Frontiers in Nonlinear and Stochastic Modeling of Mass Extinction

Ben Abbott:
The biggest terrestrial tipping point or a potential carbon sink? Local and global consequences of thawing permafrost
Video

Arctic tundra and Boreal forest contain approximately half of all terrestrial organic carbon and represent a quarter of the terrestrial habitat in the Northern Hemisphere. As the permafrost region warms, more of this immense carbon pool will be exposed to decomposition, combustion, and hydrologic export. This permafrost carbon feedback has been described as the largest terrestrial feedback to climate change as well as one of the most likely to occur; however, it is not included in current emissions negotiations and estimates of its strength vary by a factor of thirty. Models predict that some portion of this release will be offset by increased Arctic and boreal biomass, but the lack of robust estimates of net carbon balance increases the risk of further overshooting international emissions targets with serious societal and environmental consequences. Because precise empirical or model-based assessments of the critical factors driving carbon balance and biodiversity in the permafrost zone are unlikely in the near future, creative mathematical and methodological approaches are needed. In this talk, I will synthesize recent understanding of the permafrost zone generated by the Permafrost Carbon Network (PCN). The PCN is a coalition of ~450 researchers spanning the natural and social sciences. I will explore sources of uncertainty in current estimates of greenhouse gas release and present several promising approaches for identifying tipping points in biosphere integrity and permafrost-climate coupling.

Bjorn Birnir:
The Canary in the Coalmine: Capelin as a Probe for Climate Change
Video

It was suggested by Rose (2005) that because of the migratory and responsive nature of the capelin, a small pelagic fish that is key to the ecology and fisheries of the North Atlantic, it can be viewed as the "canary in the coalmine" to detect signals of environmental changes in the Arctic Ocean. In this talk we will combine analysis of data and extensive simulations of the migrations of the capelin and its physiology to analyze the changes in the ocean environment taking place over the last half-century. Our goals will be to understand and predict the migrations of the capelin and its interactions with the ocean environment. We will explain how these have changed over time and how they are likely to change in the future. Then we will explain how our simulations can be compared with data, with the aim of finding out the rate of the temperature changes in the Arctic Ocean and when thresholds for major disruptions in Arctic environments are likely to be reached.

B. B. Cael:
The temperature dependence of marine biological carbon sequestration

The ocean's biologically mediated carbon reservoirs are an integral component of the global carbon cycle, and may feed back on climate if the total carbon exported out of the surface ocean is affected by surface temperatures. A simple mechanistic model is presented relating temperature to the fraction of primary production removed from the surface ocean, based on thermodynamic dependencies of autotrophic and heterotrophic metabolisms. The model captures the temperature dependence of observations. The model is then used to estimate the amplitude of the resulting climate-biosphere feedback. This mechanism's ability to explain paleoceanographic proxies is compared to that of the more convoluted explanations in the literature.

Fabo Feng:
Investigate the influence of astronomical phenomena on the Earth
Video

Previous studies claimed various periodicity in the biodiversity variation recorded by fossils and the paleo-geological data. Considering the influence of various astronomical phenomena such as cosmic rays, asteroid impacts, and supernova explosion on the Earth, we build astronomical models of mass extinctions, climate change, and terrestrial impact rate. The occurrence rate of such phenomena are typically modulated by the motion of the Sun in the Galaxy and the motion of the Earth in the Solar System. We investigate the uncertainty in the motions of the Sun and the Earth and account for such uncertainty in Bayesian model comparison. By comparing the astronomical models with null hypotheses, we find strong connection between the Earth’s obliquity and the terrestrial climate change (so-called "Milankovitch cycle") but failed to find strong influence of the solar motion on various terrestrial records. Thus the solar motion at most plays a minor role in the triggering of terrestrial mass extinctions.

Punit Gandhi:
Using pattern formation in the presence of spatial heterogeneity to learn about dryland ecosystems
Video

Regular spatial patterns in the vegetation growth of dryland ecosystems are thought to arise through self-organization in response to water scarcity. This behavior has been qualitatively reproduced by reaction-advection-diffusion systems that model various interactions between the plants and their environment. The patterns most often appear on very gentle slopes as bands of vegetation separated by bare soil with characteristic spacing on the order of 100 meters. I will use a simple modeling framework and an idealized topography to discuss the role of water transport in determining (1) the shape of individual vegetation bands and (2) the region of the landscape occupied vegetation patterns. The results are in qualitative agreement with observations from remote sensing data, and suggest that the placement of the patterns relative to ridges and valleys on the terrain may provide some indication of resilience to ecosystem collapse under aridity stress.

Vladimir Kozlov:
Biodiversity and stability of ecosystems with extinctions
Video

Existence and stability of large food webs, where many species share a few of resources, is one of key problems in ecology. We consider an ecological system, where several species compete for few limited resources. Typical examples are plant or plankton ecosystems. Sunlight, water, nitrogen, phosphorus and iron are all abiotic essential resources for phytoplankton and plant species. Resource competition models link the population dynamics of competing species with the dynamics of the resources. The extinction in the model is described with the help of extinction thresholds (if a species distribution reaches the threshold then we remove the species from the system).

A complete description of the system large time behavior is obtained in the case of sufficiently large turnover rates and zero extinction thresholds. This result holds due to two principal properties of our system. First, the system has a typical fast/slow structure for large turnover rates. Second, the system obeys a monotonicity property: if resources increase then species abundances also increase.

If extinction thresholds are non-vanishing, the ecosystem behavior exhibits new interesting effects. The limit equilibrium state still exists but it depends on the initial ecosystem state. This implies in particular that there can a priori exist several distinct equilibrium states.

We establish explicit upper and lower estimates of biodiversity in terms of the fundamental ecosystem parameters (species mortalities, resource consuming rate etc.). These results use no assumptions on the system dynamics (in particular our theorem on global stability).

This is a joint work with S. Vakulenko, Institute of Mechanical Engineering, St Petersburg, Russia, V. Tkachev, Department of Mathematics, Linkoping University, and Uno Wennergren, Department of Physics , Chemistry and Biology, Linkoping University.

Shaun Lovejoy:
Scaling, extremes and mass extinctions in the megaclimate regime
Video

Our atmospheric environment is variable from milliseconds to the age of the planet, from tenths of a millimeter to its size: scale ratios of 1020 and 1010 respectively. The simplest assumption about wide space-time scale range processes is that its dynamics even though complex and highly nonlinear - are nonetheless scaling (i.e. they respect a scale symmetry). The scaling principle can thus be used to classify the various dynamical regimes that are in operation.

Using modern instrumental and paleo data, and with the help of Haar fluctuations, in 2015 it was pointed out that the conventional picture of atmospheric variability - essentially a white noise background continuum spectrum interspersed with oscillatory processes - was in error by a factor of at least 1015. Instead, modern data and paleo data show that there are 4 or possibly 5 regimes - from dissipation scales up to the end of the Phanerozoic eon (5.5x108 years): weather, macroweather, climate, macroclimate and megaclimate. The time scales transitional from one regime to another were broadly estimated as 10 days, 300yrs, 105 yrs, 5x105 yrs. (the 300 yr macroweather- climate transition is a pre-industrial estimate; in the anthropocene, it is closer to 20 years). It should be noted that the status of the narrow macroclimate regime is not clear; it may instead turn out to be a broad astronomically forced cycle.

Scaling regimes have a number of generic statistical properties that we outline. These include intermittent spiky, highly nonGaussian transitions as well as power-law extreme probabilities associated with black swan events. We show that this (real space) intermittency is associated with large, random spectral spikes that can easily be spuriously attributed to oscillatory processes. Indeed, we argue that sophisticated Fourier techniques combined with inappropriate null hypotheses have often misinterpreted random spectral peaks in terms of real physical phenomena.

We focus on the megaclimate regime whose statistical properties are investigated with the help of data from benthic stacks (ocean sediment isotope measurements) that cover the range of scales from roughly half a million to half a billion years. We show that in mega-climate the paleotemperature fluctuation exponent is positive indicating that the temperature is unstable, that it tends to wander instead of tending to converge to any particular value, it tends to diverge. This already invalidates Gaia hypothesis at least over the Phanerozoic. We also show that paleotemperatures are intermittent, we quantify this with (multifractal) scaling exponents and we also confirm that the extreme fluctuations are power laws. This implies that it is difficult to distinguish relatively frequent extreme temperature fluctuations from genuine tipping points.

Finally, we show that this picture is compatible with analyses of mass extinction events.

Matthew Pound:
Cenozoic paleoclimates, vegetation and extinctions
Video

The Cenozoic era (66 million years ago to today) followed the extinction of the dinosaurs and other Mesozoic life. This era is one characterised by the rise of the mammals and the modernisation of global floras. These evolutionary and extinction events have played out against the backdrop trend of fluctuating, but progressively cooling, global climates. The general trend of Cenozoic global cooling is punctuated by a number of short-lived, or step-change events that have had sometimes profound impacts on life and sometimes not. After presenting a broad overview of Cenozoic climate and contextualising this era against the history of life and the big extinction events. We will then focus on a few key time intervals, within the Cenozoic. Using these case studies, to explore the role of climate change in reorganising global vegetation, causing extinctions and promoting evolution and expansion.

Daniel Rothman:
Earth's Excitable Carbon Cycle

The history of the carbon cycle is punctuated by enigmatic transient changes in the ocean's store of carbon. Mass extinction is always accompanied by such a disruption, but most disruptions are relatively benign. The less calamitous group exhibits a characteristic rate of change whereas greater surges accompany mass extinctions. But why? Analysis of a two-component dynamical system suggests that disruptions are initiated by perturbation of a permanently stable steady state beyond a threshold. The ensuing excitation exhibits the characteristic surge of real disruptions. In this view, the magnitude and timescale of the disruption are properties of the carbon cycle itself rather than its perturbation. Surges associated with mass extinction, however, require additional inputs from external sources such as massive volcanism. Modern inputs from anthropogenic emissions may exceed the excitation threshold during the present century.

Sebastian Schreiber:
When do factors promoting genetic diversity in stochastic environments also promote population persistence? A demographic perspective on Gillespie's SAS-CFF model
Video

Classical stochasticity demography predicts that environmental stochasticity reduces population growth rates and, thereby, can increase extinction risk. In contrast, J.H. Gillespie demonstrated with his SAS-CFF model that environmental stochasticity can promote genetic diversity. Extending the SAS-CFF to account for demography, I examine the simultaneous effects of environmental stochasticity on genetic diversity and population persistence. Explicit expressions for the per-capita growth rates of rare alleles and the population at low-density are derived. These expressions determine when genetic diversity is maintained and the population persists i.e. allelic frequencies and population densities tend to stay away from zero almost-surely and in probability. Using these results, I will discuss (i) how mechanisms promoting population persistence may be at odds with mechanisms promoting genetic diversity, and (ii) provide conditions under which population persistence in stochastic environments relies on existing standing genetic variation.

Ivan Sudakov:
The feedback mechanisms in climate-biosphere coupling leading to species extinction in large ecosystems
Video

We propose a model of multispecies populations surviving on distributed resources. System dynamics are investigated under changes in abiotic factors such as the climate, as parameterized through environmental temperature. In particular, we introduce a feedback between species abundances and resources via abiotic factors. This model is apparently the first of its kind to include a feedback mechanism coupling climate and ecosystem dynamics. The model explains the coexistence of many species, yet also displays the possibility of catastrophic bifurcations, where all species become extinct under the influence of abiotic factors. Also, we consider the dynamic model with random parameters for the climate-biosphere coupling to explain why the climate may stay stable over long-time intervals even if mass extinction in large ecosystems frequently occurs. The model shows that climate stability can be explained by mutual annihilation of many independent factors. One of the important consequences is that if biodiversity decreases then the random evolution of the biosphere can lead to global climate changes.

Brian Thomas:
Astrophysics and Mass Extinctions
Video

A variety of astrophysical events may have affected life on Earth during the Phanerozoic. While most of these events with intensity and proximity great enough to have major impacts are relatively rare, over 100s of millions of years they become likely. Such events include supernovae, gamma-ray bursts, extreme solar activity, and possibly outbursts of the Galaxy's central supermassive black hole. Impacts on life can be direct, through direct radiation exposure, or indirect, through modification of a planet's atmosphere. Much work has focused on radiation-induced destruction of stratospheric ozone, leading to increased Solar ultraviolet (UV) radiation at Earth's surface. Studies of the subsequent biological effect of this increased UV have yielded mixed results, with primary productivity of marine phytoplankton less drastically affected than originally assumed. More work is needed, however, to evaluate both survivability under long-term depletion, as well as the ecological impacts of UV damage. Recent work for the case of supernovae has found that the more direct effects of cosmic ray air-shower secondaries (muons) are likely significant even in the case of less severe ozone depletion. Atmospheric ionization (common to all radiation events) may have other effects as well, including climate change (through changes in cloud cover, however this assertion is controversial), and possibly an increase in the global lightning rate, which may lead to increased wildfire and thereby ecosystem changes. I will review the various types of astrophysical events that may be important, their likely rates and terrestrial effects, and possible connections to mass extinctions.

Uno Wennergren:
Modelling climate and land use change to identify risks of mass extinctions
Video

Mass extinctions are severe events that completely disrupt the system of biological interactions known as the food web. Given today's knowledge of the dynamics and complexity of food-webs one may ask what can cause three-fourths of species to go extinct? Two major causes and pathways will be explored: climate change and land use change. Special consideration will be taken to: (i) rate of change and generation times of species, (2) expected rates of evolution, (3) dynamical properties of food webs, (4) total biomass of a food web.

James Witts:
Catastrophe at the end of the Cretaceous? The shallow marine biotic and geochemical record of the Cretaceous-Paleogene (K-Pg) mass extinction event
Video

The Cretaceous-Paleogene (K-Pg) mass extinction event 66 million years ago is the most recent of the 'Big Five' Phanerozoic extinction events, and is most famously associated with the loss of non-avian dinosaur-dominated ecosystems on land, and marine reptiles and ammonoid cephalopod mollusks in the oceans. It is now almost forty years since the famous paper by Alvarez et al. (1980) proposed this extinction was caused by the catastrophic impact of a 10 km-diameter bolide (responsible for the formation of the Chicxulub crater in the Yucatan Peninsula, Mexico), and a vast body of work exists which supports this hypothesis. However, the extinction also coincides with the emplacement of the Deccan Traps Large Igneous Province (LIP) in continental India, which based on new high-precision dating, occurred over a <750 thousand year period of the latest Cretaceous and early Paleogene. Given the widespread evidence that LIP volcanism is ultimately responsible for at least three of the other 'Big Five' events, disentangling the effects of volcanically-driven climate and oceanographic changes from the effects of the bolide impact is critical to understanding the fate of various groups of organisms during this interval of rapid global environmental change. Did volcanism cause extinctions and ecosystem instability prior to the Chicxulub impact event (the 'Press-Pulse' hypothesis)? I have been investigating this question using faunal and geochemical data from shallow marine K-Pg successions in Antarctica and the United States Atlantic and Gulf Coastal Plains which demonstrate the complexities of the K-Pg extinction event.