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ObjectiveTo analyze Hospital Acquired Infection (HAI) outbreaks using microbial population biology dynamics in order to understand outbreaks as a biological system.DesignComputational modeling study.MethodsThe majority of HAI transmission models describe dynamics on the level of the host rather than on the level of the pathogens themselves. Accordingly, epidemiologists often cannot complete transmission chains without direct evidence of either host-host contact or large reservoir populations. Here, we propose an ecology-based model to explain the transmission of pathogens in hospitals. The model is based upon metapopulation biology, which describes a group of interacting localized populations and island biogeography, which provides a basis for how pathogens may be moving between locales. Computational simulation trials are used to assess the applicability of the model.ResultsResults indicate that pathogens survive for extended periods without the need for large reservoirs by living in localized ephemeral populations while continuously transmitting pathogens to new seed populations. Computational simulations show small populations spending significant portions of time at sizes too small to be detected by most surveillance protocols. The number and type of these ephemeral populations enable the overall pathogen population to be sustained.ConclusionsBy modeling hospital pathogens as a metapopulation, observations characteristic of hospital acquired infection outbreaks for which there has previously been no sufficient biological explanation, including how and why empirically successful interventions work, can now be accounted for using population dynamic hypotheses. Epidemiological links between temporally isolated outbreaks are explained via pathogen population dynamics and potential outbreak intervention targets are identified.

Food chains are short, rarely more than five trophic levels long. The cause of this pattern remains unresolved, and no current hypothesis fully explains this phenomenon. We offer an explanation based on the stability of food chains that have been shifted away from linearity to be more web-like. We start with a simple example of food webs of two to six species arranged so that species consume all those with a trophic level less than their own. The probability of stability, for such “universal omnivory” chains declined strongly with chain length, and was as low as 1% with six level chains but highest for two and three level chains. We further explored the influence of chain length on food web stability by testing food webs with varying levels of connectance that were constructed either randomly or with the niche model. By additionally altering the relative impacts of predators on prey, and vice-versa, we test the role of our assumptions on the relationship between chain length and stability. Food webs characterized by low to moderate degrees of connectance, asymmetrical interactions, and relatively weak density dependence showed a pattern of reduced stability with longer trophic chains. The simple view that food webs characterized by long trophic chains are less stable seems to resolve the long-standing question of why there are so few trophic levels in nature.

Preface, S.E. Jorgensen and R.A. Pastorok Introduction, R.A. Pastorok Methods, R.A. Pastorok and H.R. Akcakaya Results of the Evaluation of Ecological Models: Introduction, R.A. Pastorok Population Models-Scalar Abundance, S. Ferson Population Models-Life History, S. Carroll Population Models-Individual-Based, H.M. Regan Population Models-Metapopulations, H.R. Akcakaya and H. M. Regan Ecosystem Models-Food Webs, S. Carroll Ecosystem Models-Aquatic, S.M. Bartell Ecosystem Models-Terrestrial, C.E. Mackay and R.A. Pastorok Landscape Models-Aquatic and Terrestrial, C.E. Mackay and R.A. Pastorok Toxicity-Extrapolation Models, J.A. Colton Profiles of Selected Models, R.A. Pastorok Enhancing the Use of Ecological Models in Environmental Decision-Making, L.R. Ginzburg and H. R. Akcakaya Conclusions and Recommendations, R.A. Pastorok and L.R. Ginzburg Summary, R.A. Pastorok and H.R. Akcakaya References Appendix A: Fish Population Modeling: Data Needs and Case Study, S.J. Pauwels Appendix B: Classification Systems, K.V. Root Appendix C: Results of the Initial Screening of Ecological Models, Model Analysis Team

In the language of mathematics, one needs minimally two interacting variables (two dimensions) to describe repeatable periodic behaviour, and in the language of density dependence, one needs delayed, not immediate, density dependence to produce cyclicity. Neither language specifies the causal mechanism. There are two major potential mechanisms: exogenous mechanisms involving species interactions as in predator–prey or host–parasite, and endogenous mechanisms such as maternal effects where population growth results from the cross-generational transmission of individual quality. The species interactions view stemming from a major observation of Elton and a simultaneous independent theory by Lotka and Volterra is currently dominant. Most ecologists, when faced with cyclic phenomena, automatically look for an interacting species one step below or above in a food chain in order to find an explanation. Maternal effects hypothesis, verbally suggested in the 1950s, had only found its theoretical implementation in the 1990s. In a relatively short time, the degree of acceptance of this view grew to the level of a ‘minority opinion’ as evidenced by the widely used textbook of Begon et al . This short review attempts to describe the arguments for and against this internal two-dimensional approach.

Much of the focus in evolutionary biology has been on the adaptive differentiation among organisms. It is equally important to understand the processes that result in similarities of structure among systems. Here, we discuss examples of similarities occurring at different ecological scales, from predator–prey relations (attack rates and handling times) through communities (food-web structures) to ecosystem properties. Selection among systemic configurations or patterns that differ in their intrinsic stability should lead generally to increased representation of relatively stable structures. Such nonadaptive, but selective processes that shape ecological communities offer an enticing mechanism for generating widely observed similarities, and have sparked new interest in stability properties. This nonadaptive systemic selection operates not in opposition to, but in parallel with, adaptive evolution.

The cause of mammalian cycles—the rise and fall of populations over a predictable period of time—has remained controversial since these patterns were first observed over a century ago. In spite of extensive work on observable mammalian cycles, the field has remained divided upon what the true cause is, with a majority of opinions attributing it to either predation or to intra-species mechanisms. Here we unite the eigenperiod hypothesis, which describes an internal, maternal effect-based mechanism to explain the cycles’ periods with a recent generalization explaining the amplitude of snowshoe hare cycles in northwestern North America based on initial predator abundance. By explaining the period and the amplitude of the cycle with separate mechanisms, a unified and consistent view of the causation of cycles is reached. Based on our suggested theory, we forecast the next snowshoe hare cycle (predicted peak in 2016) to be of extraordinarily low amplitude.

We focus on two paradoxes of ecological theory: the paradox of enrichment and the enrichment response. Both are counterintuitive theoretical predictions that have received little empirical support. We argue that both enrichment paradoxes could be theoretical artifacts and suggest that further experimental work is necessary to determine whether these paradoxes deserve their current status as ecological axioms.

We address the question of whether there are laws in ecology. Although there has been a great deal of recent interest in this topic, much of the relevant debate has been conducted under some common misconceptions about what laws of nature are. Once these misconceptions are cleared up, the case for ecology having laws is much stronger. Indeed, we suggest that the case for laws in ecology is no better or worse than the case for laws in physics.

The conservation of ecosystems focuses on evaluating individual sites or landscapes based on their component species. To produce a map of conservation values, we developed a method to weight habitat-suitability maps for individual species by species-specific extinction risks. The value of a particular site reflects the importance and magnitude of the threats facing the component species of the ecological community. We applied this approach to a set of species from the California Gap Analysis Project. The resulting map of multispecies conservation values identified the areas with the best habitat for the species most vulnerable to extinction. These methods are flexible and can accommodate the quantity and quality of data available for each individual species in both the development of the habitat-suitability maps and the estimation of the extinction risks. Additionally, the multispecies conservation value can accommodate specific conservation goals, such as preservation of local endemics, making it useful for prioritizing conservation and management actions. This approach provides an estimate of the ecological worth of a site based on habitat characteristics and quantitative models in terms of all the ecological components of a site, rather than a single threatened or endangered species. Resumen: La conservacion de los ecosistemas se enfoca en la evaluacion de sitios individuales o paisajes en base a las especies que lo componen. Para producir un mapa de valores para la conservacion, desarrollamos un metodo que valora mapas de aptitud del habitat para especies a nivel individual en base a los riesgos de extincion especie-especificos. El valor de un sitio en particular refleja la importancia y la magnitud de las amenazas que enfrentan las especies que componen la comunidad ecologica. Aplicamos esta metodologia a un grupo de especies del Proyecto de Analisis de Aberturas de California. El mapa de valores de conservacion para multiples especies resultante identifico las areas con el mejor habitat para las especies mas vulnerables a la extincion. Estos metodos son flexibles y pueden abarcar la cantidad y calidad de los datos disponibles para cada especie individual tanto para el desarrollo de mapas de aptitud del habitat, como para la eliminacion de los riesgos de extincion. Ademas, los valores de conservacion multi-especie pueden abarcar metas especificas de conservacion, como lo es la preservacion de endemias locales, haciendolos utiles para priorizar las acciones de conservacion y manejo. Esta metodologia provee una estimacion del merito ecologico de un sitio en base a las caracteristicas y modelos cuantitativos en terminos de todos los componentes ecologicos de un sitio, y no en una sola especie amenazada o en peligro.

The occurrence of an appreciable phase shift between the predator and prey curves is a characteristic signature of predator–prey cycles. The magnitude of the phase shift can be used for assessing whether the direct effect of predation is likely to cause the observed cyclic dynamics. The statistical estimation of the phase shift requires having simultaneous, long-term data series for predator and prey in the same locality, a condition that is almost never satisfied by long-term data of most cyclic populations. A method for estimating the magnitude of the phase shift between the predator and prey trajectories using only single species data. This method is applied to two cases in which predation has been suggested to be the ecological cause of the cycles: the lynx–hare cycles in boreal Canada and the gyrfalcon–ptarmigan cycles in northern Iceland. The estimates of the phase shift indicate that while the lynx–hare cycles are unlikely to be due by the direct effect of lynx predation, those of gyrfalcon–ptarmigan are consistent with predator–prey causation.

1. Voles undergo pronounced oscillations over periods of 3–5 years in northern Europe. A latitudinal gradient of cycle periods and amplitudes has been reported for Fennoscandia, with periods and amplitudes increasing towards northern latitudes. 2. This study formulates a discrete time model based on maternal effects to explain the density fluctuation patterns of microtine rodents. The phenotypic transmission of quality from mothers to offspring generates delayed density dependence, which produces cyclic behaviour in the model. 3. The dynamic patterns predicted by the maternal effect model agree with data. We conclude that the maternal effect hypothesis is a plausible, parsimonious explanation for vole-density cycles in northern Europe.

Results from toxicological bioassays can express the likely impact of environmental contamination on biochemical function, histopathology, development, reproduction and survivorship. However, justifying environmental regulatory decisions and management plans requires predictions of the consequent effects on ecological populations and communities. Although extrapolating the results of toxicity bioassays to potential effects on the ecosystem may be beyond the current scientific capacity of ecology, it is possible to make detailed forecasts at the level of a population. We give examples in which toxicological impacts are either magnified or diminished by population-dynamic phenomena and argue that ecological risk assessments should be conducted at a level no lower than the population. Although methods recently proposed by EPA acknowledge that ecological risk evaluations should reflect population-level effects, they adopt approaches from human health risk analysis that focus on individuals.

Conflict between ratio-dependent and prey-dependent views of trophic in- teractions finds its simplest resolution in the comparison of steady-state responses of trophic chains to increases in primary productivity. We analyze data on trophic abundances of lake ecosystems with a general trophic-chain model that is intermediate between prey dependence and ratio dependence, and can describe either of the two extremes, depending on parameter values. We estimate, for all trophic levels, the set of interference coefficients that predicts the observed statistical relationship between biomasses of adjacent trophic levels. This constitutes a test of two competing theories, since the model we use is a prey-dependent model if all interference coefficients are -O, and a ratio-dependent model if they are 1. The results show that the observed relationships among trophic levels in lake ecosystems are compatible with a ratio-dependent parameterization of this model, with interference distributed relatively evenly across trophic chains, and are incompatible with a pure prey- dependent parameterization. We suggest that approximate ratio dependence applied uni- formly across trophic chains is a more plausible description of lake ecosystems than either pure prey dependence (non-interference) or "concentrated interference" (prey dependence at some trophic levels and partial interference in others).

Recent papers opposing ratio dependence focus on four main criticisms: (1) the empirical evidence we present is insufficient or biased, (2) ratio-dependent models exhibit pathological behavior, (3) ratio dependence lacks a logical or mechanistic base, and (4) more general models incorporate both prey and ratio dependence and there is no need for either of the two simplifications. We review these arguments in the light of empirical evidence from field and experimental studies. We argue that (1) empirical evidence shows that most natural systems are closer to ratio dependence than to prey dependence, (2) pathological dynamics in a mathematical sense is not only realistic, but the lack of such dynamics in prey-dependent models actually makes them pathological in a biological sense, (3) the mechanistic base of ratio dependence is (direct and indirect) interference and resource sharing, and (4) although more general models (with extra parameters) can never fit natural patterns worse than either prey- or ratio-dependent models, there are theoretical, practical, and pedagogical reasons for attempting to find simpler models that can capture the essential dynamics of natural systems.

Ratio-dependent and prey-dependent models of trophic interactions make very different predictions about the steady-state (equilibrial) properties of ecosystems, such as the response of equilibrium abundance and biomass of organisms in each trophic level to increased primary productivity or nutrient input. Prey-dependent theory predicts alter- nating positive, negative, and zero responses of trophic levels to increased productivity, whereas ratio-dependent theory predicts proportional increase in all trophic level bio- masses. We analyzed data on the nutrient input and the biomasses of phytoplankton, zooplankton, and fish across lakes to distinguish between ratio-dependent and prey-de- pendent models. The results show parallel increases in all trophic levels as a result of increased nutrient input, demonstrating that natural systems are closer to ratio dependence than to prey dependence.

The probability of extinction is sensitive to the presence and character of density dependence controlling the dynamics of a population. This means that our capacity to estimate a population's risks of extinction under varying environmental conditions or competing management re- gimes is linked to our ability to reconstruct from data the density-dependence relationships governing the natural dy- namics, especially when data do not reveal a trend of pop- ulation growth or decline. In an example using Gadus morhua, we show that even 10- or 20-year data sets are too short to make precise estimates of these risks. We also ob- serve, however, that under moderate or weak density depen- dence, the computed risks are lower than when density de- pendence is not included in the model. We propose, therefore, that when available data sets are insufficient for recon- structing reliable measurements of density dependence, con- servative estimates of extinction probabilities can be made from models that simply omit density dependence. Resumen: La probabilidad de extinci6n es sensible a la presencia y al cardcter de la dependencia de densidad que controla la dinamica de una poblaci6n. Esto significa que nuestra capacidad para estimar los riesgos de extinci6n de una poblacion bajo condiciones ambientales cambiantes, o diferentes regimenes de manejo, esta relacionada a nuestra capacidad de reconstruir, en base a datos, las relaciones de dependencia de densidad que gobiernan la dinamica natu- ral de poblaciones, especialmente cuando no se dispone de informaci6n que revele tendencias de crecimiento o decli- naci6n de poblaciones. En un ejemplo, utilizando Gadus morhua, demostramos que aun los datos sobre un periodo de 10 6 20 anios son insuficientes para hacer estimaciones pre- cisas sobre estos riesgos. Sin embargo, observamos que in- cluso en una situaci6n de dependencia de densidad mo- derada o debil, los riesgos calculados son mas bajos que cuando la dependencia de densidad no es incluida en el modelo. Por ello proponemos, que, cuando no se dispone de datos suficientes para reconstruir estimados confiables de dependencia de densidad, se pueden hacer estimaciones con- servadoras de probabilidades de extinci6n a partir de mo- delos que simplemente omiten los aspectos de dependencia de densidad.

Consumer-resource system dynamics hinge upon the rate at which consumers capture, consume, and convert resources into biomass. In classical functional and numerical response theory, this rate is assumed to depend on resource density but not on consumer density (reviewed in Jeschke et al. [2002]). In assuming that both densities determine this rate, consumer-dependent func tional responses (e.g., Hassell and Varley 1969, Bed dington 1975, DeAngelis et al. 1975, Arditi and Ginzburg 1989) challenge the resource-dependent tradi tion. This challenge has produced a long-standing debate (reviewed in Abrams and Ginzburg 2000). The traditional approach of fitting functional response models to time series data has yielded equivocal results (e.g., Jost and Arditi 2001) and may not be capable of resolving the debate (Lundberg and Fryxell 1995). In a recent issue of Ecology, Fussmann et al. (2005) tried to enrich the debate with empirical data. They described functional response experiments in the rotifer-algae system Brachionus calyciflorus-Monoraphidium minutum that detected consumer dependence only at unnaturally high Brachionus densities and concluded that consumer dependence plays only a minor rule for planktonic rotifers in natural environments. Here, we outline why this conclusion is an over-interpretation of their results. Their experimental approach only considers direct physical interference between Brachionus and excludes all other and more important forms of consumer dependent effects (e.g., chemically mediated interfer

1. Predator−prey models that abide by the conversion rule (reproduction rate of predators is a function of the consumption rate) are more plausible. 2. Although the conversion rule is quite general, many predator−prey models in current ecological literature fail to coordinate the arguments of the functional and numerical responses.

An impressive fit to historical data suggests to biologists that a given ecological model is highly valid. Models often achieve this fit at the expense of exaggerated complexity that is not justified by empirical evidence. Because overfitted theories complement the traditional assumption that ecology is 'messy', they generally remain unquestioned. Using predation theory as an example, we suggest that a fit-driven appraisal of model value is commonly misdirected; although fit to historical data can be important, the simplicity and generality of a theory--and thus its ecological value--are of comparable importance. In particular, we argue that theories whose complexity greatly exceeds the complexity of the problem that they address should be rejected. We suggest heuristics for distinguishing between valuable ecological theories and their overfitted brethren.

We thank the editor in chief, Alan Hastings, for giving us the opportunity to publish this response to the critical paper in this issue (Barraquand 2013). Since we were asked to write a short response, we will focus only on the author’s main point. The critique addresses many details of our book (Arditi and Ginzburg 2012), but responding to all of it would require repeating much of the book because it already contains most answers. The controversy about ratio dependence was substantially settled with the joint paper of Abrams and Ginzburg (2000). So, focusing only on the author’s main point will lead us to an explanation of how this critique originates and will allow us to address a more general issue that may be of interest to the readers of Theoretical Ecology. The main argument constructed by Frederic Barraquand (FB) is that the prey-dependent model is a “straw man” artificially erected by us in order to cut it down in favor of the opposing “limit myth” of ratio dependence. FB’s position is that there are many other models besides these two classes, and all have their places under the sun; different models are needed for different purposes. The latter statement is so general that it is bound to be correct. We never said that the ratio-dependent model would give an exact description of every existing trophic community. What we say is that it is a good “null model,” i.e., a good starting point. All ecologists, even the most empirical, have some theory in their minds, and what ecologists view as the “default theory” can serve as another definition of the null model. Our meaning in this regard was clear, as shown by the various reviewers who understood fully our book’s purpose (DeAngelis 2013; Fryxell 2013; Krebs 2013; Peterson 2013). (We note in passing that, while FB uses some of Krebs’s work on cycles in support of his critique, Charles Krebs actually wrote a very favorable review of our book.) As we explained in our book, our theory can be traced back to a number of precursors; we mentioned Kolmogorov, Leslie (in part only), and Contois, and we recently found out that Ivlev too had been led to the same idea in his work with fish (Ivlev 1961). Both Contois and Ivlev were experimentalists and developed ratio-dependent models on empirical grounds. Although FB calls for pragmatism, he hardly mentions the many direct tests of functional responses against data that we present in our book, chapter 2. There, we show that most experimental estimates of interference fall on a spectrum of intermediate values, but closer to the ratio-dependent end than to the prey-dependent. If we simplify by choosing the ratiodependent end, not only do we gain in parsimony (admittedly, a little), but we obtain a very satisfactory model on theoretical grounds because of its symmetry (see below). FB’s proposition to use various models to explain a variety of trophic relations is unsatisfactory. Given that our theory, which he criticizes, unifies the explanation of all of these phenomena, we see no compelling reason for preferring a multiplicity of approaches. Moreover, beyond criticism of our theory, FB targets the whole theoretical school that uses deterministic models. He suggests instead stochastic population models and time series analysis. We have nothing against log-linear Gompertz-like predator–prey stochastic R. Arditi Ecologie et Evolution, Universite Pierre et Marie Curie, Sorbonne Universites, Case 237, 75231 Paris Cedex 05, France

The analysis of time series of 20 species of forest insects and vertebrates showed that cyclic populations take longer, typically 50% more time, to grow than to decline. The asymmetry of cycles does not differ significantly among different taxa (insects, small and large mammals and birds) and is not associated with the periods of oscillation. The asymmetric nature of population cycles may be due to the existence of a maximum value of the per capita growth rate that constrains the growing phase of the cycle but does not impose a limit in the rate of decline. By including the constraint on the population growth rate, a second order model can produce stable limit cycles regardless of the actual ecological mechanism generating the cyclic dynamics.

Many species of forest Lepidoptera have cyclic population dynamics. Although there are numerous potential causes, including interactions with predators, parasitoids, pathogens, and food-plant quality, strongly density-dependent interactions are often difficult to demonstrate. Both autocorrelation analysis and attractor-reconstruction methods have recently been applied to a number of species' time series. Results suggest that complex dynamics, i.e. cycles or deterministic chaos, may be more prevalent than once thought, and that higher-dimensioned models are necessary. We develop a two-dimensional difference equation model that relates the average quality of individuals to patterns of abundance

Keystone species and community effects of biological introductions planned introductions in biological control surface transport of micro-organisms soil and groundwater transport of micro-organisms aerial transport of bacteria physiochemical and biological factors affect the transfer of genetic information among micro-organisms genetic exchange and genetic stability in bacterial populations models for the population dynamics of transposable elements in bacteria fitness and gene stability quantitative approaches to questions about the spread of recombinant genes or recombinant organisms.

A simple theoretical argument shows that the evolutionary process will look gradual if it is considered on too fine or too coarse a time scale. There exists an intermediate time scale in which the distribution of evolutionary rates will appear as bimodal.

Approaches to modeling the evolution of community structures are reviewed and criticized; a new approach is proposed. New species introduced to a model community are chosen as “ecologically continuous” mutants of their progenitors. Although competition is strong in every step of such a process, the community is shown to evolve towards non-interaction.

In continuous-time predator-prey models, the per capita rate of consumption (the functional response or “trophic function”) is usually interpreted as a behavioral phenomenon. The classical assumptions are that predators encounter prey at random and that the trophic function depends on prey abundance only. We argue that this approach is not always appropriate. The trophic function must be considered on the slow time scale of population dynamics at which the models operate—not on the fast behavioral time scale. We propose that, in cases where these two time scales differ, it is reasonable to assume that the trophic function depends on the ratio of prey to predator abundances. Several field and laboratory observations support this hypothesis. We compare the consequences of the two types of dependence with respect to the dynamical properties of the models and the responses of population equilibria to variations in primary production. In traditional prey-dependent models, only the predator population responds to primary production, while both levels respond in ratio-dependent models. This result is generalized to food chains. We suggest that the ratio-dependent form of the trophic function is a simple way of accounting for many types of heterogeneity that occur in large scale natural systems, while the prey-dependent form may be more appropriate for homogeneous systems like chemostats.

The stability problem for multiallelic genetic polymorphisms for n populations coexisting in stable ecosystems is considered. Taking into account only density-dependent interactions a generalization of Fisher's theorem is obtained. Specifically, the average fitness of a population must be locally maximized subject to the constraint that the equilibrium population sizes are fixed if the polymorphism is stable. Further, the quasi-equilibrium population sizes Ni corresponding to fixing the genetic structure of all populations in the ecosystem at various values have extrema at the equilibrium point. Such an equilibrium can be a maximum, minimum or saddle point depending upon the type of ecosystem under consideration. A simple test separating these cases on the basis of the so-called ecosystem matrix is suggested. The general equilibrium problem is reformulated as a maximization problem under some restrictions. Conditions under which the maximized function can be expressed as sigma ni=1 Ni are formulated.