In this talk, I shall examine the problems of species extinction at the macro- and micro-levels. At the macro-level, I shall consider the statistics of extinction in the fossil record. At the micro-level, I shall try to extract a few facts from the limited data we have about the thylacine population in the late nineteenth and early twentieth centuries.
Extinctions of families over time Time measured in millions of years (Ma) before present. Graph shows the number of families of organisms which went extinct in each time period. Source: The Fossil Record 2 Database, M. J. Benton.
Extinctions (EXT) against time interval (INT): Taxonomic families have become extinct at a rate of 5.858 families/Ma over the last 550 MY.
Pearson residuals of extinctions Permian-Triassic (251 Ma). Ordovician-Silurian (444 Ma). Triassic-Jurassic (200 Ma). Devonian-Carboniferous series of extinctions (360 Ma). Cretaceous-Tertiary (65 Ma). Goodbye T-rex! End Eocene event (33 Ma). Holocene extinction (0 Ma). Goodbye us?
Mass extinctions: standard? Variation in size of extinctions far exceeds “background noise.” I.e., extinctions of taxa are clustered not independent. Mass extinctions are extreme but not exceptional. (David Raup, 1991). Mass extinctions are both extreme and exceptional (Richard Bambach & Andrew Knoll, 2001).
Extinctions have occurred at a fairly constant rate on average over time despite occasional mass extinctions.
New taxa have been appearing at a fairly constant rate over time (with a slight increase in speed over the last 50 Ma).
Diversity over time (Ma) The diversity of taxa (in this case families) at any given time has been steadily increasing (with a slight drop at the end of the Palaeozoic).
The hazards of extinction The statistical approach to studying these extinctions is to treat each species or family as subject to an ongoing hazard of extinction. This hazard is quantified by means of a hazard function whose value can change over time. The probability of extinction will depend upon the value of the hazard integrated over time.
Winners and losers Winner? (> 10 8 years) Loser? (4 x 10 6 years)
Estimating nonconstant hazard functions To estimate the hazard function, we would like to observe extinctions in the fossil record and when they happened. So we would like to know the precise number of taxa that are extant at different times. Unfortunately, this is difficult: counts are binned into time periods, dating of individual fossils is uncertain pseudoextinction, Lazarus taxa, Elvis taxa. At best we use proxy variables at any time we can determine the taxa that appear before and after that time.
Comments Most extinctions are “mass extinctions.” The Generalised BD model is useful for hazards, but does not fit other aspects of data well. Models for extinctions must explain the homogeneity of extinctions and originations in the face of increasing diversity of taxa. Research may be concentrating too much on taxa and not enough on ecological niches (D. H. Erwin, 2006). We should be modelling hazards and not simply fitting them. Current work is investigating modelling the extinction rate as a nonnegative strongly stationary process. Without modelling there are no null hypotheses: 26 Ma cycles of extinction? (Raup and Sepkoski,1984). Statistical artefact? (Stigler and Wagner). The error analysis of proxy variables is nontrivial. It is formally equivalent to the problem of estimating the support of a distribution. C. Marshall (1994), but more work necessary!
Possible sources of thylacine decline: Hunting and trapping (the latter for zoos worldwide). Destruction of habitat. Competition with wild dogs. Disease (esp. reports of a “distemper-like” disease, 1910).
This time series is the outcome of a number of factors including thylacine demographics human demographics, and socio-economic factors associated with the settlement of Tasmania at the time. It is difficult to extract information about the thylacine from such data sets because they have information about both humans and thylacines. These factors are confounded. To extract information about the thylacine demographics alone, we must either find additional ancillary information about the socio-economic activity, or find a mathematical model for the socio-economic activity. Both approaches can be viable, but the second is difficult because, to put it simply, human beings rarely obey the equations imposed on them.
Records at VDL Company, Woolnorth (E. Guiler, 1985) 189926 Aug.Tom went to the Mount to look after a tiger with his dogs. 2 Nov.Sent some men to hunt tiger out of Studland Bay run. 11 Nov.All hands in a.m. hunting a tiger out of the Forest. Set snares for a tiger on Saltwater Creek fence. 18906 Feb.Tracks seen in Forest. 27 MayChasing tiger in the Forest. 17 JulyTiger at Studland Bay, at the Knolls. 18911 Aug.Laid poison at Harcus for hunters’ dogs. 189226 Aug.Two men to Studland Bay to shift tiger. 1893No comments.
Records at VDL Company, Woolnorth (continued) 189820 Feb.One tiger caught, no locality given. 20 JulyOne tiger caught, McCabe’s Paddock 31 Dec.Snaring in the Forest. 18993 JulySaw two tigers at Swan Bay. 6 JulyCaught two tigers in Forest and Three Sticks 22 JulyTiger scaring on Three Sticks and Studland Bay 23 Nov.One tiger caught, probably at the Mount. 190024 Jan.One tiger caught, locality not stated. 8 Feb.Tiger scaring at Three Sticks
Thylacine Population around Woolnorth 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 189818991900190119021903190419051906 Year Population estimate Exponential fit from regression
Comments The data suggest that by the beginning of the twentieth century the decline in the thylacine population was substantial. While a “distemper-like” disease may have contributed to thylacine decline, the evidence is that the thylacine was disappearing before this. Habitat, dogs and hunting are the main factors to be considered.
References Bambach, R. K. & Knoll, H. (2001). “Is there a separate class of `mass extinctions?’” GSA Annual Meeting, 5—8 November 2001. Erwin, Douglas H. (2006). Extinction: How Life on Earth Nearly Ended 250 Million Years Ago. Princeton University. Guiler, Eric R. (1985). Thylacine: The Tragedy of the Tasmanian Tiger, Oxford University. Marshall, C. R. (1994). “Confidence intervals on stratigraphic ranges: partial relaxation of the assumption of randomly distributed fossil horizons.” Paleobiology 20, 459—469. Raup, D. M. (1991). Extinction: Bad Genes or Bad Luck? Norton. Raup, D. M. & Sepkoski, J. J. Jr. (1984). “Periodicity of extinction in the geologic past.” Proc. Nat. Acad. Sci. USA 81, 801—805. Stigler, S. M. & Wagner, M. J. (1987). “A substantial bias in nonparametric tests for periodicity in geophysical data.” Science 13, 940—945. Stoyan, D. (1980). “Estimation of transition rates of inhomogeneous birth- death processes with a paleontological application.” Elektronische Informationsverabeitung u. Kybernetic 16, 647—649.