Whatever,
Given that the phylogenies (cladistic analyses) under study are independent of stratigraphy, it is possible to compare the two to see how well they match. There are two main reasons for disagreement. 1/ The phylogeny is wrong, & 2/ the fossil record is so poor that the daughter species is found in older rock than the parent. Given that this is the case, we should expect a very low SCI (SCI is the ratio of consistent to inconsistent nodes in a cladogram) value if evolution were not indicative of reality. ie. Nodes (in complex trees) match by chance rather than signal. In other words, the null hypothesis is that the SCI value will be a low value.
Cladistics & stratigraphy
Stratigraphic Consistency Index
The SCI metric may also be summarized either as a mean value for each taxonomic group or as a proportion of cladograms that score SCI values of 0.500 or more, an indication that half, or more, of the branches are consistent with stratigraphic evidence. By both measures, fishes and echinoderms score better than tetrapods. Mean SCI values are: echinoderms (0.773), fishes (0.757), and tetrapods (0.701). Proportions of cladograms with SCI values $0.500 are tetrapods (100%), echinoderms (94%), and fishes (93%). For both measures, values for all three groups are indistinguishable according to binomial error bars (Fig. 3).
Within the sample of echinoderm cladograms, nonechinoids show somewhat better results than echinoids but not significantly so (Fig. 3). The mean SCI value for echinoids is 0.724, and for nonechinoids 0.849; moreover, 90%of echinoid cladograms have SCI values $ 0.500,compared with 100% for nonechinoids.
SCI values for fish groups are variable but not significantly different (Fig. 3). For mean SCI values, the order is as follows: sarcopterygians (0.904), teleosts (0.744), placoderms(0.741), agnathans (0.733), and actinopterygians (0.722). In all cases, all sampled cladograms show SCI values > 0.500. The rankings of tetrapod groups by both aspects of the SCI metric are comparable. Mean SCI values give this sequence: mammals (0.837), mammallike reptiles (0.729), lepidosauromorphs (0.714), dinosaurs (0.698), archosauromorphs (0.660), and turtles (0.586). The low value for turtles is significantly lower than the high values for synapsids, mammals, and mammallike reptiles. Proportions of cladograms with SCI values $ 0.500 give this sequence: mammals (100%), mammallike reptiles (100%), lepidosauromorphs (100%), turtles (100%), dinosaurs (86%), and archosauromorphs (78%)."
Why is the SCI so high? Why do cladograms & stratigraphy match on the whole if evolution is not indicative of reality? Given that cladograms & stratigraphy match relatively well, how do you explain this significant correlation?
Given there is a clear signal of "evolution" in the rock stratigraphy & morphology combined, & that the null hypothesis is falsified, it therefore stands to reason that where these phylogenies would infer large scale morphological change (Cetaceans, basal tetrapoda, & basal amniotes, for example). Evolution can be reliably inferred.
What are the chances of this occurring by chance? (Thanks to Rrhain for the maths help.)
The average cladogram has six taxa, meaning five nodes. Giving you the benefit of the doubt for ease of calculation we’ll assume only 60% (average) nodes (rather than ~75%) corroborate for ease of calculation.
C(n,k) * r! * {1 - [1 - 1/2! + 1/3! - 1/4! + ... + (-1)^(r+1)*1/r!]} / n!
n= total no. of nodes
K= correct nodes
r= n-k= incorrect no. of nodes
C(5,3) * 2! * [1 - (1 - 1/2!)] / 5!
10 * 2 * (1/2) / 120
10/120
1/12
There is a 12:1 chance of getting the average cladogram to match stratigraphy as well as it does. There is therefore a 12^300:1 chance of getting 300 cladograms to match stratigraphy in this way.
5.68*10^323:1
568,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 : 1 ....chance of 300 cladograms
only enjoying a 60% (as opposed to a 75% corroboration with stratigraphy).
What this means is once all else is accounted for, is that there is a stratigraphic signal supporting evolution beyond all reasonable doubt.
The questions I would like answered, Whatever, is this; how does liquefaction/flooding produce an evolutionary pattern?
Good luck.
Mark
"Physical Reality of Matchette’s EVOLUTIONARY zero-atom-unit in a transcendental c/e illusion" - Brad McFall
[This message has been edited by mark24, 01-27-2004]