The end-Permian extinction was the most severe mass extinction in the history of life, yet its causes are not well understood. Here, we use probabilistic food web models to explore how disruption of primary production could have caused the collapse of end-Permian terrestrial ecosystems. This poster was presented in the Geological Society of America's Annual Conference (Baltimore, 2015)

1. Conclusion and Future Research
References
Results and Verification
Introduction
1Brandon Chow, 1Meghana Ranganathan, 1Steve C. Wang, 2Peter Roopnarine, 3Kenneth Angielczyk
1Dept. of Mathematics and Statistics, Swarthmore College; 2Dept. of Invertebrate Zoology and Geology, California Academy of Sciences; 3Integrative Research Center, Field Museum
Inferring Primary Extinction Levels in Late Permian Food Webs Using
Approximate Bayesian Computation
Methods: ABC SMC
The end-Permian extinction was the most severe mass
extinction in the history of life, yet its causes are not well
understood. Here we use probabilistic food web models to
explore how disruption of primary production could have caused
the collapse of end-Permian terrestrial ecosystems.
We know the total extinction as a result of the end-Permian
extinction: that is, how many species ultimately went extinct. To
examine the causes of this mass extinction, we want to infer the
level of primary extinction, or the proportion of species that went
extinct as a direct effect of the cause of this extinction.
First, we construct food webs for the Late Permian Dicynodon
Assemblage Zone community of the Karoo Basin, South Africa.
Next, we use the computer program CEG (Cascading
Extinctions on Graphs) [1] to simulate the effect of applying
varying levels of primary extinction to guilds in these food webs.
This probabilistic forward model allows us to estimate the total
extinction that would result from such primary extinctions in
these terrestrial communities.
(3) Continue simulating
total extinctions and keep
primary extinction levels
that yield values within
distance εi of the
observed total extinction,
until the Nth distribution is
centered on true level of
primary extinction
This research has two main purposes. First, we
hope to better understand the causes of the end-
Permian extinction. Second, we aim to explore a
new method for investigating problems in
statistical paleontology that are computationally
intensive. In the future, we hope to further refine
our ABC model to improve our estimates of the
level of primary extinction leading to the Permian
extinction.
The posteriors estimated by ABC indicate high levels of primary extinction for
most guilds. This suggests that most species went extinct immediately, rather
than indirectly, during the end-Permian extinction. To verify our estimates, we
sample levels of primary extinction from the posterior of each guild, use CEG
to simulate the resulting total extinction, and compare these results to the
observed values. The simulated values were consistent with the observed
values, demonstrating that the methodology is sound.
To check: Sample
primary extinction from
posterior, simulate total
extinction using CEG,
compare to observed
total extinction (red
line).
Inferred Primary Extinction
Prior
ε1 ε2
. . .
εN-1 εN
PosteriorIntermediate Distributions
(1) Begin with
uniform prior
distribution over
possible levels
of primary
extinctions
(2) Use CEG to simulate total
extinction resulting from this
level of primary extinction.
Keep this primary extinction
level if simulated total
extinction is within distance εi
of observed value; otherwise
discard it.
[1] PD Roopnarine, KD Angielczyk, SC Wang, R Hertog (2007): Trophic
network models explain instability of Early Triassic terrestrial
communities. Proc. Royal Society B 274.
[2] T Toni, D Welch, N Strelkowa, A Ipsen, MPH Stumpf (2009):
Approximate Bayesian computation scheme for parameter inference and
model selection in dynamical systems. J. Royal Society Interface 6.
[3] FV Bonassi, M West (2015): Sequential Monte Carlo with adaptive
weights for approximate Bayesian computation. Bayesian Analysis 10.
[4] K Scranton, J Knape, P de Valpine (2014): An approximate Bayesian
computation approach to parameter estimation in a stochastic stage-
structured population model. Ecology 95.
[5] BM Turner, T Van Zandt (2012): A tutorial on approximate Bayesian
computation. J. Math. Psychology 56.
Simulated Total Extinction
We then use Approximate Bayesian Computation Sequential
Monte Carlo (ABC SMC) [2–5] to solve the inverse problem:
namely, inferring the level of primary extinction responsible for
the end-Permian extinction. ABC SMC works by randomly
sampling primary extinction values from a prior distribution and
keeping only those that result in output (i.e., total extinctions)
similar to the observed data. This process is then iterated to
sequentially narrow the range of plausible perturbations,
thereby arriving at the posterior distribution of perturbation
levels.
CEG
ABC SMC
Total
Extinction
Primary
Extinction