Stability Of Population Dynamics Research Articles

Finding analytical approximations for discrete, stochastic, individual-based models of ecology

Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how ’bottom up’, individual-based models can be approximated by ’top down’ models of dynamics. Here, we study a class of spatially explicit individual-based models with contest competition: where species compete for space in local cells and then disperse to nearby cells. We start by describing simulations of the model, which exhibit large-scale discrete oscillations and characterize these oscillations by measuring spatial correlations. We then develop two new approximate descriptions of the resulting spatial population dynamics. The first is based on local interactions of the individuals and allows us to give a difference equation approximation of the system over small dispersal distances. The second approximates the long-range interactions of the individual-based model. These approximations capture demographic stochasticity from the individual-based model and show that dispersal stabilizes population dynamics. We calculate extinction probability for the individual-based model and show convergence between the local approximation and the non-spatial global approximation of the individual-based model as dispersal distance and population size simultaneously tend to infinity. Our results provide new approximate analytical descriptions of a complex bottom-up model and deepen understanding of spatial population dynamics.

Is negative density-dependent reproduction regulated by density-induced stress in root voles? Two field experiments.

Density dependence in reproduction plays an important role in stabilizing population dynamics via immediate negative feedback from population density to reproductive output. Although previous studies have shown that negative density‐dependent reproduction is associated with strong spacing behavior and social interaction between individuals, the proximal mechanism for generating negative density‐dependent reproduction remains unclear. In this study, we investigated the effects of density‐induced stress on reproduction in root voles. Enclosed founder populations were established by introducing 6 (low density) and 30 (high density) adults per sex into per enclosure (four enclosures per density in total) during the breeding season from April to July 2012 and from May to August 2015. Fecal corticosterone metabolite (FCM) levels, reproductive traits (recruitment rate and the proportion of reproductively active individuals), and founder population numbers were measured following repeated live trapping in both years. The number of founders was negatively associated with recruitment rates and the proportion of reproductively active individuals, displaying a negative density‐dependent reproduction. FCM level was positively associated with the number of founders. The number of founder females directly affected the proportion of reproductive females, and directly and indirectly through their FCM levels affected the recruitment rate; the effect of the number of male founders on the proportion of reproductive males was mediated by their FCM level. Our results showed that density‐induced stress negatively affected reproductive traits and that density‐induced stress is one ecological factor generating negative density‐dependent reproduction.

A comparative approach to stabilizing mechanisms between discrete- and continuous-time consumer-resource models.

There is rich literature on using continuous-time and discrete-time models for studying population dynamics of consumer-resource interactions. A key focus of this contribution is to systematically compare between the two modeling formalisms the stabilizing/destabilizing impacts of diverse ecological processes that result in a density-dependent consumer attack rate. Inspired by the Nicholson-Bailey/Lotka-Volterra models in discrete-time/continuous-time, respectively, we consider host-parasitoid interactions with an arbitrary parasitoid attack rate that is a function of both the host/parasitoid population densities. Our analysis shows that a Type II functional response is stabilizing in both modeling frameworks only when combined with other mechanisms, such as mutual interference between parasitoids. A Type III functional response is by itself stabilizing, but the extent of attack-rate acceleration needed is much higher in the discrete-time framework, and its stability regime expands with increasing host reproduction. Finally, our results show that while mutual parasitoid interference can stabilize population dynamics, cooperation between parasitoids to handle hosts is destabilizing in both frameworks. In summary, our comparative analysis systematically characterizes diverse ecological processes driving stable population dynamics in discrete-time and continuous-time consumer-resource models.

Attack by a common parasitoid stabilizes population dynamics of multi-host communities

We model the population dynamics of two host species attacked by a common parasitoid using a discrete-time formalism that captures their population densities from year to year. It is well known starting from the seminal work of Nicholson and Bailey that a constant parasitoid attack rate leads to an unstable host-parasitoid interaction. However, a Type III functional response, where the parasitoid attack rate accelerates with increasing host density stabilizes the population dynamics. We first consider a scenario where both host species are attacked by a parasitoid with the same Type III functional response. Our results show that sufficient fast acceleration of the parasitoid attack rate stabilizes the population dynamics of all three species. For two symmetric host species, the extent of acceleration needed to stabilize the three-species equilibrium is exactly the same as that needed for a single host-parasitoid interaction. However, asymmetry can lead to scenarios where the removal of a host species from a stable interaction destabilizes the interaction between the remaining host species and the parasitoid. Next, we consider a situation where one of the host species is attacked at a constant rate (i.e., Type I functional response), and the other species is attacked via a Type III functional response. We identify parameter regimes where a Type III functional response to just one of the host species stabilizes the three species interaction. In summary, our results show that a generalist parasitoid with a Type III functional response to one or many host species can play a key role in stabilizing population dynamics of host-parasitoid communities in apparent competition.

Parentage analyses identify local dispersal events and sibling aggregations in a natural population of Millepora hydrocorals, a free‐spawning marine invertebrate

Dispersal is a critical process for the persistence and productivity of marine populations. For many reef species, there is increasing evidence that local demography and self-recruitment have major consequences on their genetic diversity and adaptation to environmental change. Yet empirical data of dispersal patterns in reef-building species remain scarce. Here, we document the first genetic estimates of self-recruitment and dispersal distances in a free-spawning marine invertebrate, the hydrocoral Millepora cf. platyphylla. Using twelve microsatellite markers, we gathered genotypic information from 3,160 georeferenced colonies collected over 27,000m2 of a single reef in three adjacent habitats in Moorea, French Polynesia; the mid slope, upper slope, and back reef. Although the adult population was predominantly clonal (85% were clones), our parentage analysis revealed a moderate self-recruitment rate with a minimum of 8% of sexual propagules produced locally. Assigned offspring often settled at <10m from their parents and dispersal events decrease with increasing geographic distance. There were no discrepancies between the dispersal distances of offspring assigned to parents belonging to clonal versus nonclonal genotypes. Interhabitat dispersal events via cross-reef transport were also detected for sexual and asexual propagules. Sibship analysis showed that full siblings recruit nearby on the reef (more than 40% settled at <30m), resulting in sibling aggregations. Our findings highlight the importance of self-recruitment together with clonality in stabilizing population dynamics, which may ultimately enhance local sustainability and resilience to disturbance.

The ecology and significance of below-ground bud banks in plants.

Below-ground bud banks have experienced much recent interest due to discoveries that they (1) account for the majority of seasonal population renewal in many communities, (2) are crucial to regeneration following disturbance, and (3) have important consequences for plant population dynamics and plant and ecosystem function across a number of habitats. This review presents an overview of the role of bud banks in plant population renewal, examines bud bank life history, summarizes bud bank traits and their potential ecological implications, synthesizes the response of bud banks to disturbance, and highlights gaps to guide future research. The characteristics and life history of buds, including their natality, dormancy, protection and longevity, provide a useful framework for advancing our understanding of bud banks. The fate of buds depends on their age, size, type, location, and biotic and abiotic factors that collectively regulate bud bank dynamics. A bud bank can provide a demographic storage effect stabilizing population dynamics, and also confer resistance to disturbance and invasion. Regeneration capacity following disturbance is determined by interactions among the rates of bud natality, depletion and dormancy (meristem limitation), and the resources available to support the regeneration process. The resulting response of plants and their bud banks to disturbances such as fire, herbivory and anthropogenic sources determines the community's regenerative capacity. Vegetation responses to environmental change may be mediated through changes in bud bank dynamics and phenology. Environmental change that depletes the bud bank or prohibits its formation likely results in a loss of vegetation resilience and plant species diversity. Standardization of bud sampling, examination of bud banks in more ecosystems and their response to environmental variation and disturbance regimes, employment of stage-structured bud bank modelling and evaluation of the cost of bud bank construction and maintenance will benefit this expanding field of research.

More frequent extreme climate events stabilize reindeer population dynamics

Extreme climate events often cause population crashes but are difficult to account for in population-dynamic studies. Especially in long-lived animals, density dependence and demography may induce lagged impacts of perturbations on population growth. In Arctic ungulates, extreme rain-on-snow and ice-locked pastures have led to severe population crashes, indicating that increasingly frequent rain-on-snow events could destabilize populations. Here, using empirically parameterized, stochastic population models for High-Arctic wild reindeer, we show that more frequent rain-on-snow events actually reduce extinction risk and stabilize population dynamics due to interactions with age structure and density dependence. Extreme rain-on-snow events mainly suppress vital rates of vulnerable ages at high population densities, resulting in a crash and a new population state with resilient ages and reduced population sensitivity to subsequent icy winters. Thus, observed responses to single extreme events are poor predictors of population dynamics and persistence because internal density-dependent feedbacks act as a buffer against more frequent events.

A mathematical model of intraguild predation with prey switching

Intraguild predation (IGP) is widespread in nature. In this paper, a mathematical model of a tri-trophic food web with IGP and prey switching is considered, where the IG predator tends to consume disproportionately more of the relatively abundant prey. Bifurcation analysis shows that prey switching may (i) enhance the persistence of the IG prey when it is an inferior competitor for resources; (ii) enhance the persistence of the IG predator when one of the prey species is at least moderately abundant; (iii) facilitate coexistence of all species; and (iv) stabilize the population dynamics. It has been found that prey switching combined with predator interference may have a synergistic effect on enhancing coexistence and stabilizing population dynamics. Bistability and chaotic attractors are also observed in the mathematical model for a small range of parameter values.

Ecological drift and competitive interactions predict unique patterns in temporal fluctuations of population size.

Recent studies have highlighted the importance of higher-order competitive interactions in stabilizing population dynamics in multi-species communities. But how does the structure of competitive hierarchies affect population dynamics and extinction processes? We tackled this important question by using spatially explicit simulations of ecological drift (10 species in a homogeneous landscape of 64 patches) in which birth rates were influenced by interspecific competition. Specifically, we examined how transitive (linear pecking orders) and intransitive (pecking orders with loops) competitive hierarchies affected extinction rates and population dynamics in simulated communities through time. In comparison to a pure neutral model, an ecological drift model including transitive competition increased extinction rates, caused synchronous density-dependent population fluctuations, and generated a white-noise distribution of population sizes. In contrast, the drift model with intransitive competitive interactions decreased extinctions rates, caused asynchronous (compensatory) density-dependent population fluctuations, and generated a brown noise distribution of population sizes. We also explored the effect on community stability of more complex patterns of competitive interactions in which pairwise competitive relationships were assigned probabilistically. These probabilistic competition models also generated density-dependent trajectories and a brown noise distribution of population sizes. However, extinction rates and the degree of population synchrony were comparable to those observed in purely neutral communities. Collectively, our results confirm that intransitive competition has a strong and stabilizing effect on local populations in species-poor communities. This effect wanes with increasing species richness. Empirical assemblages characterized by brown spectral noise, density-dependent regulation, and asynchronous (compensatory) population fluctuations may indicate a signature of intransitive competitive interactions.

Influence of Harvest on the Dynamics of Populations with Age and Sex Structures

The paper investigates influence of sex- and age-specific harvest on the dynamics of structured populations based on the mathematical model with discrete time. We assume birth rate depends on the population sex ratio and is described by the modified harmonic mating function with switching. The population size is regulated by decreasing juvenile survival rate with growth of sex-age class sizes. The aim is to study the mechanisms of formation and evolution of dynamic modes for the exploited structured population models due to harvesting intensity. Conditions for sustainable development of the exploited population are received. Dynamic modes of the population models are studied. Influence of birth, survival, and self-regulation rates, the formation process of the mating pairs, and sex- and age-specific harvest on transitions between different dynamic modes are investigated. Sex-specific harvest of mature females or males will change the pair formation if the sex class, whose number of individuals is more, is exploited. Depending on values of the population parameters, the sex- and age-specific harvest (juveniles, mature females or males) can result in both damping of the oscillations, which stabilizes population dynamics, and the oscillation appearance, including two-year or quasiperiodic population fluctuations. The model of exploited population reveals the phenomenon of multistability, which is typical for a population without harvesting. The multistability is the result of complex bifurcations occurring due to both the system nonlinearity and the changing pair formation principle.

Crop yield gap and stability in organic and conventional farming systems

A key challenge for sustainable intensification of agriculture is to produce increasing amounts of food and feed with minimal biodiversity loss, nutrient leaching, and greenhouse gas emissions. Organic farming is considered more sustainable, however, less productive than conventional farming. We analysed results from an experiment started under identical soil conditions comparing one organic and two conventional farming systems. Initially, yields in the organic farming system were lower, but approached those of both conventional systems after 10–13 years, while requiring lower nitrogen inputs. Unexpectedly, organic farming resulted in lower coefficient of variation, indicating enhanced spatial stability, of pH, nutrient mineralization, nutrient availability, and abundance of soil biota. Organic farming also resulted in improved soil structure with higher organic matter concentrations and higher soil aggregation, a profound reduction in groundwater nitrate concentrations, and fewer plant-parasitic nematodes. Temporal stability between the three farming systems was similar, but when excluding years of Phytophthora outbreaks in potato, temporal stability was higher in the organic farming system. There are two non-mutually exclusive mechanistic explanations for these results. First, the enhanced spatial stability in the organic farming system could result from changes in resource-based (i.e. bottom-up) processes, which coincides with the observed higher nutrient provisioning throughout the season in soils with more organic matter. Second, enhanced resource inputs may also affect stability via increased predator-based (i.e. top-down) control. According to this explanation, predators stabilize population dynamics of soil organisms, which is supported by the observed higher soil food web biomass in the organic farming system.We conclude that closure of the yield gap between organic and conventional farming can be a matter of time and that organic farming may result in greater spatial stability of soil biotic and abiotic properties and soil processes. This is likely due to the time required to fundamentally alter soil properties.

Temperature-based spawning habitat selection by capelin (Mallotus villosus) in Newfoundland

Abstract The location of reproduction is a key life history trait, as it influences the bio-physical conditions that offspring experience and, thus, fitness. Capelin Mallotus villosus is a small (&amp;lt; 200 mm), short-lived forage fish that spawns in two habitats in coastal Newfoundland: warm beaches and cool, deep water (15–40 m). From 2009 to 2014, we investigated temperature-dependent spawning habitat use by quantifying hourly temperature at spawning sites during July within each habitat along with population-level spawning site use. Capelin did not spawn at sites with temperatures &amp;lt;2 °C or consistently &amp;gt;12 °C, supporting the estimated suitable spawning temperature range (2–12 °C). Spawning typically occurred exclusively at beaches early in July when deep-water habitat was too cold (i.e. &amp;lt;2 °C), and then switched to deep-water habitat later in July when beaches became too warm (i.e. &amp;gt;12 °C). Spawning overlapped for 1–3 d in both habitats when temperatures were within suitable ranges (2011, 2013), but capelin also spawned exclusively in one habitat when temperatures remained suitable in the other. The latter suggests that other factors influence spawning habitat selection, such as conspecific egg densities and other environmental conditions. Overall, the flexible use of spawning habitats, along with wide tolerance ranges of capelin eggs to environmental conditions, are likely key adaptations to maximize fitness and stabilize population dynamics of this important forage fish species in an unpredictable environment.

Evolution of Site-Selection Stabilizes Population Dynamics, Promotes Even Distribution of Individuals, and Occasionally Causes Evolutionary Suicide

Species that compete for access to or use of sites, such as parasitic mites attaching to honey bees or apple maggots laying eggs in fruits, can potentially increase their fitness by carefully selecting sites at which they face little or no competition. Here, we systematically investigate the evolution of site-selection strategies among animals competing for discrete sites. By developing and analyzing a mechanistic and population-dynamical model of site selection in which searching individuals encounter sites sequentially and can choose to accept or continue to search based on how many conspecifics are already there, we give a complete characterization of the different site-selection strategies that can evolve. We find that evolution of site-selection stabilizes population dynamics, promotes even distribution of individuals among sites, and occasionally causes evolutionary suicide. We also discuss the broader implications of our findings and propose how they can be reconciled with an earlier study (Nonaka et al. in J Theor Biol 317:96–104, 2013) that reported selection toward ever higher levels of aggregation among sites as a consequence of site-selection.

Stress tolerance and population stability of rock pool Daphnia in relation to local conditions and population isolation

Small fragmented populations can lose genetic variability, which reduces population viability through inbreeding and loss of adaptability. Current and previous environmental conditions can also alter the viability of populations, by creating local adaptations that determine responses to stress. Yet, most studies on stress tolerance usually consider either the effect of genetic diversity or the local environment, missing a more holistic perspective of the factors contributing to stress tolerance among natural populations. Here, we studied how salinity stress affects population growth of Daphnialongispina, Daphnia magna, and Daphnia pulex from rock pools with varying degrees of population isolation and salinity conditions. Standing variation of in situ rock pool salinity conditions explained more variation in salt tolerance than the standing variation of population isolation or genetic diversity, in both a pulse and a press disturbance experiment. This indicates that the level of stress, which these natural populations experience, influences their response to that stress, which may have important consequences for the conservation of fragmented populations. However, long-term population stability in the field decreased with population isolation, indicating that natural populations experience a variety of stresses; thus, population isolation and genetic diversity may stabilize population dynamics over larger spatiotemporal scales.

A comparison of six methods for stabilizing population dynamics

Over the last two decades, several methods have been proposed for stabilizing the dynamics of biological populations. However, these methods have typically been evaluated using different population dynamics models and in the context of very different concepts of stability, which makes it difficult to compare their relative efficiencies. Moreover, since the dynamics of populations are dependent on the life-history of the species and its environment, it is conceivable that the stabilizing effects of control methods would also be affected by such factors, a complication that has typically not been investigated. In this study, we compare six different control methods with respect to their efficiency at inducing a common level of enhancement (defined as 50% increase) for two kinds of stability (constancy and persistence) under four different life-history/environment combinations. Since these methods have been analytically studied elsewhere, we concentrate on an intuitive understanding of realistic simulations incorporating noise, extinction probability and lattice effect. We show that for these six methods, even when the magnitude of stabilization attained is the same, other aspects of the dynamics like population size distribution can be very different. Consequently, correlated aspects of stability, like the amount of persistence for a given degree of constancy stability (and vice versa) or the corresponding effective population size (a measure of resistance to genetic drift) vary widely among the methods. Moreover, the number of organisms needed to be added or removed to attain similar levels of stabilization also varies for these methods, a fact that has economic implications. Finally, we compare the relative efficiencies of these methods through a composite index of various stability related measures. Our results suggest that Lower Limiter Control (LLC) seems to be the optimal method under most conditions, with the recently proposed Adaptive Limiter Control (ALC) being a close second.

Environmental stress, facilitation, competition, and coexistence

The major theories regarding the combined influence of the environment and species interactions on population and community dynamics appear to conflict. Stress/ disturbance gradient models of community organization, such as the stress gradient hypothesis, emphasize a diminished role for competition in harsh environments whereas modern coexistence theory does not. Confusion about the role of species interactions in harsh environments is perpetuated by a disconnect between population dynamics theory and data. We linked theory and data using response surface experiments done in the field to parameterize mathematical, population-dynamic competition models. We replicated our experiment across two environments that spanned a common and important environmental stress gradient for determining community structure in benthic marine systems. We generated quantitative estimates of the effects of environmental stress on population growth rates and the direction and strength of intra- and interspecific interactions within each environment. Our approach directly addressed a perpetual blind spot in this field by showing how the effects of competition can be intensified in stressful environments even though the apparent strength of competition remains unchanged. Furthermore, we showed how simultaneous, reciprocal competitive and facilitative effects can stabilize population dynamics in multispecies communities in stressful environments.

Maximal feeding with active prey-switching: A kill-the-winner functional response and its effect on global diversity and biogeography

Predators’ switching towards the most abundant prey is a mechanism that stabilizes population dynamics and helps overcome competitive exclusion of species in food webs. Current formulations of active prey-switching, however, display non-maximal feeding in which the predators’ total ingestion decays exponentially with the number prey species (i.e. the diet breadth) even though the total prey biomass stays constant. We analyse three previously published multi-species functional responses which have either active switching or maximal feeding, but not both. We identify the cause of this apparent incompatibility and describe a kill-the-winner formulation that combines active switching with maximal feeding. Active switching is shown to be a community response in which some predators become prey-selective and the formulations with maximal or non-maximal feeding are implicitly assuming different food web configurations. Global simulations using a marine ecosystem model with 64 phytoplankton species belonging to 4 major functional groups show that the species richness and biogeography of phytoplankton are very sensitive to the choice of the functional response for grazing. The phytoplankton biogeography reflects the balance between the competitive abilities for nutrient uptake and the degree of apparent competition which occurs indirectly between species that share a common predator species. The phytoplankton diversity significantly increases when active switching is combined with maximal feeding through predator-mediated coexistence.

Post‐reproductive life span and demographic stability

Recent field studies suggest that it is common in nature for animals to outlive their reproductive viability. Post‐reproductive life span has been observed in a broad range of vertebrate and invertebrate species. But post‐reproductive life span poses a paradox for traditional theories of life history evolution. The only commonly‐cited explanation is the ‘grandmother hypothesis’, which is limited to higher, social mammals. We propose that post‐reproductive life span evolves to stabilize population dynamics, avoiding local extinctions. Predator–prey and other ecosystem interactions tend to produce volatility that can create population crashes and local extinctions. Total fertility rates that exceed the ecosystem's recovery rate contribute to population overshoot, followed by collapse. These local extinctions may constitute a potent group selection mechanism, driving evolution toward controlled rates of population growth, even when there is a significant individual cost. In this paper, we consider the question: what life history characteristics support demographic homeostasis at the least cost to individual fitness? In individual‐based evolutionary simulations, we find that reduction in fertility is sufficient to avoid population instabilities leading to extinction, but that life histories that include senescence can accomplish the same thing at a lower cost to individual fitness. Furthermore, life histories that include the potential for a post‐reproductive period are yet more efficient at stabilizing population dynamics, while minimizing the impact on individual fitness.

Comparing the Effects of Rapid Evolution and Phenotypic Plasticity on Predator-Prey Dynamics

Ecologists have increasingly focused on how rapid adaptive trait changes can affect population dynamics. Rapid adaptation can result from either rapid evolution or phenotypic plasticity, but their effects on population dynamics are seldom compared directly. Here we examine theoretically the effects of rapid evolution and phenotypic plasticity of antipredatory defense on predator-prey dynamics. Our analyses reveal that phenotypic plasticity tends to stabilize population dynamics more strongly than rapid evolution. It is therefore important to know the mechanism by which phenotypic variation is generated for predicting the dynamics of rapidly adapting populations. We next examine an advantage of a phenotypically plastic prey genotype over the polymorphism of specialist prey genotypes. Numerical analyses reveal that the plastic genotype, if there is a small cost for maintaining it, cannot coexist with the pairs of specialist counterparts unless the system has a limit cycle. Furthermore, for the plastic genotype to replace specialist genotypes, a forced environmental fluctuation is critical in a broad parameter range. When these results are combined, the plastic genotype enjoys an advantage with population oscillations, but plasticity tends to lose its advantage by stabilizing the oscillations. This dilemma leads to an interesting intermittent limit cycle with the changing frequency of phenotypic plasticity.

Reproductive conflict delays the recovery of an endangered social species

1. Evolutionary theory predicts that individuals, in order to increase their relative fitness, can evolve behaviours that are detrimental for the group or population. This mismatch is particularly visible in social organisms. Despite its potential to affect the population dynamics of social animals, this principle has not yet been applied to real-life conservation. 2. Social group structure has been argued to stabilize population dynamics due to the buffering effects of nonreproducing subordinates. However, competition for breeding positions in such species can also interfere with the reproduction of breeding pairs. 3. Seychelles magpie robins, Copsychus sechellarum, live in social groups where subordinate individuals do not breed. Analysis of long-term individual-based data and short-term behavioural observations show that subordinates increase the territorial takeover frequency of established breeders. Such takeovers delay offspring production and decrease territory productivity. 4. Individual-based simulations of the Seychelles magpie robin population parameterized with the long-term data show that this process has significantly postponed the recovery of the species from the Critically Endangered status. 5. Social conflict thus can extend the period of high extinction risk, which we show to have population consequences that should be taken into account in management programmes. This is the first quantitative assessment of the effects of social conflict on conservation.