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.

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.

Abyssal hydrothermal springs-Cryptic incubators for brooding octopus

Does warmth from hydrothermal springs play a vital role in the biology and ecology of abyssal animals? Deep off central California, thousands of octopus (Muusoctopus robustus) migrate through cold dark waters to hydrothermal springs near an extinct volcano to mate, nest, and die, forming the largest known aggregation of octopus on Earth. Warmth from the springs plays a key role by raising metabolic rates, speeding embryonic development, and presumably increasing reproductive success; we show that brood times for females are ~1.8 years, far faster than expected for abyssal octopods. Using a high-resolution subsea mapping system, we created landscape-scale maps and image mosaics that reveal 6000 octopus in a 2.5-ha area. Because octopuses die after reproducing, hydrothermal springs indirectly provide a food supplement to the local energy budget. Although localized deep-sea heat sources may be essential to octopuses and other warm-tolerant species, most of these unique and often cryptic habitats remain undiscovered and unexplored.

CDC (Cindy and David's Conversations) game: Advising President to survive pandemic

Ongoing debates on anti-COVID19 policies have been focused on coexistence-with versus zero-out (virus) strategies, which can be simplified as "always open (AO)" versus "always closed (AC)." We postulate that a middle ground, dubbed LOHC (low-risk-open and high-risk-closed), is likely favorable, precluding obviously irrational HOLC (high-risk-open and low-risk-closed). From a meta-strategy perspective, these four policies cover the full spectrum of anti-pandemic policies. By emulating the reality of anti-pandemic policies today, the study aims to identify possible cognitive gaps and traps by harnessing the power of evolutionary game-theoretic analysis and simulations, which suggest that (1) AO and AC seem to be "high-probability" events (0.412-0.533); (2) counter-intuitively, the middle ground-LOHC-seems to be small-probability event (0.053), possibly mirroring its wide adoptions but broad failures. Besides devising specific policies, an equally important challenge seems to deal with often hardly avoidable policy transitions along the process from emergence, epidemic, through pandemic, to endemic state.

Modelling the ecological dynamics of mosquito populations with multiple co-circulating Wolbachia strains

Wolbachia intracellular bacteria successfully reduce the transmissibility of arthropod-borne viruses (arboviruses) when introduced into virus-carrying vectors such as mosquitoes. Despite the progress made by introducing Wolbachia bacteria into the Aedes aegypti wild-type population to control arboviral infections, reports suggest that heat-induced loss-of-Wolbachia-infection as a result of climate change may reverse these gains. Novel, supplemental Wolbachia strains that are more resilient to increased temperatures may circumvent these concerns, and could potentially act synergistically with existing variants. In this article, we model the ecological dynamics among three distinct mosquito (sub)populations: a wild-type population free of any Wolbachia infection; an invading population infected with a particular Wolbachia strain; and a second invading population infected with a distinct Wolbachia strain from that of the first invader. We explore how the range of possible characteristics of each Wolbachia strain impacts mosquito prevalence. Further, we analyse the differential system governing the mosquito populations and the Wolbachia infection dynamics by computing the full set of basic and invasive reproduction numbers and use these to establish stability of identified equilibria. Our results show that releasing mosquitoes with two different strains of Wolbachia did not increase their prevalence, compared with a single-strain Wolbachia-infected mosquito introduction and only delayed Wolbachia dominance.

Incorporating Microbial Species Interaction in Management of Freshwater Toxic Cyanobacteria: A Systems Science Challenge

Water resources are critically important, but also pose risks of exposure to toxic and pathogenic microbes. Increasingly, a concern is toxic cyanobacteria, which have been linked to the death and disease of humans, domesticated animals, and wildlife in freshwater systems worldwide. Management approaches successful at reducing cyanobacterial abundance and toxin production have tended to be short-term solutions applied on small scales (e.g., algaecide application) or solutions that entail difficult multifaceted investments (e.g., modification of landscape and land use to reduce nutrient inputs). However, implementation of these approaches can be undermined by microbial species interactions that (a) provide toxic cyanobacteria with protection against the method of control or (b) permit toxic cyanobacteria to be replaced by other significant microbial threats. Understanding these interactions is necessary to avoid such scenarios and can provide a framework for novel strategies to enhance freshwater resource management via systems science (e.g., pairing existing physical and chemical approaches against cyanobacteria with ecological strategies such as manipulation of natural enemies, targeting of facilitators, and reduction of benthic occupancy and recruitment). Here, we review pertinent examples of the interactions and highlight potential applications of what is known.

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.

Hopping on: Conspecific traveller density within a vehicle regulates parasitic hitchhiking between ephemeral microcosms

Hitchhikers (phoretic organisms) identify their vehicles using species-specific visual, chemical and vibrational cues. However, what factors influence their choice between vehicles of the same species has rarely been investigated. Hitchhikers must not only avoid overcrowded vehicles but may also need to travel with conspecifics to ensure mates at their destination. Hence, a trade-off between overcrowding and presence of conspecifics likely determines the choice of a vehicle especially when destination sites are distant, ephemeral and unique. Here, we investigate whether a trade-off between the presence of conspecifics versus overcrowding by conspecifics or heterospecifics on a vehicle affects hitchhiker choice. We also investigate the sensory modality responsible for this choice. We experimentally examine these questions using a phoretic nematode community (containing plant- and animal-parasitic taxa) obligately associated with a brood-site pollination mutualism. In this model system, nematodes co-travel with conspecifics and heterospecifics on pollinators as vehicles, between ephemeral plant brood sites to complete their developmental life cycle. In this system, hitchhiker overcrowding has proven negative impacts on vehicle and plant fitness. We expected nematodes to respond to conspecifics and heterospecific density on offered vehicles when making their choice. We found that animal-parasitic nematodes preferred vehicles containing some conspecifics within a certain density range. However, plant-parasitic nematodes preferentially boarded vehicles that were devoid of conspecifics or had few conspecifics. Plant parasites that preferred empty vehicles likely hitchhiked in pairs. Both nematode types employed volatile cues to discriminate between vehicles with different conspecific nematode densities. Our results suggest that vehicle overcrowding by conspecifics, most likely, guaranteed access to mates at the destination determined hitchhiker choice. Surprisingly, and contrary to our expectations, plant- and animal-parasitic nematodes did not respond to heterospecific crowding on vehicles and did not discriminate between vehicles with different heterospecific nematode densities. The reason for this lack of response to heterospecific presence is unknown. This study not only shows that phoretic organisms use different strategies while choosing a vehicle but also confirms that density-dependent effects can ensure the stability and persistence of phoretic interactions in a mutualism by balancing overcrowding against reproductive assurance.

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.

Sperm storage reduces the strength of the mate-finding Allee effect

Mate searching is a key component of sexual reproduction that can have important implications for population viability, especially for the mate-finding Allee effect. Interannual sperm storage by females may be an adaptation that potentially attenuates mate limitation, but the demographic consequences of this functional trait have not been studied. Our goal is to assess the effect of female sperm storage durability on the strength of the mate-finding Allee effect and the viability of populations subject to low population density and habitat alteration. We used an individual-based simulation model that incorporates realistic representations of the demographic and spatial processes of our model species, the spur-thighed tortoise (Testudo graeca). This allowed for a detailed assessment of reproductive rates, population growth rates, and extinction probabilities. We also studied the relationship between the number of reproductive males and the reproductive rates for scenarios combining different levels of sperm storage durability, initial population density, and landscape alteration. Our results showed that simulated populations parameterized with the field-observed demographic rates collapsed for short sperm storage durability, but were viable for a durability of one year or longer. In contrast, the simulated populations with a low initial density were only viable in human-altered landscapes for sperm storage durability of 4 years. We find that sperm storage is an effective mechanism that can reduce the strength of the mate-finding Allee effect and contribute to the persistence of low-density populations. Our study highlights the key role of sperm storage in the dynamics of species with limited movement ability to facilitate reproduction in patchy landscapes or during population expansion. This study represents the first quantification of the effect of sperm storage durability on population dynamics in different landscapes and population scenarios.

Stress response and population dynamics: Is Allee effect hormesis?

Hormesis is a fundamental notion in ecotoxicology while competition between organisms is an essential notion in population ecology and species adaptation and evolution. Both sub-disciplines of ecology deal with the response of organisms to abiotic and biotic stresses. In ecotoxicology, the Linear-non-Threshold (LNT), Threshold and Hormetic models are used to describe the dominant responses of a plethora of endpoints to abiotic stress. In population ecology, the logistic, theta-logistic and the Allee effect models are used to describe the growth of populations under different responses to (biotic) stress induced by population density. The per capita rate of population increase (r) measures species fitness. When it is used as endpoint, the responses to population density seem to perfectly correspond to LNT, Threshold and Hormetic responses to abiotic stress, respectively. Our analysis suggests the Allee effect is a hormetic-like response of r to population density, an ultimate biotic stress. This biphasic dose-response model appears across different systems and situations (from molecules to tumor growth to population dynamics), is highly supported by ecological and evolutionary theory, and has important implications in most sub-disciplines of biology as well as in environmental and earth sciences. Joined multi-disciplinary efforts would facilitate the development and application of advanced research approaches for better understanding potential planetary-scale implications.