Setting population targets for mammals using body mass as a predictor of population persistence

Conservation planning and biodiversity assessments need quantitative targets to optimize planning options and assess the adequacy of current species protection. However, targets aiming at persistence require population‐specific data, which limit their use in favor of fixed and nonspecific targets, likely leading to unequal distribution of conservation efforts among species. We devised a method to derive equitable population targets; that is, quantitative targets of population size that ensure equal probabilities of persistence across a set of species and that can be easily inferred from species‐specific traits. In our method, we used models of population dynamics across a range of life‐history traits related to species’ body mass to estimate minimum viable population targets. We applied our method to a range of body masses of mammals, from 2 g to 3825 kg. The minimum viable population targets decreased asymptotically with increasing body mass and were on the same order of magnitude as minimum viable population estimates from species‐ and context‐specific studies. Our approach provides a compromise between pragmatic, nonspecific population targets and detailed context‐specific estimates of population viability for which only limited data are available. It enables a first estimation of species‐specific population targets based on a readily available trait and thus allows setting equitable targets for population persistence in large‐scale and multispecies conservation assessments and planning.     

Information processing in models for density-dependent emigration: A comparison

Density-dependent emigration has been recognized as a fitness enhancing strategy. Yet, especially in the modelling literature there is no consensus about how density-dependent emigration should quantitatively be incorporated into metapopulation models. In this paper we compare the performance of five different dispersal strategies (defined by the functional link between density and emigration probability). Four of these strategies are based on published functional relationships between local population density and emigration probability, one assumes density-independent dispersal. We use individual-based simulations of time-discrete metapopulation dynamics and conduct evolution experiments for a broad range of values for dispersal mortality and environmental stochasticity. For each set of these conditions we analyze the evolution of emigration rates in ‘monoculture experiments’ (with only one type of dispersal strategy used by all individuals in the metapopulation) as well as in selection experiments that allow a pair-wise comparison of the performance of each functional type. We find that a single-parameter ‘asymptotic threshold’ strategy - derived from the marginal value theorem - with a decelerating increase of emigration rate with increasing population density, out-competes any other strategy, i.e. density-independent emigration, a ‘linear threshold’ strategy and a flexible three-parameter strategy. Only when environmental conditions select for extremely high emigration probabilities (close to one), strategies may perform approximately equally. A simple threshold strategy derived for the case of continuous population growth performs even worse than the density-independent strategy. As the functional type of the dispersal function implemented in metapopulation models may severely affect predictions concerning the survival of populations, range expansion, or community changes we clearly recommend to carefully select adequate functions to model density-dependent dispersal.     

A comparison of three Eulerian numerical methods for fractional-order transport models

Tracer transport in complex systems like turbulent flows or heterogeneous porous media is now more and more regarded as a non-local process that can hardly be represented by second-order diffusion models. In this work, we consider diffusion models that assume that tracer particles follow a heavy-tail Lévy distribution, which allows for large displacements. We show that such an assumption leads to a fractional-order diffusion operator in the governing equation for tracer concentration. A comparison of three Eulerian numerical methods to discretize that equation is then performed. These consist of the finite difference, finite element and spectral element methods. We suggest that non-local methods, like the spectral element method, are better suited to transport models with fractional-order diffusion operators.     

Divergence in sink contributions to population persistence

Population sinks present unique conservation challenges. The loss of individuals in sinks can compromise persistence; but conversely, sinks can improve viability by improving connectivity and facilitating the recolonization of vacant sources. To assess the contribution of sinks to regional population persistence of declining populations, we simulated source–sink dynamics for 3 very different endangered species: Black‐capped Vireos (Vireo atricapilla) at Fort Hood, Texas, Ord's kangaroo rats (Dipodomys ordii) in Alberta, and Northern Spotted Owls (Strix occidentalis caurina) in the northwestern United States. We used empirical data from these case studies to parameterize spatially explicit individual‐based models. We then used the models to quantify population abundance and persistence with and without long‐term sinks. The contributions of sink habitats varied widely. Sinks were detrimental, particularly when they functioned as strong sinks with few emigrants in declining populations (e.g., Alberta's Ord's kangaroo rat) and benign in robust populations (e.g., Black‐capped Vireos) when Brown‐headed Cowbird (Molothrus ater) parasitism was controlled. Sinks, including ecological traps, were also crucial in delaying declines when there were few sources (e.g., in Black‐capped Vireo populations with no Cowbird control). Sink contributions were also nuanced. For example, sinks that supported large, variable populations were subject to greater extinction risk (e.g., Northern Spotted Owls). In each of our case studies, new context‐dependent sinks emerged, underscoring the dynamic nature of sources and sinks and the need for frequent re‐assessment. Our results imply that management actions based on assumptions that sink habitats are generally harmful or helpful risk undermining conservation efforts for declining populations.     

Robust population management under uncertainty for structured population models.

Structured population models are increasingly used in decision making, but typically have many entries that are unknown or highly uncertain. We present an approach for the systematic analysis of the effect of uncertainties on long-term population growth or decay. Many decisions for threatened and endangered species are made with poor or no information. We can still make decisions under these circumstances in a manner that is highly defensible, even without making assumptions about the distribution of uncertainty, or limiting ourselves to discussions of single, infinitesimally small changes in the parameters. Suppose that the model (determined by the data) for the population in question predicts long-term growth. Our goal is to determine how uncertain the data can be before the model loses this property. Some uncertainties will maintain long-term growth, and some will lead to long-term decay. The uncertainties are typically structured, and can be described by several parameters. We show how to determine which parameters maintain long-term growth. We illustrate the advantages of the method by applying it to a Peregrine Falcon population. The U.S. Fish and Wildlife Service recently decided to allow minimal harvesting of Peregrine Falcons after their recent removal from the Endangered Species List. Based on published demographic rates, we find that an asymptotic growth rate lambda > 1 is guaranteed with 5% harvest rate up to 3% error in adult survival if no two-year-olds breed, and up to 11% error if all two-year-olds breed. If a population growth rate of 3% or greater is desired, the acceptable error in adult survival decreases to between 1% and 6% depending of the proportion of two-year-olds that breed. These results clearly show the interactions between uncertainties in different parameters, and suggest that a harvest decision at this stage may be premature without solid data on adult survival and the frequency of breeding by young adults.     

Analysing sperm competition data: simple models for predicting mechanisms

Summary Prospective models are developed for analysing sperm competition data so as to predict the underlying mechanisms determining paternity in multiply mated females. The models require: 1) estimations of proportion of offspring sired by the last male to mate (P ₂), 2) knowledge of the number of sperm transferred by each male, and 3) knowledge of the sperm storage capacity of the female, should this be limited. They will distinguish between raffles (sperm mixing without displacement) and sperm displacement mechanisms. The sensitivity of the techniques can be increased by manipulating the number of sperm transferred by each male. Typically, this can be done by manipulating copula duration or number of ejaculations, given a knowledge of the rate of sperm transfer. Data from two contrasting insect species are fitted to the models to demonstrate the techniques. These models are prospective only, and their limitations are discussed. The principal limitation is that we assume that sperm used for fertilization mix randomly in a fertilization set immediately prior to fertilization; in reality this may be difficult to identify. When sperm mixing is very rapid, the fertilization set will often be equivalent to the sperm stores, but with slow mixing, the fertilization set may be equivalent to a much more restricted zone and may change with time. Offprint requests to: G.A. Parker     

A note on density dependence in population models

One of the most studied phenomena in ecology is density dependent regulation. The model most frequently used to study this behaviour is the theta-logistic model. However, disagreement has developed within the ecology community pertaining to the interpretation of this model’s parameters, and thus as to appropriate values for the parameters to assume. In particular, the parameter θ$\theta$ has been allowed to take negative values, resulting in the ‘growth rate parameter’ estimated to be negative for species which are extant and exhibit no signs of becoming extinct in the short-term. Here we explain this phenomenon by formulating the theta-logistic model in the manner in which the original logistic model was formulated by Verhulst (1838), in doing so providing a simple interpretation of model parameters and thus restrictions on values the parameters may assume. We conclude that θ$\theta$ should (almost always) be restricted to values greater than −1$-1$. This has implications for studies assessing the form of density dependence from data. Additionally, another model appearing in the literature is presented which provides a more flexible model of density dependence at the expense of only one additional parameter.     

QSAR models for predicting the toxicity of halogenated phenols to Tetrahymena

Halogenated phenols are industrial pollutants which may cause serious damage to the environment. In this work, a two-dimensional (2D) and two three-dimensional (3D) quantitative structure–activity relationship models for the toxicity prediction of halogenated phenols in Tetrahymena were developed. The structural factors that mainly influence toxicity were explored, agreeing with previously reported data. The results obtained with the 3D model were in agreement with those obtained with the 2D model. According to our findings, several new molecules with different predicted activities were designed.     

Use of individual-based models for population parameters estimation

A method for parameters estimation of stage-specific mortality and fecundity rate functions in poikilotherm organisms, and in particular for arthropod structured population, is proposed. The application of this method requires three types of information: stage-frequency data of a sampled population, development rate function and time evolution of forcing variables affecting the rate functions. By means of an individual-based model (a microscopic model) the number of eggs produced by the adults is generated starting from the number of individuals collected at each sampling time. Using a compartmental model (a macroscopic model) a stage-structured population dynamics is described and compared with observations. Non-linear regression methods based on least square principle are used to estimate the optimal parameters of the mortality and fecundity rate functions combining microscopic and macroscopic models. As a case study, the parameter estimation of the temperature-dependent mortality function of olives fruit fly Bactrocera oleae is presented.     

Habitat selection models to account for seasonal persistence in radio telemetry data

Models for the analysis of habitat selection data incorporate covariates in an independent multinomial selections model (McCracken et al. 1998) Ramsey and Usner 2003 and an extension of that model to include a persistence parameter (2003). In both cases, all parameters are assumed to be fixed through time. Radio telemetry data collected for habitat selection studies typically consist of animal relocations through time, suggesting the need for an extension to these models. We use a Bayesian approach that allows for the habitat selection probabilities, persistence parameter, or both, to change with season. These extensions are particularly important when movement patterns are expected to differ seasonally and/or when availabilities of habitats change throughout the study period due to weather or migration. We implement and compare the models using radio telemetry data for westslope cutthroat trout in two streams in eastern Oregon.     

Enhancement of semi-theoretical models for predicting peak discharges in breached embankment dams

Environmental Fluid Mechanics - During the application of semi-theoretical models to predict peak discharges for breached embankment dams, it is often encountered to be lack of necessary model...     

Hidden process models for animal population dynamics.

Hidden process models are a conceptually useful and practical way to simultaneously account for process variation in animal population dynamics and measurement errors in observations and estimates made on the population. Process variation, which can be both demographic and environmental, is modeled by linking a series of stochastic and deterministic subprocesses that characterize processes such as birth, survival, maturation, and movement. Observations of the population can be modeled as functions of true abundance with realistic probability distributions to describe observation or estimation error. Computer-intensive procedures, such as sequential Monte Carlo methods or Markov chain Monte Carlo, condition on the observed data to yield estimates of both the underlying true population abundances and the unknown population dynamics parameters. Formulation and fitting of a hidden process model are demonstrated for Sacramento River winter-run chinook salmon (Oncorhynchus tshawytsha).     

Switching state-space models for modeling penguin population dynamics

Environmental and Ecological Statistics - Tracking individual animals through time using mark-recapture methods is the gold standard for understanding how environmental conditions influence...     

Spatial uncertainty analysis of population models

This paper describes an approach for conducting spatial uncertainty analysis of spatial population models, and illustrates the ecological consequences of spatial uncertainty for landscapes with different properties. Spatial population models typically simulate birth, death, and migration on an input map that describes habitat. Typically, only a single “reference” map is available, but we can imagine that a collection of other, slightly different, maps could be drawn to represent a particular species’ habitat. As a first approximation, our approach assumes that spatial uncertainty (i.e., the variation among values assigned to a location by such a collection of maps) is constrained by characteristics of the reference map, regardless of how the map was produced. Our approach produces lower levels of uncertainty than alternative methods used in landscape ecology because we condition our alternative landscapes on local properties of the reference map. Simulated spatial uncertainty was higher near the borders of patches. Consequently, average uncertainty was highest for reference maps with equal proportions of suitable and unsuitable habitat, and no spatial autocorrelation. We used two population viability models to evaluate the ecological consequences of spatial uncertainty for landscapes with different properties. Spatial uncertainty produced larger variation among predictions of a spatially explicit model than those of a spatially implicit model. Spatially explicit model predictions of final female population size varied most among landscapes with enough clustered habitat to allow persistence. In contrast, predictions of population growth rate varied most among landscapes with only enough clustered habitat to support a small population, i.e., near a spatially mediated extinction threshold. We conclude that spatial uncertainty has the greatest effect on persistence when the amount and arrangement of suitable habitat are such that habitat capacity is near the minimum required for persistence.     

Ungulate population dynamics and optimization models

Optimal harvesting strategies for an ungulate population are estimated using stochastic dynamic programming. Data on the Llano Basin white-tailed deer (Odocoileus virginianus) population were used to construct a 2-variable population dynamics model. The model provided the basis for estimating optimal harvesting strategies as a feedback function of the current values of the state variables (prefawning older deer and juveniles). Optimal harvest strategies were insensitive to assumptions about the probability distributions of the stochastic variable (rainfall). The response of the population components to harvesting and the returns obtained from applying optimal strategies were explored through simulation. Mean annual harvest is about 15% of the population. Simplified harvesting strategies based on age-ratios as well as a simplified version based on optimal strategies—but assuming persisting equilibrium juvenile deer density—were compared to optimal strategies through examining values of information. Simplified harvesting strategies lead to a lower harvest over a 50-year simulation period.     

RIVPACS models for predicting the expected macroinvertebrate fauna and assessing the ecological quality of rivers

The European Union Water Framework Directive recognises the need for and value of biological monitoring. This paper reviews the modelling approach known as River Invertebrate Prediction and Classification System (RIVPACS for assessing the ecological quality of river sites using macroinvertebrate sampling. The RIVPACS philosophy is to develop statistical relationships between the fauna and the environmental characteristics of a large set of high quality reference sites which can be used to predict the macroinvertebrate fauna to be expected at any site in the absence of pollution or other environmental stress. The observed fauna at new test sites can then be compared with their site-specific expected fauna to derive indices of ecological quality. All methodological decisions in any such model development have implications for the reliability, precision and robustness of any resulting indices for assessing the ecological quality and ecological grade (‘status’) of individual river stretches. The choice of reference sites and environmental predictor variables, the site classification and discrimination methods, the estimation of the expected fauna, and indices for comparing the agreement, or lack of it, between the observed and expected fauna, are all discussed. The indices are assessed on the reference sites and on a separate test set of 340 sites, which are subject to a wide range of types and degrees of impairment.     

Age-structured population models and their numerical solution

This paper considers the state of the art of the numerical solution of age-structured population models. The different numerical approaches to this kind of problems and the stability and convergence results for them are reviewed. Both characteristic curves methods and finite difference methods are compared with regards to accuracy, efficiency and their qualitative behaviour depending on the compatibility conditions between initial and boundary data of the problems. The paper is the first of a series of two considering the numerical solution of general structured population models.     

Fitting probability models to population dynamics data

Methods for modeling population dynamics in probability using the generalized point process approach are developed. The life history of these populations is such that seasonal reproduction occurs during a short time. Several models are developed and analyzed. Data about two species: colonial spiders (Stegodyphus dumicola) and a migratory bird (wood thrush, Hylocichla mustelina) are used to estimate model parameters with appropriate log maximum likelihood functions. For the spiders, the model is fitted to provide evolutionary feasible colony size based on maximum likelihood estimates of fecundity and survival data. For the migratory bird species, a maximum likelihood estimates are derived for the fecundity and survival rates of young and adult birds and immigration rate. The presented approach allows computation of quantities of interest such as probability of extinction and average time to extinction.