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.     

The relative roles of density and climatic variation on population dynamics and fecundity rates in three contrasting ungulate species

The relative influences of density-dependent and -independent processes on vital rates and population dynamics have been debated in ecology for over half a century, yet it is only recently that both processes have been shown to operate within the same population. However, generalizations on the role of each process across species are rare. Using a process-orientated generalized linear modelling approach we show that variations in fecundity rates in populations of three species of ungulates with contrasting life histories are associated with density and winter weather in a remarkably similar manner. However, there are differences and we speculate that they are a result of differences in size between the species. Much previous research exploring the association between vital rates, population dynamics and density-dependent and -independent processes has used pattern-orientated approaches to decompose time-series into contributions from density-dependent and -independent processes. Results from these analyses are sometimes used to infer associations between vital rates, density and climatic variables. We compare results from pattern-orientated analyses of time-series with process-orientated analyses and report that the two approaches give different results. The approach of analysing relationships between vital rates, density and climatic variables may detect important processes influencing population dynamics that time-series methodologies may overlook.     

Formulating variable carrying capacity by exploring a resource dynamics-based feedback mechanism underlying the population growth models

Most of the population growth models comprise the concept of carrying capacity presume that a stable population would have a saturation level characteristic. This indicates that the population growth models have a common implicit feature of resource-limited growth, which contributes at a later stage of population growth by forming a numerical upper bound on the population size. However, a general underlying resource dynamics of the models has not been previously explored, which is the focus of present study. In this paper, we found that there exists a conservation of energy relationship comprising the terms of available resource and population density, jointly interpreted here as total available vital energy in a confined environment. We showed that this relationship determines a density-dependent functional form of relative population growth rate and consequently the parametric equations are in the form depending upon the population density, resource concentration, and time. Thus, the derived form of relative population growth rate is essentially a feedback type, i.e., updating parametric values for the corresponding population density. This resource dynamics-based feedback approach has been implemented for formulating variable carrying capacity in a confined environment. Particularly, at a constant resource replenishment rate, a density-dependent population growth equation similar to the classic logistic equation is derived, while one of the regulating factors of the underlying resource dynamics is that the resource consumption rate is directly proportional to the resource concentration. Likewise two other population growth equations similar to two known popular growth equations are derived based on this resource dynamics-based feedback approach. Using microcosm-derived data of fungus T. virens, we fitted one derived population growth model against the datasets, and concluded that this approach is practically implementable for studying a single population growth regulation in a confined environment.     

Estimating Allee Dynamics before They Can Be Observed: Polar Bears as a Case Study

Allee effects are an important component in the population dynamics of numerous species. Accounting for these Allee effects in population viability analyses generally requires estimates of low-density population growth rates, but such data are unavailable for most species and particularly difficult to obtain for large mammals. Here, we present a mechanistic modeling framework that allows estimating the expected low-density growth rates under a mate-finding Allee effect before the Allee effect occurs or can be observed. The approach relies on representing the mechanisms causing the Allee effect in a process-based model, which can be parameterized and validated from data on the mechanisms rather than data on population growth. We illustrate the approach using polar bears (Ursus maritimus), and estimate their expected low-density growth by linking a mating dynamics model to a matrix projection model. The Allee threshold, defined as the population density below which growth becomes negative, is shown to depend on age-structure, sex ratio, and the life history parameters determining reproduction and survival. The Allee threshold is thus both density- and frequency-dependent. Sensitivity analyses of the Allee threshold show that different combinations of the parameters determining reproduction and survival can lead to differing Allee thresholds, even if these differing combinations imply the same stable-stage population growth rate. The approach further shows how mate-limitation can induce long transient dynamics, even in populations that eventually grow to carrying capacity. Applying the models to the overharvested low-density polar bear population of Viscount Melville Sound, Canada, shows that a mate-finding Allee effect is a plausible mechanism for slow recovery of this population. Our approach is generalizable to any mating system and life cycle, and could aid proactive management and conservation strategies, for example, by providing a priori estimates of minimum conservation targets for rare species or minimum eradication targets for pests and invasive species.     

From dispersal to landscapes: progress in the understanding of population dynamics

The development of our understanding of population dynamics over the past 50 years is reviewed from a personal perspective. An early emphasis on population vital rates was superceded by recognition of the importance of the specific community context of focal populations, and most recently has in turn been enriched by a landscape perspective. Certain basic principles are outlined including the value of a systems context for population analyses, the power of a dual mechanistic and contextual perspective, and the inevitability of density control in a finite biosphere. Numbers are determined by the balance of two complex parameters:p — the per capita growth promoting (enhancing) forces, ands — the per capita growth suppressing forces. Multiple factor explanations of demographic behavior are therefore to be expected, as well as temporal and spatial variations in them. An appreciation for the potential role of dispersal as a population vital rate led to the development of metapopulation theory. A renewed understanding of the role of community context in population dynamics provoked the realization that a multi-factor approach was required. This in turn allowed us to reconcile the reality of local demographic complexity with global generalizations. Finally, the introduction of landscape ecology into demographic thinking added many new insights. It is now appreciated that a spatially explicit mosaic of habitat patches, edge effects, corridors, and even the proportion of favorable to marginal habitats can all be critically important factors in influencing population dynamics.     

Causal and Mechanistic Explanations in Ecology

How are scientific explanations possible in ecology, given that there do not appear to be many-if any-ecological laws? To answer this question, I present and defend an account of scientific causal explanation in which ecological generalizations are explanatory if they are invariant rather than lawlike. An invariant generalization continues to hold or be valid under a special change-called an intervention-that changes the value of its variables. According to this account, causes are difference-makers that can be intervened upon to manipulate or control their effects. I apply the account to ecological generalizations to show that invariance under interventions as a criterion of explanatory relevance provides interesting interpretations for the explanatory status of many ecological generalizations. Thus, I argue that there could be causal explanations in ecology by generalizations that are not, in a strict sense, laws. I also address the issue of mechanistic explanations in ecology by arguing that invariance and modularity constitute such explanations.     

Pitfalls and challenges of estimating population growth rate from empirical data: consequences for allometric scaling relations

The intrinsic rate of increase is a fundamental concept in population ecology, and a variety of problems require that estimates of population growth rate be obtained from empirical data. However, depending on the extent and type of data available (e.g. time series, life tables, life history traits), several alternative empirical estimators of population growth rate are possible. Because these estimators make different assumptions about the nature of age‐dependent mortality and density‐dependence of population dynamics, among other factors, these quantities capture fundamentally different aspects of population growth and are not interchangeable. Nevertheless, they have been routinely commingled in recent ecoinformatic analyses relating to allometry and conservation biology. Here we clarify some of the confusion regarding the empirical estimation of population growth rate and present separate analyses of the frequency distributions and allometric scaling of three alternative, non‐interchangeable measures of population growth. Studies of allometric scaling of population growth rate with body size are additionally sensitive to the statistical line fitting approach used, and we find that different approaches yield different allometric scaling slopes. Across the mix of population growth estimators and line fitting techniques, we find scattered and limited support for the key allometric prediction from the metabolic theory of ecology, namely that log₁₀(population growth rate) should scale as ?0.25 power of log₁₀(body mass). More importantly, we conclude that the question of allometric scaling of population growth rate with body size is highly sensitive to previously unexamined assumptions regarding both the appropriate population growth parameter to be compared and the line fitting approach used to examine the data. Finally, we suggest that the ultimate test of allometric scaling of maximum population growth rates with body size has not been done and, moreover, may require data that are not currently available.     

Ten principles from evolutionary ecology essential for effective marine conservation

Sustainably managing marine species is crucial for the future health of the human population. Yet there are diverse perspectives concerning which species can be exploited sustainably, and how best to do so. Motivated by recent debates in the published literature over marine conservation challenges, we review ten principles connecting life‐history traits, population growth rate, and density‐dependent population regulation. We introduce a framework for categorizing life histories, POSE (Precocial–Opportunistic–Survivor–Episodic), which illustrates how a species’ life‐history traits determine a population's compensatory capacity. We show why considering the evolutionary context that has shaped life histories is crucial to sustainable management. We then review recent work that connects our framework to specific opportunities where the life‐history traits of marine species can be used to improve current conservation practices.     

The relative importance of reproduction and survival for the conservation of two dolphin populations

It has been proposed that in slow‐growing vertebrate populations survival generally has a greater influence on population growth than reproduction. Despite many studies cautioning against such generalizations for conservation, wildlife management for slow‐growing populations still often focuses on perturbing survival without careful evaluation as to whether those changes are likely or feasible. Here, we evaluate the relative importance of reproduction and survival for the conservation of two bottlenose dolphin (Tursiops cf aduncus) populations: a large, apparently stable population and a smaller one that is forecast to decline. We also assessed the feasibility and effectiveness of wildlife management objectives aimed at boosting either reproduction or survival. Consistent with other analytically based elasticity studies, survival had the greatest effect on population trajectories when altering vital rates by equal proportions. However, the findings of our alternative analytical approaches are in stark contrast to commonly used proportional sensitivity analyses and suggest that reproduction is considerably more important. We show that

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Variation in Allee effects: evidence,unknowns, and directions forward

Allee effects, positive effects of population size or density on per-capita fitness, are of broad interest in ecology and conservation due to their importance to the persistence of small populations and to range boundary dynamics. A number of recent studies have highlighted the importance of spatiotemporal variation in Allee effects and the resulting impacts on population dynamics. These advances challenge conventional understanding of Allee effects by reframing them as a dynamic factor affecting populations instead of a static condition. First, we synthesize evidence for variation in Allee effects and highlight potential mechanisms. Second, we emphasize the “Allee slope,” i.e., the magnitude of the positive effect of density on the per-capita growth rate, as a metric for demographic Allee effects. The more commonly used quantitative metric, the Allee threshold, provides only a partial picture of the underlying forces acting on population growth despite its implications for population extinction. Third, we identify remaining unknowns and strategies for addressing them. Outstanding questions about variation in Allee effects fall broadly under three categories: (1) characterizing patterns of natural variability; (2) understanding mechanisms of variation; and (3) implications for populations, including applications to conservation and management. Future insights are best achieved through robust interactions between theory and empiricism, especially through mechanistic models. Understanding spatiotemporal variation in the demographic processes contributing to the dynamics of small populations is a critical step in the advancement of population ecology.     

Parameterization of photosystem II photoinactivation and repair

The photoinactivation (also termed photoinhibition or photodamage) of Photosystem II (PSII) and the counteracting repair reactions are fundamental elements of the metabolism and ecophysiology of oxygenic photoautotrophs. Differences in the quantification, parameterization and terminology of Photosystem II photoinactivation and repair can erect barriers to understanding, and particular parameterizations are sometimes incorrectly associated with particular mechanistic models. These issues lead to problems for ecophysiologists seeking robust methods to include photoinhibition in ecological models. We present a comparative analysis of terms and parameterizations applied to photoinactivation and repair of Photosystem II. In particular, we show that the target size and quantum yield approaches are interconvertible generalizations of the rate constant of photoinactivation across a range of incident light levels. Our particular emphasis is on phytoplankton, although we draw upon the literature from vascular plants. This article is part of a Special Issue entitled: Photosystem II.     

Thirty Years of Research in Kibale National Park,Uganda, Reveals a Complex Picture for Conservation

Kibale National Park, Uganda, has a rich and abundant primate community and a complicated history of anthropogenic disturbance. Moreover, it has been the focus of over 30 yr of research and has received considerable attention from nongovernmental and governmental conservation organizations. As a result, Kibale serves as a valuable case study with which to evaluate the factors that regulate primate population density and the challenges of deriving generalizations for conservation. We review the impact of logging and forest fragmentation on primate population density and trace the efficacy of various conservation strategies. A 28-yr comparison of primate abundance in logged and unlogged forests and a 10-yr study of forest dynamics showed that primate recovery in logged areas is generally slow or not occurring at all for some species, which is likely driven by the fact that the forest is not recovering as expected. No primate species characteristic predicted their ability to live in forest fragments around Kibale. While a nutritional model was useful to predict the abundance of colobus in forest fragments outside of Kibale, a 5-yr study revealed that human land-use practices are more fundamentally shaping population dynamics. We evaluate data on primate abundance in light of Milton’s protein/fiber model to predict colobine biomass. We demonstrate that while the model can predict colobus biomass in pristine habitats, the 2 colobus species respond differently to disturbance. We offer suggestions for future conservation research and consider strategies to conserve forested national parks based on experiences gained over 30 yr.     

Demographic,mechanistic and density-dependent determinants of population growth rate: a case study in an avian predator

Identifying the determinants of population growth rate is a central topic in population ecology. Three approaches (demographic, mechanistic and density-dependent) used historically to describe the determinants of population growth rate are here compared and combined for an avian predator, the barn owl (Tyto alba). The owl population remained approximately stable (r approximately 0) throughout the period from 1979 to 1991. There was no evidence of density dependence as assessed by goodness of fit to logistic population growth. The finite (lambda) and instantaneous (r) population growth rates were significantly positively related to food (field vole) availability. The demographic rates, annual adult mortality, juvenile mortality and annual fecundity were reported to be correlated with vole abundance. The best fit (R(2) = 0.82) numerical response of the owl population described a positive effect of food (field voles) and a negative additive effect of owl abundance on r. The numerical response of the barn owl population to food availability was estimated from both census and demographic data, with very similar results. Our analysis shows how the demographic and mechanistic determinants of population growth rate are linked; food availability determines demographic rates, and demographic rates determine population growth rate. The effects of food availability on population growth rate are modified by predator abundance.     

Graphical models of residue coupling in protein families

Many statistical measures and algorithmic techniques have been proposed for studying residue coupling in protein families. Generally speaking, two residue positions are considered coupled if, in the sequence record, some of their amino acid type combinations are significantly more common than others. While the proposed approaches have proven useful in finding and describing coupling, a significant missing component is a formal probabilistic model that explicates and compactly represents the coupling, integrates information about sequence,structure, and function, and supports inferential procedures for analysis, diagnosis, and prediction.We present an approach to learning and using probabilistic graphical models of residue coupling. These models capture significant conservation and coupling constraints observable ina multiply-aligned set of sequences. Our approach can place a structural prior on considered couplings, so that all identified relationships have direct mechanistic explanations. It can also incorporate information about functional classes, and thereby learn a differential graphical model that distinguishes constraints common to all classes from those unique to individual classes.Such differential models separately account for class-specific conservation and family-wide coupling, two different sources of sequence covariation. They are then able to perform interpretable functional classification of new sequences, explaining classification decisions in terms of the underlying conservation and coupling constraints. We apply our approach in studies of both G protein-coupled receptors and PDZ domains, identifying and analyzing family-wide and class-specific constraints, and performing functional classification. The results demonstrate that graphical models of residue coupling provide a powerful tool for uncovering, representing, and utilizing significant sequence structure-function relationships in protein families.     

Equivalence relationships between stage-structured population models

Matrix population models are widely applied in conservation ecology to help predict future population trends and guide conservation effort. Researchers must decide upon an appropriate level of model complexity, yet there is little theoretical work to guide such decisions. In this paper we present an analysis of a stage-structured model, and prove that the model's structure can be simplified and parameterised in such a way that the long-term growth rate, the stable-stage distribution and the generation time are all invariant to the simplification. We further show that for certain structures of model the simplified models require less effort in data collection. We also discuss features of the models which are not invariant to the simplification and the implications of our results for the selection of an appropriate model. We illustrate the ideas using a population model for short-tailed shearwaters (Puffinus tenuirostris). In this example, model simplification can increase parameter elasticity, indicating that an intermediate level of complexity is likely to be preferred.     

Food for folivores: nutritional explanations linking diets to population density

Ecologists want to explain why populations of animals are not evenly distributed across landscapes and often turn to nutritional explanations. In seeking to link population attributes with food quality, they often contrast nutritionally positive traits, such as the concentration of nitrogen, against negative ones, such as fibre concentration, by using a ratio of these traits. This specific ratio has attracted attention because it sometimes correlates with the biomass of colobine primates across sites in Asia and Africa. Although empirically successful, we have identified problems with the ratio that may explain why it fails under some conditions to predict colobine biomass. First, available nitrogen, rather than total nitrogen, is nutritionally important, while the presence of tannins is the major factor reducing the availability of nitrogen in browse plant species. Second, tannin complexes inflate measures of fibre. Finally, simple ratios may be unsound statistically because they implicitly assume isometric relationships between variables. We used data on the chemical composition of plants from three continents to examine the relationships between the concentrations of nitrogen, available nitrogen, fibre and tannins in foliage and to evaluate the nitrogen to fibre ratio. Our results suggest that the ratio of the concentration of nitrogen to fibre in leaves does sometimes closely correlate with the concentration of available nitrogen. However, the ratio may give misleading results when leaves contain high concentrations of tannins. The concentration of available nitrogen, which incorporates measures of total nitrogen, dry matter digestibility and tannins, should give a better indication of the nutritional value of leaves for herbivorous mammals that can readily be extrapolated to habitats.     

Parasite abundance, body size, life histories, and the energetic equivalence rule

If common processes generate size-abundance relationships among all animals, then similar patterns should be observed across groups with different ecologies, such as parasites and free-living animals. We studied relationships among body size, life-history traits, and population intensity (density in infected hosts) among nematodes parasitizing mammals. Parasite size and intensity were negatively correlated independently of all other parasite and host factors considered and regardless of type of analyses (i.e., nonphylogenetic or phylogenetically based statistical analyses, and across or within communities). No other nematode life-history traits had independent effects on intensity. Slopes of size-intensity relationships were consistently shallow, around -0.20 on log-log scale, and thus inconsistent with the energetic equivalence rule. Within communities, slopes converged toward this global value as size range increased. A summary of published values suggests similar convergence toward a global value around -0.75 among free-living animals. Steeper slopes of size-abundance relationships among free-living animals could be related to fundamental differences in ecologies between parasites and free-living animals, although such generalizations require reexamination of size-abundance relationships among free-living animals with regard to confounding factors, in particular by use of phylogenetically based statistical methods. In any case, our analyses caution against simple generalizations about patterns of animal abundance.     

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.     

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.