Demographic stochasticity and extinction in populations with Allee effect

Escape from a metastable state in non-Markovian population dynamics

We study the long-time dynamics in non-Markovian single-population stochastic models, where one or more reactions are modeled as a stochastic process with a fat-tailed nonexponential distribution of waiting times, mimicking long-term memory. We focus on three prototypical examples: genetic switching, population establishment, and population extinction, all with nonexponential production rates. The system is studied in two regimes. In the first, the distribution of waiting times has a finite mean. Here, the system approaches a (quasi)stationary steady state at long times, and we develop a general Wentzel-Kramers-Brillouin approach for these non-Markovian systems. We derive explicit results for the mean population size and mean escape time from the metastable state of the stochastic dynamics. In this realm, we reveal that for sufficiently strong memory, a memory-induced (meta)stable state can emerge in the system. In the second regime, the waiting time distribution is assumed to have an infinite mean. Here, for bistable systems we find two distinct scaling regimes, separated by an exponentially long time which may strongly depend on the initial conditions of the system.

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.

Hydrological disturbances enhance stochastic assembly processes and decrease network stability of algae communities in a highland floodplain system

Floodplains are hotspots for biodiversity research and conservation worldwide. Hydrological disturbances can profoundly influence the ecological processes and functions of floodplain systems by altering key biological groups such as algae communities. However, the impacts of flood disturbance on the assembly processes and co-occurrence patterns of algae communities in floodplain ecosystems are still unclear. To ascertain the response patterns of algae communities to flood disturbance, we characterized planktonic and benthic algae communities in 144 water and sediment samples collected from the Tibetan floodplain during non-flood and flood periods based on 23S ribosomal RNA gene sequencing. Results showed that planktonic algae exhibited higher diversity and greater compositional variations compared with benthic communities after flood disturbance. Flooding promoted algae community homogenization at horizontal (rivers vs. oxbow lakes) and vertical levels (water vs. sediment). Stochastic processes governed the assembly of distinct algae communities, and their ecological impacts were enhanced in response to flooding. In the non-flood period, dispersal limitation (81.78 %) was the primary ecological process driving algae community assembly. In the flood period, the relative contribution of ecological drift (72.91 %) to algae community assembly markedly increased, with dispersal limitation (22.61 %) being less important. Flooding reduced the interactions among algae taxa, resulting in lower network complexity and stability. Compared with the planktonic algae subnetworks, the benthic subnetworks showed greater stability in the face of flooding. Findings of this study broaden our understanding of how algae communities respond to hydrological disturbances from an ecological perspective and could be useful for the management of highland floodplain ecosystems.

Analysis of modified Holling-Tanner model with strong Allee effect

In this paper, we study a predator-prey system, the modified Holling-Tanner model with strong Allee effect. The existence and stability of the non-negative equilibria are discussed first. Several kinds of bifurcation phenomena, which the model may undergo, such as saddle-node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation, are studied second. Bifurcation diagram for Bogdanov-Takens bifurcation of codimension 2 is given. Then, possible dynamical behaviors of this model are illustrated by numerical simulations. This paper appears to be the first study of the modified Holling-Tanner model that includes the influence of a strong Allee effect.

Optimal management of stochastic invasion in a metapopulation with Allee effects

Invasive species account for incalculable damages worldwide, in both ecological and bioeconomic terms. The question of how a network of invasive populations can be optimally managed is one that deserves further exploration. A study accounting for partial observability and imperfect detection, in particular, could yield useful insights into species eradication efforts. Here, we generalized a simple model system that we developed in previous work. This model consists of three interacting populations with underlying strong Allee effects and stochastic dynamics, inhabiting distinct locations connected by dispersal, which can generate bistability. To explore the stochastic dynamics, we formulated an individual-based modeling approach. Next, using the theory of continuous-time Markov chains, we approximated the original high-dimensional model by a Markov chain with eight states, with each state corresponding to a combination of population thresholds. We then used the reduced model as the core for a powerful decision-making tool, referred to as a Partially Observable Markov Decision Process (POMDP). Analysis of this POMDP indicates when the system results in optimal management outcomes.

Dispersal-induced resilience to stochastic environmental fluctuations in populations with Allee effect

Many species are unsustainable at small population densities (Allee effect); i.e., below the so-called Allee threshold, the population decreases instead of growing. In a closed local population, environmental fluctuations always lead to extinction. Here, we show how, in spatially extended habitats, dispersal can lead to a sustainable population in a region, provided the amplitude of environmental fluctuations is below an extinction threshold. We have identified two types of sustainable populations: high-density and low-density populations (through a mean-field approximation, valid in the limit of large dispersal length). Our results show that patches where population is high, low, or extinct coexist when the population is close to global extinction (even for homogeneous habitats). The extinction threshold is maximum for characteristic dispersal distances much larger than the spatial scale of synchrony of environmental fluctuations. The extinction threshold increases proportionally to the square root of the dispersal rate and decreases with the Allee threshold. The low-population-density solution can allow understanding of difficulties in recovery after harvesting. This theoretical framework provides a unique approach to address other factors, such as habitat fragmentation or harvesting, impacting population resilience to environmental fluctuations.

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

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

Trait convergence and trait divergence in lake phytoplankton reflect community assembly rules

Environmental filtering and limiting similarity are those locally acting processes that influence community structure. These mechanisms acting on the traits of species result in trait convergence or divergence within the communities. The role of these processes might change along environmental gradients, and it has been conceptualised in the stress-dominance hypothesis, which predicts that the relative importance of environmental filtering increases and competition decreases with increasing environmental stress. Analysing trait convergence and divergence in lake phytoplankton assemblages, we studied how the concepts of ‘limiting similarity’ versus ‘environmental filtering’ can be applied to these microscopic aquatic communities, and how they support or contradict the stress-dominance hypothesis. Using a null model approach, we investigated the divergence and convergence of phytoplankton traits along environmental gradients represented by canonical axes of an RDA. We used Rao’s quadratic entropy as a measure of functional diversity and calculated effect size (ES) values for each sample. Negative ES values refer to trait convergence, i.e., to the higher probability of the environmental filtering in community assembly, while positive values indicate trait divergence, stressing the importance of limiting similarity (niche partitioning), that is, the competition between the phytoplankters. Our results revealed that limiting similarity and environmental filtering may operate simultaneously in phytoplankton communities, but these assembly mechanisms influenced the distribution of phytoplankton traits differently, and the effects show considerable changes along with the studied scales. Studying the changes of ES values along with the various scales, our results partly supported the stress-dominance hypothesis, which predicts that the relative importance of environmental filtering increases and competition decreases with increasing environmental stress.

Freshwater phytoplankton diversity: models, drivers and implications for ecosystem properties

Our understanding on phytoplankton diversity has largely been progressing since the publication of Hutchinson on the paradox of the plankton. In this paper, we summarise some major steps in phytoplankton ecology in the context of mechanisms underlying phytoplankton diversity. Here, we provide a framework for phytoplankton community assembly and an overview of measures on taxonomic and functional diversity. We show how ecological theories on species competition together with modelling approaches and laboratory experiments helped understand species coexistence and maintenance of diversity in phytoplankton. The non-equilibrium nature of phytoplankton and the role of disturbances in shaping diversity are also discussed. Furthermore, we discuss the role of water body size, productivity of habitats and temperature on phytoplankton species richness, and how diversity may affect the functioning of lake ecosystems. At last, we give an insight into molecular tools that have emerged in the last decades and argue how it has broadened our perspective on microbial diversity. Besides historical backgrounds, some critical comments have also been made.

The boon and bane of boldness: movement syndrome as saviour and sink for population genetic diversity

BACKGROUND

Many felid species are of high conservation concern, and with increasing human disturbance the situation is worsening. Small isolated populations are at risk of genetic impoverishment decreasing within-species biodiversity. Movement is known to be a key behavioural trait that shapes both demographic and genetic dynamics and affects population survival. However, we have limited knowledge on how different manifestations of movement behaviour translate to population processes. In this study, we aimed to 1) understand the potential effects of movement behaviour on the genetic diversity of small felid populations in heterogeneous landscapes, while 2) presenting a simulation tool that can help inform conservation practitioners following, or considering, population management actions targeting the risk of genetic impoverishment.

METHODS

We developed a spatially explicit individual-based population model including neutral genetic markers for felids and applied this to the example of Eurasian lynx. Using a neutral landscape approach, we simulated reintroductions into a three-patch system, comprising two breeding patches separated by a larger patch of differing landscape heterogeneity, and tested for the effects of various behavioural movement syndromes and founder population sizes. We explored a range of movement syndromes by simulating populations with various movement model parametrisations that range from 'shy' to 'bold' movement behaviour.

RESULTS

We find that movement syndromes can lead to a higher loss of genetic diversity and an increase in between population genetic structure for both "bold" and "shy" movement behaviours, depending on landscape conditions, with larger decreases in genetic diversity and larger increases in genetic differentiation associated with bold movement syndromes, where the first colonisers quickly reproduce and subsequently dominate the gene pool. In addition, we underline the fact that a larger founder population can offset the genetic losses associated with subpopulation isolation and gene pool dominance.

CONCLUSIONS

We identified a movement syndrome trade-off for population genetic variation, whereby bold-explorers could be saviours - by connecting populations and promoting panmixia, or sinks - by increasing genetic losses via a 'founder takes all' effect, whereas shy-stayers maintain a more gradual genetic drift due to their more cautious behaviour. Simulations should incorporate movement behaviour to provide better projections of long-term population viability and within-species biodiversity, which includes genetic diversity. Simulations incorporating demographics and genetics have great potential for informing conservation management actions, such as population reintroductions or reinforcements. Here, we present such a simulation tool for solitary felids.

Population switching under a time-varying environment

We study the switching dynamics of a stochastic population subjected to a deterministically time-varying environment. Our approach is demonstrated on a problem of population establishment, which is important in ecology. At the deterministic level, the model we study gives rise to a critical population size beyond which the system experiences establishment. Notably the latter has been shown to be strongly influenced by the interplay between demographic and environmental variations. Here we consider two prototypical examples of a time-varying environment: a temporary change in the environment, and a periodically varying environment. By employing a semiclassical approximation we compute, within exponential accuracy, the change in the establishment probability and mean establishment time of the population, due to the environmental variability. Our analytical results are verified by using a modified Gillespie algorithm which accounts for explicitly time-dependent reaction rates. Importantly, our theoretical approach can also be useful in studying switching dynamics in gene regulatory networks under external variations.

Extinction risk of a metapopulation under bistable local dynamics

We study the extinction risk of a fragmented population residing on a network of patches coupled by migration, where the local patch dynamics includes deterministic bistability. Mixing between patches is shown to dramatically influence the population's viability. We demonstrate that slow migration always increases the population's global extinction risk compared to the isolated case, while at fast migration synchrony between patches minimizes the population's extinction risk. Moreover, we discover a critical migration rate that maximizes the extinction risk of the population, and identify an early-warning signal when approaching this state. Our theoretical results are confirmed via the highly efficient weighted ensemble method. Notably, our theoretical formalism can also be applied to studying switching in gene regulatory networks with multiple transcriptional states.