Allometry: the study of the relationship between size and shape

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 1834-1919 • 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. 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 r selection vs K selection

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