is there a mechanism deficit in ecology? intecol 2013
TRANSCRIPT
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Is there a mechanism deficit in ecology?
INTECOL 2013
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Agenda
Macroecology is mechanism-less? Mechanism in ecology Mechanism in physics Example 1 – distribution &
abundance Example 2 - biogeography
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Macroecology – a mechanism deficit?
“If you can do a regression and pull data out of a journal you can do macroecology”
MachineLearning
p<0.05 I did science!?
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Agenda
Macroecology is mechanism-less? Mechanism in ecology Mechanism in physics Example 1 – distribution &
abundance Example 2 - biogeography
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Reductionism
Sadava et al
Causality
Biology is hierarchical reified
Causality moves up
Mechanism comes from below
Ricklefs
Potochkin & McGill 2012
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Generalized Lotka Volterra
[𝑎1 1 ⋯ 𝑎1𝑆
⋮ ⋱ ⋮𝑎𝑆 1 … 𝑎𝑆𝑆 ]
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-2 0 2 40
2000
4000
0.2
Navg
log10
(N)
(A)
0 5 100
5000
10000 0.9
CV of N(B)
0 0.5 10
500
10000.1
Nmin
vs. Nmax
(C)
0 0.5 10
500
10000.2
Nmin
vs. top 5 N(D)
0 0.5 10
500
1000
0.3
Bottom 5 N vs top 5 N(E)
0 0.5 10
500
1000
0.4
% Nt<(top 5 N)/2(F)
But does it work?
1970 1990 20100
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Nt
(A)
1970 1990 20100
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Nt
(B)
1970 1990 20100
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(C)
1970 1990 20100
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Nt
(D)
1970 1990 2010200
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Nt
(E)
1970 1990 20100
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(F)
1970 1990 20100
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Nt
(G)
1970 1990 20100
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Year
Nt
(H)
1970 1990 20100
1
2
Year
Nt
(I)-2 0 2 40
2000
4000
0.2
Navg
log10
(N)
(A)
0 5 100
5000
10000 0.9
CV of N(B)
0 0.5 10
500
10000.1
Nmin
vs. Nmax
(C)
0 0.5 10
500
10000.2
Nmin
vs. top 5 N(D)
0 0.5 10
500
1000
0.3
Bottom 5 N vs top 5 N(E)
0 0.5 10
500
1000
0.4
% Nt<(top 5 N)/2(F)
0 20 400
1
2
3
Nt
t
(A)
0 20 40 600
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2
3
Nt
t
(B)
0 10 200
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2
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Nt
t
(C)
0 50 1000
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Nt
t
(D)
0 200 400 6000
1
2
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Nt
t
(E)
0 0.5 10
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0.3
r2(F)
McGill 2013 (in The Balance of Nature and Human Impact ed. Rohde)
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The equilibrial target is always moving!
27.20%
16.20%
16.40%22.70%
17.50%
Frequency HorizontalLinear sloping upLinear sloping downQuadratic convex upQuadratic convex down
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Agenda
Macroecology is mechanism-less? Mechanism in ecology Mechanism in physics Example 1 – distribution &
abundance Example 2 - biogeography
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Physics 1687
Newton:1. F=Ma2. F=GM1M2/d2
3. Inertia & equal/opposite reactions Descartes clockwork universe
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Physics 2013
Quantum mechanics
Statistical mechanics
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Mechanism in physics Practical
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)
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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
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Agenda
Macroecology is mechanism-less? Mechanism in ecology Mechanism in physics Example 1 – distribution &
abundance Example 2 - biogeography
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A thought experiment – sampling from the region
Region
Small localcommunityN=2, S=2
Larger localcommunityN=4, S=3
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We can write sampling idea as equations
S, N, Ni, A from region are inputsPivotal idea is sampling function:
P=(ni|Ni,a,A,)
McGill 2011 American Journal Botany
Also see:Etienne & Alonso 2005Green & Plotkin 2007He & Legendre 2002Dewdney 1998Pielou multiple
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How are we doing?
Surprisingly not too bad, but we’re missing something (too much , not enough )
0 10 20 30 40 5050
100
150
200
250
Area (ha)
S
(A)
Actual Ni
All equal Ni=N*/S
Actual SAR
60 80 100 120 1400
5
10
15
Observed=90.78
Sampled=103.94
Equal N=78.4
Local ( α) richness s
no. s
ites
(B)
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
Actual Oi
Pred
icte
d (ran
dom
)O
i
(C)
0 0.2 0.4 0.6 0.8 10
100
200
300
400
Observed=0.67
Sampled=0.92
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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
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Clumping fixes it!
=Finite Negative Binomial (Zillio & He 2010)
0 20 40 6050
100
150
200
250
Area (ha)
# S
peci
es
ActualBinomialAgg Binom
60 80 100 1200
5
10
1590.04 91.00
α diversity
# co
mm
uniti
es0 0.5 1
0
0.5
1
Actual Oi
Agg
Bin
Pre
d O
i
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Sampling works at small scales
Scale-break100km X 100km
Deterministic absencesMoving out of range
Stochastic absencesSampling
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Spatially explicit, larger scale version
WIDTH
WIDTH
A
B
mi
RADIUSi
EXTENT
Abundance
Spatial extent
MVPi
Range Boundary
si
mi
Ni(X)=NMAXi exp(||X- mi||2/s2)
X
McGill & Collins 2003Also seeGauch & Whittaker 1972Allen & White 2003
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3 assumptions common to many theories
3 Assumptions1. Species
abundance varies logarithmically
2. Individuals in 1 species are clumped
3. All else can be random
McGill Ecology Letters 2010
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Agenda
Macroecology is mechanism-less? Mechanism in ecology Mechanism in physics Example 1 – distribution &
abundance Example 2 - biogeography
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Back to Leibig’s Law?Gause Leibig biogeographic law
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
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It appears to be very general
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It appears very general
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Bruce Martin Wikimedia under CCA
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In the lab can home in on limiting factor
CristianSolari
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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
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Non-stationarity is now helpful
80 W 90
W
Predicted
100 W 110
W
25 N
35 N
45 N
50 N
30 N
40 N
10
20
30
40
50
60
clDD
clPclTmean
clTmax
clTmin
ndvisePsd
seTrn
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Can dopredictions
10-1
100
101
102
103
10-1
100
101
102
Actual
Pre
dict
ed
10-1
100
101
102
103
100
101
102
Actual
Pre
dict
ed
r2 limit=0.47321 r2 tree=0.32954; RMSE limit=25.1077, RMSE tree=26.2827
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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