Likelihood ridges and multimodality in population growth rate models

Interconnection between density-regulation and stability in competitive ecological network

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

Separating the effects of climate, bycatch, predation and harvesting on tītī (Ardenna grisea) population dynamics in New Zealand: A model-based assessment

A suite of factors may have contributed to declines in the tītī (sooty shearwater; Ardenna grisea) population in the New Zealand region since at least the 1960s. Recent estimation of the magnitude of most sources of non-natural mortality has presented the opportunity to quantitatively assess the relative importance of these factors. We fit a range of population dynamics models to a time-series of relative abundance data from 1976 until 2005, with the various sources of mortality being modelled at the appropriate part of the life-cycle. We present estimates of effects obtained from the best-fitting model and using model averaging. The best-fitting models explained much of the variation in the abundance index when survival and fecundity were linked to the Southern Oscillation Index, with strong decreases in adult survival, juvenile survival and fecundity being related to El Niño-Southern Oscillation (ENSO) events. Predation by introduced animals, harvesting by humans, and bycatch in fisheries also appear to have contributed to the population decline. It is envisioned that the best-fitting models will form the basis for quantitative assessments of competing management strategies. Our analysis suggests that sustainability of the New Zealand tītī population will be most influenced by climate, in particular by how climate change will affect the frequency and intensity of ENSO events in the future. Removal of the effects of both depredation by introduced predators and harvesting by humans is likely to have fewer benefits for the population than alleviating climate effects.

Elk population dynamics when carrying capacities vary within and among herds

Population and land management relies on understanding population regulation and growth, which may be impacted by variation in population growth parameters within and among populations. We explored the interactions between variation in carrying capacity (K), intrinsic population growth rate (r), and strength of density dependence (β) within and among elk (Cervus elaphus) herds in a small part of the geographic range of the species. We also estimated stochastic fluctuations in abundance around K for each herd. We fit linear Ricker growth models using Bayesian statistics to seven time series of elk population survey data. Our results indicate that K and β varied among herds, and that r and β varied temporally within herds. We also found that herds with smaller K had less stochastic fluctuation in abundances around K, but higher temporal variation in β within herds. Population regulation and the rate of return to the equilibrium abundance is often understood in terms of β, but ecological populations are dynamic systems, and temporal variation in population growth parameters may also influence regulation. Population models which accommodate variation both within and among herds in population growth parameters are necessary, even in mild climates, to fully understand population dynamics and manage populations.

Ecological change points: The strength of density dependence and the loss of history

Change points in the dynamics of animal abundances have extensively been recorded in historical time series records. Little attention has been paid to the theoretical dynamic consequences of such change-points. Here we propose a change-point model of stochastic population dynamics. This investigation embodies a shift of attention from the problem of detecting when a change will occur, to another non-trivial puzzle: using ecological theory to understand and predict the post-breakpoint behavior of the population dynamics. The proposed model and the explicit expressions derived here predict and quantify how density dependence modulates the influence of the pre-breakpoint parameters into the post-breakpoint dynamics. Time series transitioning from one stationary distribution to another contain information about where the process was before the change-point, where is it heading and how long it will take to transition, and here this information is explicitly stated. Importantly, our results provide a direct connection of the strength of density dependence with theoretical properties of dynamic systems, such as the concept of resilience. Finally, we illustrate how to harness such information through maximum likelihood estimation for state-space models, and test the model robustness to widely different forms of compensatory dynamics. The model can be used to estimate important quantities in the theory and practice of population recovery.

Estimation of the dispersal distances of an aphid-borne virus in a patchy landscape

Characterising the spatio-temporal dynamics of pathogens in natura is key to ensuring their efficient prevention and control. However, it is notoriously difficult to estimate dispersal parameters at scales that are relevant to real epidemics. Epidemiological surveys can provide informative data, but parameter estimation can be hampered when the timing of the epidemiological events is uncertain, and in the presence of interactions between disease spread, surveillance, and control. Further complications arise from imperfect detection of disease and from the huge number of data on individual hosts arising from landscape-level surveys. Here, we present a Bayesian framework that overcomes these barriers by integrating over associated uncertainties in a model explicitly combining the processes of disease dispersal, surveillance and control. Using a novel computationally efficient approach to account for patch geometry, we demonstrate that disease dispersal distances can be estimated accurately in a patchy (i.e. fragmented) landscape when disease control is ongoing. Applying this model to data for an aphid-borne virus (Plum pox virus) surveyed for 15 years in 605 orchards, we obtain the first estimate of the distribution of flight distances of infectious aphids at the landscape scale. About 50% of aphid flights terminate beyond 90 m, which implies that most infectious aphids leaving a tree land outside the bounds of a 1-ha orchard. Moreover, long-distance flights are not rare-10% of flights exceed 1 km. By their impact on our quantitative understanding of winged aphid dispersal, these results can inform the design of management strategies for plant viruses, which are mainly aphid-borne.

State-space models' dirty little secrets: even simple linear Gaussian models can have estimation problems

State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results.

Overcompensation and phase effects in a cyclic common vole population: between first and second-order cycles

Population cycles in voles are often thought to be generated by one-year delayed density dependence on the annual population growth rate. In common voles, however, it has been suggested by Turchin (2003) that some populations exhibit first-order cycles, resulting from strong overcompensation (i.e. carrying capacity overshoots in peak years, with only an effect of the current year abundance on annual growth rates). We focus on a common vole (Microtus arvalis) population from western France that exhibits 3-year cycles. Several overcompensating nonlinear models for populations dynamics are fitted to the data, notably those of Hassell, and Maynard-Smith and Slatkin. Overcompensating direct density dependence (DD) provides a satisfactory description of winter crashes, and one-year delayed density dependence is not responsible for the crashes, thus these are not classical second-order cycles. A phase-driven modulation of direct density dependence maintains a low-phase, explaining why the cycles last three years instead of two. Our analyses suggest that some of this phase dependence can be expressed as one-year delayed DD, but phase dependence provides a better description. Hence, modelling suggests that cycles in this population are first-order cycles with a low phase after peaks, rather than fully second-order cycles. However, based on the popular log-linear second-order autoregressive model, we would conclude only that negative delayed density dependence exists. The additive structure of this model cannot show when delayed DD occurs (here, during lows rather than peaks). Our analyses thus call into question the automated use of second-order log-linear models, and suggests that more attention should be given to non-(log)linear models when studying cyclic populations. From a biological viewpoint, the fast crashes through overcompensation that we found suggest they might be caused by parasites or food rather than predators, though predators might have a role in maintaining the low phase and spatial synchrony.

Quantifying extinction probabilities from sighting records: inference and uncertainties

Methods are needed to estimate the probability that a population is extinct, whether to underpin decisions regarding the continuation of a invasive species eradication program, or to decide whether further searches for a rare and endangered species could be warranted. Current models for inferring extinction probability based on sighting data typically assume a constant or declining sighting rate. We develop methods to analyse these models in a Bayesian framework to estimate detection and survival probabilities of a population conditional on sighting data. We note, however, that the assumption of a constant or declining sighting rate may be hard to justify, especially for incursions of invasive species with potentially positive population growth rates. We therefore explored introducing additional process complexity via density-dependent survival and detection probabilities, with population density no longer constrained to be constant or decreasing. These models were applied to sparse carcass discoveries associated with the recent incursion of the European red fox (Vulpes vulpes) into Tasmania, Australia. While a simple model provided apparently precise estimates of parameters and extinction probability, estimates arising from the more complex model were much more uncertain, with the sparse data unable to clearly resolve the underlying population processes. The outcome of this analysis was a much higher possibility of population persistence. We conclude that if it is safe to assume detection and survival parameters are constant, then existing models can be readily applied to sighting data to estimate extinction probability. If not, methods reliant on these simple assumptions are likely overstating their accuracy, and their use to underpin decision-making potentially fraught. Instead, researchers will need to more carefully specify priors about possible population processes.

Spatial climate patterns explain negligible variation in strength of compensatory density feedbacks in birds and mammals

The use of long-term population data to separate the demographic role of climate from density-modified demographic processes has become a major topic of ecological investigation over the last two decades. Although the ecological and evolutionary mechanisms that determine the strength of density feedbacks are now well understood, the degree to which climate gradients shape those processes across taxa and broad spatial scales remains unclear. Intuitively, harsh or highly variable environmental conditions should weaken compensatory density feedbacks because populations are hypothetically unable to achieve or maintain densities at which social and trophic interactions (e.g., competition, parasitism, predation, disease) might systematically reduce population growth. Here we investigate variation in the strength of compensatory density feedback, from long-term time series of abundance over 146 species of birds and mammals, in response to spatial gradients of broad-scale temperature precipitation variables covering 97 localities in 28 countries. We use information-theoretic metrics to rank phylogenetic generalized least-squares regression models that control for sample size (time-series length) and phylogenetic non-independence. Climatic factors explained < 1% of the remaining variation in density-feedback strength across species, with the highest non-control, model-averaged effect sizes related to extreme precipitation variables. We could not link our results directly to other published studies, because ecologists use contrasting responses, predictors and statistical approaches to correlate density feedback and climate--at the expense of comparability in a macroecological context. Censuses of multiple populations within a given species, and a priori knowledge of the spatial scales at which density feedbacks interact with climate, seem to be necessary to determine cross-taxa variation in this phenomenon. Despite the availability of robust modelling tools, the appropriate data have not yet been gathered for most species, meaning that we cannot yet make any robust generalisations about how demographic feedbacks interact with climate.

Trend and fluctuations: analysis and design of population dynamics measurements in replicate ecosystems

The dynamical evolution of complex systems is often intrinsically stochastic and subject to external random forces. In order to study the resulting variability in dynamics, it is essential to make measurements on replicate systems and to separate arbitrary variation of the average dynamics of these replicates from fluctuations around the average dynamics. Here we do so for population time-series data from replicate ecosystems sharing a common average dynamics or common trend. We explain how model parameters, including the effective interactions between species and dynamical noise, can be estimated from the data and how replication reduces errors in these estimates. For this, it is essential that the model can fit a variety of average dynamics. We then show how one can judge the quality of a model, compare alternate models, and determine which combinations of parameters are poorly determined by the data. In addition we show how replicate population dynamics experiments could be designed to optimize the acquired information of interest about the systems. Our approach is illustrated on a set of time series gathered from replicate microbial closed ecosystems.

A population growth trend analysis for Neotricula aperta, the snail intermediate host of Schistosoma mekongi, after construction of the Pak-Mun dam

Background

The Pak-Mun dam is a controversial hydro-power project on the Mun River in Northeast Thailand. The dam is sited in a habitat of the freshwater snail Neotricula aperta, which is the intermediate host for the parasitic blood-fluke Schistosoma mekongi causing Mekong schistosomiasis in humans in Cambodia and Laos. Few data are available which can be used to assess the effects of water resource development on N. aperta. The aim of this study was to obtain data and to analyze the possible impact of the dam on N. aperta population growth.

Methodology/Principal Findings

Estimated population densities were recorded for an N. aperta population in the Mun River 27 km upstream of Pak-Mun, from 1990 to 2011. The Pak-Mul dam began to operate in 1994. Population growth was modeled using a linear mixed model expression of a modified Gompertz stochastic state-space exponential growth model. The N. aperta population was found to be quite stable, with the estimated growth parameter not significantly different from zero. Nevertheless, some marked changes in snail population density were observed which were coincident with changes in dam operation policy.

Conclusions/Significance

The study found that there has been no marked increase in N. aperta population growth following operation of the Pak-Mun dam. The analysis did indicate a large and statistically significant increase in population density immediately after the dam came into operation; however, this increase was not persistent. The study has provided the first vital baseline data on N. aperta population behavior near to the Pak-Mun dam and suggests that the operation policy of the dam may have an impact on snail population density. Nevertheless, additional studies are required for other N. aperta populations in the Mun River and for an extended time series, to confirm or refine the findings of this work.

There is much controversy over the effects of water resource development on the transmission of schistosomiasis in the lower Mekong Basin. Impact assessments are urgently required because there are currently 12 such projects planned in the region. The key to understanding the effects of impoundment is the impact on the snail intermediate host, which, in the case of Mekong schistosomiasis, is Neotricula aperta. Surprisingly, we have almost no data on N. aperta population trends nor on the impact of dams. To address this, the present work focused on a population near the Pak-Mun dam in Thailand. The analysis suggested that N. aperta populations were not growing significantly over the study period (1990–2011), but that the dam may have affected a spike in population density immediately after its completion. The study also revealed changes in density that were coincident on changes in operation of the dam; suggesting that keeping the dam open might lower snail population densities. This is the first scientific assessment of the impact of the Pak-Mun dam on N. aperta and suggests that dams of this kind may affect snail population density. The study also indicates an urgent need for additional independent observations and continuing regular surveys.

Model-free forecasting outperforms the correct mechanistic model for simulated and experimental data

Accurate predictions of species abundance remain one of the most vexing challenges in ecology. This observation is perhaps unsurprising, because population dynamics are often strongly forced and highly nonlinear. Recently, however, numerous statistical techniques have been proposed for fitting highly parameterized mechanistic models to complex time series, potentially providing the machinery necessary for generating useful predictions. Alternatively, there is a wide variety of comparatively simple model-free forecasting methods that could be used to predict abundance. Here we pose a rather conservative challenge and ask whether a correctly specified mechanistic model, fit with commonly used statistical techniques, can provide better forecasts than simple model-free methods for ecological systems with noisy nonlinear dynamics. Using four different control models and seven experimental time series of flour beetles, we found that Markov chain Monte Carlo procedures for fitting mechanistic models often converged on best-fit parameterizations far different from the known parameters. As a result, the correctly specified models provided inaccurate forecasts and incorrect inferences. In contrast, a model-free method based on state-space reconstruction gave the most accurate short-term forecasts, even while using only a single time series from the multivariate system. Considering the recent push for ecosystem-based management and the increasing call for ecological predictions, our results suggest that a flexible model-free approach may be the most promising way forward.

Modeling extreme risks in ecology

Extreme risks in ecology are typified by circumstances in which data are sporadic or unavailable, understanding is poor, and decisions are urgently needed. Expert judgments are pervasive and disagreements among experts are commonplace. We outline approaches to evaluating extreme risks in ecology that rely on stochastic simulation, with a particular focus on methods to evaluate the likelihood of extinction and quasi-extinction of threatened species, and the likelihood of establishment and spread of invasive pests. We evaluate the importance of assumptions in these assessments and the potential of some new approaches to account for these uncertainties, including hierarchical estimation procedures and generalized extreme value distributions. We conclude by examining the treatment of consequences in extreme risk analysis in ecology and how expert judgment may better be harnessed to evaluate extreme risks.

Strength of density feedback in census data increases from slow to fast life histories

Life-history theory predicts an increasing rate of population growth among species arranged along a continuum from slow to fast life histories. We examine the effects of this continuum on density-feedback strength estimated using long-term census data from >700 vertebrates, invertebrates, and plants. Four life-history traits (Age at first reproduction, Body size, Fertility, Longevity) were related statistically to Gompertz strength of density feedback using generalized linear mixed-effects models and multi-model inference. Life-history traits alone explained 10 to 30% of the variation in strength across species (after controlling for time-series length and phylogenetic nonindependence). Effect sizes were largest for body size in mammals and longevity in birds, and density feedback was consistently stronger for smaller-bodied and shorter-lived species. Overcompensatory density feedback (strength <-1) occurred in 20% of species, predominantly at the fast end of the life-history continuum, implying relatively high population variability. These results support the idea that life history leaves an evolutionary signal in long-term population trends as inferred from census data. Where there is a lack of detailed demographic data, broad life-history information can inform management and conservation decisions about rebound capacity from low numbers, and propensity to fluctuate, of arrays of species in areas planned for development, harvesting, protection, and population recovery.

Observations on Neotricula aperta (Gastropoda: Pomatiopsidae) population densities in Thailand and central Laos: implications for the spread of Mekong schistosomiasis

Background

The snail Neotricula aperta transmits Mekong schistosomiasis in southern Laos and Cambodia, with about 1.5 million people at risk of infection. Plans are under consideration for at least 12 hydroelectric power dams on the lower Mekong river and much controversy surrounds predictions of their environmental impacts. Unfortunately, there are almost no ecological data (such as long term population trend studies) available for N. aperta which could be used in impact assessment. Predictions currently assume that the impacts will be the same as those observed in Africa (i.e., a worsening of the schistosomiasis problem); however, marked ecological differences between the snails involved suggest that region specific models are required. The present study was performed as an initial step in providing data, which could be useful in the planning of water resource development in the Mekong. Snail population density records were analyzed for populations close to, and far downstream of, the Nam Theun 2 (NT2) project in Laos in order to detect any changes that might be attributable to impoundment.

Results

The population immediately downstream of NT2 and that sampled 400 km downstream in Thailand both showed a long term trend of slow growth from 1992 to 2005; however, both populations showed a marked decline in density between 2005 and 2011. The decline in Thailand was to a value significantly lower than that predicted by a linear mixed model for the data, whilst the population density close to NT2 fell to undetectable levels in 2011 from densities of over 5000 m^-2 in 2005. The NT2 dam began operation in 2010.

Conclusions

The impact of the NT2 dam on N. aperta population density could be more complex than first thought and may reflect the strict ecological requirements of this snail. There was no indication that responses of N. aperta populations to dam construction are similar to those observed with Bulinus and Schistosoma haematobium in Africa, for example. In view of the present findings, more ecological data (in particular population density monitoring and surveillance for new habitats) are urgently required in order to understand properly the likely impacts of water resource development on Mekong schistosomiasis.

A Scheme for Evaluating Feral Horse Management Strategies

Context. Feral horses are an increasing problem in many countries and are popular with the public, making management difficult.Aims. To develop a scheme useful in planning management strategies.Methods. A model is developed and applied to four different feral horse herds, three of which have been quite accurately counted over the years.Key Results. The selected model has been tested on a variety of data sets, with emphasis on the four sets of feral horse data. An alternative, nonparametric model is used to check the selected parametric approach.Conclusions. A density-dependent response was observed in all 4 herds, even though only 8 observations were available in each case. Consistency in the model fits suggests that small starting herds can be used to test various management techniques.Implications. Management methods can be tested on actual, confined populations.

Are patterns of density dependence in the Global Population Dynamics Database driven by uncertainty about population abundance?

Density dependence in population growth rates is of immense importance to ecological theory and application, but is difficult to estimate. The Global Population Dynamics Database (GPDD), one of the largest collections of population time series available, has been extensively used to study cross-taxa patterns in density dependence. A major difficulty with assessing density dependence from time series is that uncertainty in population abundance estimates can cause strong bias in both tests and estimates of strength. We analyse 627 data sets in the GPDD using Gompertz population models and account for uncertainty via the Kalman filter. Results suggest that at least 45% of the time series display density dependence, but that it is weak and difficult to detect for a large fraction. When uncertainty is ignored, magnitude of and evidence for density dependence is strong, illustrating that uncertainty in abundance estimates qualitatively changes conclusions about density dependence drawn from the GPDD.