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From: gallagher@husc4.UUCP
Newsgroups: sci.bio,sci.astro,sci.misc
Subject: Re: Mass extinctions
Message-ID: <1587@husc6.UUCP>
Date: Mon, 6-Apr-87 00:30:37 EST
Article-I.D.: husc6.1587
Posted: Mon Apr  6 00:30:37 1987
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Reply-To: gallagher@husc4.UUCP (paul gallagher)
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In article <7697@ut-sally.UUCP> nather@ut-sally.UUCP (Ed Nather) writes:
>...and anyone else who deals with time-series analysis of noisy data.  When
>astronomers get results as uncertain, they go back to the telescope to get
>more data.  The basic problem lies in the tranformation of noise (as well as
>signal) in the power spectrum analysis process.  The resulting noise is far
>from friendly (Gaussian) and is, I'm told, a Chi-squared distribution with
>n-1 degrees of freedom, where n is the number of data points in the spectrum.
>I *do* know it is VERY easy to get "peaks" in the power spectrum due to
>happenstance noise buildup that have no basis in reality (whatever *that* is).
>This is not to say the claimed periodicity is not real --- just not proven.
>I'd suggest more data, with less noise.
>-- 
>Ed Nather

Here is Raup and Sepkoski's reply (SciENcE, 2/21/86, Volume 231, pp.833-836):

  The claims of periodicity have produced considerable controversy.  Many of
  the negative criticisms can be summarized by two fundamental arguments: first,
  periodicity is just an artifact of uncertainties in the geologic time scale or
  in the identification of extinction events; second, periodicity is the natural
  consequence of many complex causes of extinction operating independently.

  The first argument says that inclusion of random noise in the form of spurious
  data could create the appearance of periodicity where none actually exists.
  The analyses in question start by asking whether extinction events are 
  randomly distributed in time.  This is the fundamental null hypothesis for
  formal statistical testing as well as the conventional wisdom in paleontology.
  Only if this hypothesis of randomness can be rejected with high confidence
  can a search for nonrandom patterns begin.  Inaccurate geologic dates or
  nonexistent extinction events will degrade the sample in a direction toward
  randomness and away from any regular signal.  Thus, to include uncertain
  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  data is to make statistical testing more conservative.  To argue that 
  uncertainty in data explains the observed periodicity is illogical.

  The second argument is based on a misconception of randomness.  If
  extinction events (as opposed to individual species extinctions) are 
  caused by a complex of time-independent processes, they should exhibit
  a random (Poisson) distribution in time, typified by irregular clusters
  of closely spaced events separated by gaps of widely varying length.
  Even if the individual events in a cluster cannot be distinguished
  because of poor time resolution, the clusters themselves will be
  irregularly spaced.  The surprisingly uniform spacing of extinction
  events in Mesozoic-Cenozoic time is thus distinctly atypical of phenomena
  driven by complexes of independent processes.

Raup and Sepkoski perform their time-series analysis using a method developed
by Stothers,"in which the goodness of fit of the timings of the extinction
events to a set of periodic impulse functions with differing wavelengths is
assessed.  Goodness of fit is measured by the standard deviation of the
differences between observed and expected times of extinction events for
a given period length (in its best fit position).  The lower the standard
deviation, the better the fit.  For each individual period length, the
probability that the observed fit could have occurred by chance was
computed by comparing that fit with fits obtained by a large number of
randomized versions of the same data. " The reference given is R.B.Stothers,
Astron. Astrophys. Vol. 77, 121 (1979).

Their conclusion is that the eight major extinction events of marine families
over the past 250 million years "stand significantly above local background
(P < 0.05)"; the events are more pronounced when when analyzed at the level
of genus.  Time series analysis strongly suggest a 26-million year periodicity;
"when the time series is limited to the four best-dated events..., the 
hypothesis of randomness is also rejected for the 26-million year period 
(P < 0.0002)."

Raup is very persuasive, but, unfortunately, I'm in no position to
evaluate his use of statistics, so I'll leave to others on the net to do so.
I'm well aware of the way biologists and others have misused statistics,
and I'm also aware that the paleontological record may be a very biased
sample of previously existing life.  For example, paleontologists do
most of their research close to home.  That means most of the fossil record
comes from those areas with a day's bus ride from major universities!

Paul Gallagher