Perry de Valpine

Diversification practices reduce organic to conventional yield gap

Agriculture today places great strains on biodiversity, soils, water and the atmosphere, and these strains will be exacerbated if current trends in population growth, meat and energy consumption, and food waste continue. Thus, farming systems that are both highly productive and minimize environmental harms are critically needed. How organic agriculture may contribute to world food production has been subject to vigorous debate over the past decade. Here, we revisit this topic comparing organic and conventional yields with a new meta-dataset three times larger than previously used (115 studies containing more than 1000 observations) and a new hierarchical analytical framework that can better account for the heterogeneity and structure in the data. We find organic yields are only 19.2% (±3.7%) lower than conventional yields, a smaller yield gap than previous estimates. More importantly, we find entirely different effects of crop types and management practices on the yield gap compared with previous studies. For example, we found no significant differences in yields for leguminous versus non-leguminous crops, perennials versus annuals or developed versus developing countries. Instead, we found the novel result that two agricultural diversification practices, multi-cropping and crop rotations, substantially reduce the yield gap (to 9 ± 4% and 8 ± 5%, respectively) when the methods were applied in only organic systems. These promising results, based on robust analysis of a larger meta-dataset, suggest that appropriate investment in agroecological research to improve organic management systems could greatly reduce or eliminate the yield gap for some crops or regions.

PLANT RESPONSES TO EXPERIMENTAL WARMING IN A MONTANE MEADOW

We studied the effects of a seven-year warming experiment on 11 forb species in the Rocky Mountains of Colorado in 1996 and 1997. Previous work on this experiment focused on ecosystem and community responses to warming. Our purpose here is to report on species responses. We found significant positive responses to warming for two species and negative responses for four species in terms of abundance, size, flowering, or frost damage. Because previous results from the warming experiment showed that artificial warming decreases soil moisture and increases nitrogen mineralization, we used nitrogen and water addition experiments on the two dominant forbs to determine whether species responses in the warming experiment could be due to shifts in resource availability. We found that Erigeron speciosus was limited more clearly by water than by nitrogen and Helianthella quinquenervis was limited by both nitrogen and water. These responses are consistent with the hypothesis that a primary effect of warming on plants occurs via changes in soil resource availability, but more complicated factors including competition are likely to be important to warming effects as well. Because previous work on this experiment indicated that annual forb detrital production is a key component of the carbon cycle of this system, we also asked which species responded to warming with changes in aboveground biomass. Over 1996 and 1997, four of nine perennial species had significantly lower biomass in the warmed plots, and in 1997 one species had significantly higher biomass. The biomass differences of Erigeron and Helianthella were almost equal and opposite, but while the decline in Erigeron was statistically significant the increase in Helianthella was smaller and not significant. In one year, a major effect of warming was to protect Helianthella from frost damage, which illustrates the importance of extreme weather events. Our study points to the potential importance of understanding ecosystem responses to climate change in terms of species responses.

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.

BETTER INFERENCES FROM POPULATION-DYNAMICS EXPERIMENTS USING MONTE CARLO STATE-SPACE LIKELIHOOD METHODS

In experimental population ecology, there is often a gap between realistic models used to hypothesize about population dynamics and statistical models used to analyze data. Ecologists routinely conduct experiments where the data from each replicate are short time series of estimated population abundances structured by stage, species, and/or other information, and the conventional test for treatment effects uses a general linear model (GLM) such as analysis of variance (ANOVA). However, GLMs do not incorporate demographic relationships between abundances through time. An alternative is to use population-dynamics models as frameworks for statistical hypothesis testing. This approach requires general methods for fitting structured population models that can incorporate both process noise (stochastic dynamics) and observation error (inaccurate data). This paper presents such methods and compares them to GLMs for testing population-dynamics hypotheses from experiments. The methods are Monte Carlo state-space l...

Effects of weather and climate on the dynamics of animal population time series.

Weather is one of the most basic factors impacting animal populations, but the typical strength of such impacts on population dynamics is unknown. We incorporate weather and climate index data into analysis of 492 time series of mammals, birds and insects from the global population dynamics database. A conundrum is that a multitude of weather data may a priori be considered potentially important and hence present a risk of statistical over-fitting. We find that model selection or averaging alone could spuriously indicate that weather provides strong improvements to short-term population prediction accuracy. However, a block randomization test reveals that most improvements result from over-fitting. Weather and climate variables do, in general, improve predictions, but improvements were barely detectable despite the large number of datasets considered. Climate indices such as North Atlantic Oscillation are not better predictors of population change than local weather variables. Insect time series are typically less predictable than bird or mammal time series, although all taxonomic classes display low predictability. Our results are in line with the view that population dynamics is often too complex to allow resolving mechanisms from time series, but we argue that time series analysis can still be useful for estimating net environmental effects.

Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS

1. Ecologists often use nonlinear fitting techniques to estimate the parameters of complex ecological models, with attendant frustration. This paper compares three open-source model fitting tools and discusses general strategies for defining and fitting models. 2. R is convenient and (relatively) easy to learn, AD Model Builder is fast and robust but comes with a steep learning curve, while BUGS provides the greatest flexibility at the price of speed. 3. Our model-fitting suggestions range from general cultural advice (where possible, use the tools and models that are most common in your subfield) to specific suggestions about how to change the mathematical description of models to make them more amenable to parameter estimation. 4. A companion web site (https://groups.nceas.ucsb.edu/nonlinear-modeling/projects) presents detailed examples of application of the three tools to a variety of typical ecological estimation problems; each example links both to a detailed project report and to full source code and data.

Monte Carlo State-Space Likelihoods by Weighted Posterior Kernel Density Estimation

Maximum likelihood estimation and likelihood ratio tests for nonlinear, non-Gaussian state-space models require numerical integration for likelihood calculations. Several methods, including Monte Carlo (MC) expectation maximization, MC likelihood ratios, direct MC integration, and particle filter likelihoods, are inefficient for the motivating problem of stage-structured population dynamics models in experimental settings. An MC kernel likelihood (MCKL) method is presented that estimates classical likelihoods up to a constant by weighted kernel density estimates of Bayesian posteriors. MCKL is derived by using Bayesian posteriors as importance sampling densities for unnormalized kernel smoothing integrals. MC error and mode bias due to kernel smoothing are discussed and two methods for reducing mode bias are proposed: “zooming in” on the maximum likelihood parameters using a focused prior based on an initial estimate and using a posterior cumulant-based approximation of mode bias. A simulated example shows that MCKL can be much more efficient than previous approaches for the population dynamics problem. The zooming-in and cumulant-based corrections are illustrated with a multivariate variance estimation problem for which accurate results are obtained even in 20 parameter dimensions.Maximum likelihood estimation and likelihood ratio tests for nonlinear, non-Gaussian state-space models require numerical integration for likelihood calculations. Several methods, including Monte Carlo (MC) expectation maximization, MC likelihood ratios, direct MC integration, and particle filter likelihoods, are inefficient for the motivating problem of stage-structured population dynamics models in experimental settings. An MC kernel likelihood (MCKL) method is presented that estimates classical likelihoods up to a constant by weighted kernel density estimates of Bayesian posteriors. MCKL is derived by using Bayesian posteriors as importance sampling densities for unnormalized kernel smoothing integrals. MC error and mode bias due to kernel smoothing are discussed and two methods for reducing mode bias are proposed: “zooming in” on the maximum likelihood parameters using a focused prior based on an initial estimate and using a posterior cumulant-based approximation of mode bias. A simulated example show...

Likelihood ridges and multimodality in population growth rate models

A central problem in population ecology is to use time series data to estimate the form of density dependence in the per capita growth rate (pgr). This is often accomplished with phenomenological models such as the theta-Ricker or generalized Beverton-Holt. Using the theta-Ricker model as a simple but flexible description of density dependence, we apply theory and simulations to show how multimodality and ridges in the likelihood surface can emerge even in the absence of model misspecification or observation error. The message for model fitting of real data is to consider the likelihood surface in detail, check whether the best-fit model is located on a likelihood ridge and, if so, evaluate predictive differences of biologically plausible models along the ridge. We present a detailed analysis of a focal data set showing how multimodality and ridges emerge in practice for fits of several parametric models, including a state-space model with explicit accommodation of observation error. Best-fit models for these data are biologically dubious beyond the range of the data, and likelihood ratio confidence regions include a wide range of more biologically plausible models. We demonstrate the broad relevance of these findings by presenting analyses of 25 additional data sets spanning a wide range of taxa. The results here are relevant to information-theoretic and Bayesian methods, which also rely on likelihoods. Beyond presentation of best-fit models and confidence regions around individual parameters, effort toward understanding features of the likelihood surface will help ensure the most robust translation from statistical analysis to biological interpretation.

A robust-design formulation of the incidence function model of metapopulation dynamics applied to two species of rails

The incidence function model (IFM) uses area and connectivity to predict metapopulation dynamics. However, false absences and missing data can lead to underestimates of the number of sites contributing to connectivity, resulting in overestimates of dispersal ability and turnovers (extinctions plus colonizations). We extend estimation methods for the IFM by using a hierarchical Bayesian model to account both for false absences due to imperfect detection and for missing data due to sites not surveyed in some years. We compare parameter estimates, measures of metapopulation dynamics, and forecasts using stochastic patch occupancy models (SPOMs) among three IFM models: (1) a Bayesian formulation assuming no false absences and omitting site-year combinations with missing data; (2) a hierarchical Bayesian formulation assuming no false absences but incorporating missing data; and (3) a hierarchical Bayesian formulation allowing for imperfect detection and incorporating missing data. We fit the models to multiyear data sets of occupancy for two bird species that differ in body size and presumed dispersal ability but inhabit the same network of sites: the small Black Rail (Laterallus jamaicensis) and the medium-sized Virginia Rail (Rallus limicola). Incorporating missing data affected colonization parameters and led to lower estimates of dispersal ability for the Black Rail. Detection rates were high for the Black Rail in most years but moderate for the Virginia Rail. Incorporating imperfect detection resulted in higher occupancy and lower turnover rates for both species, with largest effects for the Virginia Rail. Forecasts using SPOMs were sensitive to both missing data and false absences; persistence in models assuming no false absences was more optimistic than from robust models. Our results suggest that incorporating false absences and missing data into the IFM can improve (1) estimates of dispersal ability and the effect of connectivity on colonization, (2) the scaling of extinction risk with patch area, and (3) forecasts of occupancy and turnover rates.

Shared challenges and common ground for Bayesian and classical analysis of hierarchical statistical models

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