Early warning signals and the prosecutor's fallacy

Early warning signals have been proposed to forecast the possibility of a critical transition, such as the eutrophication of a lake, the collapse of a coral reef or the end of a glacial period. Because such transitions often unfold on temporal and spatial scales that can be difficult to approach by experimental manipulation, research has often relied on historical observations as a source of natural experiments. Here, we examine a critical difference between selecting systems for study based on the fact that we have observed a critical transition and those systems for which we wish to forecast the approach of a transition. This difference arises by conditionally selecting systems known to experience a transition of some sort and failing to account for the bias this introduces—a statistical error often known as the prosecutor''s fallacy. By analysing simulated systems that have experienced transitions purely by chance, we reveal an elevated rate of false-positives in common warning signal statistics. We further demonstrate a model-based approach that is less subject to this bias than those more commonly used summary statistics. We note that experimental studies with replicates avoid this pitfall entirely.     

Rate of forcing and the forecastability of critical transitions

Critical transitions are qualitative changes of state that occur when a stochastic dynamical system is forced through a critical point. Many critical transitions are preceded by characteristic fluctuations that may serve as model‐independent early warning signals, implying that these events may be predictable in applications ranging from physics to biology. In nonbiological systems, the strength of such early warning signals has been shown partly to be determined by the speed at which the transition occurs. It is currently unknown whether biological systems, which are inherently high dimensional and typically display low signal‐to‐noise ratios, also exhibit this property, which would have important implications for how ecosystems are managed, particularly where the forces exerted on a system are anthropogenic. We examine whether the rate of forcing can alter the strength of early warning signals in (1) a model exhibiting a fold bifurcation where a state shift is driven by the harvesting of individuals, and (2) a model exhibiting a transcritical bifurcation where a state shift is driven by increased grazing pressure. These models predict that the rate of forcing can alter the detectability of early warning signals regardless of the underlying bifurcation the system exhibits, but that this result may be more pronounced in fold bifurcations. These findings have important implications for the management of biological populations, particularly harvested systems such as fisheries, and suggest that knowing the class of bifurcations a system will manifest may help discriminate between true‐positive and false‐positive signals.     

Robustness of early warning signals for catastrophic and non‐catastrophic transitions

Early warning signals (EWS) are statistical indicators that a rapid regime shift may be forthcoming. Their development has given ecologists hope of predicting rapid regime shifts before they occur. Accurate predictions, however, rely on the signals being appropriate to the system in question. Most of the EWS commonly applied in ecology have been studied in the context of one specific type of regime shift (the type brought on by a saddle‐node bifurcation, at which one stable equilibrium point collides with an unstable equilibrium and disappears) under one particular perturbation scheme (temporally uncorrelated noise that perturbs the net population growth rate in a density independent way). Whether and when these EWS can be applied to other ecological situations remains relatively unknown, and certainly underappreciated. We study a range of models with different types of dynamical transitions (including rapid regime shifts) and several perturbation schemes (density‐dependent uncorrelated or temporally‐correlated noise) and test the ability of EWS to warn of an approaching transition. We also test the sensitivity of our results to the amount of available pre‐transition data and various decisions that must be made in the analysis (i.e. the rolling window size and smoothing bandwidth used to compute the EWS). We find that EWS generally work well to signal an impending saddle‐node bifurcation, regardless of the autocorrelation or intensity of the noise. However, EWS do not reliably appear as expected for other types of transition. EWS were often very sensitive to the length of the pre‐transition time series analyzed, and usually less sensitive to other decisions. We conclude that the EWS perform well for saddle‐node bifurcation in a range of noise environments, but different methods should be used to predict other types of regime shifts. As a consequence, knowledge of the mechanism behind a possible regime shift is needed before EWS can be used to predict it.     

Changing skewness: an early warning signal of regime shifts in ecosystems

Empirical evidence for large-scale abrupt changes in ecosystems such as lakes and vegetation of semi-arid regions is growing. Such changes, called regime shifts, can lead to degradation of ecological services. We study simple ecological models that show a catastrophic transition as a control parameter is varied and propose a novel early warning signal that exploits two ubiquitous features of ecological systems: nonlinearity and large external fluctuations. Either reduced resilience or increased external fluctuations can tip ecosystems to an alternative stable state. It is shown that changes in asymmetry in the distribution of time series data, quantified by changing skewness, is a model-independent and reliable early warning signal for both routes to regime shifts. Furthermore, using model simulations that mimic field measurements and a simple analysis of real data from abrupt climate change in the Sahara, we study the feasibility of skewness calculations using data available from routine monitoring.     

Evolutionary constraints of warning signals: A genetic trade‐off between the efficacy of larval and adult warning coloration can maintain variation in signal expression

To predict evolutionary responses of warning signals under selection, we need to determine the inheritance pattern of the signals, and how they are genetically correlated with other traits contributing to fitness. Furthermore, protective coloration often undergoes remarkable changes within an individual's lifecycle, requiring us to quantify the genetic constraints of adaptive coloration across all the relevant life stages. Based on a 12 generation pedigree with > 11,000 individuals of the wood tiger moth (Arctia plantaginis), we show that high primary defense as a larva (large warning signal) results in weaker defenses as adult (less efficient warning color), due to the negative genetic correlation between the efficacy of larval and adult warning coloration. However, production of effective warning coloration as a larva did not incur any life‐history costs and was positively genetically correlated with reproductive output. These results provide novel insights into the evolutionary constraints on protective coloration in animals, and explain the maintenance of variation in the signal expression despite the strong directional selection by predators. By analyzing the genetic and environmental effects on warning signal and life‐history traits in all relevant life stages, we can accurately determine the mechanisms shaping the evolutionary responses of phenotypic traits under different selection environments.     

Indicators of transitions in biological systems

In the face of global biodiversity declines, predicting the fate of biological systems is a key goal in ecology. One popular approach is the search for early warning signals (EWSs) based on alternative stable states theory. In this review, we cover the theory behind nonlinearity in dynamic systems and techniques to detect the loss of resilience that can indicate state transitions. We describe the research done on generic abundance‐based signals of instability that are derived from the phenomenon of critical slowing down, which represent the genesis of EWSs research. We highlight some of the issues facing the detection of such signals in biological systems – which are inherently complex and show low signal‐to‐noise ratios. We then document research on alternative signals of instability, including measuring shifts in spatial autocorrelation and trait dynamics, and discuss potential future directions for EWSs research based on detailed demographic and phenotypic data. We set EWSs research in the greater field of predictive ecology and weigh up the costs and benefits of simplicity vs. complexity in predictive models, and how the available data should steer the development of future methods. Finally, we identify some key unanswered questions that, if solved, could improve the applicability of these methods.     

Integration of Life Cycle assessment and population balance model for assessing environmental impacts of product population in a social scale case studies for the global warming potential of air conditioners in Japan

Scope  In this study, a dynamic model was built in which LCA and PBM were integrated to quantitatively assess the total environmental impacts induced by the product population in a society over time. Specifically, a determination was carried out concerning how Japan’s air conditioner population is used (lifetime distribution, number of units, etc.) and an assessment was made concerning the Global Warming Potential (GWP) associated with the air conditioner population. Methods  The proposed dynamic model was applied to air conditioners for analyzing the total GWP caused by the air conditioner population in Japan from 1990 to 2010. To create a trend forecast model for future environmental load, scenarios for air conditioner production up to 2010 were formulated and the total GWP from the air conditioner population was predicted. Conducted also were sensitivity analyses whose parameters were air conditioner performance, lifetime and the rate of refrigerant recovery when retired units are processed. Results and Discussion  Applying the PBM to the air conditioner population in 2000, it was found that 81.5 million units consumed 5.94 x 10^p10 kWh in that year, which was a 6.1 % increase in the total annual power consumption in 1990. In both a stationary scenario and a steady growth (1.5% annual increase), it was found that the total GWP would be 27.7% higher than in 1990 under the stationary scenario and 37.8% higher under the steady growth scenario. The improvements in air conditioner performance will have a small effect on reducing the total GWP from that population. Furthermore, in connection with the average lifetime, it was found that the GWP, due to refrigerant releases when units are disposed of, would be relatively large in 2000 and the following years. Conclusions  Thus, shorter product lifetimes will spur a replacement of air conditioners with new units, a situation that will only lead to the reduction of GWP if the recovery rate of refrigerant is to be achieved to more than 50% under the stationary scenario. Recommendations and Outlook  To meet COP3 targets for Japan in 2010 (i.e. to reach the same level as in 1990 for household appliances), our study shows that it will be vital to raise the refrigerant recovery rate. If the number of air conditioners in use remains unchanged, recovery would have to be 45.7%, but under the steady growth scenario it would have to be at least 60.4%. Therefore, it will be difficult to meet COP3 targets unless the refrigerant recovery rate is strongly increased. This method is applicable to assess not only the GWP of air conditioners, but also other environmental impacts caused by a variety of product populations, which will be quite effective for setting targets of products’ performance, policymaking, etc.