at low population densities is known as the Allee effect; this effect has been studied extensively in ecology, but so far lacks a good explanation in the cancer setting. Here, we formulate and analyze an individual-based model of cancer, in which cell division rates are increased by the local concentration of an autocrine growth factor produced by the cancer cells themselves. We show, analytically and by simulation, that autocrine signaling suffices to cause both strong and weak Allee effects. Whether low cell densities lead to negative (strong effect) or reduced (weak effect) growth rate depends directly on the ratio of cell death to proliferation, and indirectly on cellular dispersal. Our model is consistent with experimental observations from three patient-derived brain tumor cell lines grown at different densities. We propose that further studying and quantifying population-wide feedback, impacting cell growth, will be central for advancing our understanding of cancer dynamics and treatment, potentially exploiting Allee effects for therapy.

A common feature of tumor growth is the production, by the cancer cells themselves, of hormones known as growth factors that increase the rate of cell division. This type of signalling makes the growth rate of the tumor depend on the population size in a non-linear manner, and the growth rate might become low or negative for small population sizes. This is known as the Allee effect which has been studied extensively in ecology. We have developed a computational model that can explain the Allee effect in terms of growth factor signalling, and show by mathematical analysis of the model that the magnitude of the Allee effect depends on the ratio of cell death to proliferation, as well as the properties of the growth factor. In addition we show that the model is consistent with experimental observations from three different cell lines derived from the brain tumor glioblastoma. Our findings indicate that the Allee effect can be exploited in order to improve the treatment of glioblastoma patients.

Temporary Allee effects among non-stationary recruitment dynamics in depleted gadid and flatfish populations

Many considerably declined fish populations have not fully recovered despite reductions in fishing pressure. One of the possible causes of impaired recovery is the (demographic) Allee effect. To investigate whether low-abundance recruitment dynamics can switch between compensation and depensation, the latter implying the presence of the Allee effect, we analysed the stock-recruitment time series of 17 depleted cod-type and flatfish populations using a Bayesian change point model. The recruitment dynamics were represented with the sigmoidal Beverton-Holt and the Saila-Lorda stock-recruitment models, allowing the parameters of the models to shift at a priori unknown change points. Our synthesis study questions the common assumption that recruitment is stationary and compensatory and the high amount of scatteredness often present in stock-recruitment data is only due to random variation. When a moderate amount of such variation was assumed, stock-recruitment dynamics were best explained by a non-stationary model for 53% of the populations, which suggests that these populations exhibit temporal changes in the stock-recruitment relationship. For four populations, we found shifts between compensation and depensation, suggesting the presence of temporary Allee effects. However, the evidence of Allee effects was highly dependent on the priors of the stock-recruitment model parameters and the amount of random variation assumed. Nonetheless, detection of changes in low-abundance recruitment is essential in stock assessment since such changes affect the renewal ability of the population and, ultimately, its sustainable harvest limits.

Dynamics of a Predator–Prey Model with the Additive Predation in Prey

In this paper, we consider a predator–prey model, in which the prey’s growth is affected by the additive predation of its potential predators. Due to the additive predation term in prey, the model may exhibit the cases of the strong Allee effect, weak Allee effect and no Allee effect. In each case, the dynamics of global features of the model are investigated. Compared to the well-known Lotka–Volterra type model, the model proposed in this paper exhibits much richer and more complex dynamic behaviors, such as the Allee effect, the sensitivity to the initial conditions caused by the strong Allee effect, the oscillatory behavior and the Hopf and heteroclinic bifurcations. Furthermore, the stability and Hopf bifurcation of the model with the density dependent feedback time delay in prey are investigated. By the normal form method and center manifold theory, the explicit formulas are presented to determine the direction of Hopf bifurcation and the stability and period of Hopf-bifurcating periodic solutions. Theoretical analysis and numerical simulation indicate that the delay may destabilize the model, and cause the Hopf bifurcation not only at the interior equilibrium but also at a boundary equilibrium.

Allee effects and the Allee-effect zone in northwest Atlantic cod

According to the theory of compensatory dynamics, depleted populations should recover when the threat responsible for their decline is removed because per capita population growth is assumed to be highest when populations are at their smallest viable sizes. Yet, many seriously depleted fish populations have failed to recover despite threat mitigation. Atlantic cod (Gadus morhua) stocks off Newfoundland, despite 30 years of dramatically reduced fishing mortality and numerous fishery closures, have not recovered, suggesting that drivers other than fishing can regulate the growth of collapsed fish populations, inhibiting or preventing their recovery. Here, using Bayesian inference, we show strong evidence of Allee effects in a south Newfoundland cod population, based on data on recruitment and spawning stock biomass. We infer the Allee-effect threshold, below which recovery is impaired. We demonstrate the necessity of data at low population sizes to make inferences about the nature of low-abundance dynamics. Our work indicates that Allee effects are not negligible in commercially exploited fish populations, as commonly projected, and that they represent an inhibitory force that can effectively prevent recovery from overfishing. Our findings contrast with prevailing fisheries management practices that assume compensatory dynamics at low abundances with potential to seriously overestimate the recovery potential of collapsed populations.

A RETROSPECTIVE STUDY OF MORBIDITY AND MORTALITY IDENTIFIED AT POSTMORTEM EXAMINATION OF CAPTIVE LANGURS (TRACHYPITHECUS SPP) FROM SIX UNITED KINGDOM ZOOLOGICAL INSTITUTIONS: A 19-YEAR REVIEW

Langurs are Asian primates belonging to the Colobinae subfamily. Langur populations are declining, with most species categorized as threatened by the International Union for Conservation of Nature. Investigation into the threats to population viability and sustainability would be beneficial but there is limited literature available on common diseases or causes of death in these species, either in captive or free-ranging settings. This study aimed to evaluate the most common causes of morbidity and mortality in Trachypithecus species submitted for postmortem examination by six United Kingdom zoological institutions between 2001 and 2020, to inform best practice husbandry guidelines. Necropsy and histopathology reports from 88 individuals of Trachypithecus species from six zoological organizations in the United Kingdom were analyzed. Species included Javan langurs (Trachypithecus auratus; n = 35), dusky langurs (Trachypithecus obscurus; n = 28), François' langurs (Trachypithecus francoisi; n = 16), purple-faced langurs (Trachypithecus vetulus; n = 4), silvered langurs (Trachypithecus cristatus; n = 4), and Phayre's langur (Trachypithecus phayrei; n = 1). Morbidities and causes of death were recorded. Gastrointestinal diseases and systemic infections were the leading causes of death (27.4% and 21.0% of cases where cause of death was known, respectively); linear foreign bodies were the most common cause of death. Interstitial pneumonia was frequently observed secondary to systemic infection. Heart abnormalities, anthracosis, and hemosiderosis were common but not directly associated with mortality. Further investigation is necessary to assess the importance of these conditions and whether they predispose to other diseases. This study provides a baseline for future research evaluating captive and free-ranging langur health and highlights husbandry practices that may decrease morbidity in these species.

Extinction transition of hantavirus-infected rodents in a hostile environment

The spatial critical shelter sizes above which populations would survive are investigated for the infection of hantavirus among rodent populations surrounded by a deadly environment. We show that the critical shelter sizes for the infected population and the susceptible population are different due to symmetry breaking in the reproduction and the transmission processes. Therefore, there exists a shelter size gap within which the infected population becomes extinct while only the susceptible population survives. With the field data reported in the literature, we estimate that, if one confines the rodent population within a stripe region surrounded by a deadly environment with the shorter dimension between 335.5±27.2m and 547.9±78.3m, the infected population would become extinct. In addition, we introduce two factors that influence the movement of rodents, namely, the spatial asymmetry of the landscape and the sociality of rodents, to study their effects on the shelter size gap. The effects on the critical size due to environmental bias are twofold: it enhances the overall competition among rodents which increases the critical size, but on the other hand it promotes the spread of the hantavirus which reduces the critical size for the infected population. On the contrary, the sociality of rodents gives rise to a more localized population profile which promotes the spread of the hantavirus and reduces the shelter size gap. The results shed light on a possible strategy of eliminating hantavirus while preserving the integrity of food webs in ecosystems.

A missing cog in the wheel: an Allee effects perspective in biological invasion paradigm

Environmental stochasticity and invasive species demographical factors are considered to be fundamental aspects of species invasion. Population size, density, and intraspecific competition are the important determinants of species range expansion. Allee effects, interesting density-dependent phenomena, act as 'mechanism of population regulation' during species expansion. The study intends to understand the trend of published researches and identify research gaps pertaining to biological invasions and Allee effects with the help of bibliometric analysis. Content and citation analysis using key words 'Allee effects' AND 'biological invasion' was conducted on research articles published over a period of two and a half decades from Scopus database for global and Indian context. Understanding of Allee effects dynamics in context of biological invasion is limited, especially in India. Integrating the emerging trends pertaining to Allee effects in the biological invasion framework will strengthen the understanding on species range expansion. It is emphasized that Allee effects can emerge as an important tool to manage invasive species range expansion.

Ecological theory of mutualism: Robust patterns of stability and thresholds in two-species population models

Mutualisms are ubiquitous in nature, provide important ecosystem services, and involve many species of interest for conservation. Theoretical progress on the population dynamics of mutualistic interactions, however, comparatively lagged behind that of trophic and competitive interactions, leading to the impression that ecologists still lack a generalized framework to investigate the population dynamics of mutualisms. Yet, over the last 90 years, abundant theoretical work has accumulated, ranging from abstract to detailed. Here, we review and synthesize historical models of two-species mutualisms. We find that population dynamics of mutualisms are qualitatively robust across derivations, including levels of detail, types of benefit, and inspiring systems. Specifically, mutualisms tend to exhibit stable coexistence at high density and destabilizing thresholds at low density. These dynamics emerge when benefits of mutualism saturate, whether due to intrinsic or extrinsic density dependence in intraspecific processes, interspecific processes, or both. We distinguish between thresholds resulting from Allee effects, low partner density, and high partner density, and their mathematical and conceptual causes. Our synthesis suggests that there exists a robust population dynamic theory of mutualism that can make general predictions.

Genealogical structure changes as range expansions transition from pushed to pulled

Range expansions accelerate evolution through multiple mechanisms, including gene surfing and genetic drift. The inference and control of these evolutionary processes ultimately rely on the information contained in genealogical trees. Currently, there are two opposing views on how range expansions shape genealogies. In invasion biology, expansions are typically approximated by a series of population bottlenecks producing genealogies with only pairwise mergers between lineages-a process known as the Kingman coalescent. Conversely, traveling wave models predict a coalescent with multiple mergers, known as the Bolthausen-Sznitman coalescent. Here, we unify these two approaches and show that expansions can generate an entire spectrum of coalescent topologies. Specifically, we show that tree topology is controlled by growth dynamics at the front and exhibits large differences between pulled and pushed expansions. These differences are explained by the fluctuations in the total number of descendants left by the early founders. High growth cooperativity leads to a narrow distribution of reproductive values and the Kingman coalescent. Conversely, low growth cooperativity results in a broad distribution, whose exponent controls the merger sizes in the genealogies. These broad distribution and non-Kingman tree topologies emerge due to the fluctuations in the front shape and position and do not occur in quasi-deterministic simulations. Overall, our results show that range expansions provide a robust mechanism for generating different types of multiple mergers, which could be similar to those observed in populations with strong selection or high fecundity. Thus, caution should be exercised in making inferences about the origin of non-Kingman genealogies.

A metapopulation model of social group dynamics and disease applied to Yellowstone wolves

The population structure of social species has important consequences for both their demography and transmission of their pathogens. We develop a metapopulation model that tracks two key components of a species' social system: average group size and number of groups within a population. While the model is general, we parameterize it to mimic the dynamics of the Yellowstone wolf population and two associated pathogens: sarcoptic mange and canine distemper. In the initial absence of disease, we show that group size is mainly determined by the birth and death rates and the rates at which groups fission to form new groups. The total number of groups is determined by rates of fission and fusion, as well as environmental resources and rates of intergroup aggression. Incorporating pathogens into the models reduces the size of the host population, predominantly by reducing the number of social groups. Average group size responds in more subtle ways: infected groups decrease in size, but uninfected groups may increase when disease reduces the number of groups and thereby reduces intraspecific aggression. Our modeling approach allows for easy calculation of prevalence at multiple scales (within group, across groups, and population level), illustrating that aggregate population-level prevalence can be misleading for group-living species. The model structure is general, can be applied to other social species, and allows for a dynamic assessment of how pathogens can affect social structure and vice versa.

Integrating mechanistic models and climate change projections to predict invasion of the mussel, Mytilopsis sallei, along the southern China coast

Species invasion is an important cause of global biodiversity decline and is often mediated by shifts in environmental conditions such as climate change. To investigate this relationship, a mechanistic Dynamic Energy Budget model (DEB) approach was used to predict how climate change may affect spread of the invasive mussel Mytilopsis sallei, by predicting variation in the total reproductive output of the mussel under different scenarios. To achieve this, the DEB model was forced with present-day satellite data of sea surface temperature (SST) and chlorophyll-a concentration (Chl-a), and SST under two warming RCP scenarios and decreasing current Chl-a levels, to predict future responses. Under both warming scenarios, the DEB model predicted the reproductive output of M. sallei would enhance range extension of the mussel, especially in regions south of the Yangtze River when future declines in Chl-a were reduced by less than 10%, whereas egg production was inhibited when Chl-a decreased by 20-30%. The decrease in SST in the Yangtze River may, however, be a natural barrier to the northward expansion of M. sallei, with colder temperatures resulting in a strong decrease in egg production. Although the invasion path of M. sallei may be inhibited northwards by the Yangtze River, larger geographic regions south of the Yangtze River run the risk of invasion, with subsequent negative impacts on aquaculture through competition for food with farmed bivalves and damaging aquaculture facilities. Using a DEB model approach to characterise the life history traits of M. sallei, therefore, revealed the importance of food availability and temperature on the reproductive output of this mussel and allowed evaluation of the invasion risk for specific regions. DEB is, therefore, a powerful predictive tool for risk management of already established invasive populations and to identify regions with a high potential invasion risk.

Evidence for an Allee effect in a declining fur seal population

Allee effects play an important role in the dynamics of many populations and can increase the risk of local extinction. However, some authors have questioned the weight of evidence for Allee effects in wild populations. We therefore exploited a natural experiment provided by two adjacent breeding colonies of contrasting density to investigate the potential for Allee effects in an Antarctic fur seal (Arctocephalus gazella) population that is declining in response to climate change-induced reductions in food availability. Biometric time-series data were collected from 25 pups per colony during two consecutive breeding seasons, the first of which was among the worst on record in terms of breeding female numbers, pup birth weights and foraging trip durations. In previous decades when population densities were higher, pup mortality was consistently negatively density dependent, with rates of trauma and starvation scaling positively with density. However, we found the opposite, with higher pup mortality at low density and the majority of deaths attributable to predation. In parallel, body condition was depressed at low density, particularly in the poor-quality season. Our findings shed light on Allee effects in wild populations and highlight a potential emerging role of predators in the ongoing decline of a pinniped species.

Interpopulation variations in life history traits and reproductive tactics in Aedes aegypti: A test on populations 50 km apart

The interpopulation variation in life history traits of a species reflects evolutionary adaptation in response to a local environment regime. We examined the life history traits of Aedes aegypti populations from 2 cities in southern Taiwan separated by 50 km. Results revealed a high level of trait differentiation in immature developmental time and survival of Ae. aegypti between the 2 cities. The Kaohsiung populations exhibited total pupation of 40%-60% on day 8; this was significantly lower than that of the Tainan populations and laboratory-reared KHsm mosquitos, which exhibited a pupation rate of 70%-90%. The slow immature development of the Kaohsiung populations was reflected in the low percentage of adult emergence (22%-26%) on day 10. The prolonged immature development did not select larger adults with longer life spans because the Kaohsiung populations had a shorter life span (≈37 d) than that of the Tainan populations (≈42 d). By contrast, immature development and longevity did not differ between populations within each region, indicating weak local differentiation. Three field populations exhibited male-bias sex ratio because of differential mortality of female immatures. The effect of female size on adult life history was nonsignificant. Two reproduction tactics were detected, representing the balanced-mortality hypothesis and the bet-hedging hypothesis. Despite their differential life history strategies and reproductive tactics, these mosquito populations apparently counterbalanced any shortcomings in traits to produce similar population growth. Maintaining optimal population density is essential for Aedes mosquitos to increase the probability of encountering mates and reduce the Allee effect.

Propagule pressure and the establishment of emergent polyploid populations

BACKGROUND

Whereas the incidence or rate of polyploid speciation in flowering plants is modest, the production of polyploid individuals within local populations is widespread. Explanations for this disparity primarily have focused on properties or interactions of polyploids that limit their persistence.

HYPOTHESIS

The emergence of local polyploid populations within diploid populations is similar to the arrival of invasive species at new, suitable sites, with the exception that polyploids suffer interference from their progenitor(s). The most consistent predictor of successful colonization by invasive plants is propagule pressure, i.e. the number of seeds introduced. Therefore, insufficient propagule pressure, i.e. the formation of polyploid seeds within diploid populations, ostensibly is a prime factor limiting the establishment of newly emergent polyploids within local populations. Increasing propagule number reduces the effects of genetic, environmental and demographic stochasticity, which thwart population survival. As with invasive species, insufficient seed production within polyploid populations limits seed export, and thus reduces the chance of polyploid expansion.

CONCLUSION

The extent to which propagule pressure limits the establishment of local polyploid populations remains to be determined, because we know so little. The numbers of auto- or allopolyploid seed in diploid populations rarely have been ascertained, as have the numbers of newly emergent polyploid plants within diploid populations. Moreover, seed production by these polyploids has yet to be assessed.

An experimental test of the Allee effect range limitation hypothesis

Understanding how climate change impacts trailing‐edge populations requires information about how abiotic and biotic factors limit their distributions. Theory indicates that socially mediated Allee effects can limit species distributions by suppressing growth rates of peripheral populations when social information is scarce.

The goal of our research was to determine if socially mediated Allee effects limit the distribution of Canada warbler Cardellina canadensis at the trailing‐edge of the geographic range.

Using 4 years of observational data from 71 sites and experimental data at 10 sites, we tested two predictions of the socially mediated range limitation hypothesis: (a) local growth rates should be positively correlated with local density and (b) the addition of social cues immediately outside the trailing‐edge range boundary would result in colonization of formerly unoccupied habitat and increased growth rates. During the third breeding season, social cues were experimentally added at 10 formerly unoccupied sites within and beyond the species’ local range margin to determine if the addition of social information could increase density and effectively expand the species’ range.

No experimental sites were colonized after adding social cues and no evidence of Allee effects was found. Rather, temperature, precipitation and negative density dependence strongly influenced population growth rates.

Although theoretical models indicate that the presence of socially mediated Allee effects at species range boundaries could increase the rate of climate‐induced range shifts and local extinctions, empirical results from the first test of this hypothesis suggest that Allee effects play a minimal role in limiting species’ distributions.

A MATHEMATICAL MODEL FOR TREATMENT OF PAPILLARY THYROID CANCER USING THE ALLEE EFFECT

The incidence of thyroid cancer is rising all over the world, and the papillary subtype (PTC) is the primary factor for this increase. The presence of thyroid tumors is commonly associated with increased levels of cytokines, such as interleukin 6 (IL-6). Considering PTC patients treated with thyroidectomy and radioactive iodine [Formula: see text]I (RAI), we propose an ordinary differential system using four variables: the RAI activity, the number of cancer cells and the serum concentrations of IL-6 and thyroglobulin (Tg). Our objective is to study the efficacy of different therapeutic doses of RAI in the treatment of thyroid cancer. The Allee effect is taken into account when modeling cancer cells growth under the influence of IL-6. From the results obtained, the main factors and conditions correlated with successful treatment, such as the RAI activity used and the tumor response are addressed. The detection of minimal doses of RAI that can cause tumor extinction is performed, though this has also meant longer periods for tumor cell elimination. The critical number of tumor cells due to the Allee effect is analyzed and linked to the immune system or biological factors that can slow the progression of the tumor but are insufficient after thyroid resection surgery.

The spatial Muller's ratchet: Surfing of deleterious mutations during range expansion

During a range expansion, deleterious mutations can "surf" on the colonization front. The resultant decrease in fitness is known as expansion load. An Allee effect is known to reduce the loss of genetic diversity of expanding populations, by changing the nature of the expansion from "pulled" to "pushed". We study the impact of an Allee effect on the formation of an expansion load with a new model, in which individuals have the genetic structure of a Muller's ratchet. A key feature of Muller's ratchet is that the population fatally accumulates deleterious mutations due to the stochastic loss of the fittest individuals, an event called a click of the ratchet. We observe fast clicks of the ratchet at the colonization front owing to small population size, followed by a slow fitness recovery due to migration of fit individuals from the bulk of the population, leading to a transient expansion load. For large population size, we are able to derive quantitative features of the expansion wave, such as the wave speed and the frequency of individuals carrying a given number of mutations. Using simulations, we show that the presence of an Allee effect reduces the rate at which clicks occur at the front, and thus reduces the expansion load.