Anti-CRISPR Phages Cooperate to Overcome CRISPR-Cas Immunity.

Some phages encode anti-CRISPR (acr) genes, which antagonize bacterial CRISPR-Cas immune systems by binding components of its machinery, but it is less clear how deployment of these acr genes impacts phage replication and epidemiology. Here, we demonstrate that bacteria with CRISPR-Cas resistance are still partially immune to Acr-encoding phage. As a consequence, Acr-phages often need to cooperate in order to overcome CRISPR resistance, with a first phage blocking the host CRISPR-Cas immune system to allow a second Acr-phage to successfully replicate. This cooperation leads to epidemiological tipping points in which the initial density of Acr-phage tips the balance from phage extinction to a phage epidemic. Furthermore, both higher levels of CRISPR-Cas immunity and weaker Acr activities shift the tipping points toward higher initial phage densities. Collectively, these data help elucidate how interactions between phage-encoded immune suppressors and the CRISPR systems they target shape bacteria-phage population dynamics.

Habitat fragmentation decouples fire-stimulated flowering from plant reproductive fitness.

Many plant species in historically fire-dependent ecosystems exhibit fire-stimulated flowering. While greater reproductive effort after fire is expected to result in increased reproductive outcomes, seed production often depends on pollination, the spatial distribution of prospective mates, and the timing of their reproductive activity. Fire-stimulated flowering may thus have limited fitness benefits in small, isolated populations where mating opportunities are restricted and pollination rates are low. We conducted a 6-y study of 6,357 Echinacea angustifolia (Asteraceae) individuals across 35 remnant prairies in Minnesota (USA) to experimentally evaluate how fire effects on multiple components of reproduction vary with population size in a common species. Fire increased annual reproductive effort across populations, doubling the proportion of plants in flower and increasing the number of flower heads 65% per plant. In contrast, fire's influence on reproductive outcomes differed between large and small populations, reflecting the density-dependent effects of fire on spatiotemporal mating potential and pollination. In populations with fewer than 20 individuals, fire did not consistently increase pollination or annual seed production. Above this threshold, fire increased mating potential, leading to a 24% increase in seed set and a 71% increase in annual seed production. Our findings suggest that density-dependent effects of fire on pollination largely determine plant reproductive outcomes and could influence population dynamics across fire-dependent systems. Failure to account for the density-dependent effects of fire on seed production may lead us to overestimate the beneficial effects of fire on plant demography and the capacity of fire to maintain plant diversity, especially in fragmented habitats.

Variation in Avian Predation Pressure as a Driver for the Diversification of Periodical Cicada Broods.

AbstractPeriodical cicadas live 13 or 17 years underground as nymphs, then emerge in synchrony as adults to reproduce. Developmentally synchronized populations called broods rarely coexist, with one dominant brood locally excluding those that emerge in off years. Twelve modern 17-year cicada broods are believed to have descended from only three ancestral broods following the last glaciation. The mechanisms by which these daughter broods overcame exclusion by the ancestral brood to synchronously emerge in a different year, however, are elusive. Here, we demonstrate that temporal variation in the population density of generalist predators can allow intermittent opportunities for new broods to invade, even though a single brood remains dominant most of the time. We show that this mechanism is consistent, in terms of the type and frequency of brood replacements, with the distribution of periodical cicada broods throughout North America today. Although we investigate one particularly charismatic case study, the mechanisms involved (competitive exclusion, Allee effects, trait variation, predation, and temporal variability) are ubiquitous and could contribute to patterns of species diversity in a range of systems.

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.

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.

Spread and persistence for integro-difference equations with shifting habitat and strong Allee effect.

We study an integro-difference equation model that describes the spatial dynamics of a species with a strong Allee effect in a shifting habitat. We examine the case of a shifting semi-infinite bad habitat connected to a semi-infinite good habitat. In this case we rigorously establish species persistence (non-persistence) if the habitat shift speed is less (greater) than the asymptotic spreading speed of the species in the good habitat. We also examine the case of a finite shifting patch of hospitable habitat, and find that the habitat shift speed must be less than the asymptotic spreading speed associated with the habitat and there is a critical patch size for species persistence. Spreading speeds and traveling waves are established to address species persistence. Our numerical simulations demonstrate the theoretical results and show the dependence of the critical patch size on the shift speed.

Pushed to the edge: Spatial sorting can slow down invasions.

Our ability to understand population spread dynamics is complicated by rapid evolution, which renders simple ecological models insufficient. If dispersal ability evolves, more highly dispersive individuals may arrive at the population edge than less dispersive individuals (spatial sorting), accelerating spread. If individuals at the low-density population edge benefit (escape competition), high dispersers have a selective advantage (spatial selection). These two processes are often described as forming a positive feedback loop; they reinforce each other, leading to faster spread. Although spatial sorting is close to universal, this form of spatial selection is not: low densities can be detrimental for organisms with Allee effects. Here, we present two conceptual models to explore the feedback loops that form between spatial sorting and spatial selection. We show that the presence of an Allee effect can reverse the positive feedback loop between spatial sorting and spatial selection, creating a negative feedback loop that slows population spread.

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.

Intermittent Precipitation-Dependent Interactions, Encompassing Allee Effect, May Yield Vegetation Patterns in a Transitional Parameter Range.

We construct a spatial model that incorporates Allee-type and competition interactions for vegetation as an evolving random field of biomass density. The cumulative effect of close-range precipitation-dependent interactions is controlled by a parameter defining precipitation frequency. We identify a narrow parameter range in which the behavior of the system changes from survival of vegetation to extinction, via a transitional aggregation pattern. The aggregation pattern is tied to the initial configuration and appears to arise differently from Turing's diffusion and differential flow patterns of other models. There is close agreement of our critical transition parameter range with that of the corresponding evolving random mean-field model.

Forced Traveling Waves in a Reaction-Diffusion Equation with Strong Allee Effect and Shifting Habitat.

We study a reaction-diffusion equation that describes the growth of a population with a strong Allee effect in a bounded habitat which shifts at a speed [Formula: see text]. We demonstrate that the existence of forced positive traveling waves depends on habitat size L, and [Formula: see text], the speed of traveling wave for the corresponding reaction-diffusion equation with the same growth function all over the entire unbounded spatial domain. It is shown that for [Formula: see text] there exists a positive number [Formula: see text] such that for [Formula: see text] there are two positive traveling waves and for [Formula: see text] there is no positive traveling wave. It is also shown if [Formula: see text] for any [Formula: see text] there is no positive traveling wave. The dynamics of the equation are further explored through numerical simulations.

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.

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.

Fire synchronizes flowering and boosts reproduction in a widespread but declining prairie species.

Fire is an important determinant of habitat structure and biodiversity across ecosystems worldwide. In fire-dependent communities, similar to the North American prairie, fire suppression contributes to local plant extinctions. Yet the demographic mechanisms responsible for species loss have not been directly investigated. We conducted a 21-y longitudinal study of 778 individual plants of Echinacea angustifolia, a widespread perennial species with chronically limited mating opportunities, to explore how fire affects reproduction. In a large preserve, with management units on different burn schedules, we investigated Echinacea mating scenes, which quantify isolation from potential mates and overlap in the timing of flowering, to determine the extent to which fire influences the potential for sexual reproduction. We demonstrate that fire consistently increased mating opportunities by synchronizing reproductive effort. Each fire occurred during fall or spring and stimulated flowering in the subsequent summer, thus synchronizing reproduction among years and increasing the proximity of potential mates after a fire. Greater within-season flowering synchrony in postfire mating scenes further increased mating potential. The improved postfire mating scene enhanced reproduction by increasing pollination efficiency. Seed set in scenes postfire exceeded other scenes by 55%, and annual fecundity nearly doubled (88% increase). We predict the reproductive benefits of synchronized flowering after fire can alleviate mate-finding Allee effects, promote population growth, and forestall local extirpation in small populations of Echinacea and many other prairie species. Furthermore, the synchronization of flowering by burning may improve mating opportunities, reproduction, and the likelihood of persistence for many other plant species in fire-dependent habitats.

Fast behavioral feedbacks make ecosystems sensitive to pace and not just magnitude of anthropogenic environmental change.

Anthropogenic environmental change is altering the behavior of animals in ecosystems around the world. Although behavior typically occurs on much faster timescales than demography, it can nevertheless influence demographic processes. Here, we use detailed data on behavior and empirical estimates of demography from a coral reef ecosystem to develop a coupled behavioral-demographic ecosystem model. Analysis of the model reveals that behavior and demography feed back on one another to determine how the ecosystem responds to anthropogenic forcing. In particular, an empirically observed feedback between the density and foraging behavior of herbivorous fish leads to alternative stable ecosystem states of coral population persistence or collapse (and complete algal dominance). This feedback makes the ecosystem more prone to coral collapse under fishing pressure but also more prone to recovery as fishing is reduced. Moreover, because of the behavioral feedback, the response of the ecosystem to changes in fishing pressure depends not only on the magnitude of changes in fishing but also on the pace at which changes are imposed. For example, quickly increasing fishing to a given level can collapse an ecosystem that would persist under more gradual change. Our results reveal conditions under which the pace and not just the magnitude of external forcing can dictate the response of ecosystems to environmental change. More generally, our multiscale behavioral-demographic framework demonstrates how high-resolution behavioral data can be incorporated into ecological models to better understand how ecosystems will respond to perturbations.

A Gender-Selective Harvesting Strategy: Weak Allee Effects and a Non-hyperbolic Extinction Boundary.

Recently a gender-selective harvesting strategy has been proposed for possible control of aquatic invasive species, wherein females of the invasive species are harvested, whilst stocking the males (abbreviated as FHMS strategy) (Lyu et al. in Nat Resour Model 33(2):e12252, 2020). We consider the FHMS strategy with a weak Allee effect, and show that its extinction boundary need not be hyperbolic. To the best of our knowledge, this is the first example of a non-hyperbolic extinction boundary in two-compartment mating models structured by sex. The model possesses a rich dynamical structure, with several local co-dimension one bifurcations occurring. We also show the occurrence of a global homoclinic bifurcation, which has applicability for large scale strategic bio-control.

Dioecy Is Associated with High Genetic Diversity and Adaptation Rates in the Plant Genus Silene.

About 15,000 angiosperm species (∼6%) have separate sexes, a phenomenon known as dioecy. Why dioecious taxa are so rare is still an open question. Early work reported lower species richness in dioecious compared with nondioecious sister clades, raising the hypothesis that dioecy may be an evolutionary dead-end. This hypothesis has been recently challenged by macroevolutionary analyses that detected no or even positive effect of dioecy on diversification. However, the possible genetic consequences of dioecy at the population level, which could drive the long-term fate of dioecious lineages, have not been tested so far. Here, we used a population genomics approach in the Silene genus to look for possible effects of dioecy, especially for potential evidence of evolutionary handicaps of dioecy underlying the dead-end hypothesis. We collected individual-based RNA-seq data from several populations in 13 closely related species with different sexual systems: seven dioecious, three hermaphroditic, and three gynodioecious species. We show that dioecy is associated with increased genetic diversity, as well as higher selection efficacy both against deleterious mutations and for beneficial mutations. The results hold after controlling for phylogenetic inertia, differences in species census population sizes and geographic ranges. We conclude that dioecious Silene species neither show signs of increased mutational load nor genetic evidence for extinction risk. We discuss these observations in the light of the possible demographic differences between dioecious and self-compatible hermaphroditic species and how this could be related to alternatives to the dead-end hypothesis to explain the rarity of dioecy.

Avoiding critical thresholds through effective monitoring.

A major challenge in sustainability science is identifying targets that maximize ecosystem benefits to humanity while minimizing the risk of crossing critical system thresholds. One critical threshold is the biomass at which populations become so depleted that their population growth rates become negative-depensation. Here, we evaluate how the value of monitoring information increases as a natural resource spends more time near the critical threshold. This benefit emerges because higher monitoring precision promotes higher yield and a greater capacity to recover from overharvest. We show that precautionary buffers that trigger increased monitoring precision as resource levels decline may offer a way to minimize monitoring costs and maximize profits. In a world of finite resources, improving our understanding of the trade-off between precision in estimates of population status and the costs of mismanagement will benefit stakeholders that shoulder the burden of these economic and social costs.

Confirmation and variability of the Allee effect inDictyostelium discoideumcell populations, possible role of chemical signaling within cell clusters.

In studies of the unicellular eukaryoteDictyostelium discoideum, many have anecdotally observed that cell dilution below a certain 'threshold density' causes cells to undergo a period of slow growth (lag). However, little is documented about the slow growth phase and the reason for different growth dynamics below and above this threshold density. In this paper, we extend and correct our earlier work to report an extensive set of experiments, including the use of new cell counting technology, that set this slow-to-fast growth transition on a much firmer biological basis. We show that dilution below a certain density (around 104cells ml-1) causes cells to grow slower on average and exhibit a large degree of variability: sometimes a sample does not lag at all, while sometimes it takes many moderate density cell cycle times to recover back to fast growth. We perform conditioned media experiments to demonstrate that a chemical signal mediates this endogenous phenomenon. Finally, we argue that while simple models involving fluid transport of signal molecules or cluster-based signaling explain typical behavior, they do not capture the high degree of variability between samples but nevertheless favor an intra-cluster mechanism.

Modeling and migration-based control of depopulation.

This study deals with the problem of the population shrinking in habitats affected by aging and excessive migration outflows. First, a control-oriented population dynamics model was proposed that catches the effect of depopulation. The model also includes the effect of spatial interaction-driven migration flows on population size. The resulting model is a non-homogeneous ordinary differential equation. It includes such phenomena that are important from the control point of view, such as the influence of migration costs on population dynamics, the impact of aging on population size, or the effect of the habitats' carrying capacity on migration flows. Based on the model, controllability conditions are formulated and a control strategy was developed that is meant to avoid the depopulation of the habitat. The control method acts on the migration costs to achieve the control goal and requires only population size measurements. Simulation measurements are presented in the paper to show the effectiveness of the proposed modeling and control methods.

Propagation of invasive plant species in the presence of a road.

Invasive plant species pose a significant threat to biodiversity and the economy, yet their management is often resource-intensive and expensive, and further research is required to make control measures more efficient. Evidence suggests that roads can have an important effect on the spread of invasive plant species, although little is known about the underlying mechanisms at play. We have developed a novel mathematical model to analyse the impact of roads on the propagation of invasive plants. The integro-difference equation model is formulated for stage-structured population and incorporates a road sub-domain in the spatial domain. The results of our study reveal, that, depending on the definition of the growth function in the model, there are three distinct types of behaviour in front of the road. Roads can act as barriers to invasion, lead to a formation of a beachhead in front of the road, or act as corridors allowing the invasive species to invade the domain in front of the road. Analytical and computational findings on how roads can impact the spread of invasive species show that a small change in conditions of the environment favouring the invasive species can change the case for the road, allowing the invasive species to invade the domain in front of the road where it previously could not spread.