[QUOTE=Darwin’s Finch]
You do realize, do you not, that what you are arguing against is Wilson’s extrapolation of the species-area relationship to extinction numbers, not that the current rate of extinctions does not exceed the background rate? I, myself, am skeptical about applying the relationship across ecological zones, and the term “forest” can apply to several such zones which should not necessarily be lumped together to arrive at a single area for evaluating expected diversity. That, and the fact that the constant C in the species-area relationship formula is not constant across ecological zones, and can often vary by several orders of magnitude between them (unlike the z coefficient, which only varies between around .15 - .50, regardless of zone). As such, any hard numbers that are coming from estimated species numbers for very large areas (wherein one could reasonably argue that the extent of the area does not represent a unified ecological zone) are suspect, at best.
However:
The “background extinction rate”, based on analyses of the fossil record, is typically cited at approx. 1 species / million species / million years, or from 10-100 species per year (note that this value is for all species). For mammals alone, the rate is approximately 1 species every 200 years.
The Red List’s summary of extinctions by major taxonomic group shows 74 mammal extinctions since about 1500 CE. This is over 29x the estimated background rate. However, an additional 163 mammal species are critically endangered, and 349 more are endangered. Were these groups to go extinct within the next 100 years or so, the extinction rate would skyrocket to over 195x the background rate (from 1500 CE - 2100 CE, the expected number of mammal extinctions based on the background rate would be…3 species).
Thus, the evidence does, indeed, support a higher-than-background extinction rate over the past 500 years or so, at least. It may not be as dramatic as Wilson, et al, are claiming, but it is not a figment.
[/QUOTE]
Darwin’s Finch, thank you for a thoughtful post.
You are correct that I am making two separate arguments. One is that Wilson’s extrapolation of the species-area law does not work in reverse (to predict extinctions) on the continents.
You seem, however, to have misunderstood my second argument, which is that the extinction rate on the continents is not very different from the historical rate.
Curiously, comparing extinction rates across time is not a simple task. We can’t simply compare modern extinctions with historical extinctions as you have done above. This is because the means of discovering the two are so different (direct observation vs. examining the fossil record). Since we are here now and we weren’t there then, we would expect to discover more modern extinctions than we would discover by looking at fossils.
Instead, we have to ask ourselves a slightly different question - what would an archaeologist a million years from now calculate as the extinction rate (for continental birds or mammals) for our time? We need to determine whether future paleontologists looking back at our fossil record would say our era was above or below the background rates. That way we are comparing apples and apples.
To calculate this uncertain figure, it is useful to use “fuzzy sets.” Traditional set theory includes the idea of exclusively being or not being a member of a set. For example, an animal is either alive or dead. However, for a number of sets, no clear membership can be determined. For example, is a person “old” if they are 55?
While no yes/no answer can be given, we can use fuzzy sets to determine the ranges of these types of values. Instead of the 1 or 0 used to indicate membership in traditional sets, fuzzy sets use a number between 0 and 1 to indicate partial membership in the set.
Fuzzy sets can also be used to establish boundaries around uncertain values. In addition to upper and lower values, these boundaries can include best estimates as well. For example, the number of mammalian species is given by the IUCN as 4,629 species. However, this is known to be an estimate subject to error, which is usually quoted as ± 10%.
This range of estimates of the number of mammal species can be represented by a triangular fuzzy number written as [4166, 4629, 5092], to indicate the upper and lower bounds, as well as the best estimate .
Fuzzy numbers can be used in place of regular numbers in any type of calculation, and the resulting uncertainties propagate through the calculation. If this is done across all membership values, the result is a fuzzy number showing the range of expected answers. (See the excellent work by Regan et. al. for a full explanation of these concepts.)
To use fuzzy numbers to compare extinction rates of continental mammals, we first have to determine how many of the 3 extinct continental mammal species will likely make it into the fossil record. Only one of the species (Bluebuck) was at all widespread, so the best estimate is that 1 species would show up in the fossil record. The low estimate would be that none would make it, and the high estimate would be 4, to allow for an extinct species that we might have missed. So the fuzzy number of extinct species found in the future fossil record for our times would be [0,1,4].
Next, we need to estimate the total number of continental species present in the future fossil record. We first need to estimate how many continental species there are, and then figure how many of them will make likely make it into the fossil record.
According to the IUCN, the number of mammal species endemic to islands is 581, with an additional 206 mammals endemic to Australia, for a total of 787. The lower limit, then, would be 787 species not in the record (less 10%, as this number is inexact and we want the smallest possible value). In addition, some endemic continual species will likely not make it into the record. A reasonable upper limit would be the total number of endemic mammal species, or 1,884 species + 10% uncertainty. The most likely number is probably around 1,200 species, so the fuzzy number we need to subtract from the total count of species is [708, 1200, 2072].
Our calculation of the observed extinction rate (OER, in species/year) for the last 500 years, then, is:
OER = ( [0, 1, 4] extinct mammals)/( [4166, 4629, 5092] mammal species - [708, 1200, 2072] endemic/island mammals) x 1/500 yrs
To calculate the relationship to the background extinction rate (BER), two more steps are necessary. First, we need to allow for uncertainty in the preservation potential, the chance that a species will be preserved. Foote (1997) estimated the preservation potential for fossil mammals as 67%, with a 99% confidence interval of 65% to 70%. Accordingly, I will use [.65, .67, .70] to represent this uncertainty.
Also, there is uncertainty in the fossil rate of mammal extinctions (in species/species million years), ranging from 0.21 (Alroy 1998) to 0.46 (Foote 1997). I will represent this as [.21, .46]. To complete the calculation of the relationship with the background extinction rate (OER/BER), then, we calculate:
OER/BER = OER X (.67 preser. poten.)/[.65, .67, .70] X 10^6 years/([.21,.46] species/species.
Doing the calculation shows that the most probable value of the observed continental mammalian extinction rate relative to background for the last half millennium is between 1.2 and 2.6 times the background rate, with a maximum range between 0 and 19 times the background continental extinction rate.
Using the same analysis for the continental birds, we obtain:
OER = [2, 3, 7]/([8705, 9672, 10639] - [1239, 1500, 2636] ) x 1/500 yrs
OER/ BER = OER X .67/[.65, .67, .70] X 10^6 years/ [.84, 1.84]
Doing the math shows the observed continental bird extinction rate is most likely between 0.4 and 0.9 times the background extinction rate, with the maximum range between 0.2 and 2.8 times the background rate.
Finally, I examined whether the Red List mammal figures would give us something radically different from the CREO figures. The CREO disqualified only five continental mammal species that appear on the Red List. Four of them were disqualified by CREO as being currently extant under a valid species name, and because of this finding by the CREO, the IUCN has referred these four species back to the relevant Red List Specialist Group for reconsideration.
If current biologists have trouble deciding if these are separate species, the chance of them being identified as separate species in the fossil record is zero. The fifth mammal, whose known range is only a single meadow, would also likely not make it into the record but might conceivably do so. This makes the fuzzy number for the Red List count of extinct continental mammals [0, 1, 5] instead of [0, 1, 4]. The effect of including the Red List mammals is to increase the possible maximum value from 19 to 23, without changing the most likely value range of 1.2 to 2.6 times background rate.
Since the results for modern extinction rates for both continental mammals and birds completely overlap the historical values, we cannot say that they are statistically different. About all we can say is that best estimate for continental mammals is between 1.2 and 2.6 times background, best estimate for continental birds is 0.4 to 0.9 times background. Neither of these seem to me to be a cause for concern.
My best to everyone,
w.