Abstract
Quantifying ecological memory could be done at several levels from the rate of physiological changes in an ecosystem all the way down to responses at the genetic level. One way of unlocking the information encoded in a collective environmental memory is to examine the recorded time-series data generated by different components of an ecosystem. In this paper, we probe into the case of the Great Barrier Reef (GBR) which is threatened by elevated sea surface temperatures (SST) and ocean acidification attributed to rising atmospheric CO2 levels. Specifically, we investigate the interrelated dynamics between the degradation of the GBR, SST, and rising atmospheric CO2 levels, by considering three datasets: (a) the mean percentage hard coral cover of the GBR from the archives of the Australian Institute of Marine Science; (b) SST close to the GBR from the National Oceanic and Atmospheric Administration; and (c) the Keeling curve for atmospheric CO2 levels measured by the Mauna Loa Observatory. We show that fluctuating observables in these datasets have the same memory behavior described by a non-Markovian stochastic process. All three datasets show a good match between empirical and analytical mean square deviation. An explicit analytical form for the corresponding probability density function is obtained which obeys a modified diffusion equation with a time dependent diffusion coefficient. This study provides a new perspective on the similarities of and interaction between the GBR’s declining hard coral cover, SST, and rising atmospheric CO2 levels by putting all three systems into one unified framework indexed by a memory parameter \(\mu \) and a characteristic frequency \(\nu \). The short-time dynamics of CO2 levels and SST fall in the superdiffusive regime, while the GBR exhibits hyperballistic fluctuation in percent coral cover with the highest values for \(\mu \) and \(\nu \).
Highlights
Ecological memory where past events shape and alter future evolution of ecosystems in a changing environment has been a recurring theme in understanding the response of an ecological community to climate change (Hughes et al 2019; Schweiger et al 2018; Peterson 2002; Ogle et al 2015; Nyström and Folke 2001; Johnstone et al 2016)
Short-time behavior of the analytical probability density function (PDF) and mean square displacement (MSD) reveals that sea surface temperature (SST) and atmospheric CO2 levels are characterized by fluctuating data point values in the superdiffusive regime, while the Great Barrier Reef (GBR) degradation exhibits hyperballistic fluctuations
2.1 Observable Fluctuations in Empirical Datasets We investigate three sets of empirical time series: (a) the mean percentage coral cover of the GBR from July 1985 to June 2011 obtained from the archives of the Australian Institute of Marine Science (AIMS) accessible through the data portal data.gov.au (AIMS, 2016); (b) Sea surface temperatures from the climate monitoring division of NOAA for monthly data from January 1982 to October 2017; and (c) the Keeling curve for atmospheric CO2 levels measured by the Mauna Loa Observatory of the National Oceanic Atmospheric Administration (NOAA, www.esrl.noaa.gov) in the island of Hawaii
Summary
Ecological memory where past events shape and alter future evolution of ecosystems in a changing environment has been a recurring theme in understanding the response of an ecological community to climate change (Hughes et al 2019; Schweiger et al 2018; Peterson 2002; Ogle et al 2015; Nyström and Folke 2001; Johnstone et al 2016). In the form of heat, leaving and entering the earth climate system is continually measured in terms of radiation at the top of the atmosphere (von Schuckmann 2020; Meyssignac et al 2019). Modeling fluctuating observables in the interrelated dynamics of the coral cover of the GBR, the rise in atmospheric CO2 levels, and SST, finds a non-Markovian stochastic process most appropriate. Once the theoretical MSD has been matched with the empirically generated MSD of the fluctuating values of the observables, we obtain an explicit analytical probability density function (PDF) describing the GBR degradation, as well as SST and atmospheric CO2 levels. Short-time behavior of the analytical PDF and MSD reveals that SST and atmospheric CO2 levels are characterized by fluctuating data point values in the superdiffusive regime, while the GBR degradation exhibits hyperballistic fluctuations
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