Presentation is loading. Please wait.

Presentation is loading. Please wait.

… One by one, we go in the dark and come out Saying how we experience the animal One of us happens to touch the trunk. “A water-pipe kind of creature.”

Similar presentations


Presentation on theme: "… One by one, we go in the dark and come out Saying how we experience the animal One of us happens to touch the trunk. “A water-pipe kind of creature.”"— Presentation transcript:

1

2 … One by one, we go in the dark and come out Saying how we experience the animal One of us happens to touch the trunk. “A water-pipe kind of creature.” Another, the ear. “A very strong, always moving Back and forth, fan-animal.” Another, the leg. “I find it still, Like a column on a temple.” Another touches the curved back. “ A leathery throne” Another, the cleverest, feels the tusk. “A rounded sword made of porcelain.” He’s proud of his description. Each of us touches one place And understands the whole in that way. The palm and fingers feeling in the dark are How the senses explore the reality of the elephant If each of us held a candle there, And if we went in together, We could see it. -The Elephant in the Dark Rumi (Translated by Coleman Barks)

3 Another, touches extant populations,… “A very strong, always moving back and forth [process]”

4 Another, the fossil record, … “I find it still, like a column on a temple [with occasional punctuations]”

5 Another, the phylogeny… …Brownian Motion might be a good approximation.

6 How can the evolutionary pattern be all these things? Contemporary field studies Rapid evolution High genetic variation Strong selection Fossil record Stasis over millions of years Geographic variation Extinction and species turnover Comparative methods Variance increases through time High morphological diversity Brownian motion fits reasonably

7 How can we see the pattern across scales of time? All studies of phenotypic evolution measure comparable quantities Allochronic We measure two quantitaties: (1) “time for evolution” (2) Δ mean Pop B mean(z) Pop A mean(z) Time interval Pop X Synchronic Pop B mean(z) Pop A mean(z) Time interval

8 Estes and Arnold 2007 Field Studies Fossil Record Historic Divergence isn’t dependent on time?

9 Why is there no time-span effect? How can this be consistent with strong phylogenetic signal for body size traits? Thomas F Hansen University of Oslo

10 Body size is known to have a strong phylogenetic signal Smith et al Phylogenetic heritability of body size between sister species of mammals (think of the plot like a sib-sib regression)

11 Estes and Arnold 2007 Field Studies Fossil Record Historic Divergence isn’t dependent on time?

12 Estes & Arnold (2007)‏ Neutral drift in trait or adaptive optimum Stabilizing selection Displaced optimum Moving optimum White noise motion of the optimum Peak shift

13 Estes and Arnold 2007

14 Time (Raw timescale)

15 Example: Brownian Motion process Time (Raw timescale)

16 Example: Brownian Motion process Time (Raw timescale)

17 Example: Brownian Motion process Time (Log timescale)

18 Field Studies Fossil RecordComparative data Historic

19 Let’s combine with comparative data: Log-scaled linear body size traits e.g. ln(height) or ln( mass 1/3 ) Taxa- Many, but mostly vertebrates Field and historic data (e.g. Hendry et al. 2008) Fossil record (e.g. Gingerich 2001) Comparative data: Time-calibrated phylogenies & body size databases Mammals, Birds & Squamates

20 Microevolutionary data

21 Fossil data

22 Comparative data Mammals

23 Comparative data Birds

24 Comparative data Squamates

25 Comparative data Mammalian, Avian and Squamate body size

26

27 Comparative data Mammalian, Avian and Squamate body size “The Evolutionary Blunderbuss” ™ Stevan J Arnold

28

29

30

31

32 Study bias?

33

34 Models must explain: “The Stasis Distribution” and Longer term trends of accumulating variance

35 Two-layer process

36 Stochastic models Bounded Evolution (BE) Brownian Motion (BM) Single-burst (SB) – Exponential time to displacement Multiple-burst (MB) – Poisson Point Process

37

38 Multiple-Burst Model Punctuational change Stasis distribution: ± 10% linear size change (1 SD) (ME + phenotypic plasticity + evolutionary change + genetic drift) Burst distribution: ± 30% linear size change (1 SD) Average time to displacement = 25 my

39 Multiple-Burst Model: bootstrapped over studies

40

41 Why millions of years? What process accounts for this pattern?

42 What pattern makes evolution look like Brownian motion over macroevolutionary time? Genetic drift (Lande 1976)? – No, parameters do not work Drift of a local adaptive peak? – No, or we could never measure selection A statistical pattern in need of an interpretation

43 What then, is randomly walking? “Niches” Not a real answer We need more focus on interpretation and causation!

44 Is there anything significant about 1-5 milllion years? Species life-spans for mammals are ~1-5 million years (Alroy et al. 2000; Liow et al. 2008) Marine inverts my (Foote, 2007) Taxon cycles are suggested to occur on the order of my (Ricklefs & Bermingham 2002)

45 Liow et al. 2008

46

47 Foote 2007

48

49 What role could demography & extinction play? Similar to models proposed by Eldredge et al. (2005)‏ As fitness-related mean trait value deviates from θ, mean population fitness declines according to a Gaussian function.

50 Let the population grow at a multiplicative growth rate, Rt, such that: and, otherwise. Population growth (Burger & Lynch 1995)‏ when where B is the maximum population growth rate and K is the carrying capacity.

51 G/(ω 2 +1)=0.01 σ 2 ө = 2.25 B=1.025 λ = 1/250 N 0 = Constant population size: Divergence increases with time Addition of demography: Divergence decreases with time G/(ω 2 +1)=0.01 σ 2 ө = 2.25 λ = 1/250, Linear increase in average divergence expected

52

53

54

55 1/2501/1000 1/2000

56

57

58

59 From adaptive landscapes & G- matrices to phylogenetic stochastic models Need to account for the scaling from populations  species e.g. Futuyma’s ephemeral divergence model Demography, and the dynamics of species ranges over time (including speciation) can be factored in to explain shifts in species means The ultimate “cause” of evolutionary change is change in adaptive landscapes

60 Key parameters Birth rate must be low such that populations grow slowly, even when optimal Selection and inheritance parameters must not be so strong as to prevent any divergence at all, or the model fails to explain rapid divergence over short time scales.

61

62


Download ppt "… One by one, we go in the dark and come out Saying how we experience the animal One of us happens to touch the trunk. “A water-pipe kind of creature.”"

Similar presentations


Ads by Google