492
swarms that, of late, have provided ample probability statistics on pre-existing
levels of risk at all levels, including “partial survival and extinction,” a mathematically paradoxical condition.
46
The notion of partial comports with the idea of tendency, a subjectively held
view of observations, relations, and qualified data, considering its anthropic bias
that is inevitably tied to all empirical as well as theoretical decision making, on our
part.
47
These components of the subjective, in turn, invoke deliberation of “chance
events,” “expectation,” and “variance”.
48
Because we think of ecosystems as dynamic, forever in flux, circumvention of
punctuation marks and all, there are distinct “bifurcation points.” These philosophical junctures have taken probability theories to the threshold of an interdisciplinary
focal point on our species and its likely fate. It is a not surprising ecological obsession in the twenty-first century, that began with other mammals.
49
Its logic then
encompassed whole populations,
50
mathematical formulas for re-discovering socalled Lazarus species (those thought to be extinct that are not; or, conversely, the
“living dead,” those whose little remaining time has been all but calculated),
51
or for
re-introducing extinct species like the Passenger Pigeon.
52
Of late, this logical
stream has increasingly determined that we are among the next to go, however
prematurely.
53
46 See “Partial Survival and Extinction of Species in Discrete Nonautonomous Lotka-Volterra
Systems,” by Yoshiaki Muroya, Tokyo Journal of Mathematics, Volume 28. Number 1, 2005, 189200, Project Eucid mathematics and statistics online, https://projecteuclid.org/euclid.
tjm/1244208288, Accessed May 16, 2020. See also, ‘Extinction in competitive Lotka-Volterra systems,” by M. L. Zeeman, Proceedings Of The American Mathematical Society, 123, 1995, 87–96,
MSC: Primary 92D25; Secondary 34C05, 34D20, 34D45, 92D40, https://doi.org/10.1090/S00029939-1995-1264833-2, MathSciNet review: 1264833, https://www.ams.org/journals/proc/1995123-01/S0002-9939-1995-1264833-2/. Accessed May 16, 2020.
47 See “Probability Theory,” T. Rudas, in the International Encyclopedia of Education (Third
Edition), 2010, ScienceDirect, https://www.sciencedirect.com/topics/social-sciences/probabilitytheory, Accessed May 16, 2020.
48 “Basic Probability,” https://seeing-theory.brown.edu/basic-probability/index.html, Accessed
May 16, 2020.
49 “Investigating Anthropogenic Mammoth Extinction with Mathematical Models,” by Michael
Frank, Anneliese Slaton, Teresa Tinta and Alex Capaldi, Spora: A Journal of Biomathematics,
Volume 1, Issue 1, Article 3, 2015, https://core.ac.uk/download/pdf/48841606.pdf.
50 “Stochastic models of population extinction,” by Otso Ovaskainen and Baruch Meerson, https://
arxiv.org/pdf/1008.1162.pdf; “A math equation that predicts the end of humanity,” by William
Poundstone, Vox, July 15, 2019, https://www.vox.com/the-highlight/2019/6/28/18760585/doomsday-argument-calculation-prediction-j-richard-gott, Accessed May 16, 2020.
51 See “The mathematics of species extinction,” n.a., Mathematical Institute, University of Oxford,
January 19, 2017, https://www.maths.ox.ac.uk/node/16490, Accessed May 16, 2020.
52 “Mathematical Modeling in Ecology: Simulating the Reintroduction of the Extinct Passenger
Pigeon (Ectopistes migratorius), by Erin Boggess, Jordan Collignon, and Alanna Riederer,
VERUM 2015, Valparaiso University, University 28, 2015, https://www.valpo.edu/mathematicsstatistics/files/2014/09/Capaldi2015.pdf.
53 See, for example, “Mathematical law could anticipate the possibility of mass extinctions in ecosystems,” Newsroom, Universitat Autonoma de Barcelona, September 10, 2018, https://www.uab.
52 The Extinction Probability Era
swarms that, of late, have provided ample probability statistics on pre-existing
levels of risk at all levels, including “partial survival and extinction,” a mathematically paradoxical condition.
46
The notion of partial comports with the idea of tendency, a subjectively held
view of observations, relations, and qualified data, considering its anthropic bias
that is inevitably tied to all empirical as well as theoretical decision making, on our
part.
47
These components of the subjective, in turn, invoke deliberation of “chance
events,” “expectation,” and “variance”.
48
Because we think of ecosystems as dynamic, forever in flux, circumvention of
punctuation marks and all, there are distinct “bifurcation points.” These philosophical junctures have taken probability theories to the threshold of an interdisciplinary
focal point on our species and its likely fate. It is a not surprising ecological obsession in the twenty-first century, that began with other mammals.
49
Its logic then
encompassed whole populations,
50
mathematical formulas for re-discovering socalled Lazarus species (those thought to be extinct that are not; or, conversely, the
“living dead,” those whose little remaining time has been all but calculated),
51
or for
re-introducing extinct species like the Passenger Pigeon.
52
Of late, this logical
stream has increasingly determined that we are among the next to go, however
prematurely.
53
46 See “Partial Survival and Extinction of Species in Discrete Nonautonomous Lotka-Volterra
Systems,” by Yoshiaki Muroya, Tokyo Journal of Mathematics, Volume 28. Number 1, 2005, 189200, Project Eucid mathematics and statistics online, https://projecteuclid.org/euclid.
tjm/1244208288, Accessed May 16, 2020. See also, ‘Extinction in competitive Lotka-Volterra systems,” by M. L. Zeeman, Proceedings Of The American Mathematical Society, 123, 1995, 87–96,
MSC: Primary 92D25; Secondary 34C05, 34D20, 34D45, 92D40, https://doi.org/10.1090/S00029939-1995-1264833-2, MathSciNet review: 1264833, https://www.ams.org/journals/proc/1995123-01/S0002-9939-1995-1264833-2/. Accessed May 16, 2020.
47 See “Probability Theory,” T. Rudas, in the International Encyclopedia of Education (Third
Edition), 2010, ScienceDirect, https://www.sciencedirect.com/topics/social-sciences/probabilitytheory, Accessed May 16, 2020.
48 “Basic Probability,” https://seeing-theory.brown.edu/basic-probability/index.html, Accessed
May 16, 2020.
49 “Investigating Anthropogenic Mammoth Extinction with Mathematical Models,” by Michael
Frank, Anneliese Slaton, Teresa Tinta and Alex Capaldi, Spora: A Journal of Biomathematics,
Volume 1, Issue 1, Article 3, 2015, https://core.ac.uk/download/pdf/48841606.pdf.
50 “Stochastic models of population extinction,” by Otso Ovaskainen and Baruch Meerson, https://
arxiv.org/pdf/1008.1162.pdf; “A math equation that predicts the end of humanity,” by William
Poundstone, Vox, July 15, 2019, https://www.vox.com/the-highlight/2019/6/28/18760585/doomsday-argument-calculation-prediction-j-richard-gott, Accessed May 16, 2020.
51 See “The mathematics of species extinction,” n.a., Mathematical Institute, University of Oxford,
January 19, 2017, https://www.maths.ox.ac.uk/node/16490, Accessed May 16, 2020.
52 “Mathematical Modeling in Ecology: Simulating the Reintroduction of the Extinct Passenger
Pigeon (Ectopistes migratorius), by Erin Boggess, Jordan Collignon, and Alanna Riederer,
VERUM 2015, Valparaiso University, University 28, 2015, https://www.valpo.edu/mathematicsstatistics/files/2014/09/Capaldi2015.pdf.
53 See, for example, “Mathematical law could anticipate the possibility of mass extinctions in ecosystems,” Newsroom, Universitat Autonoma de Barcelona, September 10, 2018, https://www.uab.
52 The Extinction Probability Era