Many dynamical systems, including lakes, organisms, ocean circulation patterns, or financial markets, are now thought to have tipping points where critical transitions to a contrasting state can ...happen. Because critical transitions can occur unexpectedly and are difficult to manage, there is a need for methods that can be used to identify when a critical transition is approaching. Recent theory shows that we can identify the proximity of a system to a critical transition using a variety of so-called 'early warning signals', and successful empirical examples suggest a potential for practical applicability. However, while the range of proposed methods for predicting critical transitions is rapidly expanding, opinions on their practical use differ widely, and there is no comparative study that tests the limitations of the different methods to identify approaching critical transitions using time-series data. Here, we summarize a range of currently available early warning methods and apply them to two simulated time series that are typical of systems undergoing a critical transition. In addition to a methodological guide, our work offers a practical toolbox that may be used in a wide range of fields to help detect early warning signals of critical transitions in time series data.
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Abstract
Many researchers want to report an $R^{2}$ to measure the variance explained by a model. When the model includes correlation among data, such as phylogenetic models and mixed models, ...defining an $R^{2}$ faces two conceptual problems. (i) It is unclear how to measure the variance explained by predictor (independent) variables when the model contains covariances. (ii) Researchers may want the $R^{2}$ to include the variance explained by the covariances by asking questions such as “How much of the data is explained by phylogeny?” Here, I investigated three $R^{2}$s for phylogenetic and mixed models. $R^{2}_{resid}$ is an extension of the ordinary least-squares $R^{2}$ that weights residuals by variances and covariances estimated by the model; it is closely related to $R^{2}_{glmm}$ presented by Nakagawa and Schielzeth (2013. A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods Ecol. Evol. 4:133–142). $R^{2}_{pred}$ is based on predicting each residual from the fitted model and computing the variance between observed and predicted values. $R^{2}_{lik}$ is based on the likelihood of fitted models, and therefore, reflects the amount of information that the models contain. These three $R^{2}$s are formulated as partial $R^{2}$s, making it possible to compare the contributions of predictor variables and variance components (phylogenetic signal and random effects) to the fit of models. Because partial $R^{2}$s compare a full model with a reduced model without components of the full model, they are distinct from marginal $R^{2}$s that partition additive components of the variance. I assessed the properties of the $R^{2}$s for phylogenetic models using simulations for continuous and binary response data (phylogenetic generalized least squares and phylogenetic logistic regression). Because the $R^{2}$s are designed broadly for any model for correlated data, I also compared $R^{2}$s for linear mixed models and generalized linear mixed models. $R^{2}_{resid}$, $R^{2}_{pred}$, and $R^{2}_{lik}$ all have similar performance in describing the variance explained by different components of models. However, $R^{2}_{pred}$ gives the most direct answer to the question of how much variance in the data is explained by a model. $R^{2}_{resid}$ is most appropriate for comparing models fit to different data sets, because it does not depend on sample sizes. And $R^{2}_{lik}$ is most appropriate to assess the importance of different components within the same model applied to the same data, because it is most closely associated with statistical significance tests.
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Stability and Diversity of Ecosystems Ives, Anthony R; Carpenter, Stephen R
Science (American Association for the Advancement of Science),
07/2007, Volume:
317, Issue:
5834
Journal Article
Peer reviewed
Understanding the relationship between diversity and stability requires a knowledge of how species interact with each other and how each is affected by the environment. The relationship is also ...complex, because the concept of stability is multifaceted; different types of stability describing different properties of ecosystems lead to multiple diversity-stability relationships. A growing number of empirical studies demonstrate positive diversity-stability relationships. These studies, however, have emphasized only a few types of stability, and they rarely uncover the mechanisms responsible for stability. Because anthropogenic changes often affect stability and diversity simultaneously, diversity-stability relationships cannot be understood outside the context of the environmental drivers affecting both. This shifts attention away from diversity-stability relationships toward the multiple factors, including diversity, that dictate the stability of ecosystems.
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Summary
The rise in the use of statistical models for non‐Gaussian data, such as generalized linear models (GLMs) and generalized linear mixed models (GLMMs), is pushing aside the traditional ...approach of transforming data and applying least‐squares linear models (LMs). Nonetheless, many least‐squares statistical tests depend on the variance of the sum of residuals, which by the Central Limit Theorem converge to a Gaussian distribution for large sample sizes. Therefore, least‐squares LMs will likely have good performance in assessing the statistical significance of regression coefficients.
Using simulations of count data, I compared GLM approaches for testing whether regression coefficients differ from zero with the traditional approach of applying LMs to transformed data. Simulations assumed that variation among sample populations was either (i) negative binomial or (ii) log‐normal Poisson (i.e. log‐normal variation among populations that were then sampled by a Poisson distribution). I used the simulated data to conduct tests of the hypotheses that regression coefficients differed from zero; I did not investigate statistical properties of the coefficient estimators, such as bias and precision.
For negative binomial simulations whose assumptions closely matched the GLMs, the GLMs were nonetheless prone to type I errors (false positives) especially when there was more than one predictor (independent) variable. After correcting for type I errors, however, the GLMs provided slightly better statistical power than LMs. For log‐normal‐Poisson simulations, both a GLMM and the LMs performed well, but under some simulated conditions the GLMs had high type I error rates, a deadly sin for statistical tests.
These results show that, while GLMs have slight advantages in power when they are properly specified, they can lead to badly wrong conclusions about the significance of regression coefficients if they are mis‐specified. In contrast, transforming data and applying least‐squares linear analyses provide robust statistical tests for significance over a wide range of conditions. Thus, the traditional approach of transforming data and applying LMs is still useful.
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Recent studies suggest that environmental changes may tip the balance between interacting species, leading to the extinction of one or more species. While it is recognized that evolution will play a ...role in determining how environmental changes directly affect species, the interactions among species force us to consider the coevolutionary responses of species to environmental changes.
We use simple models of competition, predation, and mutualism to organize and synthesize the ways coevolution modifies species interactions when climatic changes favor one species over another. In cases where species have conflicting interests (i.e., selection for increased interspecific interaction strength on one species is detrimental to the other), we show that coevolution reduces the effects of climate change, leading to smaller changes in abundances and reduced chances of extinction. Conversely, when species have nonconflicting interests (i.e., selection for increased interspecific interaction strength on one species benefits the other), coevolution increases the effects of climate change.
Coevolution sets up feedback loops that either dampen or amplify the effect of environmental change on species abundances depending on whether coevolution has conflicting or nonconflicting effects on species interactions. Thus, gaining a better understanding of the coevolutionary processes between interacting species is critical for understanding how communities respond to a changing climate. We suggest experimental methods to determine which types of coevolution (conflicting or nonconflicting) drive species interactions, which should lead to better understanding of the effects of coevolution on species adaptation. Conducting these experiments across environmental gradients will test our predictions of the effects of environmental change and coevolution on ecological communities.
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Abstract Agricultural habitats are frequently disturbed, and disturbances could have major effects on species in upper trophic levels such as hymenopteran parasitoids that are important for ...biological control. A strategy for conservation biological control is to provide a diversified agricultural landscape which increases the availability of resources such as sugar required by parasitoid biological control agents. Here, we ask whether parasitoids occurring in agriculture benefit from sugar resources more or less than parasitoids occurring in natural habitats surrounding agricultural fields. We collected parasitoids from agricultural alfalfa fields, field margins, and natural prairies, and in the lab we randomly divided them into two treatments: half were given a constant supply of a sugar source to test their residual lifespan, and half were given neither sugar nor water to test their hardiness. Collected individuals were monitored daily and their day of death recorded. Parasitoids receiving a sugar source lived substantially longer than those without. Parasitoids collected in prairies lived longer than those from alfalfa fields in both the residual lifespan and hardiness treatments, with parasitoids from field margins being intermediate between them. Furthermore, the benefits of a sugar source to increase longevity was lower for parasitoids collected in agriculture than in natural habitats. This suggests that, even though parasitoid biological control agents benefit from sugar resources, their short lifespans make the benefit of sugar resources small compared to parasitoids that occur in natural habitats and have longer lifespans, and are adapted to consistent sugar sources.
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Species exist within communities of other interacting species, so an exogenous force that directly affects one species can indirectly affect all other members of the community. In the case of climate ...change, many species may be affected directly and subsequently initiate numerous indirect effects that propagate throughout the community. Therefore, the net effect of climate change on any one species is a function of the direct and indirect effects. We investigated the direct and indirect effects of climate warming on corn leaf aphids, a pest of corn and other grasses, by performing an experimental manipulation of temperature, predators, and two common aphid-tending ants. Although warming had a positive direct effect on aphid population growth rate, warming reduced aphid abundance when ants and predators were present. This occurred because winter ants, which aggressively defend aphids from predators under control temperatures, were less aggressive toward predators and less abundant when temperatures were increased. In contrast, warming increased the abundance of cornfield ants, but they did not protect aphids from predators with the same vigor as winter ants. Thus, warming broke down the ant-aphid mutualism and counterintuitively reduced the abundance of this agricultural pest.
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Abstract
During the COVID-19 pandemic, many quantitative approaches were employed to predict the course of disease spread. However, forecasting faces the challenge of inherently unpredictable spread ...dynamics, setting a limit to the accuracy of all models. Here, we analyze COVID-19 data from the USA to explain variation among jurisdictions in disease spread predictability (that is, the extent to which predictions are possible), using a combination of statistical and simulation models. We show that for half the counties and states the spread rate of COVID-19,
r
(
t
), was predictable at most 9 weeks and 8 weeks ahead, respectively, corresponding to at most 40% and 35% of an average cycle length of 23 weeks and 26 weeks. High predictability was associated with high cyclicity of
r
(
t
) and negatively associated with
R
0
values from the pandemic’s onset. Our statistical evidence suggests the following explanation: jurisdictions with a severe initial outbreak, and where individuals and authorities took strong and sustained protective measures against COVID-19, successfully curbed subsequent waves of disease spread, but at the same time unintentionally decreased its predictability. Decreased predictability of disease spread should be viewed as a by-product of positive and sustained steps that people take to protect themselves and others.
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Many statistical models currently used in ecology and evolution account for covariances among random errors. Here, I address five points: (i) correlated random errors unite many types of statistical ...models, including spatial, phylogenetic and time‐series models; (ii) random errors are neither unpredictable nor mistakes; (iii) diagnostics for correlated random errors are not useful, but simulations are; (iv) model predictions can be made with random errors; and (v) can random errors be causal?
These five points are illustrated by applying statistical models to analyse simulated spatial, phylogenetic and time‐series data. These three simulation studies are paired with three types of predictions that can be made using information from covariances among random errors: predictions for goodness‐of‐fit, interpolation, and forecasting.
In the simulation studies, models incorporating covariances among random errors improve inference about the relationship between dependent and independent variables. They also imply the existence of unmeasured variables that generate the covariances among random errors. Understanding the covariances among random errors gives information about possible processes underlying the data.
Random errors are caused by something. Therefore, to extract full information from data, covariances among random errors should not just be included in statistical models; they should also be studied in their own right. Data are hard won, and appropriate statistical analyses can make the most of them.
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Ecology Letters (2011) 14: 69–74
Climate change has led to phenological shifts in flowering plants and insect pollinators, causing concern that these shifts will disrupt plant–pollinator mutualisms. ...We experimentally investigated how shifts in flowering onset affect pollinator visitation for 14 native perennial plant species, six of which have exhibited shifts to earlier flowering over the last 70 years and eight of which have not. We manipulated flowering onset in greenhouses and then observed pollinator visitation in the field. Five of six species with historically advanced flowering received more visits when flowering was experimentally advanced, whereas seven of eight species with historically unchanged flowering received fewer visits when flowering earlier. This pattern suggests that species unconstrained by pollinators have advanced their flowering, whereas species constrained by pollinators have not. In contrast to current concern about phenological mismatches disrupting plant–pollinator mutualisms, mismatches at the onset of flowering are not occurring for most of our study species.
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