Population dynamics as related to rate of increase per generation

Interconnection between density-regulation and stability in competitive ecological network

In natural ecosystems, species can be characterized by the nonlinear density-dependent self-regulation of their growth profile. Species of many taxa show a substantial density-dependent reduction for low population size. Nevertheless, many show the opposite trend; density regulation is minimal for small populations and increases significantly when the population size is near the carrying capacity. The theta-logistic growth equation can portray the intraspecific density regulation in the growth profile, theta being the density regulation parameter. In this study, we examine the role of these different growth profiles on the stability of a competitive ecological community with the help of a mathematical model of competitive species interactions. This manuscript deals with the random matrix theory to understand the stability of the classical theta-logistic models of competitive interactions. Our results suggest that having more species with strong density dependence, which self-regulate at low densities, leads to more stable communities. With this, stability also depends on the complexity of the ecological network. Species network connectance (link density) shows a consistent trend of increasing stability, whereas community size (species richness) shows a context-dependent effect. We also interpret our results from the aspect of two different life history strategies: r and K-selection. Our results show that the stability of a competitive network increases with the fraction of r-selected species in the community. Our result is robust, irrespective of different network architectures.

Vulnerability Assessment of Pelagic Sharks in the Western North Pacific by Using an Integrated Ecological Risk Assessment

Simple Summary

A new integrated ecological risk assessment (ERA) including the IUCN Red List category, the body weight variation trend of 1989–2011 with large sample size (n > 678,000), and the inflection point of population growth curve coupled with the ERA was developed to assess the impact of longline fishery on the pelagic sharks in the western North Pacific. The intrinsic rate of population growth was used to estimate the productivity, and the susceptibility was estimated by the multiplication of the catchability, selectivity, and post-capture mortality. Five groups were identified based on the cluster analysis coupling with non-parametric multi-dimensional scaling. Rigorous management measures are recommended for the scalloped hammerhead, silky, and spinner shark at highest risk, setting total allowable catch quota is recommended for the bigeye thresher, and sandbar shark, and a consistent monitoring scheme is suggested for the smooth hammerhead, shortfin mako, pelagic thresher, oceanic whitetip, and dusky shark.

Abstract

The vulnerability of 11 pelagic shark species caught by the Taiwanese coastal and offshore longline fisheries in the western North Pacific were assessed by an ecological risk assessment (ERA) and 10 of the 11 species was assessed by using an integrated ERA developed in this study. The intrinsic rate of population growth was used to estimate the productivity of sharks, and the susceptibility of sharks was estimated by the multiplication of the catchability, selectivity, and post-capture mortality. Three indices namely, the IUCN Red List category, the body weight variation trend, and the inflection point of population growth curve coupled with ERA were used to conduct an integrated ERA. The results indicated that the scalloped hammerhead is at the highest risk (group 1), followed by the silky shark, and the spinner shark at high risk (group 2). The bigeye thresher, and sandbar shark fall in group 3, the smooth hammerhead falls in group 4, and the shortfin mako, pelagic thresher, oceanic whitetip, and dusky shark fall in group 5. Rigorous management measures for the species in groups 1 and 2, setting total allowable catch quota for group 3, and consistent monitoring schemes for groups 4 and 5 are recommended.

Density dependence can obscure nonlethal effects of disturbance on life history of medium-sized cetaceans

Nonlethal disturbance of animals can cause behavioral and physiological changes that affect individual health status and vital rates, with potential consequences at the population level. Predicting these population effects remains a major challenge in ecology and conservation. Monitoring fitness-related traits may improve detection of upcoming population changes, but the extent to which individual traits are reliable indicators of disturbance exposure is not well understood, especially for populations regulated by density dependence. Here we study how density dependence affects a population’s response to disturbance and modifies the disturbance effects on individual health and vital rates. We extend an energy budget model for a medium-sized cetacean (the long-finned pilot whale Globicephala melas) to an individual-based population model in which whales feed on a self-replenishing prey base and disturbance leads to cessation of feeding. In this coupled predator-prey system, the whale population is regulated through prey depletion and the onset of yearly repeating disturbances on the whale population at carrying capacity decreased population density and increased prey availability due to reduced top-down control. In populations faced with multiple days of continuous disturbance each year, female whales that were lactating their first calf experienced increased mortality due to depletion of energy stores. However, increased prey availability led to compensatory effects and resulted in a subsequent improvement of mean female body condition, mean age at first reproduction and higher age-specific reproductive output. These results indicate that prey-mediated density dependence can mask negative effects of disturbance on fitness-related traits and vital rates, a result with implications for the monitoring and management of marine mammal populations.

Thresholds for impaired species recovery

Studies on small and declining populations dominate research in conservation biology. This emphasis reflects two overarching frameworks: the small-population paradigm focuses on correlates of increased extinction probability; the declining-population paradigm directs attention to the causes and consequences of depletion. Neither, however, particularly informs research on the determinants, rate or uncertainty of population increase. By contrast, Allee effects (positive associations between population size and realized per capita population growth rate, r(realized), a metric of average individual fitness) offer a theoretical and empirical basis for identifying numerical and temporal thresholds at which recovery is unlikely or uncertain. Following a critique of studies on Allee effects, I quantify population-size minima and subsequent trajectories of marine fishes that have and have not recovered following threat mitigation. The data suggest that threat amelioration, albeit necessary, can be insufficient to effect recovery for populations depleted to less than 10% of maximum abundance (N(max)), especially when they remain depleted for lengthy periods of time. Comparing terrestrial and aquatic vertebrates, life-history analyses suggest that population-size thresholds for impaired recovery are likely to be comparatively low for marine fishes but high for marine mammals.Articulation of a 'recovering population paradigm' would seem warranted. It might stimulate concerted efforts to identify generic impaired recovery thresholds across species. It might also serve to reduce the confusion of terminology, and the conflation of causes and consequences with patterns currently evident in the literature on Allee effects, thus strengthening communication among researchers and enhancing the practical utility of recovery-oriented research to conservation practitioners and resource managers.

Improved estimation of intrinsic growth r(max) for long-lived species: integrating matrix models and allometry

Intrinsic population growth rate (r(max)) is an important parameter for many ecological applications, such as population risk assessment and harvest management. However, r(max) can be a difficult parameter to estimate, particularly for long-lived species, for which appropriate life table data or abundance time series are typically not obtainable. We describe a method for improving estimates of r(max) for long-lived species by integrating life-history theory (allometric models) and population-specific demographic data (life table models). Broad allometric relationships, such as those between life history traits and body size, have long been recognized by ecologists. These relationships are useful for deriving theoretical expectations for r(max), but r(max) for real populations may vary from simple allometric estimators for "archetypical" species of a given taxa or body mass. Meanwhile, life table approaches can provide population-specific estimates of r(max) from empirical data, but these may have poor precision from imprecise and missing vital rate parameter estimates. Our method borrows strength from both approaches to provide estimates that are consistent with both life-history theory and population-specific empirical data, and are likely to be more robust than estimates provided by either method alone. Our method uses an' allometric constant: the product of r(max) and the associated generation time for a stable-age population growing at this rate. We conducted a meta-analysis to estimate the mean and variance of this allometric constant across well-studied populations from three vertebrate taxa (birds, mammals, and elasmobranchs) and found that the mean was approximately 1.0 for each taxon. We used these as informative Bayesian priors that determine how much to "shrink" imprecise vital rate estimates for a data-limited population toward the allometric expectation. The approach ultimately provides estimates of r(max) (and other vital rates) that reflect a balance of information from the individual studied population, theoretical expectation, and meta-analysis of other populations. We applied the method specifically to an archetypical petrel (representing the genus Procellaria) and to white sharks (Carcharodon carcharias) in the context of estimating sustainable-fishery bycatch limits.

A generic target for species recovery

Recovery targets for threatened species are typically developed on a species- or population-specific basis. Such narrow taxonomic specificity stands in contrast with widely applied species-independent metrics of conservation status. Here, we propose a generic protocol that can be used to specify broadly applicable targets intended to recover the ecological and evolutionary functionality of threatened species. The method is based on basic density-dependent population dynamics, draws on first principles related to population growth, and explicitly incorporates habitat by accounting for changes in carrying capacity. It offers a consistently applied, methodologically transparent, and predictable biological benchmark for recovery purposes. The benefits of a generic method for articulating recovery targets, particularly from a policy- and statute-implementation perspective, are substantive.

A new method for identifying rapid decline dynamics in wild vertebrate populations

Tracking trends in the abundance of wildlife populations is a sensitive method for assessing biodiversity change due to the short time-lag between human pressures and corresponding shifts in population trends. This study tests for proposed associations between different types of human pressures and wildlife population abundance decline-curves and introduces a method to distinguish decline trajectories from natural fluctuations in population time-series. First, we simulated typical mammalian population time-series under different human pressure types and intensities and identified significant distinctions in population dynamics. Based on the concavity of the smoothed population trend and the algebraic function which was the closest fit to the data, we determined those differences in decline dynamics that were consistently attributable to each pressure type. We examined the robustness of the attribution of pressure type to population decline dynamics under more realistic conditions by simulating populations under different levels of environmental stochasticity and time-series data quality. Finally, we applied our newly developed method to 124 wildlife population time-series and investigated how those threat types diagnosed by our method compare to the specific threatening processes reported for those populations. We show how wildlife population decline curves can be used to discern between broad categories of pressure or threat types, but do not work for detailed threat attributions. More usefully, we find that differences in population decline curves can reliably identify populations where pressure is increasing over time, even when data quality is poor, and propose this method as a cost-effective technique for prioritizing conservation actions between populations.

Comparative demography of skates: life-history correlates of productivity and implications for management

Age-structured demographic models were constructed based on empirical estimates of longevity and maturity for five deepwater Bering Sea skates to investigate how observed differences in life history parameters affect population growth rates. Monte Carlo simulations were used to incorporate parameter uncertainty. Estimated population growth rates ranged from 1.045 to 1.129 yr(-1) and were lower than those reported for other Alaskan skates and most chondrichthyans. Population growth rates of these and other high-latitude skates increased with relative reproductive lifespan, but displayed no significant relationship with body size or depth distribution, suggesting that assemblage shifts may be difficult to predict for data-poor taxa. Elasticity analyses indicated that juvenile and adult survival had greater per-unit effects on population growth rates than did egg-case survival or fecundity. Population growth rate was affected more by uncertainty in age at maturity than maximum age. The results of this study indicate that if skates are deemed to be a management concern, gear modifications or depth-specific effort controls may be effective.

Drivers and hotspots of extinction risk in marine mammals

The world's oceans are undergoing profound changes as a result of human activities. However, the consequences of escalating human impacts on marine mammal biodiversity remain poorly understood. The International Union for the Conservation of Nature (IUCN) identifies 25% of marine mammals as at risk of extinction, but the conservation status of nearly 40% of marine mammals remains unknown due to insufficient data. Predictive models of extinction risk are crucial to informing present and future conservation needs, yet such models have not been developed for marine mammals. In this paper, we: (i) used powerful machine-learning and spatial-modeling approaches to understand the intrinsic and extrinsic drivers of marine mammal extinction risk; (ii) used this information to predict risk across all marine mammals, including IUCN "Data Deficient" species; and (iii) conducted a spatially explicit assessment of these results to understand how risk is distributed across the world's oceans. Rate of offspring production was the most important predictor of risk. Additional predictors included taxonomic group, small geographic range area, and small social group size. Although the interaction of both intrinsic and extrinsic variables was important in predicting risk, overall, intrinsic traits were more important than extrinsic variables. In addition to the 32 species already on the IUCN Red List, our model identified 15 more species, suggesting that 37% of all marine mammals are at risk of extinction. Most at-risk species occur in coastal areas and in productive regions of the high seas. We identify 13 global hotspots of risk and show how they overlap with human impacts and Marine Protected Areas.

The May threshold and life-history allometry

One of Robert May's classic results was finding that population dynamics become chaotic when the average lifetime rate of reproduction exceeds a certain value. Populations whose reproductive rates exceed this May threshold probably become extinct. The May threshold in each case depends upon the shape of the density-dependence curve, which differs among models of population growth. However, species of different sizes and generation times that share a roughly similar density-dependence curve will also share a similar May threshold. Here, we argue that this fact predicts a striking allometric regularity among animal taxa: lifetime reproductive rate should be roughly independent of body size. Such independence has been observed in diverse taxa, but has usually been ascribed to a fortuitous combination of physiologically based life-history allometries. We suggest, instead, that the ecological elimination of unstable populations within groups that share a value of the May threshold is a likely cause of this allometry.

Resource variability, aggregation and direct density dependence in an open context: the local regulation of an African elephant population

1. An emerging perspective in the study of density dependence is the importance of the spatial and temporal heterogeneity of resources. Although this is well understood in temperate ungulates, few studies have been conducted in tropical environments where both food and water are limiting resources. 2. We studied the regulation of one of the world's largest elephant populations in Hwange National Park, Zimbabwe. The study period started in 1986 when the population was released from culling. Using census data we investigated changes in elephant abundance with respect to rainfall and density across the entire park and across waterholes. 3. The population more than doubled since culling stopped. The population increased continuously during the first 6 years, and then fluctuated widely at about 30,000 individuals. Immigration processes must have been involved in the increase of the population size. 4. Population growth rates were negatively related to previous population density by a convex relationship, and negatively related to the ratio of previous population density on annual rainfall by a linear relationship. However, only this latter model (i.e. assuming a fluctuating carrying capacity related to annual rainfall) produced realistic dynamics. Overall, population decreased during dry years when the elephant density was high. 5. During dry years there were fewer waterholes retaining water during the dry season and consequently elephant numbers at waterholes increased, while their aggregation level across waterholes decreased. On the long-run elephant numbers increased only at the less crowded waterholes. 6. We suggest that the interaction between population size and the available foraging range determined by the number of active waterholes during the dry season controls the park population. 7. Our results emphasize the need to understand how key-resource areas cause resource-based aggregation, which ultimately influences the strength of density dependence. More specifically, this study suggests that climate variability strongly affects local elephant population dynamics through changes in surface-water availability. Finally, as dispersal is likely to be an important driver of the dynamics of this population, our results support views that a metapopulation framework should be endorsed for elephant management in open contexts.

Mammal population regulation, keystone processes and ecosystem dynamics

The theory of regulation in animal populations is fundamental to understanding the dynamics of populations, the causes of mortality and how natural selection shapes the life history of species. In mammals, the great range in body size allows us to see how allometric relationships affect the mode of regulation. Resource limitation is the fundamental cause of regulation. Top-down limitation through predators is determined by four factors: (i). body size; (ii). the diversity of predators and prey in the system; (iii). whether prey are resident or migratory; and (iv). the presence of alternative prey for predators. Body size in mammals has two important consequences. First, mammals, particularly large species, can act as keystones that determine the diversity of an ecosystem. I show how keystone processes can, in principle, be measured using the example of the wildebeest in the Serengeti ecosystem. Second, mammals act as ecological landscapers by altering vegetation succession. Mammals alter physical structure, ecological function and species diversity in most terrestrial biomes. In general, there is a close interaction between allometry, population regulation, life history and ecosystem dynamics. These relationships are relevant to applied aspects of conservation and pest management.

Pattern of variation in avian population growth rates

A central question in population ecology is to understand why population growth rates differ over time. Here, we describe how the long-term growth of populations is not only influenced by parameters affecting the expected dynamics, for example form of density dependence and specific population growth rate, but is also affected by environmental and demographic stochasticity. Using long-term studies of fluctuations of bird populations, we show an interaction between the stochastic and the deterministic components of the population dynamics: high specific growth rates at small densities r(1) are typically positively correlated with the environmental variance sigma(e)(2). Furthermore, theta, a single parameter describing the form of the density regulation in the theta-logistic density-regulation model, is negatively correlated with r(1). These patterns are in turn correlated with interspecific differences in life-history characteristics. Higher specific growth rates, larger stochastic effects on the population dynamics and stronger density regulation at small densities are found in species with large clutch sizes or high adult mortality rates than in long-lived species. Unfortunately, large uncertainties in parameter estimates, as well as strong stochastic effects on the population dynamics, will often make even short-term population projections unreliable. We illustrate that the concept of population prediction interval can be useful in evaluating the consequences of these uncertainties in the population projections for the choice of management actions.

Complex numerical responses to top-down and bottom-up processes in vertebrate populations

Population growth rate is determined in all vertebrate populations by food supplies, and we postulate bottom-up control as the universal primary standard. But this primary control system can be overridden by three secondary controls: top-down processes from predators, social interactions within the species and disturbances. Different combinations of these processes affect population growth rates in different ways. Thus, some relationships between growth rate and density can be hyperbolic or even have multiple nodes. We illustrate some of these in marsupial, ungulate and rabbit populations. Complex interactions between food, predators, environmental disturbance and social behaviour produce the myriad observations of population growth in nature, and we need to develop generalizations to classify populations. Different animal groups differ in the combination of these four processes that affect them, in their growth rates and in their vulnerability to extinction. Because conservation and management of populations depend critically on what factors drive population growth, we need to develop universal generalizations that will relieve us from the need to study every single population before we can make recommendations for management.

Population growth rate and its determinants: an overview

We argue that population growth rate is the key unifying variable linking the various facets of population ecology. The importance of population growth rate lies partly in its central role in forecasting future population trends; indeed if the form of density dependence were constant and known, then the future population dynamics could to some degree be predicted. We argue that population growth rate is also central to our understanding of environmental stress: environmental stressors should be defined as factors which when first applied to a population reduce population growth rate. The joint action of such stressors determines an organism's ecological niche, which should be defined as the set of environmental conditions where population growth rate is greater than zero (where population growth rate = r = log(e)(N(t+1)/N(t))). While environmental stressors have negative effects on population growth rate, the same is true of population density, the case of negative linear effects corresponding to the well-known logistic equation. Following Sinclair, we recognize population regulation as occurring when population growth rate is negatively density dependent. Surprisingly, given its fundamental importance in population ecology, only 25 studies were discovered in the literature in which population growth rate has been plotted against population density. In 12 of these the effects of density were linear; in all but two of the remainder the relationship was concave viewed from above. Alternative approaches to establishing the determinants of population growth rate are reviewed, paying special attention to the demographic and mechanistic approaches. The effects of population density on population growth rate may act through their effects on food availability and associated effects on somatic growth, fecundity and survival, according to a 'numerical response', the evidence for which is briefly reviewed. Alternatively, there may be effects on population growth rate of population density in addition to those that arise through the partitioning of food between competitors; this is 'interference competition'. The distinction is illustrated using a replicated laboratory experiment on a marine copepod, Tisbe battagliae. Application of these approaches in conservation biology, ecotoxicology and human demography is briefly considered. We conclude that population regulation, density dependence, resource and interference competition, the effects of environmental stress and the form of the ecological niche, are all best defined and analysed in terms of population growth rate.

Demographic characteristics and population dynamical patterns of solitary birds

In birds and many other animals, there are large interspecific differences in the magnitude of annual variation in population size. Using time-series data on populations of solitary bird species, we found that fluctuations in population size of solitary birds were affected by the deterministic characteristics of the population dynamics as well as the stochastic factors. In species with highly variable populations, annual variation in recruitment was positively related to the return rate of adults between successive breeding seasons. In stable populations, more recruits were found in years with low return rates of breeding adults. This identifies a gradient, associated with the position of the species along a "slow-fast" continuum of life history variation, from highly variable populations with a recruitment-driven demography to stable, strongly density-regulated populations with a survival-restricted demography. These results suggest that patterns in avian population fluctuations can be predicted from a knowledge of life-history characteristics and/or temporal variation in certain demographic traits.

Possible indirect interactions between transient and resident killer whales: implications for the evolution of foraging specializations in the genus Orcinus

Two distinct forms of killer whale (Orcinus orca) occur off the coast of British Columbia, Alaska and Washington State. These have different diets, and may be reproductively isolated. Because the primary food of transient whales (pinnipeds) is a potential competitor for the primary food of resident whales (salmon), or for the smaller fishes on which salmon feed, there should be an indirect interaction between the two forms of killer whale. We use simple mathematical models to show that this interaction will be either of a "plus-minus" type, or a "plus-plus" type (indirect mutualism), depending on whether or not pinnipeds and residents are on the same trophic level. In the case of the "plus-minus" interaction, increasing the population density or improving the environmental conditions of transients will increase the population density of residents, while increasing resident populations will reduce the equilibrium population size of transients. In the case of the "plus-plus" interaction, increasing the population density or improving the environmental conditions of transients will increase the population density of residents, while increasing resident populations will reduce the equilibrium population size of transients. In the case of the "plus-plus" interaction, increasing the population density or improving the environmental conditions of transients will increase the population density of residents, and vice versa. Such effects may not be currently manifest due to reduced populations at most levels in the food web. Regardless, considering such indirect interactions may be important for the management of many of the species involved, and can also provide a valuable framework for examining the evolution of the two forms of killer whales. Frequency-dependent indirect interactions, acting in concert with density-dependence within populations and disruptive selection on prey-type specific foraging characteristics, may have favoured reproductive isolation of the two forms of killer whales. We suggest that these two forms of whale are in the process of speciating, i.e., the two forms are incipient species.