Dispersal limitation and fire feedbacks maintain mesic savannas in Madagascar

Madagascar is regarded by some as one of the most degraded landscapes on Earth, with estimates suggesting that 90% of forests have been lost to indigenous Tavy farming. However, the extent of this degradation has been challenged: paleoecological data, phylogeographic analysis, and species richness indicate that pyrogenic savannas in central Madagascar predate human arrival, even though rainfall is sufficient to allow forest expansion into central Madagascar. These observations raise a question—if savannas in Madagascar are not anthropogenic, how then are they maintained in regions where the climate can support forest? Observation reveals that the savanna–forest boundary coincides with a dispersal barrier—the escarpment of the Central Plateau. Using a stepping-stone model, we show that in a limited dispersal landscape, a stable savanna–forest boundary can form because of fire–vegetation feedbacks. This phenomenon, referred to as range pinning, could explain why eastern lowland forests have not expanded into the mesic savannas of the Central Highlands. This work challenges the view that highland savannas in Madagascar are derived by human-lit fires and, more importantly, suggests that partial dispersal barriers and strong nonlinear feedbacks can pin biogeographical boundaries over a wide range of environmental conditions, providing a temporary buffer against climate change

An Empiricist’s Guide to Using Ecological Theory

A scientific understanding of the biological world arises when ideas about how nature works are formalized, tested, refined, and then tested again. Although the benefits of feedback between theoretical and empirical research are widely acknowledged by ecologists, this link is still not as strong as it could be in ecological research. This is in part because theory, particularly when expressed mathematically, can feel inaccessible to empiricists who may have little formal training in advanced math. To address this persistent barrier, we provide a general and accessible guide that covers the basic, step-by-step process of how to approach, understand, and use ecological theory in empirical work. We first give an overview of how and why mathematical theory is created, then outline four specific ways to use both mathematical and verbal theory to motivate empirical work, and finally present a practical tool kit for reading and understanding the mathematical aspects of ecological theory.We hope that empowering empiricists to embrace theory in their work will help move the field closer to a full integration of theoretical and empirical research

Lack of critical slowing down suggests that financial meltdowns are not critical transitions, yet rising variability could signal systemic risk

Complex systems inspired analysis suggests a hypothesis that financial meltdowns are abrupt critical transitions that occur when the system reaches a tipping point. Theoretical and empirical studies on climatic and ecological dynamical systems have shown that approach to tipping points is preceded by a generic phenomenon called critical slowing down, i.e. an increasingly slow response of the system to perturbations. Therefore, it has been suggested that critical slowing down may be used as an early warning signal of imminent critical transitions. Whether financial markets exhibit critical slowing down prior to meltdowns remains unclear. Here, our analysis reveals that three major US (Dow Jones Index, S&P 500 and NASDAQ) and two European markets (DAX and FTSE) did not exhibit critical slowing down prior to major financial crashes over the last century. However, all markets showed strong trends of rising variability, quantified by time series variance and spectral function at low frequencies, prior to crashes. These results suggest that financial crashes are not critical transitions that occur in the vicinity of a tipping point. Using a simple model, we argue that financial crashes are likely to be stochastic transitions which can occur even when the system is far away from the tipping point. Specifically, we show that a gradually increasing strength of stochastic perturbations may have caused to abrupt transitions in the financial markets. Broadly, our results highlight the importance of stochastically driven abrupt transitions in real world scenarios. Our study offers rising variability as a precursor of financial meltdowns albeit with a limitation that they may signal false alarms

Scale invariance in the spatial-dynamics of biological invasions

Despite the enormous negative consequences of biological invasions, we have a limited understanding of how spatial demography during invasions creates population patterns observed at different spatial scales. Early stages of invasions, arrival and establishment, are considered distinct from the later stage of spread, but the processes of population growth and dispersal underlie all invasion phases. Here, we argue that the spread of invading species, to a first approximation, exhibits scale invariant spatial-dynamic patterns that transcend multiple spatial scales. Dispersal from a source population creates smaller satellite colonies, which in turn act as sources for secondary invasions; the scale invariant pattern of coalescing colonies can be seen at multiple scales. This self-similar pattern is referred to as “stratified diffusion” at landscape scales and the “bridgehead effect” at the global scale. The extent to which invasions exhibit such scale-invariant spatial dynamics may be limited by the form of the organisms’ dispersal kernel and by the connectivity of the habitat. Recognition of this self-similar pattern suggests that certain concepts for understanding and managing invasions might be widely transferable across spatial scales

Lack of Critical Slowing Down Suggests that Financial Meltdowns Are Not Critical Transitions, yet Rising Variability Could Signal Systemic Risk

<div><p>Complex systems inspired analysis suggests a hypothesis that financial meltdowns are abrupt critical transitions that occur when the system reaches a tipping point. Theoretical and empirical studies on climatic and ecological dynamical systems have shown that approach to tipping points is preceded by a generic phenomenon called critical slowing down, i.e. an increasingly slow response of the system to perturbations. Therefore, it has been suggested that critical slowing down may be used as an early warning signal of imminent critical transitions. Whether financial markets exhibit critical slowing down prior to meltdowns remains unclear. Here, our analysis reveals that three major US (Dow Jones Index, S&P 500 and NASDAQ) and two European markets (DAX and FTSE) did not exhibit critical slowing down prior to major financial crashes over the last century. However, all markets showed strong trends of rising variability, quantified by time series variance and spectral function at low frequencies, prior to crashes. These results suggest that financial crashes are not critical transitions that occur in the vicinity of a tipping point. Using a simple model, we argue that financial crashes are likely to be stochastic transitions which can occur even when the system is far away from the tipping point. Specifically, we show that a gradually increasing strength of stochastic perturbations may have caused to abrupt transitions in the financial markets. Broadly, our results highlight the importance of stochastically driven abrupt transitions in real world scenarios. Our study offers rising variability as a precursor of financial meltdowns albeit with a limitation that they may signal false alarms.</p></div

Strength of trends, as measured by Kendall-<i>τ</i>, in all three indicators for DJI as a function of time over the last century.

<p>The blue line is a threshold value of Kendall-<i>τ</i> (0.9) which is sufficiently large to conclude a strong increasing trend. Clearly, the trends for acf at lag 1 are weak and never exceed this threshold. For both variance and power spectrum, a total of sixteen events of crossing the threshold value were found and they are all listed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0144198#pone.0144198.t001" target="_blank">Table 1</a>. Four of them indicated in red squares in the middle and the lower panel correspond to four major financial crashes, namely 1929, 1987, 2000 and 2008 whereas five others correspond to minor economic crises of last century. This figure also illustrates instances of strong trends of EWS that were not followed by any crash, suggesting that they were false alarms.</p

Early warning signals of critical transitions versus stochastic transitions.

<p>(A) The bifurcation diagram for the model <math><mrow><mi>x</mi><mo>˙</mo><mo>=</mo><mo>-</mo><mi>h</mi><mo>+</mo><mi>r</mi><mi>x</mi><mo>-</mo><mi>x</mi><mn>3</mn></mrow></math>, where <i>x</i> represents system state and <i>h</i> and <i>r</i> are system parameters (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0144198#sec016" target="_blank">Methods A</a>)). Solid lines represent stable equilibria and the dotted line represents unstable equilibria. In the left column, we show the dynamics and the early warning signals of the system, <math><mrow><mi>x</mi><mo>˙</mo><mo>=</mo><mo>-</mo><mi>h</mi><mo>+</mo><mi>r</mi><mi>x</mi><mo>-</mo><mi>x</mi><mn>3</mn><mo>+</mo><mi>σ</mi><mi>η</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math>, where <i>η</i>(<i>t</i>) is a Guassian white noise, i.e. 〈<i>η</i>(<i>t</i>)<i>η</i>(<i>t</i>′)〉 = <i>δ</i>(<i>t</i>−<i>t</i>′), as the system approaches critical point (the driver <i>h</i> → <i>h</i>_<i>c</i> = 2 with <i>r</i> = 3 and <i>σ</i> = 0.1). The right column shows abrupt transitions driven by increasing strength of perturbations (we increase <i>σ</i> with constant <i>r</i> = 3 and <i>h</i> = 0).</p

Lack of significant increasing trends of indicators for DJI data for the duration 17/09/2011 to 16/09/2015.

<p>Parameters used to analyze data are same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0144198#pone.0144198.g001" target="_blank">Fig 1</a>. The insets show a distribution of Kendall-<i>τ</i> for the corresponding indicator obtained by a parameter scan of over 1.25 million combinations. Lack of consistent value in Kendall−<i>τ</i> and relatively high p-values (> 0.1) for all EWS suggest that there are no clear trends. For the inset: x-axis scale is from −1 to 1 and the y-axis is from 0 to 0.11 (See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0144198#sec023" target="_blank">Methods B</a>).</p

Early warning signals of major financial crashes of Dow Jones Index (DJI).

<p>The columns correspond to analysis of each crash. The solid vertical line together with the arrow in the residual plots, which were obtained after detrending the data, shows the length of the rolling window (<i>l</i>_<i>rw</i>) over which all indicators are estimated. The symbol k-<i>τ</i> represents Kendall’s rank correlation coefficient estimated for each indicator for 250 days prior to the crash. The p-value denoted by <i>p</i>_<i>hist</i> quantifies how likely such trends are in years far away from the crash. The other three p-values quantify likelihood of such trends occurring by chance (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0144198#sec023" target="_blank">Methods B</a>). Parameters: <i>l</i>_<i>rw</i> = 500 days, <i>bw</i> = 25, <i>l</i>_<i>kw</i> = 250 days, <i>l</i>_<i>Kend</i> = 0 days.</p