Overcompensatory Density Dependence Research Articles

Patterns of spawning and settlement of reef fishes as strategic responses to post-settlement competition

Settlement is a critical transition in the life history of reef fish, and the timing of this event can have a strong effect on fitness. Key factors that influence settlement timing are predictable lunar cyclic variation in tidal currents, moonlight, and nocturnal predation risk as larvae transition from pelagic to benthic environments. However, populations typically display wide variation in the arrival of settlers over the lunar cycle. This variation is often hypothesized to result from unpredictable conditions in the pelagic environment and bet-hedging by spawning adults. Here, we consider the hypothesis that the timing of spawning and settlement is a strategic response to post-settlement competition. We use a game theoretic model to predict spawning and settlement distributions when fish face a tradeoff between minimizing density-independent predation risk while crossing the reef crest vs. avoiding high competitor density on settlement habitat. In general, we expect competition to spread spawning over time such that settlement is distributed around the lunar phase with the lowest predation risk, similar to an ideal free distribution in which competition spreads competitors across space. We examine the effects of overcompensating density dependence, age-dependent competition, and competition among daily settler cohorts. Our model predicts that even in the absence of stochastic variation in the larval environment, competition can result in qualitative divergence between spawning and settlement distributions. Furthermore, we show that if competitive strength increases with settler age, competition results in covariation between settler age and settlement date, with older larvae settling when predation risk is minimal. We predict that competition between daily cohorts delays peak settlement, with priority effects potentially selecting for a multimodal settlement distribution.

Resource Translocation Modelling Highlights Density-Dependence Effects in Fruit Production at Various Levels of Organisation.

The size of fruit cells, seeds and fruits depends on their number. Could this density-dependence effect result from sugar resource sharing and, if so, does it involve phloem sugar flow or the intensity of sugar unloading to the sink? A density-dependence model (DDM) describing these processes was designed and parameterised for six species at five levels of organisation: cells and seeds within fruits, fruits within clusters, fruits within plants and plants within plots. Sugar flow was driven by phloem conductance, determined by parameters α, governing the shape of its relationship to population size, and κ, its value for a population size of one. Sugar unloading followed Michaelis–Menten kinetics with parameters Vm (maximal unloading rate) and Km (Michaelis constant). The DDM effectively reproduced the observed individual mass dynamics, the undercompensating density dependence observed in most species at all sub-plant levels and the undercompensating, exact and overcompensating density dependence observed at the plant level. Conductance (κ) was a scaling factor varying with the level of organisation. Vm was positively correlated with density dependence, and α was negatively correlated with density dependence only if the plant-within-plot level was not considered. Analysis of the model’s behaviour indicates that density dependence of fruit growth could be a result of sugar sharing, and that both phloem sugar flow and sugar unloading contribute to these effects.

Strong Allee effect and basins of attraction in a discrete‐time zoonotic infectious disease model

AbstractMotivated by the Feline immunodeficiency virus, the virus that causes AIDS in cat populations, we use discrete‐time infectious disease models with demographic strong Allee effect to examine the impact of the fatal susceptible‐infected (SI) infections on two different types of growth functions: Holling type III or modified Beverton–Holt per‐capita growth function (compensatory density dependence), and Ricker per‐capita growth function with mating (overcompensatory density dependence). The occurrence of the strong Allee effect in the disease‐free equation renders the SI population model bistable, where the two coexisting locally asymptotically stable equilibrium points are either the origin (catastrophic extinction state) and the second fixed point (compensatory dynamics) or the origin and an intrinsically generated demographic period population cycle (overcompensatory dynamics). We use the basic reproduction number, , and the spectral radius, , to examine the structures of the coexisting attractors. In particular, we use MATLAB simulations to show that the fatal disease is not only capable of enlarging or shrinking the basin of attraction of the catastrophic extinction state, but it is also capable of fracturing the basins of attraction into several disjoint sets. Thus, making it difficult to specify the asymptotic zoonotic SI disease outcome in terms of all initial infections. The complexity of the basins of attractions appears to increase with an increase in the period of the intrinsically generated demographic population cycles.Recommendations for Resource Managers: Worldwide, disease agents which originate from animals or products of animal origin, such as Ebola virus, COVID‐19, West Nile virus, or malaria are responsible for millions of deaths each year. To help improve control and ultimately eradicate future pandemics in human populations, we use a Feline immunodeficiency virus disease model with the strong Allee effect to understand outbreaks of zoonotic diseases. In general, the strong Allee effect renders a population bistable with a catastrophic extinction state coexisting with a persistence state. We use the basic reproduction number and the spectral radius to obtain conditions for outbreaks of zoonotic diseases and conditions for zoonotic disease extinction. We show that a fatal zoonotic disease is not only capable of enlarging or shrinking the basin of attraction of the catastrophic extinction state, but it is also capable of fracturing the basins of attraction into several disjoint sets. Thus, making it difficult to specify the asymptotic zoonotic disease outcome in terms of all initial infections. The complexity of the basins of attractions appears to increase with an increase in the period of the demographic population cycles.

Cost-benefit evaluation of management strategies for an invasive amphibian with a stage-structured model

Management strategies for invasive populations should be designed to maximise efficacy and efficiency, i.e. to accomplish their goals while operating with the least resource consumption. This optimisation is often difficult to achieve in stage-structured populations, because costs, benefits and feasibility of removing individuals may vary with stage. We use a spatially-explicit stage-structured model to assess efficacy of past, present and alternative control strategies for invasive guttural toads, Sclerophrys gutturalis, in Cape Town. The strategies involve removal of variable proportions of individuals at different life-history stages and spatial scales. We also quantify the time necessary to implement each strategy as a proxy of financial resources and we correct strategy outcomes by implementation of time to estimate efficiency. We found that the strategy initially pursued in Cape Town, which did not target any specific stage, was less efficient than the present strategy, which prioritises adult removal. The initial strategy was particularly inefficient because it did not reduce the population size despite allocating consistent resources to remove eggs and tadpoles. We also found that such removal might be detrimental when applied at high levels. This counter-intuitive outcome is due to the ‘hydra effect’: an undesired increase in population size caused by removing individuals before overcompensatory density dependence. Strategies that exclusively remove adults ensure much greater management efficiency than those that also remove eggs and tadpoles. Available management resources should rather be allocated to increase the proportion of adult guttural toads that are removed or the spatial extent at which this removal is pursued.

Climate variability and density-dependent population dynamics: Lessons from a simple High Arctic ecosystem

Ecologists are still puzzled by the diverse population dynamics of herbivorous small mammals that range from high-amplitude, multiannual cycles to stable dynamics. Theory predicts that this diversity results from combinations of climatic seasonality, weather stochasticity, and density-dependent food web interactions. The almost ubiquitous 3- to 5-y cycles in boreal and arctic climates may theoretically result from bottom-up (plant-herbivore) and top-down (predator-prey) interactions. Assessing, empirically, the roles of such interactions and how they are influenced by environmental stochasticity has been hampered by food web complexity. Here, we take advantage of a uniquely simple High Arctic food web, which allowed us to analyze the dynamics of a graminivorous vole population not subjected to top-down regulation. This population exhibited high-amplitude, noncyclic fluctuations-partly driven by weather stochasticity. However, the predominant driver of the dynamics was overcompensatory density dependence in winter that caused the population to frequently crash. Model simulations showed that the seasonal pattern of density dependence would yield regular 2-y cycles in the absence of stochasticity. While such short cycles have not yet been observed in mammals, they are theoretically plausible if graminivorous vole populations are deterministically bottom-up regulated. When incorporating weather stochasticity in the model simulations, cyclicity became disrupted and the amplitude was increased-akin to the observed dynamics. Our findings contrast with the 3- to 5-y population cycles that are typical of graminivorous small mammals in more complex food webs, suggesting that top-down regulation is normally an important component of such dynamics.

Compensatory and overcompensatory dynamics in prey\u2013predator systems exposed to harvest

Density dependent prey–predator systems under the impact of harvest are considered. The recruitment functions for both the prey and predator belong to the Deriso–Schnute family which allow us to study how the dynamical behaviour of both populations changes when compensatory density dependence turns overcompensatory. Depending on the degree of overcompensation, we show in the case of no harvest that an increase of the fecundity of the prey always acts in a destabilizing fashion. If the degree of overcompensation becomes sufficiently large, such an increase can lead to large amplitude chaotic oscillations of the prey, which actually may drive the predator population to extinction. The impact of harvest also depends on the degree of overcompensatory density dependence. If only the prey is the target population, increased harvest in general seems to stabilize the dynamics. On the other hand, harvesting only the predator may in some cases tend to stabilize dynamics, but there are also parameter regions where this turns out to be a strong destabilizing effect.

Tail associations in ecological variables and their impact on extinction risk

AbstractExtreme climatic events (ECEs) are becoming more frequent and more intense due to climate change. Furthermore, there is reason to believe ECEs may modify "tail associations" between distinct population vital rates, or between values of an environmental variable measured in different locations. "Tail associations" between two variables are associations that occur between values in the left or right tails of the distributions of the variables. Two positively associated variables can be principally "left‐tail associated" (i.e., more correlated when they take low values than when they take high values) or "right‐tail associated" (more correlated when they take high than low values), even with the same overall correlation coefficient in both cases. We tested, in the context of non‐spatial stage‐structured matrix models, whether tail associations between stage‐specific vital rates may influence extinction risk. We also tested whether the nature of spatial tail associations of environmental variables can influence metapopulation extinction risk. For instance, if low values of an environmental variable reduce the growth rates of local populations, one may expect that left‐tail associations increase metapopulation extinction risks because then environmental "catastrophes" are spatially synchronized, presumably reducing the potential for rescue effects. For the non‐spatial, stage‐structured models we considered, left‐tail associations between vital rates did accentuate extinction risk compared to right‐tail associations, but the effect was small. In contrast, we showed that density dependence interacts with tail associations to influence metapopulation extinction risk substantially: For population models showing undercompensatory density dependence, left‐tail associations in environmental variables often strongly accentuated and right‐tail associations mitigated extinction risk, whereas the reverse was usually true for models showing overcompensatory density dependence. Tail associations and their asymmetries are taken into account in assessing risks in finance and other fields, but to our knowledge, our study is one of the first to consider how tail associations influence population extinction risk. Our modeling results provide an initial demonstration of a new mechanism influencing extinction risks and, in our view, should help motivate more comprehensive study of the mechanism and its importance for real populations in future work.

Interannual population dynamics of the green spruce aphid Elatobium abietinum (Walker) in France

AbstractThe hypothesis that similar processes govern interannual dynamics of green spruce aphid in the UK and France, is generally supported by the application of a general discrete model. A simple model based on relatively few parameters was able to closely characterise interannual population dynamics from completely independent aerial and arboreal samples of aphids. Long‐term field population estimates of the green spruce aphid Elatobium abietinum (Walker) in France have provided the opportunity to select and evaluate the generality of a model, which was developed in the UK to explain the year‐to‐year variations in peak abundance of the aphid. The objective was to observe the influence of the local climates and disturbing climate factors on the population densities of the insect in two regions of France. The model uses climate variables and aphid population data from regular samples in the two regions that were investigated. A general discrete model was used to predict aphid population densities. The model performed well in tracking the interannual patterns of population but was less likely to predict absolute population density. To improve predictions, further account would need to be taken of additional site‐specific climate variables and the strength of overcompensating density dependence. Nevertheless, it is clear that broadly similar processes are at work in the population dynamics of this insect across its biogeographical range.

A note on the Lasota discrete model for blood cell production

In an attempt to explain experimental evidence of chaotic oscillations in blood cell population, A. Lasota suggested in 1977 a discrete-time one-dimensional model for the production of blood cells, and he showed that this equation allows to model the behavior of blood cell population in many clinical cases. Our main aim in this note is to carry out a detailed study of Lasota's equation, in particular revisiting the results in the original paper and showing new interesting phenomena. The considered equation is also suitable to model the dynamics of populations with discrete reproductive seasons, adult survivorship, overcompensating density dependence, and Allee effects. In this context, our results show the rich dynamics of this type of models and point out the subtle interplay between adult survivorship rates and strength of density dependence (including Allee effects).

Mechanism matters: the cause of fluctuations in boom-bust populations governs optimal habitat restoration strategy.

Many populations exhibit boom-bust dynamics in which abundance fluctuates dramatically over time. Past research has focused on identifying whether the cause of fluctuations is primarily exogenous, e.g., environmental stochasticity coupled with weak density dependence, or endogenous, e.g., over-compensatory density dependence. Far fewer studies have addressed whether the mechanism responsible for boom-bust dynamics matters with respect to at-risk species management. Here, we ask whether the best strategy for restoring habitat across a landscape differs under exogenously vs. endogenously driven boom-bust dynamics. We used spatially explicit individual-based models to assess how butterfly populations governed by the two mechanisms would respond to habitat restoration strategies that varied in the level of resource patchiness, from a single large patch to multiple patches spaced at different distances. Our models showed that the restoration strategy that minimized extinction risk and boom-bust dynamics would be markedly different depending on the governing mechanism. Exogenously governed populations fared best in a single large habitat patch, whereas for endogenously driven populations, boom-bust dynamics were dampened and extinction risk declined when the total restored area was split into multiple patches with low to moderate inter-patch spacing. Adding environmental stochasticity to the endogenous model did not alter this result. Habitat fragmentation lowered extinction risk in the endogenously driven populations by reducing their growth rate, precluding both "boom" phases and, more importantly, "bust" phases. Our findings suggest that (1) successful restoration will depend on understanding the causes of fluctuations in at-risk populations, (2) the level and pattern of spatiotemporal environmental heterogeneity will also affect the ideal management approach, and (3) counterintuitively, for at-risk species with endogenously governed boom-bust dynamics, lowering the intrinsic population growth rate may decrease extinction risk.

Mean and variance of population density and temporal Taylor’s law in stochastic stage-structured density-dependent models of exploited fish populations

How does fishing affect the mean and variance of population density in the presence of environmental fluctuations? Several recent authors have suggested that an increasing ratio of standard deviation to mean (coefficient of variation, or CV) in population density indicates declining population stability. We investigated the relationship between the mean and variance of population density in stochastic, density-dependent, stage-structured fish population models. Our models included either compensatory or overcompensatory density dependence affecting either fertility or juvenile survival. Environmental stochasticity affected either juvenile survival (when density dependence affected fertility) or fertility (when density dependence affected juvenile survival). The mean and variance of population density were compared as fishing mortality changed. In some cases, the relationship between the natural logarithms of mean and variance is linear under some parameters (life history strategy) of some models (the type of density dependence and the timing of density dependence and stochasticity), supporting Taylor’s law. In other cases, the relationship can be non-linear, especially when density dependence is overcompensatory, and depends on the stage observed. For example, the variance of adult density may increase with its mean while the variance of juvenile density of the same population may decline, or vice versa. The sequence in which individuals experience stochasticity and density dependence matters because density dependence can attenuate or magnify the fluctuation. In conclusion, the use of the CV as a proxy for population instability is not appropriate, and the CV of population density has to be interpreted carefully for other purposes.

Understanding the interplay between density dependent birth function and maturation time delay using a reaction-diffusion population model

The present work employs a nonlocal delay reaction-diffusion model to study the impacts of the density dependent birth function, maturation time delay and population dispersal on single species dynamics (i.e., extinction, survival, extinction-survival). It is shown that the maturation time and the birth function are two major factors determining the fate of single species. Whereas the dispersal acts as a subsidiary factor that only affects the spatial patterns of population densities. When the birth function has a compensating density dependence, maturation time delay cannot destabilize the population survival at the positive equilibrium. Nevertheless, when the birth function has an over-compensating density dependence, the population densities of single species fluctuate in the spatial domain due to the increased maturation time delay. With the Allee effect and over-compensating density dependence, the increases in the maturation time may cause extinction of the single species in the entire spatial domain. The numerical simulations suggest that the solutions of the general model may temporarily remain nearby a stationary wave pulse or a stationary wavefront of the reduced model. The former indicates the survival of single species in a narrow region of the spatial domain. Whereas the latter represents the survival in the entire left-half or right-half of the spatial domain.

Effects of spatial structure of population size on the population dynamics of barnacles across their elevational range.

Explanations for why population dynamics vary across the range of a species reflect two contrasting hypotheses: (i) temporal variability of populations is larger in the centre of the range compared to the margins because overcompensatory density dependence destabilizes population dynamics and (ii) population variability is larger near the margins, where populations are more susceptible to environmental fluctuations. In both of these hypotheses, positions within the range are assumed to affect population variability. In contrast, the fact that population variability is often related to mean population size implies that the spatial structure of the population size within the range of a species may also be a useful predictor of the spatial variation in temporal variability of population size over the range of the species. To explore how population temporal variability varies spatially and the underlying processes responsible for the spatial variation, we focused on the intertidal barnacle Chthamalus dalli and examined differences in its population dynamics along the tidal levels it inhabits. Changes in coverage of barnacle populations were monitored for 10.5 years at 25 plots spanning the elevational range of this species. Data were analysed by fitting a population dynamics model to estimate the effects of density-dependent and density-independent processes on population growth. We also examined the temporal mean-variance relationship of population size with parameters estimated from the population dynamics model. We found that the relative variability of populations tended to increase from the centre of the elevational range towards the margins because of an increase in the magnitude of stochastic fluctuations of growth rates. Thus, our results supported hypothesis (2). We also found that spatial variations in temporal population variability were well characterized by Taylor's power law, the relative population variability being inversely related to the mean population size. Results suggest that understanding the population dynamics of a species over its range may be facilitated by taking the spatial structure of population size into account as well as by considering changes in population processes as a function of position within the range of the species.

The hydra effect, bubbles, and chaos in a simple discrete population model with constant effort harvesting

We analyze the effects of a strategy of constant effort harvesting in the global dynamics of a one-dimensional discrete population model that includes density-independent survivorship of adults and overcompensating density dependence. We discuss the phenomenon of bubbling (which indicates that harvesting can magnify fluctuations in population abundance) and the hydra effect, which means that the stock size gets larger as harvesting rate increases. Moreover, we show that the system displays chaotic behaviour under the combination of high per capita recruitment and small survivorship rates.

Testing the Janzen‐Connell mechanism: pathogens cause overcompensating density dependence in a tropical tree

The Janzen-Connell hypothesis is a leading explanation for plant-species diversity in tropical forests. It suggests that specialized natural enemies decrease offspring survival at high densities beneath parents, giving locally rarer species an advantage. This mechanism, in its original form, assumes that density dependence is overcompensating: mortality must be disproportionately high at the highest densities, with few offspring recruiting below their parents. We tested this assumption using parallel shadehouse and field density-series experiments on seedlings of a tropical tree, Pleradenophora longicuspis. We found strong, overcompensating mortality driven by fungal pathogens, causing 90% (shadehouse) or 100% (field) mortality within 4 weeks of germination, and generating a negative relationship between initial and final seedling densities. Fungicide treatment led to much lower, density-independent, mortality. Overcompensating mortality was extremely rapid, and could be missed without detailed monitoring. Such dynamics may prevent dead trees from being replaced by conspecifics, promoting coexistence as envisioned by the Janzen-Connell hypothesis.

Complex dynamics of survival and extinction in simple population models with harvesting

We study the effects of constant harvesting in a discrete population model that includes density-independent survivorship of adults in a population with overcompensating density dependence. The interaction between the survival parameter and other parameters of the model (harvesting rate, natural growth rate) reveal new phenomena of survival and extinction. The main differences with the dynamics of survival and extinction reported for semelparous populations with overcompensatory density dependence are that there can be multiple windows of extinction and conditional persistence as harvesting increases or the intrinsic growth rate is increased, and that, in case of bistability, the basin of attraction of the nontrivial attractor may consist of an arbitrary number of disjoint connected components.

When does greater mortality increase population size? The long history and diverse mechanisms underlying the hydra effect

The phenomenon of a population increasing in response to an increase in its per-capita mortality rate has recently been termed the 'hydra effect'. This article reviews and unifies previous work on this phenomenon. Some discrete models of density-dependent growth were shown to exhibit hydra effects in 1954, but the topic was then ignored for decades. Here the history of research on the hydra effect is reviewed, and the key factors producing it are explored. Mortality that precedes overcompensatory density dependence always has the potential to produce hydra effects. Even when mortality follows density dependence, hydra effects may occur in unstable systems due to changes in the amplitude and/or form of population cycles. An increase in resource productivity due to lower consumption rates following increased consumer mortality can also produce a hydra effect. Lower consumption can come about as the result of increased satiation of the consumers or changes in behaviour of either consumer or resource species that reduce the mean attack rate. Changes in species composition of a resource community may also decrease the average attack rate. Population structure can promote hydra effects by allowing separation of the timing of density dependence and mortality, although stage-specific density dependence usually decreases hydra effects.

The form of host density-dependence and the likelihood of host–pathogen cycles in forest-insect systems

Forest-insect systems frequently show cyclic dynamics which has been of considerable interest to both experimental and theoretical ecologists. One important issue has been the manner in which density-dependence acting on the host population through resource competition influences the likelihood of population cycles. Existing models make contradictory predictions. Here, we explore two models that allow different forms of density-dependence to be examined. We find that host density-dependence can influence the persistence of the host–pathogen interaction, the likelihood of population cycles and the stability of the host–pathogen interaction. In particular, over-compensatory density-dependence is likely to lead to host–pathogen cycles while under-compensatory density-dependence can promote stability. We discuss these differences with reference to the different forms of intraspecific competition and recent developments in insect population ecology.

A host–parasitoid interaction with Allee effects on the host

We explore the addition of Allee effects to single-species discrete-time models with overcompensatory density dependence. When the intrinsic growth rate of the population, r , is large, the population bifurcates into chaos. The population goes extinct if r is either below a threshold level or very large. The model is then used to study host–parasitoid interactions with and without Allee effects in the host. The coexistence of the host and parasitoid populations both depends on threshold levels of r , threshold levels of the host population size, and the parasitoid potential, which is the product of the searching efficiency of the parasitoid for the host, and the fecundity of the parasitoid. The addition of Allee effects has a negative impact on the coexistence of both populations.

Does Red Noise Increase or Decrease Extinction Risk? Single Extreme Events versus Series of Unfavorable Conditions

Recent theoretical studies have shown contrasting effects of temporal correlation of environmental fluctuations (red noise) on the risk of population extinction. It is still debated whether and under which conditions red noise increases or decreases extinction risk compared with uncorrelated (white) noise. Here, we explain the opposing effects by introducing two features of red noise time series. On the one hand, positive autocorrelation increases the probability of series of poor environmental conditions, implying increasing extinction risk. On the other hand, for a given time period, the probability of at least one extremely bad year ("catastrophe") is reduced compared with white noise, implying decreasing extinction risk. Which of these two features determines extinction risk depends on the strength of environmental fluctuations and the sensitivity of population dynamics to these fluctuations. If extreme (catastrophic) events can occur (strong noise) or sensitivity is high (overcompensatory density dependence), then temporal correlation decreases extinction risk; otherwise, it increases it. Thus, our results provide a simple explanation for the contrasting previous findings and are a crucial step toward a general understanding of the effect of noise color on extinction risk.