Norman MacLeod

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Introduction to Allometry
Norman MacLeod Department of Palaeontology, The
Natural History Museum
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Scale of Life
108
105
102
10-1
10-4
10-7
10-10
10-13
Mycoplasm
Tetrahymena
Bee
Human
Malarial Parasite
Large Amoeba
Blue Whale
Hamster
In terms of physical scale, life covers 21 orders
of magnitude
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Scale of Life
Organisms at one end of the scale have different
shapes from those at the other
A.
B.
C.
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Size-Related Constraints
Comparative anatomy is largely the history of
lifes attempts to increase area in relation to
volume. J.B.S. Haldane
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Size-Related Constraints
Consider the meaning of size-related
shape changes in the skull of this Triassic
dinosaur
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Size-Related Constraints
Consider the meaning of size-related
shape changes in this modern mammal
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Size-Related Constraints
Note how the complexity of these changes masks a
simple underlying geometric transformation
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Types of Form Variation

• Position - object centroids located at different
  positions
• Rotation - corresponding point locations oriented
  in different directions
• Size - a co-ordinated, constant or proportional
  metric increase or decrease in the spatial
  dimension of all parts of the form
• Shape - a localized, metric increase or decrease
  in spatial dimension

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Expected Pattern of Form Variation
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Analysis of Form Variation
Consider the cuboids
Surface Area Length2
Volume Length3
Surface Area Volume2/3
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Analysis of Form Variation
Area Length2
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Relative Growth
In the early 1900s Julian Huxley noticed that,
when plotted on logarithmically ruled paper, the
pattern of size increase for structures in a
large number of animals and plants looked
remarkably simple.
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Analysis of Allometry
Log Area 2(Log Length)
Area Length2
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Examples of Allometry
from Roth (1990)
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Examples of Allometry
Mammals
from Van Valkenburgh (1990)
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Examples of Allometry
Mammals
from Van Valkenburgh (1990)
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Examples of Allometry
from McMahon Bonner (1983)
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Examples of Allometry
from McMahon Bonner (1983)
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Examples of Allometry
from McMahon Bonner (1983)
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Examples of Allometry
from McNab (1990)
from Martin (1990)
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Allometry
The study of the influence of body size on form
and function
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Types of Allometry
Static Allometry The analysis of allometry
between different individuals of the same species
at the comparable levels of development
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Types of Allometry
Ontogenetic Allometry The analysis of allometry
in an individual over the course of different
developmental stages
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Types of Allometry
Evolutionary Allometry The analysis of allometry
between individuals of different sister species
at comparable developmental stages
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Allometry Nomenclature
Positive Allometry Slope gt 1.0
Isometry Slope 1.0
Negative Allometry Slope lt 1.0
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Example Radiolaria
Descriptive Morphology Morphological Integration
MacLeod et al. 1986
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Example Radiolaria
Descriptive Morphology Morphological Integration
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Example Radiolaria
Descriptive Morphology Morphological Integration
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Example Foraminifera
Descriptive Morphology
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Example Irish Elk
Evolutionary Trends Targets of Selection
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Example Brontotheres
Evolutionary Trends Targets of Selection
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Heterochrony
The study of changes in the relative timing of
appearance and development rate for characters
present in ancestors and descendants (or sister
taxa)
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Types of Heterochrony

• Paedomorphosis - changes in the differential
  growth rate or offset signal that cause adult
  descendant species to be morphologically similar
  to the juvenile forms of ancestors
• Peramorphosis - changes in the differential
  growth rate or offset signal that cause adult
  descendant species to extrapolate the
  developmental trends of ancestors

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What Type of Heterochrony?
In Human Evolution
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What Type of Heterochrony?
Paedomorphosis
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What Type of Heterochrony?
In Echinoid Evolution
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What Type of Heterochrony?
Peramorphosis
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Allometry Heterochrony
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Developmental Trajectories
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Allometry Heterochrony
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Introduction to Allometry
Norman MacLeod Department of Palaeontology, The
Natural History Museum