TOWARDS A STATISTICAL DEFINITION OF A SPECIES IN TERMS OF PROBABILITIES OF CONSPECIFICITY,

1. TOWARDS A STATISTICAL DEFINITION OF A SPECIES IN TERMS OF PROBABILITIES OF CONSPECIFICITY, WITH EXAMPLES DRAWN FROM THE STUDY OF AFRICAN PLIO-PLEISTOCENE HOMINIDS FRANCIS THACKERAY DIRECTOR, TRANSVAAL MUSEUM PRETORIA SOUTH AFRICA Director, Human Origins and Past Environments Programme (HOPE) mrsples@global.co.za

2. PROBLEM: HOW TO RECOGNISE DIFFERENT SPECIES WHICH ARE DISTANT RELATIVES OF HUMANKIND?

3. PROBLEM: HOW TO RECOGNISE DIFFERENT SPECIES WHICH ARE DISTANT RELATIVES OF HUMANKIND POTENTIAL SOLUTION: MORPHOMETRIC ANALYSES OF MODERN SPECIMENS WHICH ARE KNOWN TO BELONG TO THE SAME SPECIES, USING LEAST SQUARES REGRESSION ANALYSIS

4. Y AXIS REGRESSION LINE y = mx + c B X AXIS MEASUREMENTS OF SPECIMEN A

5. Y AXIS REGRESSION LINE y = mx + c m: slope B STANDARD ERROR OF THE m COEFFICIENT “DEGREE OF SCATTER AROUND REGRESSION LINE” X AXIS MEASUREMENTS OF SPECIMEN A

6. ULTIMATE OBJECTIVES: • 1. TO FIND A WAY TO DEFINE A SPECIES STATISTICALLY • TO ASSESS “PROBABILITIES OF CONSPECIFICITY” (THE PROBABILITY THAT TWO SPECIMENS REPRESENT THE SAME SPECIES) • WHEN TWO SPECIMENS ARE COMPARED

7. ULTIMATE OBJECTIVES: • 1. TO FIND A WAY TO DEFINE A SPECIES STATISTICALLY • TO ASSESS “PROBABILITIES OF CONSPECIFICITY” (THE PROBABILITY THAT TWO SPECIMENS REPRESENT THE SAME SPECIES) • WHEN TWO SPECIMENS ARE COMPARED • RECOGNISING THAT • BOUNDARIES BETWEEN SPECIES • ARE NOT NECESSARILY ALWAYS CLEAR

8. APPLICATION TO FOSSILS FROM THE “CRADLE OF HUMANKIND” WORLD HERITAGE SITE, SOUTH AFRICA, AND TO FOSSILS FROM OTHER AREAS OF AFRICA, THE CONTINENT FROM WHICH “PROGENITORS” OF HUMANKIND EVOLVED

9. DARWIN NOTED THAT OF ALL LIVING PRIMATES, IT IS THE CHIMPANZEE AND GORILLA THAT ARE MOST SIMILAR TO HOMO SAPIENS, IN TERMS OF SKELETAL AND CRANIAL ANATOMY

10. DARWIN NOTED THAT OF ALL LIVING PRIMATES, IT IS THE CHIMPANZEE AND GORILLA THAT ARE MOST SIMILAR TO HOMO SAPIENS, IN TERMS OF SKELETAL AND CRANIAL ANATOMY SECONDLY, HE NOTED THAT IT WAS ONLY IN AFRICA THAT CHIMPANZEES AND GORILLA ARE DISTRIBUTED

11. DARWIN NOTED THAT OF ALL LIVING PRIMATES, IT IS THE CHIMPANZEE AND GORILLA THAT ARE MOST SIMILAR TO HOMO SAPIENS, IN TERMS OF SKELETAL AND CRANIAL ANATOMY SECONDLY, HE NOTED THAT IT WAS ONLY IN AFRICA THAT CHIMPANZEES AND GORILLA ARE DISTRIBUTED DARWIN CONCLUDED THAT THE “PROGENITORS” (ANCESTORS) OF HUMANKIND EVOLVED ON THE AFRICAN CONTINENT, “THE CRADLE OF HUMANKIND”

12. CRADLE OF HUMANKIND ZIMBABWE MOZAMBIQUE BOTSWANA NAMIBIE Makapansgat Pretoria Cradle of Humankind SWAZILAND Johannesburg Taung N LESOTHO Durban 0 200 Cape Town km (UNESCO World Heritage Site since 1999)

13. SWARTKRANS STERKFONTEIN KROMDRAAI STERKFONTEIN: “MRS PLES” PLESIANTHROPUS: “ALMOST HUMAN” FOSSIL HOMINID, 2.15 MILLION YEARS OLD AUSTRALOPITHECUS AFRICANUS, A DISTANT RELATIVE OF ALL HUMANKIND

14. “MRS PLES”: AUSTRALOPITHECUS AFRICANUS

17. SWARTKRANS STERKFONTEIN KROMDRAAI SWARTKRANS: “ROBUST” HOMINIDS PARANTHROPUS FOSSIL HOMINID, 1.0 – 1.7 MILLION YEARS OLD

18. PARANTHROPUS (AUSTRALOPITHECUS) ROBUSTUS

19. HOMO HABILIS, HOMO ERECTUS, HOMO ERGASTER

21. SWARTKRANS STERKFONTEIN KROMDRAAI KROMDRAAI: “ROBUST” HOMINIDS PARANTHROPUS ROBUSTUS FOSSIL HOMINID, 1.0 – 2.0 MILLION YEARS OLD

22. PARANTHROPUS (AUSTRALOPITHECUS) ROBUSTUS

23. EARLY HOMO

26. KROMDRAAI TM 1517 PARANTHROPUS ROBUSTUS

27. 3 DIMENSIONAL RECONSTRUCTION OF “MRS PLES” BASED ON CT SCANS (BRAGA, TREIL, THACKERAY)

28. PARTIAL SKELETON OF “MRS PLES” AUSTRALOPITHECUS AFRICANUS STERKFONTEIN, 2.15 MILLION YEARS OLD

29. ALGEBRAIC BIOLOGY SKULL MEASUREMENTS or TOOTH MEASUREMENTS or SKELETAL MEASUREMENTS B MEASUREMENTS OF SPECIMEN A

30. B MEASUREMENTS OF SPECIMEN A

31. Y AXIS REGRESSION LINE y = mx + c B X AXIS MEASUREMENTS OF SPECIMEN A

32. SPECIMENS A AND B ARE SAME SPECIES LITTLE SCATTER AROUND REGRESSION LINE SIMILAR SHAPE B MEASUREMENTS OF SPECIMEN A

33. SPECIMENS A AND B ARE SAME SPECIES LITTLE SCATTER AROUND REGRESSION LINE SIMILAR SHAPE B y = mx + c Low standard error of m coefficient: (sem) MEASUREMENTS OF SPECIMEN A

34. SPECIMENS A AND B ARE DIFFERENT SPECIES MUCH SCATTER AROUND REGRESSION LINE DIFFERENT SHAPE B MEASUREMENTS OF SPECIMEN A

35. SPECIMENS A AND B ARE DIFFERENT SPECIES MUCH SCATTER AROUND REGRESSION LINE DIFFERENT SHAPE B y = mx + c High standard error of m coefficient: (sem) MEASUREMENTS OF SPECIMEN A

36. FOSSILS A AND B HAVE A HIGH PROBABILITY OF CONSPECIFICITY LITTLE SCATTER AROUND REGRESSION LINE SIMILAR SHAPE B y = mx + c Low standard error of m coefficient: (sem) MEASUREMENTS OF SPECIMEN A

37. FOSSILS A AND B HAVE A LOW PROBABILITY OF CONSPECIFICITY MUCH SCATTER AROUND REGRESSION LINE DIFFERENT SHAPE B y = mx + c High standard error of m coefficient: (sem) MEASUREMENTS OF SPECIMEN A

38. CHALLENGE • WHAT IS THE FRAME OF REFERENCE FOR ASSESSING “PROBABILITIES OF CONSPECIFICITY” ?

39. EXPLORATORY STUDY: PAIRWISE COMPARISONS OF SPECIMENS OF EXTANT ANIMALS THAT CERTAINLY BELONG TO THE SAME SPECIES

40. EXPLORATORY STUDY: PAIRWISE COMPARISONS OF SPECIMENS OF EXTANT ANIMALS THAT CERTAINLY BELONG TO THE SAME SPECIES FOR EXAMPLE: SKULL MEASUREMENTS OF WILDEBEEST A SKULL MEASUREMENTS OF WILDEBEEST B

41. SPECIMENS A AND B LITTLE SCATTER AROUND REGRESSION LINE (sem =0,031) SIMILAR SHAPE B y = 1.103x - 0.234sem = 0.031 Low standard error of m coefficient: (sem) MEASUREMENTS OF WILDEBEEST SPECIMEN A

42. EXPLORATORY STUDY: PAIRWISE COMPARISONS OF SPECIMENS OF EXTANT ANIMALS THAT CERTAINLY BELONG TO DIFFERENT SPECIES FOR EXAMPLE: SKULL MEASUREMENTS OF WILDEBEEST A SKULL MEASUREMENTS OF HARTEBEEST B

43. SPECIMENS A AND B HAVE A LOW PROBABILITY OF CONSPECIFICITY MUCH SCATTER AROUND REGRESSION LINE DIFFERENT SHAPE B y = 1.103 x - 0.04 sem = 0.073 High standard error of m coefficient: (sem) MEASUREMENTS OF SPECIMEN A

44. SPECIMENS A AND B LITTLE SCATTER AROUND REGRESSION LINE (sem =0,021) SIMILAR SHAPE B y = 1.103x - 0.234sem = 0.031 Low standard error of m coefficient: (sem) MEASUREMENTS OF WILDEBEEST SPECIMEN A

45. MEAN sem = 0.03 BASED ON 25 MODERN TAXA VERTEBRATES (CONSPECIFICS) N 0.03 0.07 SEM (STANDARD ERROR) BASED ON PAIRWISE COMPARISONS

46. MEAN sem = 0.03 BASED ON 25 MODERN TAXA VERTEBRATES (CONSPECIFICS) N WILDEBEEST A AND B 0.03 0.07 SEM (STANDARD ERROR) BASED ON PAIRWISE COMPARISONS

47. MEAN sem = 0.03 BASED ON 25 MODERN TAXA VERTEBRATES (CONSPECIFICS) WILDEBEEST A HARTEBEEST B N WILDEBEEST A AND B 0.03 0.07 SEM (STANDARD ERROR) BASED ON PAIRWISE COMPARISONS

48. ASSYMETRIC DISTRIBUTION OF sem VALUES MEAN sem = 0.03 BASED ON 25 MODERN TAXA VERTEBRATES (CONSPECIFICS) N WILDEBEEST A AND B 0.03 0.07 SEM (STANDARD ERROR) BASED ON PAIRWISE COMPARISONS

49. ASSYMETRIC DISTRIBUTION OF sem VALUES MEAN sem = 0.03 WHAT HAPPENS WITH LOG TRANSFORMATION (BASE 10 ?) N 0.03 0.07 SEM (STANDARD ERROR) BASED ON PAIRWISE COMPARISONS

50. LOG NORMAL DISTRIBUTION OF sem VALUES OBTAINED FROM CONSPECIFIC PAIRS LOG MEAN SEM = -1.78 +/- 0.27 BASED ON 76 MODERN TAXA VERTEBRATES AND INVERTEBRATES N LOG STANDARD ERROR OF m (LOG sem) BASED ON PAIRWISE COMPARISONS