TOWARDS A STATISTICAL DEFINITIONOF A SPECIES IN TERMS OF PROBABILITIES OF CONSPECIFICITY,WITH EXAMPLES DRAWN FROM THE STUDYOF AFRICAN PLIO-PLEISTOCENE HOMINIDS
FRANCIS THACKERAY DIRECTOR, TRANSVAAL MUSEUM PRETORIA SOUTH AFRICA
Director, Human Origins and Past Environments Programme (HOPE)
PROBLEM:
HOW TO RECOGNISE DIFFERENT SPECIES WHICH ARE DISTANT RELATIVES OF HUMANKIND?
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
MEASUREMENTS OF SPECIMEN A
B
REGRESSION LINE
y = mx + c
Y AXIS
X AXIS
MEASUREMENTS OF SPECIMEN A
B
REGRESSION LINE
y = mx + c
m: slope
Y AXIS
X AXIS
STANDARD ERROR
OF THE m COEFFICIENT
“DEGREE OF SCATTER AROUND REGRESSION LINE”
ULTIMATE OBJECTIVES:
1. TO FIND A WAY TO DEFINE A SPECIES STATISTICALLY
2. TO ASSESS “PROBABILITIES OF CONSPECIFICITY” (THE PROBABILITY THAT TWO SPECIMENS REPRESENT THE SAME SPECIES)
WHEN TWO SPECIMENS ARE COMPARED
ULTIMATE OBJECTIVES:
1. TO FIND A WAY TO DEFINE A SPECIES STATISTICALLY
2. 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
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
DARWIN NOTED THAT OF ALL LIVING PRIMATES,IT IS THE CHIMPANZEE AND GORILLATHAT ARE MOST SIMILAR TO HOMO SAPIENS,IN TERMS OF SKELETAL AND CRANIAL ANATOMY
DARWIN NOTED THAT OF ALL LIVING PRIMATES,IT IS THE CHIMPANZEE AND GORILLATHAT 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 NOTED THAT OF ALL LIVING PRIMATES,IT IS THE CHIMPANZEE AND GORILLATHAT 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 HUMANKINDEVOLVED ON THE AFRICAN CONTINENT,“THE CRADLE OF HUMANKIND”
Cape Town 0 200
km
LESOTHO
SWAZILAND
MOZAMBIQUE
ZIMBABWE
BOTSWANA
NAMIBIE
Durban
Pretoria
Johannesburg
N
Cradle of Humankind
Makapansgat
CRADLE OF HUMANKIND
Taung
(UNESCO World Heritage Site since 1999)
SWARTKRANS
STERKFONTEIN
KROMDRAAI
STERKFONTEIN: “MRS PLES”
PLESIANTHROPUS: “ALMOST HUMAN”
FOSSIL HOMINID, 2.15 MILLION YEARS OLD
AUSTRALOPITHECUS AFRICANUS, A DISTANT RELATIVE OF ALL HUMANKIND
“MRS PLES”: AUSTRALOPITHECUS AFRICANUS
SWARTKRANS
STERKFONTEIN
KROMDRAAI
SWARTKRANS: “ROBUST” HOMINIDS
PARANTHROPUS
FOSSIL HOMINID, 1.0 – 1.7 MILLION YEARS OLD
PARANTHROPUS (AUSTRALOPITHECUS) ROBUSTUS
HOMO HABILIS, HOMO ERECTUS, HOMO ERGASTER
SWARTKRANS
STERKFONTEIN
KROMDRAAI
KROMDRAAI: “ROBUST” HOMINIDS
PARANTHROPUS ROBUSTUS
FOSSIL HOMINID, 1.0 – 2.0 MILLION YEARS OLD
PARANTHROPUS (AUSTRALOPITHECUS) ROBUSTUS
EARLY HOMO
KROMDRAAI TM 1517
PARANTHROPUS ROBUSTUS
3 DIMENSIONAL RECONSTRUCTION OF “MRS PLES”
BASED ON CT SCANS (BRAGA, TREIL, THACKERAY)
PARTIAL SKELETON OF “MRS PLES”AUSTRALOPITHECUS AFRICANUSSTERKFONTEIN, 2.15 MILLION YEARS OLD
MEASUREMENTS OF SPECIMEN A
B
SKULL MEASUREMENTS
or
TOOTH MEASUREMENTS
or
SKELETAL MEASUREMENTS
ALGEBRAIC BIOLOGY
MEASUREMENTS OF SPECIMEN A
B
MEASUREMENTS OF SPECIMEN A
B
REGRESSION LINE
y = mx + c
Y AXIS
X AXIS
MEASUREMENTS OF SPECIMEN A
B
SPECIMENS A AND B
ARE SAME SPECIES
LITTLE SCATTER AROUND REGRESSION LINE
SIMILAR SHAPE
MEASUREMENTS OF SPECIMEN A
B
SPECIMENS A AND B
ARE SAME SPECIES
LITTLE SCATTER AROUND REGRESSION LINE
SIMILAR SHAPE
Low standard error of m coefficient: (sem)
y = mx + c
MEASUREMENTS OF SPECIMEN A
B
SPECIMENS A AND B
ARE DIFFERENT SPECIES
MUCH SCATTER AROUND REGRESSION LINE
DIFFERENT SHAPE
MEASUREMENTS OF SPECIMEN A
B
SPECIMENS A AND B
ARE DIFFERENT SPECIES
MUCH SCATTER AROUND REGRESSION LINE
DIFFERENT SHAPE
High standard error of m coefficient: (sem)
y = mx + c
MEASUREMENTS OF SPECIMEN A
B
FOSSILS A AND B
HAVE A HIGH PROBABILITY OF CONSPECIFICITY
LITTLE SCATTER AROUND REGRESSION LINE
SIMILAR SHAPE
Low standard error of m coefficient: (sem)
y = mx + c
MEASUREMENTS OF SPECIMEN A
B
FOSSILS A AND B
HAVE A LOW PROBABILITY
OF CONSPECIFICITY
MUCH SCATTER AROUND REGRESSION LINE
DIFFERENT SHAPE
High standard error of m coefficient: (sem)
y = mx + c
CHALLENGE
• WHAT IS THE FRAME OF REFERENCE FOR ASSESSING “PROBABILITIES OF CONSPECIFICITY” ?
EXPLORATORY STUDY:
PAIRWISE COMPARISONS OF SPECIMENS
OF EXTANT ANIMALS THAT CERTAINLY
BELONG TO THE SAME SPECIES
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
MEASUREMENTS OF WILDEBEEST SPECIMEN A
B
SPECIMENS A AND B
LITTLE SCATTER AROUND REGRESSION LINE (sem =0,031)
SIMILAR SHAPE
Low standard error of m coefficient: (sem)
y = 1.103x - 0.234 sem = 0.031
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
MEASUREMENTS OF SPECIMEN A
B
SPECIMENS A AND B
HAVE A LOW PROBABILITY
OF CONSPECIFICITY
MUCH SCATTER AROUND REGRESSION LINE
DIFFERENT SHAPE
High standard error of m coefficient: (sem)
y = 1.103 x - 0.04 sem = 0.073
MEASUREMENTS OF WILDEBEEST SPECIMEN A
B
SPECIMENS A AND B
LITTLE SCATTER AROUND REGRESSION LINE (sem =0,021)
SIMILAR SHAPE
Low standard error of m coefficient: (sem)
y = 1.103x - 0.234 sem = 0.031
SEM (STANDARD ERROR) BASED ON PAIRWISE COMPARISONS
N
MEAN sem = 0.03
BASED ON 25 MODERN TAXA
VERTEBRATES (CONSPECIFICS)
0.03 0.07
SEM (STANDARD ERROR) BASED ON PAIRWISE COMPARISONS
N
MEAN sem = 0.03
BASED ON 25 MODERN TAXA
VERTEBRATES (CONSPECIFICS)
0.03 0.07
WILDEBEEST A AND B
SEM (STANDARD ERROR) BASED ON PAIRWISE COMPARISONS
N
MEAN sem = 0.03
BASED ON 25 MODERN TAXA
VERTEBRATES (CONSPECIFICS)
0.03 0.07
WILDEBEEST A AND B
WILDEBEEST A
HARTEBEEST B
SEM (STANDARD ERROR) BASED ON PAIRWISE COMPARISONS
N
MEAN sem = 0.03
BASED ON 25 MODERN TAXA
VERTEBRATES (CONSPECIFICS)
0.03 0.07
WILDEBEEST A AND B
ASSYMETRIC DISTRIBUTION OF sem VALUES
SEM (STANDARD ERROR) BASED ON PAIRWISE COMPARISONS
N
MEAN sem = 0.03
0.03 0.07
ASSYMETRIC DISTRIBUTION OF sem VALUES
WHAT HAPPENS WITH LOG TRANSFORMATION (BASE 10 ?)
LOG STANDARD ERROR OF m (LOG sem) BASED ON PAIRWISE COMPARISONS
N
LOG MEAN SEM = -1.78 +/- 0.27
BASED ON 76 MODERN TAXA
VERTEBRATES AND INVERTEBRATES
LOG NORMAL DISTRIBUTION OF sem VALUES
OBTAINED FROM CONSPECIFIC PAIRS
LOG STANDARD ERROR OF m (LOG sem) BASED ON PAIRWISE COMPARISONS
N
LOG MEAN SEM = -1.78 +/- 0.27
BASED ON 76 MODERN TAXA
VERTEBRATES AND INVERTEBRATES
TOWARDS A STATISTICAL DEFINITION OF A SPECIES !
LOG STANDARD ERROR OF m (LOG sem) BASED ON PAIRWISE COMPARISONS
N
LOG MEAN SEM = -1.78 +/- 0.27
BASED ON 76 MODERN TAXA
VERTEBRATES AND INVERTEBRATES
TOWARDS A STATISTICAL DEFINITION OF A SPECIES !
+ 2 sigma- 2 sigma
-1.78
LOG STANDARD ERROR OF m (LOG sem) BASED ON PAIRWISE COMPARISONS
N
LOG MEAN SEM = -1.78 +/- 0.27
95 % CONFIDENCE LIMITS OF THE DISTRIBUTION OF LOG sem VALUES
TOWARDS A STATISTICAL DEFINITION OF A SPECIES !
+ 2 sigma- 2 sigma
-1.78
-1.78 + (2 x 0.27)-1.78 - (2 x 0.27)
LOG STANDARD ERROR OF m (LOG sem) BASED ON PAIRWISE COMPARISONS
N
LOG MEAN SEM = -1.78 +/- 0.27
95 % CONFIDENCE LIMITS OF THE DISTRIBUTION OF LOG sem VALUES
TOWARDS A STATISTICAL DEFINITION OF A SPECIES !
+ 2 sigma- 2 sigma
-1.78
-1.78 + (2 x 0.27)-1.78 - (2 x 0.27)
Two specimens attributed toAustralopithecus africanus
LOG STANDARD ERROR OF m (LOG sem) BASED ON PAIRWISE COMPARISONS
N
LOG MEAN SEM = -1.78 +/- 0.27
95 % CONFIDENCE LIMITS OF THE DISTRIBUTION OF LOG sem VALUES
TOWARDS A STATISTICAL DEFINITION OF A SPECIES !
+ 2 sigma- 2 sigma
-1.78
-1.78 + (2 x 0.27)-1.78 - (2 x 0.27)
Two specimens, one attributed toAustralopithecus africanus,another attributed to Homo habilis
LOG STANDARD ERROR OF m (LOG sem) BASED ON PAIRWISE COMPARISONS
N
LOG MEAN SEM = -1.78 +/- 0.27
95 % CONFIDENCE LIMITS OF THE DISTRIBUTION OF LOG sem VALUES
TOWARDS A STATISTICAL DEFINITION OF A SPECIES !
+ 2 sigma- 2 sigma
-1.78
-1.78 + (2 x 0.27)-1.78 - (2 x 0.27)
Two specimens, one attributed toParanthropus robustus,another attributed to Homo habilis
IMPLICATION:
REGARDING FOSSIL SPECIMENSATTRIBUTED TO
AUSTRALOPITHECUSPARANTHROPUS orHOMO,
THE BOUNDARIES BETWEEN TAXA
ARE NOT NECESSARILY DISTINCT !
CONCLUSIONS:
1. LEAST SQUARES REGRESSION ANALYSIS HAS THE POTENTIAL TO FACILITATE A STATISTICAL DEFINITION OF A SPECIES
CONCLUSIONS:
1. LEAST SQUARES REGRESSION ANALYSIS HAS THE POTENTIAL TO FACILITATE A STATISTICAL DEFINITION OF A SPECIES
2. WHEN TWO FOSSIL SKULLS ARE COMPARED, IT IS POSSIBLE TO USE THE LOG sem VALUES (BASED ON REGRESSION ANALYSES) TO ASSESS THE PROBABILITY THAT THOSE SPECIMENS ARE CONSPECIFIC.
CONCLUSIONS:
1. LEAST SQUARES REGRESSION ANALYSIS HAS THE POTENTIAL TO FACILITATE A STATISTICAL DEFINITION OF A SPECIES
2. WHEN TWO FOSSIL SKULLS ARE COMPARED, IT IS POSSIBLE TO USE THE LOG sem VALUE (BASED ON REGRESSION ANALYSES) TO ASSESS THE PROBABILITY THAT THOSE SPECIMENS ARE CONSPECIFIC.
3. BOUNDARIES BETWEEN SPECIES MAY NOT ALWAYS BE CLEAR, BUT LOG sem VALUES HAVE THE POTENTIAL TO ADDRESS THIS ISSUE.
ACKNOWLEDGEMENTS
BRUNO BUCHBERGER
TEMUR KUTSIA
TRANSVAAL MUSEUM
NATIONAL RESEARCH FOUNDATION
FRENCH EMBASSY IN SOUTH AFRICA
