Graph theory as a proxy for spatially explicit population models in conservation planning.

Spatially explicit population models (SEPMs) are often considered the best way to predict and manage species distributions in spatially heterogeneous landscapes. However, they are computationally intensive and require extensive knowledge of species' biology and behavior, limiting their application in many cases. An alternative to SEPMs is graph theory, which has minimal data requirements and efficient algorithms. Although only recently introduced to landscape ecology, graph theory is well suited to ecological applications concerned with connectivity or movement. This paper compares the performance of graph theory to a SEPM in selecting important habitat patches for Wood Thrush (Hylocichla mustelina) conservation. We use both models to identify habitat patches that act as population sources and persistent patches and also use graph theory to identify patches that act as stepping stones for dispersal. Correlations of patch rankings were very high between the two models. In addition, graph theory offers the ability to identify patches that are very important to habitat connectivity and thus long-term population persistence across the landscape. We show that graph theory makes very similar predictions in most cases and in other cases offers insight not available from the SEPM, and we conclude that graph theory is a suitable and possibly preferable alternative to SEPMs for species conservation in heterogeneous landscapes.     

Uncertainty analysis of transient population dynamics

Two types of demographic analyses, perturbation analysis and uncertainty analysis, can be conducted to gain insights about matrix population models and guide population management. Perturbation analysis studies how the perturbation of demographic parameters (survival, growth, and reproduction parameters) may affect the population projection, while uncertainty analysis evaluates how much uncertainty there is in population dynamic predictions and where the uncertainty comes from. Previously, both perturbation analysis and uncertainty analysis were conducted on the long-term population growth rate. However, the population may not reach its equilibrium state, especially when there is management by harvesting or hunting. Recently, there has been an increased interest in short-term transient dynamics, which can differ from asymptotic long-term dynamics. There are currently techniques to conduct perturbation analyses of short-term transient dynamics, but no techniques have been proposed for uncertainty analysis of such dynamics. In this study, we introduced an uncertainty analysis technique, the general Fourier Amplitude Sensitivity Test (FAST), to study uncertainties in transient population dynamics. The general FAST is able to identify the amount of uncertainty in transient dynamics and contributions by different demographic parameters. We applied the general FAST to a mountain goat (Oreamnos americanus) matrix population model to give a clear illustration of how uncertainty analysis can be conducted for transient dynamics arising from matrix population models.     

Why are metapopulations so rare?

Roughly 40 years after its introduction, the metapopulation concept is central to population ecology. The notion that local populations and their dynamics may be coupled by dispersal is without any doubt of great importance for our understanding of population-level processes. A metapopulation describes a set of subpopulations linked by (rare) dispersal events in a dynamic equilibrium of extinctions and recolonizations. In the large body of literature that has accumulated, the term "metapopulation" is often used in a very broad sense; most of the time it simply implies spatial heterogeneity. A number of reviews have recently addressed this problem and have pointed out that, despite the large and still growing popularity of the metapopulation concept, there are only very few empirical examples that conform with the strict classical metapopulation (CM) definition. In order to understand this discrepancy between theory and observation, we use an individual-based modeling approach that allows us to pinpoint the environmental conditions and the life-history attributes required for the emergence of a CM structure. We find that CM dynamics are restricted to a specific parameter range at the border between spatially structured but completely occupied and globally extinct populations. Considering general life-history attributes, our simulations suggest that CMs are more likely to occur in arthropod species than in (large) vertebrates. Since the specific type of spatial population structure determines conservation concepts, our findings have important implications for conservation biology. Our model suggests that most spatially structured populations are panmictic, patchy, or of mainland-island type, which makes efforts spent on increasing connectivity (e.g., corridors) questionable. If one does observe a true CM structure, this means that the focal metapopulation is on the brink of extinction and that drastic conservation measures are needed.     

Methods for joint inference from panel survey and demographic data

A number of methods for joint inference from animal abundance and demographic data have been proposed in recent years, each with its own advantages. A new approach to analyzing panel survey and demographic data simultaneously is described. The approach fits population-dynamics models to the survey data, rather than to a single index of abundance derived from them and thus avoids disadvantages inherent in analyzing such an index. The methodology is developed and illustrated with British Lapwing data, and the results are compared with those obtained from existing approaches. The estimates of demographic parameters and population indices are similar for all methods. The results of a simulation study show that the new method performs well in terms of mean squared error.     

Integral projection models for finite populations in a stochastic environment

Continuous types of population structure occur when continuous variables such as body size or habitat quality affect the vital parameters of individuals. These structures can give rise to complex population dynamics and interact with environmental conditions. Here we present a model for continuously structured populations with finite size, including both demographic and environmental stochasticity in the dynamics. Using recent methods developed for discrete age-structured models we derive the demographic and environmental variance of the population growth as functions of a continuous state variable. These two parameters, together with the expected population growth rate, are used to define a one-dimensional diffusion approximation of the population dynamics. Thus, a substantial reduction in complexity is achieved as the dynamics of the complex structured model can be described by only three population parameters. We provide methods for numerical calculation of the model parameters and demonstrate the accuracy of the diffusion approximation by computer simulation of specific examples. The general modeling framework makes it possible to analyze and predict future dynamics and extinction risk of populations with various types of structure, and to explore consequences of changes in demography caused by, e.g., climate change or different management decisions. Our results are especially relevant for small populations that are often of conservation concern.     

Ein Indikator für den Einsatz gefährlicher Stoffe in Produkten und Prozessen: Monoethylenglykol-Äquivalente

In order to quantify hazardous substance use in production processes, a special methodology has been designed within the context of the EcoGrade integrated environmental assessment method developed by the Öko-Institut, Institute for Applied Ecology. This methodology uses monoethylene glycol (MEG) equivalents as an indicator value for hazardous substance use. MEG equivalents permit direct, noxious-substance-focussed comparison of processes and products (Bunke 2001). The assessment is based upon the standardized risk phrases assigned to the component substances. The MEG equivalent methodology is a refinement and application of the potency factor model (Wirkfaktorenmodell) of the German Technical Rule for Hazardous Substances (Technische Regel für Gefahrstoffe, TRGS) 440 (AGS 2001). The data required for the assessment procedure are available within companies (safety data sheets) or are readily accessible publicly (hazardous substance databanks). A further benefit is that inventory analysis of hazardous substances using the method presented here makes it possible to take hazardous substance use into account in a systematic manner within life-cycle assessment (LCA) studies. The methodology has been tested for the example of residential buildings. Note: The terms ‘hazardous substance’, ‘noxious substance’ and ‘hazardous constituent’ are used in this paper in the sense of substances that have one of the hazard attributes set out in Article 3 of the German Chemicals Act (Chemikaliengesetz).     

Population inertia and its sensitivity to changes in vital rates and population structure

Because the (st)age structure of a population may rarely be stable, studies of transient population dynamics and population momentum are becoming ever more popular. Yet, studies of "population momentum" are restricted in the sense that they describe the inertia of population size resulting from a demographic transition to the stationary population growth rate. Although rarely mentioned, inertia in population size is a general phenomenon and can be produced by any demographic transition or perturbation. Because population size is of central importance in demography, conservation, and management, formulas relating the sensitivity of population inertia to changes in underlying vital rates and population structure could provide much-needed insight into the dynamics of populations with unstable (st)age structure. Here, we derive such formulas, which are readily computable, and provide examples of their potential use in studies of life history and applied arenas of population study.     

Quantifying Relative Extinction Risks and Targeting Intervention for the Orchid Flora of a Natural Park in the European Prealps

Abstract:  Conservation currently relies largely on hindsight because demographic studies identify population decline after the event. Nevertheless, the degree of aggregation within a population is an "instantaneous" characteristic with the potential to identify populations presently at greatest risk of genetic impoverishment (via Allee effects and in-breeding depression) and local decline. We sought to determine the relative extinction risk for sympatric orchid species throughout Monte Barro natural park (Lecco, Italy), based on an index of dispersion ( I ) calculated from the size and location of subpopulations (recorded with GPS and mapped with GIS). Three population dispersion types were identified: (1) highly aggregated and locally abundant (large subpopulations restricted to particular sites; e.g., Gymnadenia conopsea [L.] R.Br.; I = 54.5); (2) widespread and moderately aggregated (opportunistic throughout the elevational range of the mountain; e.g., Listera ovata [L.] R.Br.; I = 18.9); and (3) weakly aggregated and locally rare (small, highly diffuse subpopulations; e.g., endemic Ophrys benacensis [Reisigl] O. & E. Danesch & Ehrend.; I = 4.4). Type 1 populations are more likely to respond to in situ intervention, whereas type 2 are relatively invasive species for which conservation intervention is not necessary, and type 3 are rare species that are least likely to respond to habitat management, for which ex situ conservation and population reinforcement would be most appropriate. Although our methodology provides only a "snapshot" of aboveground patterns of population dispersion, it can help target the application of in situ and ex situ conservation activities proactively and is of particular utility for parks for which a rapid assessment of local extinction risks is needed.     

Reconstructing the historic demography of an endangered seabird

Reducing extinction risk for threatened species requires determining which demographic parameters are depressed and causing population declines. Museum collections may constitute a unique, underutilized resource for measuring demographic changes over long time periods using age-ratio analysis. We reconstruct the historic demography of a U.S. federally endangered seabird, the Marbled Murrelet (Brachyramphus marmoratus), from specimens collected approximately 100 years ago for comparison with predictions from comparative analyses and with results from contemporary field studies using both age-ratio analysis and conventional demographic estimators. Reproduction in the late 1800s and early 1900s matched predictions from comparative analysis, but was 8-9 times greater than contemporary estimates, whereas adult survival was unchanged. Historic reproductive rates would support stable populations, but contemporary levels should result in population declines. Contemporary demographic estimates derived from age-ratio analysis were similar to estimates from conventional estimators. Using museum specimens to reconstruct historic demography provides a unique approach to identify causes of decline and to set demographic benchmarks for recovery of endangered species that meet most assumptions of age-ratio analysis.     

Factors Leading to Different Viability Predictions for a Grizzly Bear Data Set

Population viability analysis programs are being used increasingly in research and management applications, but there has not been a systematic study of the congruence of different program predictions based on a single data set. We performed such an analysis using four population viability analysis computer programs: GAPPS, INMAT, RAMAS/AGE, and VORTEX. The standardized demographic rates used in all programs were generalized from hypothetical increasing and decreasing grizzly bear ( Ursus arctos horribilis ) populations. Idiosyncracies of input format for each program led to minor differences in intrinsic growth rates that translated into striking differences in estimates of extinction rates and expected population size. In contrast, the addition of demographic stochasticity, environmental stochasticity, and inbreeding costs caused only a small divergence in viability predictions. But, the addition of density dependence caused large deviations between the programs despite our best attempts to use the same density-dependent functions. Population viability programs differ in how density dependence is incorporated, and the necessary functions are difficult to parameterize accurately. Thus, we recommend that unless data clearly suggest a particular density-dependent model, predictions based on population viability analysis should include at least one scenario without density dependence. Further, we describe output metrics that may differ between programs; development of future software could benefit from standardized input and output formats across different programs.     

Age,stages, and the role of generation time in matrix models

The earliest matrix models, proposed in the 1940s, consider age classes, and were later proved to be equivalent to the discrete time version of the stable population theory. In this theory and models, besides the asymptotic growth rate, a very important characteristic is the turnover of individuals, measured in various ways by generation time. Models considering stages, on the contrary, do not take into account the age of individuals and seem largely preferable to age-structured models for many populations in which demographic characteristics are related to biological stages (such a seed, rosette, flowering plant, etc.) rather than to age per itself. These two kinds of models can be embedded as particular cases of stage by age models or multistate models. Theses general models can be used to develop a multistate stable population theory with many advantages. This general theory is reviewed with emphasis on general rules for sensitivity analyses in which generation time plays a central role.     

Characterizing source-sink dynamics with genetic parentage assignments

Source-sink dynamics have been suggested to characterize the population structure of many species, but the prevalence of source-sink systems in nature is uncertain because of inherent challenges in estimating migration rates among populations. Migration rates are often difficult to estimate directly with demographic methods, and indirect genetic methods are subject to a variety of assumptions that are difficult to meet or to apply to evolutionary timescales. Furthermore, such methods cannot be rigorously applied to high-gene-flow species. Here, we employ genetic parentage assignments in conjunction with demographic simulations to infer the level of immigration into a putative sink population. We use individual-based demographic models to estimate expected distributions of parent-offspring dyads under competing sink and closed-population models. By comparing the actual number of parent-offspring dyads (identified from multilocus genetic profiles) in a random sample of individuals taken from a population to expectations under these two contrasting demographic models, it is possible to estimate the rate of immigration and test hypotheses related to the role of immigration on population processes on an ecological timescale. The difference in the expected number of parent-offspring dyads between the two population models was greatest when immigration into the sink population was high, indicating that unlike traditional population genetic inference models, the highest degree of statistical power is achieved for the approach presented here when migration rates are high. We used the proposed genetic parentage approach to demonstrate that a threatened population of Marbled Murrelets (Braclhyrarmphus marmotus) appears to be supplemented by a low level of immigration (approximately 2-6% annually) from other populations.     

Applying Metapopulation Theory to Conservation of Migratory Birds

Abstract: Metapopulation theory has proven useful for understanding the population structure and dynamics of many species of conservation concern. The metapopulation concept has been applied almost exclusively to nonmigratory species, however, for which subpopulation demographic independence—a requirement for a classically defined metapopulation—is explicitly related to geographic distribution and dispersal probabilities. Defining the degree of demographic independence among subpopulations of migratory animals, and thus the applicability of metapopulation theory as a conceptual framework for understanding population dynamics, is much more difficult. Unlike nonmigratory species, subpopulations of migratory animals cannot be defined as synonymous with geographic areas. Groups of migratory birds that are geographically separate at one part of the annual cycle may occur together at others, but co-occurrence in time and space does not preclude the demographic independence of subpopulations. I suggest that metapopulation theory can be applied to migratory species but that understanding the degree of subpopulation independence may require information about both spatial distribution throughout the annual cycle and behavioral mechanisms that may lead to subpopulation demographic independence. The key for applying metapopulation theory to migratory animals lies in identifying demographically independent subpopulations, even as they move during the annual cycle and potentially co-occur with other subpopulations. Using examples of migratory bird species, I demonstrate that spatial and temporal modes of subpopulation independence can interact with behavioral mechanisms to create demographically independent subpopulations, including cases in which subpopulations are not spatially distinct in some parts of the annual cycle.     

System theory formulation of site-specific water quality standards and protocols

Habitat variability makes site-specific considerations a necessity in the specification of water quality standards. The U.S. Environmental Protection Agency (EPA) has recognized this in its development of procedures for site-specific modification of national standards. These procedures involves translation of laboratory toxicology data into field situations where such data are often poor predictors of biotoxicity. The whole problem is poorly specified.This paper formulates a system theory approach to better specification of the problems associated with setting water quality standards. A state space model of the general environmental protection problem is presented: Find a set of diagnostic variables whose maintenance within specifiable limits (standards) is both necessary and sufficient to protect all variables of a subject ecosystem. The program for this comprises a site-specific protocol.Stages in such a protocol include (1) choice of diagnostic variables, (2) establishment of necessity and sufficiency for these variables, and (3) determination of standards through (4) toxicity testing. Problems associated with the latter include (a) spatiotemporal variability, system (b) linearity-nonlinearity, and (c) stationarity-nonstationarity, and (d) monitoring for: baseline information, impact detection, determining compliance, establishing causality and making predictions. Each of these problems is structured in terms of the state space model. Then, current procedures of the EPA site-specific methodology are reviewed, and a set of recommendations proposed for their improvement using the system theory formulation to guide further developments.     

Disarming the population bomb

This paper argues for a renewed international focus on managed population reduction as a key enabler of sustainable development. The paper presents development data that demonstrate why population reduction should be elevated to share top priority with poverty alleviation, as the two over-arching goals of international development strategy. The critical analysis put forth in this paper argues that the current ‘unsustainable’ approach to sustainable development stems from (1) ‘empty world’ economic growth theory applied to a ‘full world’, which is (2) supported and driven by socioeconomic incentives to expand population, (3) justified through flawed interpretation of demographic transition theory, (4) bolstered by the exaggerated efficacy of environmental economic theory applied in a resource-constrained world, (5) insulated from challenge by limitations of scientific knowledge and (6) perpetuated by herd behavior. This paper concludes that failure to reduce global population will inhibit attainment of poverty alleviation and worsen environmental degradation.     

Using Modeling to Improve Monitoring of Structured Populations: Are We Collecting the Right Data?

Abstract:  Population monitoring is central to most demographic studies and conservation efforts, but it may not always be directed at the most appropriate life stage. We used stochastic simulation modeling to evaluate the effectiveness of a monitoring program for a well-studied population of Eastern Imperial Eagles ( Aquila heliaca ) in Kazakhstan. Specifically, we asked whether the most appropriate data were being collected to understand system state and population dynamics. Our models were parameterized with data collected over the course of 25 years of study of this population. We used the models to conduct simulation experiments to evaluate relationships between monitored or potentially monitored parameters and the demographic variables of interest—population size ( N ) and population growth (λ). Static analyses showed that traditional territory-based monitoring was a poor indicator of eagle population size and growth and that monitoring survivorship would provide more information about these parameters. Nevertheless, these same traditionally monitored territory-based parameters had greater power to detect long-term changes in population size than did survivorship or population structure. Regardless of the taxa considered, threats can have immediate impacts on population size and growth or longer-term impacts on population dynamics. Prudently designed monitoring programs for any species will detect the demographic effects of both types of threats.     

Hummingbird isolegs in an experimental system

Summary Optimal foraging theory was first looked upon as a tool to study the evolution of niches in community ecology. Isoleg theory is being developed to reestablish it as such a tool. Isoleg theories are maps of isolegs in a graph whose axes are population densities. There are two kinds of isolegs: some are lines of equal optimal behavior in the graph; others mark threshold combinations of densities past which sudden shifts in behavior should occur. A technique for determining whether isolegs exist is described and applied to hummingbird data. These data were collected experimentally in the field expressly to test one isoleg model. All three species of hummingbird exhibited at least one of the sudden-shift type of isoleg. Their behaviors map onto the density graph in the predicted portions of the graph with only one exception. The data also support the prediction that behavior in the field is disjunct, i.e. subject to substantial, abrupt, discontinuous changes produced by very small continuous changes in a control variable. Some evidence for continuous control was also found, but it is ambiguous. Theory predicts that the two forms of control should be found together in some optimal systems.     

Effect of stage-specific vital rates on population growth rates and effective population sizes in an endangered iteroparous plant

Effective population size (N(e)) determines the strength of genetic drift and can influence the level of genetic diversity a population can maintain. Assessing how changes in demographic rates associated with environmental variables and management actions affect N(e) thus can be crucial to the conservation of endangered species. Calculation of N(e) through demographic models makes it possible to use elasticity analyses to study this issue. The elasticity of N(e) to a given vital rate is the proportional change in N(e) associated with a proportional increase in that vital rate. In addition, demographic models can be used to study N(e) and population growth rate (λ) simultaneously. Simultaneous examination is important because some vital rates differ diametrically in their associations with λ and N(e). For example, in some cases increasing these vital rates increases λ and decreases N(e). We used elasticity analysis to study the effect of stage-specific survival and flowering rates on N(e), annual effective population size (N(a)), and λ in seven populations of the endangered plant Austrian dragonhead (Dracocephalum austriacum). In populations with λ ≥ 1, the elasticities of N(e) and N(a) were similar to those of λ. Survival rates of adults were associated with greater elasticities than survival rates of juveniles, flowering rates, or fecundity. In populations with λ < 1, N(e) and N(a) exhibited greater elasticities to juvenile than to adult vital rates. These patterns are similar to those observed in other species with similar life histories. We did not observe contrasting effects of any vital rate on λ and N(e); thus, management actions that increase the λ of populations of Austrian dragonhead will not increase genetic drift. Our results show that elasticity analyses of N(e) and N(a) can complement elasticity analysis of λ. Moreover, such analyses do not require more data than standard matrix models of population dynamics.     

Use of Integrated Modeling to Enhance Estimates of Population Dynamics Obtained from Limited Data

Abstract:  Demographic data of rare and endangered species are often too sparse to estimate vital rates and population size with sufficient precision for understanding population growth and decline. Yet, the combination of different sources of demographic data into one statistical model holds promise. We applied Bayesian integrated population modeling to demographic data from a colony of the endangered greater horseshoe bats (Rhinolophus ferrumequinum) . Available data were the number of subadults and adults emerging from the colony roost at dusk, the number of newborns from 1991 to 2005, and recapture data of subadults and adults from 2004 and 2005. Survival rates did not differ between sexes, and demographic rates remained constant across time. The greater horseshoe bat is a long-lived species with high survival rates (first year: 0.49 [SD 0.06]; adults: 0.91 [SD 0.02]) and low fecundity (0.74 [SD 0.12]). The yearly average population growth was 4.4% (SD 0.1%) and there were 92 (SD 10) adults in the colony in year 2005. Had we analyzed each data set separately, we would not have been able to estimate fecundity, the estimates of survival would have been less precise, and the estimate of population growth biased. Our results demonstrate that integrated models are suitable for obtaining crucial demographic information from limited data.