1. Allometry: the study of the relationship between size and shape
Galileo, 1636: Discorsi

2. Allometry of Stegosaur plates

4. Allometry in Tyrannosaurus forelegs
Adaptive explanations
Allometry in combination with Cope’s Rule

5. Surface/volume considerations and Allometry

6. Assume a spherical cow . . .
Surface area of sphere:
4p r 2
Volume of sphere:
4/3 p r 3

7. Julian Huxley and Georges Tessier
Exponential form
y=bx a
Linear form:
log(y) = a log(x)+log(b)

8. Surface/volume and respiration in arthropods

9. Problems of scaling to larger size

10. Problems of scale at smaller size

11. Surface/volume and locomotion
Surface area of wings vs mass
Cross sectional surface area of legs vs mass

12. The “Irish Elk”
Actually a deer
Lived across N. Europe and Asia

13. But a very large deer . . .

14. Antler span up to 12 feet

15. Prospecting for fossil Megaloceras in Irish peat bogs

16. Allometry in the white-tailed deer
Allometry can be measured within a species, usually by comparing juveniles to adults

17. Allometry in Megaloceras
Allometry of antler size comparing adults of different species of deer
“M” indicates the Irish Elk, Megaloceras

18. Negative allometry of metabolic heat production on body weight

19. Do we really have big brains?
Allometric curve has slope of 0.667, indicating the real relationship is between surface area of brain and size of animal
Reptiles have the same slope, lower intercept on the y axis

20. Primate brain weights plotted on the same field
The real measure of brain size is neither simple weight nor a ratio of brain to body weight, but deflection from the allometric curve

21. Heterochrony: the evolution of allometry (rate) and timing in organismal development
Ernst Haeckel
Met Darwin in 1866 and became defender of Natural Selection
“Ontogeny recapitulates Phylogeny”

22. Ontogeny and Phylogeny defined
Ontogeny: the developmental sequence of an individual organism
Phylogeny: the evolutionary history of a species or lineage (phylogeny is to a species as genealogy is to an individual)

23. Evolution in fish tails
Diphycercal tail in lungfish Protopterus

24. Evolution in fish tails
Heterocercal tail in the sturgeon and other intermediate fish

25. Evolution in fish tails
Heterocercal tail in modern teleostean fish (e.g. perch, bass)
Note vestigial internal assymmetry of axial skeleton

26. Ontogeny and phylogeny in fish tail evolution
A good example of recapitulation, consistent with Haeckel’s theory

27. However . . . The Axolotl salamander: an inconvenient counter-example
Descendant (bottom) resembles juvenile of the ancestor (top)

28. Synthesizing the literature on heterochrony
Paedomorphosis (juvenilization)
Neoteny (K, slope, decreases)
Progenesis (b, offset, moves left)
Post-displacement (a , onset, moves right)
Peramorphosis (“adultization”)
Acceleration (K, slope, increases)
Hypermorphosis (b, offset, moves right)
Pre-displacement (a , onset, moves left)

29. Neoteny in Mountain Sheep
Study by Geist compares ontogenies of male to female sheep

30. Synthesizing the literature on heterochrony
Paedomorphosis (juvenilization)
Neoteny (K, slope, decreases)
Progenesis (b, offset, moves left)
Post-displacement (a , onset, moves right)
Peramorphosis (“adultization”)
Acceleration (K, slope, increases)
Hypermorphosis (b, offset, moves right)
Pre-displacement (a , onset, moves left)

31. Progenesis in Micromalthus, the gall midge
Wingless females reproduce and feed on mushrooms and other fungi

32. r selection vs K selection
No=ert
Small
High juvenile mortality
Unstable environments
Large # offspring
No parental care
No=ert (K-N)/K
Large
Low juvenile mortality
Stable environments
Small # offspring
Parental care

33. Synthesizing the literature on heterochrony
Paedomorphosis (juvenilization)
Neoteny (K, slope, decreases)
Progenesis (b, offset, moves left)
Post-displacement (a , onset, moves right)
Peramorphosis (“adultization”)
Acceleration (K, slope, increases)
Hypermorphosis (b, offset, moves right)
Pre-displacement (a , onset, moves left)

34. Post-displacement in the Dachshund
Legs begin developing late and never catch up

35. Astogeny (colonial development) recapitulates phylogeny?
Earliest colonial forms (analogous to juveniles) carried forward into later astogeny

36. Synthesizing the literature on heterochrony
Paedomorphosis (juvenilization)
Neoteny (K, slope, decreases)
Progenesis (b, offset, moves left)
Post-displacement (a , onset, moves right)
Peramorphosis (“adultization”)
Acceleration (K, slope, increases)
Hypermorphosis (b, offset, moves right)
Pre-displacement (a , onset, moves left)

37. Hypermorphosis in the Irish Elk
Postponing the offset of development leads to a larger adult – one way of achieving Cope’s Rule of phyletic size increase

38. Acceleration in ammonite phylogeny

39. Heterochrony in Paleozoic zaphrentid corals
Note adult shape compressed back into early ontogeny, resulting in recapitulation in descendant
Acceleration of development

40. Human allometry

41. Primate allometric patterns
Positive allometry of jaw, brow ridge on skull
Negative allometry of cranial vault on skull

42. Human skull allometry
Follows same allometric pattern as primate ancestors, but slowed down (neotenic)

43. Allometry in Pan troglodites
Note:
upright posture
Vaulted cranium
Flattened alveolar
Region
Less pronounced
Brow ridge
Of juvenile

44. Primate allometry of birth weight
Humans retain rapid fetal growth rates longer, hence a relatively larger fetus

45. Effect of neoteny on brain weight
Humans retain rapid fetal growth rate of brain longer, shifting flexure in brain-body curve to right, resulting in larger brains

46. Allometry in toy dogs: King Charles Spaniel (top)
Irish Wolfhound (bottom)
Note negative allometry of cranial cavity and positive allometry of prognathous jaw – both standard mammalian ontogenetic patterns

47. Paedomorphosis in foraminifera: Paleogene genus Morozovella
Juvenile form angulose (visible in lower cross section), carried forward to adult morphology in descendant

48. Ecological heterochrony?
Note steepening curve showing increasing angularity (left)
Increasing isotopic difference between juvenile and adult in descendant (right)

49. Adult vs juvenile morphology in Mickey

50. Paedomorphosis in Mickey

51. Comparative embryology and heterochrony
Early embryonic stages are comparable
Differentiation is increasingly expressed later in ontogeny

52. Allometry in birth weight
Birth weight compared to gestation time in mammals