1. Is there a mechanism deficit in ecology?
INTECOL 2013

2. Agenda Macroecology is mechanism-less? Mechanism in ecology
Mechanism in physics
Example 1 – distribution & abundance
Example 2 - biogeography

3. Macroecology – a mechanism deficit?
“If you can do a regression and pull data out of a journal you can do macroecology”
Machine
Learning ?
p<0.05
I did science!

4. Agenda Macroecology is mechanism-less? Mechanism in ecology
Mechanism in physics
Example 1 – distribution & abundance
Example 2 - biogeography

5. Reductionism Biology is hierarchical reified Causality moves up
Mechanism comes from below
Ricklefs
Sadava et al
Potochkin & McGill 2012

6. Generalized Lotka Volterra
1 𝑁 𝑑𝑁 𝑑𝑡 = 𝑟 𝑖 + 𝑗=1 𝑆 𝑟 𝑖 𝛼 𝑖𝑗 𝑁 𝑗 𝐾 𝑖 1 𝑁 𝑑 𝑁 𝑑𝑡 = 𝑟 +𝐴 𝑁
𝑎 11 ⋯ 𝑎 1𝑆 ⋮ ⋱ ⋮ 𝑎 𝑆1 … 𝑎 𝑆𝑆

7. But does it work?
McGill 2013 (in The Balance of Nature and Human Impact ed. Rohde)

8. The equilibrial target is always moving!

9. Agenda Macroecology is mechanism-less? Mechanism in ecology
Mechanism in physics
Example 1 – distribution & abundance
Example 2 - biogeography

10. Physics 1687 Newton: Descartes clockwork universe F=Ma F=GM1M2/d2
Inertia & equal/opposite reactions
Descartes clockwork universe

11. Physics 2013
Quantum mechanics
Statistical mechanics

12. Mechanism in physics Practical Laddered Statistical
If you have an equation that is useful/predictive you have a mechanism (or maybe you’re just done and don’t care about mechanism?)
Laddered
Quantum mechanics gives Bohr atom
Physical chemistry gives multi-atom systems
Ideal gas law/statistical mechanics gives relation of macro-properties
Statistical
Quantum mechanics
Statistical mechanics (avoids intermediate numbers problem)
As general as possible
Only occasionally reductionist (more often self-contained)
Context aware (external forcing, environment)

13. Conclusion Macroecology Doesn’t have a mechanism deficit
Has a mechanism recognition deficit
Mechanisms in ecology: AWOL or Purloined Letter. Towards a practical view of mechanism McGill & Nekola

14. Agenda Macroecology is mechanism-less? Mechanism in ecology
Mechanism in physics
Example 1 – distribution & abundance
Example 2 - biogeography

15. A thought experiment – sampling from the region
Larger local
community
N=4, S=3
Region
Small local
community
N=2, S=2

16. We can write sampling idea as equations
S, N, Ni, A from region are inputs
Pivotal idea is sampling function:
P=(ni|Ni,a,A,)
Also see:
Etienne & Alonso 2005
Green & Plotkin 2007
He & Legendre 2002
Dewdney 1998
Pielou multiple
McGill 2011 American Journal Botany

17. How are we doing?
Surprisingly not too bad, but we’re missing something (too much , not enough )

18. Need another assumption
Have been using sampling function, , as spatially random (binomial or Poisson form)
We know clumped in nature
Clumping would fix problems (reduce , increase )
More individuals from same species in sample lowers 
More individuals from same species in one sample, likely to be underrepresented in other sample increases 
Condit et al 2000

19. Clumping fixes it!
=Finite Negative Binomial (Zillio & He 2010)

20. Sampling works at small scales
Stochastic absences
Sampling
Deterministic absences
Moving out of range
Scale-break
100km X 100km

21. Spatially explicit, larger scale version
Abundance
Spatial extent
MVPi
Range Boundary si mi
Ni(X)=NMAXi exp(||X- mi||2/s2) X
WIDTH A B mi
RADIUSi
EXTENT
McGill & Collins 2003
Also see
Gauch & Whittaker 1972
Allen & White 2003

22. 3 assumptions common to many theories
Species abundance varies logarithmically
Individuals in 1 species are clumped
All else can be random
McGill Ecology Letters 2010

23. Agenda Macroecology is mechanism-less? Mechanism in ecology
Mechanism in physics
Example 1 – distribution & abundance
Example 2 - biogeography

24. Back to Leibig’s Law? Gause Leibig biogeographic law
This figure has been removed as the work is unpublished
Any one variable sets an upper limit according to a Gause’s law (Gaussian bell-curve)
But most sites at the optimum are limited by something else

25. It appears to be very general
This figure has been removed as the work is unpublished

26. It appears very general
This figure has been removed as the work is unpublished

27. Bruce Martin Wikimedia under CCA
This figure has been removed as the work is unpublished

28. In the lab can home in on limiting factor
Cristian Solari
In the lab can home in on limiting factor
This figure has been removed as the work is unpublished

29. Environment and Organisms
What
Dozens of GIS layers of climate that are biologically relevant for use in distribution modelling
Bioagricultural (e.g. degree days, frost free days, drought)
Extreme events (10-year coldest day, 50 year drought)
Topographic (slope, aspect, moisture indices)
Landcover
Traditional climate
Publically served, global 1km co-registered
Status
Funding from 3 organizations, >30 people involved
Pieces starting to become publically available

30. Non-stationarity is now helpful

31. Can do predictions

32. Summary Mechanism is not deterministic and reductionist
Mechanism is often stochastic, self-referential, context-sensitive, more general than biology
Macroecology already has many mechanisms!
Sampling w/ clumping
Gause’s normal curve & Liebig’s Law