Density-dependent Population Research Articles

Density dependent survival drives variation in density dependent population growth of an insect pest

Several ecological processes – from population dynamics to species co‐existence – are driven by density dependence (DD) in population growth rate. Thus, to predict and manage ecological outcomes, we need a deep understanding of which factors and demographic traits drive variation in DD. In the insect pest Tribolium castaneum, we found large variation in DD across habitats but not across source populations. We modeled DD in population growth as the product of DD in fecundity and survival, experimentally estimating each parameter. Across habitats, survival parameters varied more than fecundity, including in simulations with varying parameter values. Thus, DD in survival drives variation in density‐dependent population growth. Hence, under strong density‐dependent selection, we expect evolutionary change in density‐dependent survival, provided sufficient genetic variance. Our general framework combining detailed experiments and simulations with a simple model can be used for other species to better understand the causes and consequences of density dependent population growth.

Revisiting Fishery Sustainability Targets

Density-dependent population dynamic models strongly influence many of the world’s most important harvest policies. Nearly all classic models (e.g. Beverton-Holt and Ricker) recommend that managers maintain a population size of roughly 40–50 percent of carrying capacity to maximize sustainable harvest, no matter the species’ population growth rate. Such insights are the foundational logic behind most sustainability targets and biomass reference points for fisheries. However, a simple, less-commonly used model, called the Hockey-Stick model, yields very different recommendations. We show that the optimal population size to maintain in this model, as a proportion of carrying capacity, is one over the population growth rate. This leads to more conservative optimal harvest policies for slow-growing species, compared to other models, if all models use the same growth rate and carrying capacity values. However, parameters typically are not fixed; they are estimated after model-fitting. If the Hockey-Stick model leads to lower estimates of carrying capacity than other models, then the Hockey-Stick policy could yield lower absolute population size targets in practice. Therefore, to better understand the population size targets that may be recommended across real fisheries, we fit the Hockey-Stick, Ricker and Beverton-Holt models to population time series data across 284 fished species from the RAM Stock Assessment database. We found that the Hockey-Stick model usually recommended fisheries maintain population sizes higher than all other models (in 69–81% of the data sets). Furthermore, in 77% of the datasets, the Hockey-Stick model recommended an optimal population target even higher than 60% of carrying capacity (a widely used target, thought to be conservative). However, there was considerable uncertainty in the model fitting. While Beverton-Holt fit several of the data sets best, Hockey-Stick also frequently fit similarly well. In general, the best-fitting model rarely had overwhelming support (a model probability of greater than 95% was achieved in less than five percent of the datasets). A computational experiment, where time series data were simulated from all three models, revealed that Beverton-Holt often fit best even when it was not the true model, suggesting that fisheries data are likely too small and too noisy to resolve uncertainties in the functional forms of density-dependent growth. Therefore, sustainability targets may warrant revisiting, especially for slow-growing species.

Evolutionary rescue in resistance to pesticides.

Evolutionary rescue occurs when the genetic evolution of adaptation saves a population from decline or extinction after environmental change. The evolution of resistance to pesticides is a special scenario of abrupt environmental change, where rescue occurs under (very) strong selection for one or a few de novo resistance mutations of large effect. Here, a population genetic model of evolutionary rescue with density-dependent population change is developed, with a focus on deriving results that are important to resistance management. Massive stochastic simulations are used to generate observations, which are accurately predicted using analytical approximations. Key results include the probability density function for the time to resistance and the probability of population extinction. The distribution of resistance times shows a lag period, a narrow peak and a long tail. Surprisingly, the mean time to resistance can increase with the strength of selection because, if a mutation does not occur early on, then its emergence is delayed by the pesticide reducing the population size. The probability of population extinction shows a sharp transition, in that when extinction is possible, it is also highly likely. Consequently, population suppression and (local) eradication can be theoretically achievable goals, as novel strategies to delay resistance evolution.

Dynamic analysis of a fuzzy Bobwhite quail population model under g-division law

This paper is concerned with a kind of Bobwhite quail population model xn+1=A+Bxn+xnxn-1xn-2,n=0,1,⋯,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} x_{n+1}=A+Bx_n+\\frac{x_n}{x_{n-1}x_{n-2}},\\ \\ n=0,1,\\cdots , \\end{aligned}$$\\end{document}where the parameters and initial values are positive parabolic fuzzy numbers. According to g-division of fuzzy sets and based on the symmetrical parabolic fuzzy numbers, the conditional stability of this model is proved. Besides the existence, boundedness and persistence of its unique positive fuzzy solution. When some fuzzy stability conditions are satisfied, the model evolution exhibits oscillations with return to a fixed fuzzy equilibrium no matter what the initial value is. This phenomena provided a vivid counterexample to Allee effect in density-dependent populations of organisms. As a supplement, two numerical examples with data-table are interspersed to illustrate the effectiveness. Our findings have been verified precise with collected northern bobwhite data in Texas, and will help to form some efficient density estimates for wildlife populations of universal applications.

Weak evidence of density dependent population regulation when using the ability of two simple density dependent models to predict population size

The relative importance of density dependence regulation in natural population fluctuations has long been debated. The concept of density dependence implies that current abundance is determined by historical abundance. We have developed four models—two density dependent and two density independent—to predict population size one year beyond the training set and used predictive performance on more than 16,000 populations from 14 datasets to compare the understanding captured by those models. For 4 of 14 datasets the density dependent models make better predictions (i.e., density dependent regulated) than either of the density independent models. However, neither of the density dependent models is statistically significantly superior to density independent models for any of the 14 datasets. We conclude that the evidence for widespread density dependent population regulation in the forms represented by these two simple density-dependent models is weak. However, the density dependent models used here—the Logistic and Gompertz models—are simple representations of how population density might regulate natural populations and only examine density-dependent effects on population size. A comprehensive assessment of the relative importance of density-dependent population regulation will require testing the predictive ability of a wider range of density-dependent models including models examining effects on population characteristics other than population size.

Superinfection and the hypnozoite reservoir for Plasmodium vivax: a general framework

A characteristic of malaria in all its forms is the potential for superinfection (that is, multiple concurrent blood-stage infections). An additional characteristic of Plasmodium vivax malaria is a reservoir of latent parasites (hypnozoites) within the host liver, which activate to cause (blood-stage) relapses. Here, we present a model of hypnozoite accrual and superinfection for P. vivax. To couple host and vector dynamics for a homogeneously-mixing population, we construct a density-dependent Markov population process with countably many types, for which disease extinction is shown to occur almost surely. We also establish a functional law of large numbers, taking the form of an infinite-dimensional system of ordinary differential equations that can also be recovered by coupling expected host and vector dynamics (i.e. a hybrid approximation) or through a standard compartment modelling approach. Recognising that the subset of these equations that model the infection status of the human hosts has precisely the same form as the Kolmogorov forward equations for a Markovian network of infinite server queues with an inhomogeneous batch arrival process, we use physical insight into the evolution of the latter process to write down a time-dependent multivariate generating function for the solution. We use this characterisation to collapse the infinite-compartment model into a single integrodifferential equation (IDE) governing the intensity of mosquito-to-human transmission. Through a steady state analysis, we recover a threshold phenomenon for this IDE in terms of a parameter R_0 expressible in terms of the primitives of the model, with the disease-free equilibrium shown to be uniformly asymptotically stable if R_0<1 and an endemic equilibrium solution emerging if R_0>1. Our work provides a theoretical basis to explore the epidemiology of P. vivax, and introduces a strategy for constructing tractable population-level models of malarial superinfection that can be generalised to allow for greater biological realism in a number of directions.

Population growth rates of pronghorn: influence of temporally and spatially explicit conditions, density dependence, and scale

Density-independent and density-dependent population regulation has long been a subject of investigation. We examined density-dependent and density-independent factors on growth rates of pronghorn ( Antilocapra americana (Ord, 1815)) using a retrospective analysis of population survey data. Across Idaho, we found that as the proportion of the subpopulation harvested the previous year increased, growth rates increased. Similarly, as fawn recruitment increased, growth rates increased. We also found when the growth rate in the previous year increased, the growth rate the subsequent year decreased. When subpopulations were examined independently, we found that in a low-elevation desert subpopulation, growth rates were influenced by growth the previous year. In an agricultural-dominated site, growth rates were influenced by fawn recruitment in the current year and maximum temperature the previous fall. Growth rates in a mid-elevation shrub–steppe site were influenced by drought severity prior to parturition and the growth rates from the previous year. Growth rates in two mountain valley subpopulations were influenced by measures of vegetative greenness. At the statewide scale, while managers may strive for increased numbers of pronghorn, density dependence will limit the ability for a region-wide numerical response. On the localized scale, drivers of growth were temporally and spatially explicit, and biologists must consider site-specific actions.

Global Asymptotic Stability Analysis of Fixed Points for a Density-Dependent Single-Species Population Growth Model

In a density-dependent single-species population growth model, a simple method is proposed to explicitly and directly derive the analytic expressions of reliable regions for local and global asymptotic stability. Specifically, first, a reliable region ΛLAS is explicitly represented by solving the fixed point and utilizing the asymptotic stability criterion, over which the fixed point is locally asymptotically stable. Then, two types of auxiliary Liapunov functions are constructed, where the variation of the Liapunov function is decomposed into the product of two functions and is always negative at the non-equilibrium state. Finally, based on the Liapunov stability theorem, a closed-form expression of reliable region ΛGAS is obtained, where the fixed point is globally asymptotically stable in the sense that all the solutions tend to fixed point. Numerical results show that our analytic expressions of reliable regions are accurate for both local and global asymptotic stability.

Density-dependent population regulation in freshwater fishes and small mammals: A literature review and insights for Ecological Risk Assessment.

The regulation of populations through density dependence (DD) has long been a central tenet of studies of ecological systems. As an important factor in regulating populations, DD is also crucial for understanding risks to populations from stressors, including its incorporation into population models applied for this purpose. However, study of density-dependent regulation is challenging because it can occur through various mechanisms, and their identification in the field, as well as the quantification of the consequences on individuals and populations, can be difficult. We conducted a targeted literature review specifically focusing on empirical laboratory or field studies addressing negative DD in freshwater fish and small rodent populations, two vertebrate groups considered in pesticide Ecological Risk Assessment (ERA). We found that the most commonly recognized causes of negative DD were food (63% of 19 reviewed fish studies, 40% of 25 mammal studies) or space limitations (32% of mammal studies). In addition, trophic interactions were reported as causes of population regulation, with predation shaping mostly small mammal populations (36% of the mammal studies) and cannibalism impacting freshwater fish (26%). In the case of freshwater fish, 63% of the studies were experimental (i.e., with a length of weeks or months). They generally focused on the individual-level causes and effects of DD, and had a short duration. Moreover, DD affected mostly juvenile growth and survival of fish (68%). On the other hand, studies on small mammals were mainly based on time series analyzing field population properties over longer timespans (68%). Density dependence primarily affected survival in subadult and adult mammal stages and, to a lesser extent, reproduction (60% vs. 36%). Furthermore, delayed DD was often observed (56%). We conclude by making suggestions on future research paths, providing recommendations for including DD in population models developed for ERA, and making the best use of the available data. Integr Environ Assess Manag 2024;20:1225-1236. © 2023 Syngenta Crop Protection. Integrated Environmental Assessment and Management published by Wiley Periodicals LLC on behalf of Society of Environmental Toxicology & Chemistry (SETAC).

The effect of dispersal on asymptotic total population size in discrete- and continuous-time two-patch models

Many populations occupy spatially fragmented landscapes. How dispersal affects the asymptotic total population size is a key question for conservation management and the design of ecological corridors. Here, we provide a comprehensive overview of two-patch models with symmetric dispersal and two standard density-dependent population growth functions, one in discrete and one in continuous time. A complete analysis of the discrete-time model reveals four response scenarios of the asymptotic total population size to increasing dispersal rate: (1) monotonically beneficial, (2) unimodally beneficial, (3) beneficial turning detrimental, and (4) monotonically detrimental. The same response scenarios exist for the continuous-time model, and we show that the parameter conditions are analogous between the discrete- and continuous-time setting. A detailed biological interpretation offers insight into the mechanisms underlying the response scenarios that thus improve our general understanding how potential conservation efforts affect population size.

Testing Density-Dependent and Path-Dependent Population Dynamics in Greece with Spatial Quantile and Geographically Weighted Regressions

Regional variability in the spatial distribution of resident population and across-country density divides have consolidated heterogeneous demographic patterns at the base of modern urban systems in Europe. Although economic, historical, institutional, and cultural factors have demonstrated to affect the spatial distribution of resident population, density-dependence and path-dependence are mechanisms persistently shaping demographic dynamics at both local and regional scale. Analysis of density-dependent patterns of population growth (and decline) over sufficiently long time intervals allows a refined comprehension of socioeconomic processes underlying demographic divides. Despite a long settlement history, empirical investigation of the role of density-dependence in the long-term evolution of human populations along urban–rural gradients is relatively scarce especially in Mediterranean countries. The present study performs a comparative analysis of population distribution in 1033 Greek municipalities identifying (and testing the significance of) density-dependent and path-dependent mechanisms of population growth between 1961 and 2011, using spatially implicit and explicit econometric approaches. Results highlight a positive impact of density on population growth where settlements are concentrated. Assuming goodness of fit of the tested models as a proxy of density-dependence, the empirical findings clarify how density-dependent mechanisms were not significant all over the study period, being instead associated with specific phases of the city life cycle—basically urbanization with population concentrating in central locations. Density-dependence was less intense with suburbanization and counter-urbanization—when population sprawled over larger areas at medium–low density. An improved understanding of density-dependent and path-dependent mechanisms of population growth contributes to rethink spatial planning, regional development strategies, and socio-demographic policies adapting to heterogeneous (and rapidly changing) local contexts.

Modelling population growth and sustainable harvesting

In this paper, we discuss how a professor could have students, using rational and exponential functions, develop models for several different density-dependent populations based on characteristics of the species. Students would then need to choose an appropriate method from among three different analytic methods (find a solution, phase-line analysis, graphing approximate solutions) to analyse their models. We then discuss how to use aspects of a species' behaviour to choose an appropriate model from among the ones developed. Finally, we show how a professor could apply what students have learned to develop general principles for sustainable harvesting of such species.

What is needed to make a simple density-dependent response population model consistent with data for eastern North Pacific gray whales?

Census estimates indicate that the eastern North Pacific gray whale population showed an increase rate of some 3.2% per annum from 1968-1988. Further, historic records suggest that the population was ‘commercially extinct’ at the end of the 19th century. The standard HITTER-FITTER population model trajectories which pass through the 1987-88 census estimate of some 21,113, and utilise the customary historic commercial catch series, are inconsistent with both of these features; in particular, they generally show a decrease over the 1968-1988 period. The quantitative extent of various possible adjustment factors that would be needed to resolve these inconsistencies is examined. Depensation effects alone cannot account for the inconsistencies, while a model used to incorporate an additional response delay in recovery from exploitation produces unrealistic population oscillations. Other adjustment factors can, however, produce a 1968-1988 annual population increase rate of 2% or more, and all also correspond to a depletion of the population in 1900 to less than 25% of its size at the onset of commercial whaling in 1846. These are: an increase in the carrying capacity from 1846-1988 of at least 2.5 times; an underestimation of the historic commercial catch from 1846-1900 of at least 60%; or annual aboriginal catch levels prior to the commercial fishery at least three times those estimated by the 1990 Special Meeting of the Scientific Committee (IWC, 1993). These limits weaken if the adjustment factors are considered in combination rather than separately. The results appear insensitive to values assumed for the biological parameters of the population model (natural mortality, age at first parturition, age at recruitment and MSY level). However, they are sensitive to assumptions concerning data inputs, viz the accuracy of the 1987-88 census estimate used, and a 2:1 female:male ratio assumed for the commercial catches for which this information is not available. All trajectories which reflect a 1968-88 annual increase rate of 2% or more correspond to MSYR values (in terms of a 5+ exploitable population) of at least 4%. Fits of the population model to the series of gray whale census estimates are mis-specified, unless either or both of the historic commercial and aboriginal catches have been substantially underestimated (or carrying capacity has increased). The precision of these fits, conditional on fixed levels for such underestimation, is quite high, with coefficients of variation of about 10% for historic population sizes and about 20% for MSYR. There are indications that even if allowance was made for the uncertainty about these levels of underestimation, MSYR would remain relatively robustly estimated to be some 5% (or about 4% if expressed in terms of uniform selectivity on the 1+ population).

Evidence of a compensatory response in invasive Rusty Crayfish (Faxonius rusticus) following intensive harvest removal from northern Lake Michigan fish spawning reefs.

The online version contains supplementary material available at 10.1007/s10530-023-03076-6.

On the control of density-dependent stochastic population processes with time-varying behavior

The study of density-dependent stochastic population processes (DDSPPs) is important from a historical perspective as well as from the perspective of a number of existing and emerging applications today. In more recent applications of these processes, it can be especially important to include time-varying parameters for the rates that impact the density-dependent population structures and behaviors. Under a mean-field scaling, we show that such time-inhomogeneous DDSPPs converge to a corresponding nonautonomous dynamical system. We then analogously establish that the optimal control of such time-inhomogeneous DDSPPs converges to the optimal control of the limiting dynamical system. An analysis of both the dynamical system and its optimal control renders various important mathematical properties of interest.

An experimental analysis of density dependence in meadow voles: Within-season and delayed effects.

Wild mammal populations exhibit a variety of dynamics, ranging from fairly stable with little change in population size over time to high-amplitude cyclic or erratic fluctuations. A persistent question in population ecology is why populations fluctuate as they do. Answering this seemingly simple question has proven to be challenging. Broadly, density-dependent feedback mechanisms should allow populations to grow at low density and slow or halt growth at high density. However, experimental tests of what demographic processes result in density-dependent feedback and on what timescale have proven elusive. Here, we used replicated density perturbation experiments and capture-mark-recapture analyses to test density-dependent population growth in populations of meadow voles (Microtus pennsylvanicus) during the summer breeding season by manipulating founding population density and observing the pattern of survival, reproduction, and population growth. High population density had no consistent effect on survival rates but generally negatively influenced recruitment and population growth rates. However, these density-dependent effects varied within the breeding season and across years. Our study provides evidence that density-dependent feedback mechanisms operate at finer time scales than previously believed and that process, additively with delayed year effects, is key to understanding multiyear population demography.

Inferring density-dependent population dynamics mechanisms through rate disambiguation for logistic birth-death processes.

Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can manifest in birth processes, death processes, or both. Therefore, we utilize the mean and variance of cell number fluctuations to separately identify birth and death rates from time series that follow stochastic birth-death processes with logistic growth. Our nonparametric method provides a novel perspective on stochastic parameter identifiability, which we validate by analyzing the accuracy in terms of the discretization bin size. We apply our method to the scenario where a homogeneous cell population goes through three stages: (1) grows naturally to its carrying capacity, (2) is treated with a drug that reduces its carrying capacity, and (3) overcomes the drug effect to restore its original carrying capacity. In each stage, we disambiguate whether the dynamics occur through the birth process, death process, or some combination of the two, which contributes to understanding drug resistance mechanisms. In the case of limited sample sizes, we provide an alternative method based on maximum likelihood and solve a constrained nonlinear optimization problem to identify the most likely density dependence parameter for a given cell number time series. Our methods can be applied to other biological systems at different scales to disambiguate density-dependent mechanisms underlying the same net growth rate.

Estimating Density Dependence, Environmental Variance, and Long-Term Selection on a Stage-Structured Life History.

AbstractA method for analyzing long-term demographic data on density-dependent stage-structured populations in a stochastic environment is derived to facilitate comparison of populations and species with different life histories. We assume that a weighted sum of stage abundances, N, exerts density dependence on stage-specific vital rates of survival and reproduction and that N has a small or moderate coefficient of variation. The dynamics of N are approximated as a univariate stochastic process governed by three key parameters: the density-independent growth rate, the net density dependence, and environmental variance in the life history. We show how to estimate the relative weighs of stages in N and the key parameters. Life history evolution represents a stochastic maximization of a simple function of the key parameters. The long-term selection gradient on the life history can be expressed as a vector of sensitivities of this function with respect to density-independent, density-dependent, and stochastic components of the vital rates. To illustrate the method, we analyze 38 years of demographic data on a great tit population, estimating the key parameters, which accurately predict the observed mean, coefficient of variation, and fluctuation rate of N; we also evaluate the long-term selection gradient on the life history.

Population size regulation is density-dependent in Rhodnius prolixus (Hemiptera: Reduviidae) through an irritability mechanism.

Physical factors can determine the level of triatomine abundance, but do not regulate their population densities, and neither do natural enemies. To identify the processes associated with density-dependent triatomine population regulation. We set-up a laboratory experiment with four interconnected boxes; the central box harbored Rhodnius prolixus bugs and one hamster. Stage 5 and adult densities of 10, 20, 30, 40, and 60 bugs per hamster, were replicated four times (except the density of 60 bugs). Hamster's irritability and several triatomine responses were measured: feeding, development time and longevity, mortality, fecundity, dispersal, and the net reproductive value (R o ). Density had a statistically significant effect on irritability, but not on the percent of bugs feeding. Density was significant on blood meal size ingested in bugs that did not move between boxes, but not significant when the bugs moved. Density and irritability affected the proportion of stage 5 nymphs molting, and the proportion of adult bugs dying per day and over a three-week period. There was a highly significant effect of density and irritability on R o . We showed that a density-dependent mechanism, acting through the irritability of the host, seems the most plausible process regulating populations in triatomines.

Seasonality, density dependence, and spatial population synchrony

Studies of spatial population synchrony constitute a central approach for understanding the drivers of ecological dynamics. Recently, identifying the ecological impacts of climate change has emerged as a new important focus in population synchrony studies. However, while it is well known that climatic seasonality and sequential density dependence influences local population dynamics, the role of season-specific density dependence in shaping large-scale population synchrony has not received attention. Here, we present a widely applicable analytical protocol that allows us to account for both season and geographic context-specific density dependence to better elucidate the relative roles of deterministic and stochastic sources of population synchrony, including the renowned Moran effect. We exemplify our protocol by analyzing time series of seasonal (spring and fall) abundance estimates of cyclic rodent populations, revealing that season-specific density dependence is a major component of population synchrony. By accounting for deterministic sources of synchrony (in particular season-specific density dependence), we are able to identify stochastic components. These stochastic components include mild winter weather events, which are expected to increase in frequency under climate warming in boreal and Arctic ecosystems. Interestingly, these weather effects act both directly and delayed on the vole populations, thus enhancing the Moran effect. Our study demonstrates how different drivers of population synchrony, presently altered by climate warming, can be disentangled based on seasonally sampled population time-series data and adequate population models.