Effects of nitrogen deposition on the interaction between an aphid and its host plant

Abstract 1. Anthropogenic increases in nitrogen deposition are impacting terrestrial ecosystems worldwide. While some of the direct ecosystem‐level effects of nitrogen deposition are understood, the effects of nitrogen deposition on plant–insect interactions and on herbivore population dynamics have received less attention. 2. Nitrogen deposition will potentially influence both plant resource availability and herbivore population growth. If increases in herbivore population growth outstrip increases in resource availability, then increases in the strength of density dependence expressed within the herbivore population would be predicted. Alternatively, if plant resources respond more vigorously to nitrogen deposition than do herbivore populations, a decline in the strength of density dependence would be expected. No change in the strength of density dependence acting upon the herbivore population would suggest equivalent responses by herbivores and plants. 3. A density manipulation experiment was performed to examine the effect of nitrogen deposition on the interaction between a host plant, Asclepias tuberosa, and its herbivore, Aphis nerii. Aphid maximum per capita growth rate (R_max), carrying capacity (K), and the strength of density dependence were measured under three nitrogen deposition treatments. The effect of nitrogen deposition on the relationship among these three measures of insect population dynamics was explored. 4. Simulated nitrogen deposition increased aphid per capita population growth, plant foliar nitrogen concentrations, and plant biomass. Nitrogen deposition caused R_max and K to increase proportionally, leading to no overall change in the strength of density dependence. In this system, potential changes in the negative feedback processes operating on herbivore populations following nitrogen deposition appear to be buffered by concomitant changes in resource availability.     

Plant defense and density dependence in the population growth of herbivores

Long-standing theory has predicted that plant defensive and nutritional traits contribute to the population dynamics of insect herbivores. To examine the role of plant variation in density dependence, I took a comparative approach by conducting density manipulation experiments with the specialist aphid, Aphis nerii, on 18 species of milkweed (Asclepias spp.). The strength of density dependence varied on the plant species. Variation in plant secondary compounds (cardenolides), trichomes, leaf carbon and nitrogen concentrations, and seed mass of the milkweed species predicted the R(max) of aphid populations, while specific leaf weight, carbon concentration, latex, water content, and trichome density were significant predictors of the strength of density dependence. Thus, plant traits that probably evolved for primary and defensive functions contribute to the ecological dynamics of herbivore populations.     

Variation in plant quality and the population dynamics of herbivores: there is nothing average about aphids

In the attempt to use results from small-scale studies to make large-scale predictions, it is critical that we take into account the greater spatial heterogeneity encountered at larger spatial scales. An important component of this heterogeneity is variation in plant quality, which can have a profound influence on herbivore population dynamics. This influence is particularly relevant when we consider that the strength of density dependence can vary among host plants and that the strength of density dependence determines the difference between exponential and density- dependent growth. Here, we present some simple models and analyses designed to examine the impact of variable plant quality on the dynamics of insect herbivore populations, and specifically the consequences of variation in the strength of density dependence among host plants. We show that average values of herbivore population growth parameters, calculated from plants that vary in quality, do not predict overall population growth. Furthermore, we illustrate that the quality of a few individual plants within a larger plant population can dominate herbivore population growth. Our results demonstrate that ignoring spatial heterogeneity that exists in herbivore population growth on plants that differ in quality can lead to a misunderstanding of the mechanisms that underlie population dynamics.     

Intraspecific variation in the strength of density dependence in aphid populations

Abstract.  1. Experimental evidence is presented for positive, negative, and no density dependence from 32 independent density manipulations of milkweed aphids ( Aphis nerii ) in laboratory and field experiments. This substantial variation in intraspecific density dependence is associated with temperature and host-plant species.
2. It is reported that as population growth rate increases, density dependence becomes more strongly negative, suggesting that the monotonic definition of density dependence used in many common population models is appropriate for these aphids, and that population growth rate and carrying capacity are not directly proportional.
3. For populations that conform to these assumptions, population growth rate may be widely applicable as a predictor of the strength of density dependence.     

Ecological drivers of guanaco recruitment: variable carrying capacity and density dependence

Ungulates living in predator-free reserves offer the opportunity to study the influence of food limitation on population dynamics without the potentially confounding effects of top-down regulation or livestock competition. We assessed the influence of relative forage availability and population density on guanaco recruitment in two predator-free reserves in eastern Patagonia, with contrasting scenarios of population density. We also explored the relative contribution of the observed recruitment to population growth using a deterministic linear model to test the assumption that the studied populations were closed units. The observed densities increased twice as fast as our theoretical populations, indicating that marked immigration has taken place during the recovery phase experienced by both populations, thus we rejected the closed-population assumption. Regarding the factors driving variation in recruitment, in the low- to medium-density setting, we found a positive linear relationship between recruitment and surrogates of annual primary production, whereas no density dependence was detected. In contrast, in the high-density scenario, both annual primary production and population density showed marked effects, indicating a positive relationship between recruitment and per capita food availability above a food-limitation threshold. Our results support the idea that environmental carrying capacity fluctuates in response to climatic variation, and that these fluctuations have relevant consequences for herbivore dynamics, such as amplifying density dependence in drier years. We conclude that including the coupling between environmental variability in resources and density dependence is crucial to model ungulate population dynamics; to overlook temporal changes in carrying capacity may even mask density dependence as well as other important processes.     

Plant genotypic diversity increases population size of a herbivorous insect

It is critical to incorporate the process of population dynamics into community genetics studies to identify the mechanisms of the linkage between host plant genetics and associated communities. We studied the effects of plant genotypic diversity of tall goldenrod Solidago altissima on the population dynamics of the aphid Uroleucon nigrotuberculatum. We found genotypic variation in plant resistance to the aphid in our experiments. To determine the impact of plant genotypic diversity on aphid population dynamics, we compared aphid densities under conditions of three treatments: single-genotype plots, mixed-genotype plots and mixed-genotype-with-cages plots. In the latter treatment plants were individually caged to prevent natural enemy attack and aphid movement among plants. The synergistic effects of genotypes on population size were demonstrated by the greater aphid population size in the mixed-genotype treatment than expected from additive effects alone. Two non-exclusive hypotheses are proposed to explain this pattern. First, there is a source-sink relationship among plant genotypes: aphids move from plant genotypes where their reproduction is high to genotypes where their reproduction is low. Second, natural enemy mortality is reduced in mixed plots in a matrix of diverse plant genotypes.     

Differing contributions of density dependence and climate to the population dynamics of three eruptive herbivores

1. Although both endogenous and exogenous processes regulate populations, the current understanding of the contributions from density dependence and climate to the population dynamics of eruptive herbivores remains limited. 2. Using a 17‐year time series of three cereal aphid species [Rhopalosiphum padi L., Metopolophium dirhodum (Walker), and Diuraphis noxia (Kurdumov)] compiled from a trapping network spanning the northwestern U.S.A., temporal and spatial patterns associated with population fluctuations, and modelled density dependence in aphid abundances were tested. These models were used to analyse correlations between climate and aphid abundances in the presence and absence of residual variance as a result of density‐dependent effects. 3. The temporal dynamics of aphid population fluctuations indicated periodicity, with no clear evidence for a spatial pattern underlying population fluctuations. 4. Aphid abundances oscillated in a manner consistent with delayed density dependence for all three aphid species, although the strength of these feedbacks differed among species. 5. Diuraphis noxia abundances were negatively correlated with increasing temperatures in the absence of density‐dependent effects, whereas M. dirhodum abundances were positively correlated with increasing cumulative precipitation in the presence of density‐dependent effects; yet, R. padi abundances were unrelated to climate variables irrespective of population feedbacks. 6. Our analysis suggests that endogenous feedbacks differentially regulate aphid populations in the northwestern U.S.A., and these feedbacks may operate at an expansive spatial scale. It is concluded that the contributions of density dependence and climate to aphid population dynamics are species‐specific in spite of similar ecological niches, with implications for assessing species responses to climate variability.     

Effects of variation among plant species on the interaction between a herbivore and its parasitoid

Abstract.  1. Previous studies have demonstrated that phenotypic traits of plants have the potential to affect interactions between herbivores and their natural enemies. Consequently, the impact of natural enemies on herbivore vital rates and population dynamics may vary among plant species. This study was designed to investigate the potential for density-dependent parasitism of an aphid herbivore feeding on six different host plant species.
2. Population densities of the aphid Aphis nerii B de F (Homoptera: Aphididae) and its parasitoid Lysiphlebus testaceipes Cresson (Hymenoptera: Braconidae) were recorded within a single growing season on six different species of milkweed in the genus Asclepias L. (Asclepiadaceae). Asclepias species are known to vary in their quality as food for herbivores. Although data on plant quality were not available in this study, population data were analysed to determine the effects of different Asclepias species on rates of parasitism and aphid population growth.
3. Parasitism rates of A. nerii varied among Asclepias species but were temporally density dependent over at least some range of aphid density on all plant species. Aphid population growth rates also varied among Asclepias species, and declined with an increase in the maximum parasitism rates among plant species; however, in no case was density-dependent parasitism sufficient to prevent exponential population growth of aphids within the growing season. The results serve to emphasise that, if natural enemies are to regulate herbivore populations, density-dependent mortality is a necessary, but not sufficient, condition for regulation.     

The generality of management recommendations across populations of an invasive perennial herb

Demographic models are widely used to produce management recommendations for different species. For invasive plants, current management recommendations to control local population growth are often based on data from a limited number of populations per species, and the assumption of stable population structure (asymptotic dynamics). However, spatial variation in population dynamics and deviation from a stable structure may affect these recommendations, calling into question their generality across populations of an invasive species. Here, I focused on intraspecific variation in population dynamics and investigated management recommendations generated by demographic models across 37 populations of a short-lived, invasive perennial herb (Lupinus polyphyllus). Models that relied on the proportional perturbations of vital rates (asymptotic elasticities) indicated an essential role for plant survival in long-term population dynamics. The rank order of elasticities for different vital rates (survival, growth, retrogression, fecundity) varied little among the 37 study populations regardless of population status (increasing or declining asymptotically). Summed elasticities for fecundity increased, while summed elasticities for survival decreased with increasing long-term population growth rate. Transient dynamics differed from asymptotic dynamics, but were qualitatively similar among populations, that is, depending on the initial size structure, populations tended to either increase or decline in density more rapidly than predicted by asymptotic growth rate. These findings indicate that although populations are likely to exhibit transient dynamics, management recommendations based on asymptotic elasticities for vital rates might be to some extent generalised across established populations of a given short-lived invasive plant species.     

Local environment and density-dependent feedbacks determine population growth in a forest herb

Linking spatial variation in environmental factors to variation in demographic rates is essential for a mechanistic understanding of the dynamics of populations. However, we still know relatively little about such links, partly because feedbacks via intraspecific density make them difficult to observe in natural populations. We conducted a detailed field study and investigated simultaneous effects of environmental factors and the intraspecific density of individuals on the demography of the herb Lathyrus vernus. In regression models of vital rates we identified effects associated with spring shade on survival and growth, while density was negatively correlated with these vital rates. Density was also negatively correlated with average individual size in the study plots, which is consistent with self-thinning. In addition, average plant sizes were larger than predicted by density in plots that were less shaded by the tree canopy, indicating an environmentally determined carrying capacity. A size-structured integral projection model based on the vital rate regressions revealed that the identified effects of shade and density were strong enough to produce differences in stable population sizes similar to those observed in the field. The results illustrate how the local environment can determine dynamics of populations and that intraspecific density may have to be more carefully considered in studies of plant demography and population viability analyses of threatened species. We conclude that demographic approaches incorporating information about both density and key environmental factors are powerful tools for understanding the processes that interact to determine population dynamics and abundances.     

Phenological responses in a sycamore–aphid–parasitoid system and consequences for aphid population dynamics: A 20 year case study

Species interactions have a spatiotemporal component driven by environmental cues, which if altered by climate change can drive shifts in community dynamics. There is insufficient understanding of the precise time windows during which inter‐annual variation in weather drives phenological shifts and the consequences for mismatches between interacting species and resultant population dynamics—particularly for insects. We use a 20 year study on a tri‐trophic system: sycamore Acer pseudoplatanus, two associated aphid species Drepanosiphum platanoidis and Periphyllus testudinaceus and their hymenopteran parasitoids. Using a sliding window approach, we assess climatic drivers of phenology in all three trophic levels. We quantify the magnitude of resultant trophic mismatches between aphids and their plant hosts and parasitoids, and then model the impacts of these mismatches, direct weather effects and density dependence on local‐scale aphid population dynamics. Warmer temperatures in mid‐March to late‐April were associated with advanced sycamore budburst, parasitoid attack and (marginally) D. platanoidis emergence. The precise time window during which spring weather advances phenology varies considerably across each species. Crucially, warmer temperatures in late winter delayed the emergence of both aphid species. Seasonal variation in warming rates thus generates marked shifts in the relative timing of spring events across trophic levels and mismatches in the phenology of interacting species. Despite this, we found no evidence that aphid population growth rates were adversely impacted by the magnitude of mismatch with their host plants or parasitoids, or direct impacts of temperature and precipitation. Strong density dependence effects occurred in both aphid species and probably buffered populations, through density‐dependent compensation, from adverse impacts of the marked inter‐annual climatic variation that occurred during the study period. These findings explain the resilience of aphid populations to climate change and uncover a key mechanism, warmer winter temperatures delaying insect phenology, by which climate change drives asynchronous shifts between interacting species.     

Effects of grazing on above-ground biomass on a mountain snowbed, NW Finland

The density-dependent effect of induced plant resistance on herbivore populations depends on the relationship between the amount of herbivore damage and the level of induced resistance produced by the plant. This relationship should influence the interaction of induced resistance and herbivore population dynamics, and if the relationship varies among plant genotypes, it could be subject to natural selection by herbivores. In this study the relationship between percent leaf area damaged and level of induced resistance was characterized for four genotypes of soybeans grown in a greenhouse. Damage ranging from 8 to 92% of leaf area was imposed using Mexican bean beetle larvae, and induced resistance was measured by bioassay using Mexican bean beetle adults. The level of induced resistance was significantly affected by the amount of damage, and the level of induced resistance varied significantly among the four genotypes. There was also a marginally significant interaction of damage and plant genotype, suggesting that the form of density dependence varies among these four genotypes of soybeans. These results suggest that these genotypes of plants might affect herbivore populations differently. If this variation is heritable, the form of density-dependent effects of induced resistance has the potential to evolve in this system.     

Geographical gradients in the population dynamics of North American prairie ducks

1. Geographic gradients in population dynamics may occur because of spatial variation in resources that affect the deterministic components of the dynamics (i.e. carrying capacity, the specific growth rate at small densities or the strength of density regulation) or because of spatial variation in the effects of environmental stochasticity. To evaluate these, we used a hierarchical Bayesian approach to estimate parameters characterizing deterministic components and stochastic influences on population dynamics of eight species of ducks (mallard, northern pintail, blue-winged teal, gadwall, northern shoveler, American wigeon, canvasback and redhead (Anas platyrhynchos, A. acuta, A. discors, A. strepera, A. clypeata, A. americana, Aythya valisineria and Ay. americana, respectively) breeding in the North American prairies, and then tested whether these parameters varied latitudinally. 2. We also examined the influence of temporal variation in the availability of wetlands, spring temperature and winter precipitation on population dynamics to determine whether geographical gradients in population dynamics were related to large-scale variation in environmental effects. Population variability, as measured by the variance of the population fluctuations around the carrying capacity K, decreased with latitude for all species except canvasback. This decrease in population variability was caused by a combination of latitudinal gradients in the strength of density dependence, carrying capacity and process variance, for which details varied by species. 3. The effects of environmental covariates on population dynamics also varied latitudinally, particularly for mallard, northern pintail and northern shoveler. However, the proportion of the process variance explained by environmental covariates, with the exception of mallard, tended to be small. 4. Thus, geographical gradients in population dynamics of prairie ducks resulted from latitudinal gradients in both deterministic and stochastic components, and were likely influenced by spatial differences in the distribution of wetland types and shapes, agricultural practices and dispersal processes. 5. These results suggest that future management of these species could be improved by implementing harvest models that account explicitly for spatial variation in density effects and environmental stochasticity on population abundance.     

Demography in relation to population density in two herbivorous marsupials: testing for source–sink dynamics versus independent regulation of population size

We compared demography of populations along gradients of population density in two medium-sized herbivorous marsupials, the common brushtail possum Trichosurus vulpecula and the rufous bettong Aepyprymnus rufescens, to test for net dispersal from high density populations (acting as sources) to low density populations (sinks). In both species, population density was positively related to soil fertility, and variation in soil fertility produced large differences in population density of contiguous populations. We predicted that if source–sink dynamics were operating over this density gradient, we should find higher immigration rates in low-density populations, and positive relationships of measures of individual fitness—body condition, reproductive output, juvenile growth rates and survivorship—to population density. This was predicted because under source–sink dynamics, immigration from high-density sites would hold population density above carrying capacity in low-density sites. The study included 13 populations of these two species, representing a more than 50-fold range of density for each species, but we found that individual fitness, immigration rates and population turnover were similar in all populations. We conclude that net dispersal from high to low density populations had little influence on population dynamics in these species; rather, all populations appeared to be independently regulated at carrying capacity, with a balanced exchange of dispersers among populations. These two species have suffered recent reductions in range, and they are ecologically similar to other species that have declined to extinction in inland Australia. It has been argued that part of the cause of the vulnerability of species like these is that they exhibit source–sink dynamics, and disturbance to source habitats can therefore cause large-scale population collapses. The results of our study argue against this interpretation.     

Effects of body size and temperature on population growth

For at least 200 years, since the time of Malthus, population growth has been recognized as providing a critical link between the performance of individual organisms and the ecology and evolution of species. We present a theory that shows how the intrinsic rate of exponential population growth, rmax, and the carrying capacity, K, depend on individual metabolic rate and resource supply rate. To do this, we construct equations for the metabolic rates of entire populations by summing over individuals, and then we combine these population-level equations with Malthusian growth. Thus, the theory makes explicit the relationship between rates of resource supply in the environment and rates of production of new biomass and individuals. These individual-level and population-level processes are inextricably linked because metabolism sets both the demand for environmental resources and the resource allocation to survival, growth, and reproduction. We use the theory to make explicit how and why rmax exhibits its characteristic dependence on body size and temperature. Data for aerobic eukaryotes, including algae, protists, insects, zooplankton, fishes, and mammals, support these predicted scalings for rmax. The metabolic flux of energy and materials also dictates that the carrying capacity or equilibrium density of populations should decrease with increasing body size and increasing temperature. Finally, we argue that body mass and body temperature, through their effects on metabolic rate, can explain most of the variation in fecundity and mortality rates. Data for marine fishes in the field support these predictions for instantaneous rates of mortality. This theory links the rates of metabolism and resource use of individuals to life-history attributes and population dynamics for a broad assortment of organisms, from unicellular organisms to mammals.     

Demographic response of plant populations to habitat fragmentation and temporal environmental variability

Many plant species currently exist in fragmented populations of different sizes, while they also experience unpredictable climatic fluctuation over time. However, we still understand little about how plant demography responds to such spatial and temporal environmental variability. We studied population dynamics of an understory perennial herb Trillium camschatcense in the Tokachi plain of Hokkaido, Japan, where a significant effect of forest fragmentation on seedling recruitment was previously reported. Four populations across a range of fragment sizes were studied for 6 years, and the data were analyzed using matrix population models. Per capita fecundity (the number of recruits per plant) varied greatly among populations, but the variation in population growth rates (λ) was mainly driven by the variation in stasis and growth rates, suggesting that the general trend of reduced fecundity in fragmented populations may not be readily translated into subsequent dynamics. Temporal variation in λ among years was more than 2 times larger than spatial variation among populations, and this result was likely attributable to the contrasting response of correlation structures among demographic rates. The among-population variation in λ was dampened by negative covariation between matrix elements possibly due to density-dependent regulation as well as an inherent constraint that some elements are not independent, whereas positive covariation between matrix elements resulted in large temporal variation in λ. Our results show that population dynamics responded differently to habitat fragmentation and temporal variability of the environment, emphasizing the need to discriminate these spatial and temporal variations in demographic models. Although no populations were projected to be declining in stochastic simulations, correlation between current habitat size and plant density implies historical λ is positively related to habitat size.     

Temperature change and complex dynamics

Density-dependent factors, such as population growth rate and migration, influence dynamic behaviour in ecological models. Temperature, an abiotic and density-independent factor, is also an important determinant of insect population growth. We investigated the endogenous dynamics of a density-dependent response-surface model that included temperature, based on time series for two aphid species. We investigated the effects of temperature and random noise on the model dynamics. In most cases, an increase in temperature resulted in a higher predicted equilibrium density; it could induce complex dynamics. Noise at the level of the natural variation in temperature resulted in extinctions in some models. Our results from these models indicate that aphid populations might become more abundant, and less stable in some circumstances, if there is climate warming. Received: 25 November 1996 / Accepted: 30 June 1997     

Evidence for predominant clones in a cyclically parthenogenetic organism provided by combined demographic and genetic analyses

Aphids are particularly interesting models in the study of genetic and demographic components of plant adaptation because of their breeding system which combines parthenogenesis and sexual reproduction (i.e. cyclical parthenogenesis), and the frequent emergence of host-adapted races reported in this group. In this paper, patterns of host adaptation were assessed on local populations of the aphid Sitobion avenae by following their demographic and genetic structure in a maize field for two consecutive years. The existence of putative generalist (polyphagous) or specialized (host-adapted) genotypes was also investigated by comparing the genotypic distribution of this aphid on maize and other cultivated host plants, using five microsatellite loci. Although population dynamics revealed strong variation in aphid abundance during the colonization period on maize, two genotypes identified at seven additional microsatellite loci were predominant and exhibited stable frequencies over cropping season and between years. Based on present and earlier studies, these two prevalent genotypes were shown to survive on different host plants other than maize, to colonize large geographical zones and to persist parthenogenetically for several years. All these data strongly suggest that these two genotypes are asexual generalist clones that could have been favoured by agricultural practices encountered in western Europe. Besides these two clones, a continual replacement of rare genotypes was observed on maize in both years. Hypotheses involving selection via aphid-plant interactions and natural enemies were proposed for explaining the disappearance of these genotypes on maize.     

Disease ontogeny overshadows effects of climate and species interactions on population dynamics in a nonnative forest disease complex

Biotic threats to trees often arise from interactions among two or more species, frequently insects and fungi, that function together to defeat host defenses, secure resources and colonize new hosts. Feedbacks among plant enemies can have large effects on host population and disease dynamics, either by promoting stabilizing negative feedbacks or contributing to positive feedbacks that can destabilize populations and permit outbreaks. Feedbacks can be rapid and direct (e.g. within trees or among years) or can arise from slowly developing changes in host resource quantity or quality at the scale of forest stands or landscapes. Climate may also influence system dynamics by altering feedbacks within or among species or through density independent effects. We evaluated major drivers of population dynamics of beech bark disease (BBD), an important forest disease in eastern deciduous forests of North America, using data from 28 study sites in the eastern United States monitored for up to 14 yr between 1979 and 1992. Both primary causal agents of BBD – the introduced felted beech scale Cryptococcus fagisuga and native fungi Neonectria spp. – showed strong simple density dependence in all study populations. Surprisingly, densities of scale insects and fungi had little or no effects on population growth rates of the other, despite their habit of living in close physical relationships. For both insects and fungi, ecologically important features of the density dependent functions (slope, carrying capacity and density independent variance) were variable across sites. Climatic effects on density‐dependent functions (and scatter around them) were evident but generally weak and variable. The most striking predictor of patterns in density dependence was duration since establishment of BBD in the region. Apparently BBD alters forests over decades in ways that strengthen self‐regulation among causal agents without eliminating or even dramatically reducing host populations.     

The Role of Density Regulation in Extinction Processes and Population Viability Analysis

We review the role of density dependence in the stochastic extinction of populations and the role density dependence has played in population viability analysis (PVA) case studies. In total, 32 approaches have been used to model density regulation in theoretical or applied extinction models, 29 of them are mathematical functions of density dependence, and one approach uses empirical relationships between density and survival, reproduction, or growth rates. In addition, quasi-extinction levels are sometimes applied as a substitute for density dependence at low population size. Density dependence further has been modelled via explicit individual spacing behaviour and/or dispersal. We briefly summarise the features of density dependence available in standard PVA software, provide summary statistics about the use of density dependence in PVA case studies, and discuss the effects of density dependence on extinction probability. The introduction of an upper limit for population size has the effect that the probability of ultimate extinction becomes 1. Mean time to extinction increases with carrying capacity if populations start at high density, but carrying capacity often does not have any effect if populations start at low numbers. In contrast, the Allee effect is usually strong when populations start at low densities but has only a limited influence on persistence when populations start at high numbers. Contrary to previous opinions, other forms of density dependence may lead to increased or decreased persistence, depending on the type and strength of density dependence, the degree of environmental variability, and the growth rate. Furthermore, effects may be reversed for different quasi-extinction levels, making the use of arbitrary quasi-extinction levels problematic. Few systematic comparisons of the effects on persistence between different models of density dependence are available. These effects can be strikingly different among models. Our understanding of the effects of density dependence on extinction of metapopulations is rudimentary, but even opposite effects of density dependence can occur when metapopulations and single populations are contrasted. We argue that spatially explicit models hold particular promise for analysing the effects of density dependence on population viability provided a good knowledge of the biology of the species under consideration exists. Since the results of PVAs may critically depend on the way density dependence is modelled, combined efforts to advance statistical methods, field sampling, and modelling are urgently needed to elucidate the relationships between density, vital rates, and extinction probability.