Is there a mechanism deficit in ecology? INTECOL 2013

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

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!

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

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

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

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

The equilibrial target is always moving!

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

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

Physics 2013 Quantum mechanics Statistical mechanics

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)

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. 2010 McGill & Nekola

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

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

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

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

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

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

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

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

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

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

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

It appears to be very general This figure has been removed as the work is unpublished

It appears very general This figure has been removed as the work is unpublished

Bruce Martin Wikimedia under CCA This figure has been removed as the work is unpublished

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

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

Non-stationarity is now helpful

Can do predictions

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