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We analyse metapopulation dynamics in terms of an individual-based, stochastic model of a finite metapopulation. We suggest a new approach, using the number of patches in the population as a large parameter. This approach does not require that the number of individuals per patch is large, neither is it necessary to assume a time-scale separation between local population dynamics and migration. Our approach makes it possible to accurately describe the dynamics of metapopulations consisting of many small patches. We focus on metapopulations on the brink of extinction. We estimate the time to extinction and describe the most likely path to extinction. We find that the logarithm of the time to extinction is proportional to the product of two vectors, a vector characterising the distribution of patch population sizes in the quasi-steady state, and a vector -- related to Fisher's reproduction vector -- that quantifies the sensitivity of the quasi-steady state distribution to demographic fluctuations. We compare our analytical results to stochastic simulations of the model, and discuss the range of validity of the analytical expressions. By identifying fast and slow degrees of freedom in the metapopulation dynamics, we show that the dynamics of large metapopulations close to extinction is approximately described by a deterministic equation originally proposed by Levins (1969). We were able to compute the rates in Levins' equation in terms of the parameters of our stochastic, individual-based model. It turns out, however, that the interpretation of the dynamical variable depends strongly on the intrinsic growth rate and carrying capacity of the patches. Only when the growth rate and the carrying capacity are large does the slow variable correspond to the number of patches, as envisaged by Levins. Last but not least, we discuss how our findings relate to other, widely used metapopulation models.

Computations are performed to examine the effectiveness of mono-disperse water droplets in extinguishing a co-flow, propane diffusion flame by injecting the droplets into the air stream. The calculations show that the droplets entrained into the reaction kernel at the flame base are crucial for extinction. The reaction kernel detaches from the burner rim and blows-off when the droplet concentration is increased to a critical value (extinction concentration). At the critical value, the maximum chain-branching reaction (H2+O=OH+H) rate in the reaction kernel was found to be reduced by a factor of 5 in our computations. A large decrease in the reaction rate indicates that the maximum heat generations rate and Damkholer number are too low to sustain the flame, and cause the flame blow-off. Large drops are more effective than small drops, and the extinction concentration of water increases from 10.5% to 15% by mass as the size is reduced from 32 to 4 micro m. As the droplet size is increased further (32 micro m), the trend will reverse as the evaporation rates get too small despite increased penetration of flame core by the drops.

Lucia Snyderman, Middlebury College research assistant The Great Auk (Pinguinus impennis) was hunted to extinction in the year 1844. All that remains for us to piece together its extinction story are skins, bones, a few eggs, and historical testimonies. Investigating human-auk relationships and modeling extinction timing using a combination of historical and radiocarbon data across the seabird’s North Atlantic range provides insight into how its distribution contracted and why certain populations persisted longer than others. Studying the Great Auk’s range collapse also contextualizes trends for current seabirds in decline.

We study a model of a multi-species ecosystem described by Lotka-Volterra-like equations. Interactions among species form a network whose evolution is determined by the dynamics of the model. Numerical simulations show power-law distribution of intervals between extinctions, but only for ecosystems with sufficient variability of species and with networks of connectivity above certain threshold that is very close to the percolation threshold of the network. Effect of slow environmental changes on extinction dynamics, degree distribution of the network of interspecies interactions, and some emergent properties of our model are also examined.

DYNAMICS OF DROPLET COMBUSTION AND EXTINCTION GROUND TEST HARDWARE

DYNAMICS OF DROPLET COMBUSTION AND EXTINCTION GROUND TEST HARDWARE

We consider a continuum version of a previously introduced and numerically studied model of macroevolution (PRL 75, 2055, (1995)) in which agents evolve by an optimization process in a rugged fitness landscape and die due to their competitive interactions. We first formulate dynamical equations for the fitness distribution and the survival probability. Secondly we analytically derive the $t^{-2}$ law which characterizes the life time distribution of biological genera. Thirdly we discuss other dynamical properties of the model such as the rate of extinction and conclude with a brief discussion.

DYNAMICS OF DROPLET COMBUSTION AND EXTINCTION GROUND TEST HARDWARE

DYNAMICS OF DROPLET COMBUSTION AND EXTINCTION GROUND TEST HARDWARE

Symposium: The Dynamics of Possible Nuclear Extinction Two day event organized by The Helen Caldicott Foundation February 28 - March 1 2015 The New York Academy of Medicine, NYC

DYNAMICS OF DROPLET COMBUSTION AND EXTINCTION GROUND TEST HARDWARE WITH HANK KACHER AND DALE ROBINSON

DYNAMICS OF DROPLET COMBUSTION AND EXTINCTION GROUND TEST HARDWARE

DYNAMICS OF DROPLET COMBUSTION AND EXTINCTION GROUND TEST HARDWARE

DYNAMICS OF DROPLET COMBUSTION AND EXTINCTION GROUND TEST HARDWARE

We consider the spreading dynamics of two nested invasion clusters on an infinite tree. This model was defined as the chase-escape model by Kordzakhia and it admits a limit process, the birth-and-assassination process, previously introduced by Aldous and Krebs. On both models, we prove an asymptotic equivalent of the extinction probability near criticality. In the subcritical regime, we give a tail bound on the total progeny of the preys before extinction.

We consider a stochastic population model where the intrinsic or demographic noise causes cycling between states before the population eventually goes extinct. A master equation approach coupled with a WKB (Wentzel-Kramers-Brillouin) approximation is used to construct the optimal path to extinction. In addition, a probabilistic argument is used to understand the pre-extinction dynamics and approximate the mean time to extinction. Analytical results agree well with numerical Monte Carlo simulations. A control method is implemented to decrease the mean time to extinction. Analytical results quantify the effectiveness of the control and agree well with numerical simulations.

Transitions to absorbing states are of fundamental importance in non-equilibrium physics as well as ecology. In ecology, absorbing states correspond to the extinction of species. We here study the spatial population dynamics of three cyclically interacting species. The interaction scheme comprises both direct competition between species as in the cyclic Lotka-Volterra model, and separated selection and reproduction processes as in the May-Leonard model. We show that the dynamic processes leading to the transient maintenance of biodiversity are closely linked to attractors of the nonlinear dynamics for the overall species' concentrations. The characteristics of these global attractors change qualitatively at certain threshold values of the mobility, and depend on the relative strength of the different types of competition between species. They give information about the scaling of extinction times with the system size and thereby the stability of biodiversity. We define an effective free energy as the negative logarithm of the probability to find the system in a specific global state before reaching one of the absorbing states. The global attractors then correspond to minima of this effective energy landscape and determine the most probable values for the species' global concentrations. As in equilibrium thermodynamics, qualitative changes in the effective free energy landscape indicate and characterize the underlying non-equilibrium phase transitions. We provide the complete phase diagrams for the population dynamics, and give a comprehensive analysis of the spatio-temporal dynamics and routes to extinction in the respective phases.

Acquiring fear is crucial for survival (e.g., learning to avoid/escape dangerous situations). However, it is equally critical to extinguish fear when the threat abates (e.g., adapting to changing circumstances), a process known as ‘fear extinction’. Failure to adaptively extinguish fear is a key feature of anxiety disorders(1). Strikingly, diminished fear extinction is observed particularly in adolescence(2-4), possibly because of the need to stay vigilant when exploring novel environments(5). Despite the importance of fear extinction, there is a knowledge gap in how fear extinction learning develops across adolescence, the developmental period between childhood and adulthood. The lack of understanding of the process of extinction is even more surprising, because of the dramatic rise in the prevalence of mental health problems in adolescence, including social anxiety(6-8). It is likely that the mechanisms of extinction lie in the changing neurobiological systems in adolescence. Indeed, adolescence is a period of major neurobiological changes(9-11), partly driven by hormonal changes(12). Importantly, women are twice as likely as men to develop anxiety problems in adolescence (6, 13, 14). Our knowledge on fear extinction across development is merely derived from research studying extinction by learning from direct experience (2-4, 15), yet much of our learning comes from other individuals(16). This learning through social transmission, for example by observing others, is particularly important in adolescence. Adolescents are specifically sensitive to the social context and influence of peers (17-19). Therefore, it is expected that adolescents will benefit more from social learning (17, 20, 21), which have been observed in other social contexts such as risk-taking (22, 23). These prior studies showed that activity in brain regions implicated in risk-taking are enhanced under influence of peers. Likewise, evidence for the positive impact of social-extinction (i.e., extinction learning through observation) comes from our previous studies on adults, demonstrating that social-extinction prevented the return of conditioned fear responses better than direct-extinction(16, 24, 25). The general aim of this project is to understand the development of extinction learning based on both direct experience (i.e., direct-extinction) and through observation (i.e., social-extinction) from adolescence to adulthood.

Influence of climate drivers on colonization and extinction dynamics of wetland-dependent species Journal Article (Item ID: 2233032) National Parks Service (NPS) - IRMA Resource Originally published by the NPS and hosted at: https://irma.nps.gov/DataStore/Reference/Profile/2233032 Suggested Citation: Ray AM and Others. 2016. Influence of climate drivers on colonization and extinction dynamics of wetland-dependent species. Ecosphere. 7(7):1-21 Because this content was published and publicly released by the Unitesd States federal government, we believe that it is in the Public Domain and have indicated so with the appropriate licensing metadata. This item includes the following files, with JSON-formatted metadata obtained from: https://irma.nps.gov/DataStore/Reference/GetHoldings?referenceId=2233032 FileDescription : Ray_2016_Ecosphere_InfluenceClimateDriversColonizationExtinctionDynamics.pdf Accessibility : None Id : 554429 MimeType : application/pdf DisplayOrder : 1 WebServiceType : None QueueForServices : False DisableDownload : False FileManagerId : 259337 Url : https://irma.nps.gov/DataStore/DownloadFile/554429 LastVerified : /Date(-62135571600000)/ NeedsToBeQueued : False HoldingType : 0 FileSize : 3299173 ServiceTemplate : None Description : None FileDescription : None Accessibility : None Id : 563910 MimeType : None DisplayOrder : 2 WebServiceType : None QueueForServices : False DisableDownload : False FileManagerId : None Url : http://onlinelibrary.wiley.com/doi/10.1002/ecs2.1409/full LastVerified : /Date(1483686000000)/ NeedsToBeQueued : False HoldingType : 1 FileSize : 0 ServiceTemplate : None Description : Link to full profile.

Lada et al. (1994) have described a method for studying the distribution of dust in dark clouds using infrared imaging surveys. In particular they show that the method provides some information about the structure of the gas (dust) on scales smaller than their resolution. In the present work we clarify the nature of the information provided by their method. We show that: 1) the 3D density field of the gas is well described by a Log-Normal distribution down to very small scales; 2) the power spectrum and the standard deviation of the 3D density field can be constrained; 3) the origin of such a structure of the density field is likely to be the supersonic turbulence in the gas. In fact we find a qualitative and quantitative agreement between the predictions based on recent numerical simulations of supersonic turbulence (Nordlund and Padoan 1996; Padoan, Nordlund and Jones 1996) and the constraints given by the infrared dust extinction measurements.

DYNAMICS OF DROPLET COMBUSTION AND EXTINCTION GROUND TEST HARDWARE

DYNAMICS OF DROPLET COMBUSTION AND EXTINCTION GROUND TEST HARDWARE

Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 50's with the KiSS (after Kierstead, Slobodkin and Skellam) model, namely a continuous reaction-diffusion equation for a population growing on a patch of finite size $L$ surrounded by a deadly environment with infinite mortality -- i.e. an oasis in a desert. The main outcome of the model is that only patches above a critical size allow for population persistence. Here, we introduce an individual-based analogue of the KiSS model to investigate the effects of discreteness and demographic stochasticity. In particular, we study the average time to extinction both above and below the critical patch size of the continuous model and investigate the quasi-stationary distribution of the number of individuals for patch sizes above the critical threshold.

DYNAMICS OF DROPLET COMBUSTION AND EXTINCTION GROUND TEST HARDWARE