Matthew Pennell - Young Investigator Prize Talk

Matthew Pennell
University of British Columbia

This talk is dedicated to
Paul Joyce
1958–2016

Some errant thoughts on:
macroevolution,
community ecology,
phylogenetic comparative methods,
and other such matters
(with some data).

EARLY PHANEROZOIC FAMILIAL DIVERSITY 241
se kinetic model, as illustrated in Figure 11.
mbrian rates, shown in detail in Figure 6,
plotted as solid points in Figure 1 1; the
ves drawn through these points are the solid
bolas in Figure 6. Rates for the remaining
-Permian series of the Paleozoic are identi-
by letter codes; Permian rates are not in-
ed because of problems associated with the
aordinary extinctions of that period, which
not be treated explicitly with the kinetic
del (these may be "diversity independent";
Valentine 1972, 1973). The parabolas drawn
ough the post-Cambrian points represent
nd-order least-squares fits to those segments
he data; fits of the more complex functions
trated in Figure 10 were not attempted be-
se of technical problems associated with
A Me
Lil ~ ~ ~ ~ L
F 8
z
0e
L/ SLD
Z LtUS
_ MD
tr 4 - M
o UD
2 A
0 100 200 300 400
NUMBER OF FAMILIES
B
z
0U
'S -
0 ue MD
u ~~~~~~~~~~~~~~UDUSo00'
Fx 4- 6Ee _ eDs
Figure 1.4. Area-species curves, birds, showing areas and distance effects
(MacArthur and Wilson 1967).
Figure 1.5. Crossed immigration and extinction curves, with the changing in-
tersections (equilibria) predicting the area and distance effects (MacArthur and
Wilson 1963).
Sepkoski 1979 PaleobiologyMacArthur and Wilson 1963 TIB
Diversity dependent diversiﬁcation inspired by
equilibrium theories from ecology

pe I error rates for constant-rate phylogenies simulated
nder both pure birth and continuous-decline models of
iversification, assuming both complete and incomplete
xon sampling. For the pure birth model, we simulated
000 trees of NZ25 taxa under a constant speciation
rocess and tabulated the distribution of DAICTS. To further
ontrol for the possibility that incomplete taxon sampling
ould result in high type I error rates, we tabulated the
istribution of the test statistic for constant-rate phylogenies
mulated with different levels of incomplete sampling ( f ),
s described above for the g-statistic analyses.
simulation. Simulated trees were then randomly pruned to
the desired sampling level. All phylogenetic simulations
were conducted using a modified version of the birth–death
tree simulation algorithm from the GEIGER package for R
(Harmon et al. 2008).
3. RESULTS
Phylogenetic trees generated under a relaxed-clock model
of sequence evolution (figure 1) strongly supported
previous findings that diversification rates in North
D. coronata
D. discolor
D. caerulescens
D. nigrescens
D. striata
D. occidentalis
D. graciae
D. palmarum
W. citrina
D. dominica
S. ruticilla
D. fusca
D. pensylvanica
D. petechia
D. townsendi
D. cerulea
P. americana
D. tigrina
D. magnolia
D. pinus
D. kirtlandii
P. pitiayumi
D. chrysoparia
D. virens
D. castanea
0.84
*
**
*
*
*
0.71
*
*
*
*
0.75
*
0.82
*
*
0.72
*
*0.35
*
0.74
igure 1. Maximum clade credibility (MCC) tree from Bayesian analysis of all continental North American Dendroica wood
arbler species. Nodes marked with asterisks are supported by posterior probabilities of more than 0.95. Tree is based on more
han 9 kb of mtDNA and nuclear intron sequence. Branch lengths are proportional to absolute time.
366 D. L. Rabosky & I. J. Lovette Density-dependent diversification
on June 15, 2016http://rspb.royalsocietypublishing.org/Downloaded from
0 0.2 0.4 0.6 0.8 1.0
0
0.5
1.0
1.5
2.0
2.5
3.0
relative divergence time
log(lineages)frequency
25%
100%
warblers
(a)
(b)
Densi
http://rspb.royaDownloaded from
Diversity dependent diversification should (might?)
leave signature in phylogenetic tree shape
Rabosky and Lovette 2008 Proc B

D. coronata
D. discolor
D. caerulescens
D. nigrescens
D. striata
D. occidentalis
D. graciae
D. palmarum
W. citrina
D. dominica
S. ruticilla
D. fusca
D. pensylvanica
D. petechia
D. townsendi
D. cerulea
P. americana
D. tigrina
D. magnolia
D. pinus
D. kirtlandii
P. pitiayumi
D. chrysoparia
D. virens
D. castanea
0.84
*
**
*
*
*
0.71
*
*
*
*
0.75
*
0.82
*
*
0.72
*
*0.35
*
0.74
0 0.2 0.4 0.6 0.8 1.0
0
0.5
1.0
1.5
2.0
2.5
3.0
relative divergence time
log(lineages)
(a)
Rabosky and Lovette 2008 Proc B
But lots of processes/artifacts can leave early bursty patterns!
Harmon and Harrison 2015 Am Nat
Moen and Morlon 2014 TREE
Diversity dependent diversiﬁcation should (might?)
leave signature in phylogenetic tree shape

Brownian motion Ornstein-Uhlenbeck Early burst
Constant rate
“random evolution”
Most variance recent
“clade optimum”
Most variance early
“adaptive radiation”
Also predict early bursts of trait evolution

Pennell et al. 2015 Am Nat
Dataset
AICweight
Model
BM
OU
EB
Ornstein-Uhlenbeck
Brownian
motion
Early burst
Dataset
Modelsupport(AICweight)
Also predict early bursts of trait evolution
Slater and Pennell 2014 Sys Bio

dividual of species 2 compared to another of species 1. U1(R) of Fig. 1
measures the probability that an item of resource R is consumed in a unit
of time by an individual of species 1. Here the R continuum may be one of
resource quality or location. Hence, the probability of species 1 and 2
simultaneously trying for the same resource, R, is U1(R) U2(R). In terms of
this result, we now give a heuristic justification of the aX formula used in
R
FIG. 1. The form of the niche. For each resource r, U is the probability of its
utilization in a unit time by an individual. The area under each curve, therefore, is
the total resource utilization Ki for species i.
This content downloaded from 128.189.214.142 on Fri, 10 Jun 2016 18:56:02 UTC
All use subject to http://about.jstor.org/terms
How ecology looks to macroevolution folk
MacArthur and Levins 1967 Am Nat

“We’ve come a long way since the folk music days of ecology”
— Susan Harrison, ASN debate 2014

! Ecologists must broaden their concepts of community
processes and incorporate data from systematics,
biogeography, and palaeontology into analyses of
ecological patterns and tests of community theory "
— Bob Ricklefs (1987, Science)

Webb et al. 2002 AREES cited 1,741x
Webb 2000 Am Nat
ystem where the main difference between species is their
eight, in this case a competitive ability difference (Fig. 3b,
noring the phylogeny). In this scenario, competitive
in this trait is p
competition w
(Fig. 3a). By co
(a) (b)
gure 3 Competitive exclusion can drive either phylogenetic over-dispersion or cluste
reference for different soil textures, and this niche difference is phylogenetically conserv
referred soil type will compete most intensely, and competitive exclusion will eliminate spe
ffer primarily in their height, a competitive ability difference when light is limiting. Co
Competition leads to
overdispersion
Enter: phylogenetic community ecology

QE PD
MPD
MNTD AWMNTD
PSV PSC PSE Δ+ Δ- Δ
PAE
PDC HED EED HAED EAED
Simpson’s Phy
MPDcomp MPDinter MPDintra
+10 β diversity metrics +9 null models
Μiller et al. 2016 Ecography
1 theory:
Close relatives compete —
competition leads to exclusion
22 α diversity metrics

ly eliminates taxa that overlap too much in their
preferences, leaving species that are less similar
it. Now consider a hypothetical light-limited
ere the main difference between species is their
his case a competitive ability difference (Fig. 3b,
he phylogeny). In this scenario, competitive
competition example (Fig. 3). If competitive
preferentially eliminates taxa that overlap too g
their soil texture preferences, and how different sp
in this trait is positively related to phylogenetic
competition will drive phylogenetic over-d
(Fig. 3a). By contrast, if species differ greatly i
(a) (b)
mpetitive exclusion can drive either phylogenetic over-dispersion or clustering. (a) Competitors differ primari
or different soil textures, and this niche difference is phylogenetically conserved in this example. Species overlappi
l type will compete most intensely, and competitive exclusion will eliminate species that are too closely related. (b) Co
rily in their height, a competitive ability difference when light is limiting. Competitive exclusion eliminates all but
More closely related taxa have more similar heights, and competitive exclusion drives clustering.
Mayﬁeld and Levine 2010 Eco Lett
Plot twist: pattern does not imply process
overdispersion
clustering

COMMUNITY PHYLOGENETICS AND ECOSYSTEM FUNCTIONING
Species richness, but not phylogenetic diversity,
inﬂuences community biomass production and
temporal stability in a re-examination of 16 grassland
biodiversity studies
Patrick Venail*,†,1,2
, Kevin Gross3
, Todd H. Oakley4
, Anita Narwani1,5
, Eric Allan6
,
Pedro Flombaum7
, Forest Isbell8
, Jasmin Joshi9,10
, Peter B. Reich11,12
, David Tilman13,14
,
Jasper van Ruijven15
and Bradley J. Cardinale1
1
School of Natural Resources and Environment, University of Michigan, 440 Church Street, Ann Arbor, MI 48109, USA;
2
Section of Earth and Environmental Sciences, Institute F.-A. Forel, University of Geneva, Versoix, Switzerland;
3
Statistics Department, North Carolina State University, 2311 Stinson Drive, Raleigh, NC 27695-8203, USA;
4
Department of Ecology, Evolution and Marine Biology, University of California, Santa Barbara, CA 93106-9620, USA;
5
Aquatic Ecology, Eawag (Swiss Federal Institute of Aquatic Science and Technology), D€ubendorf 8600, Switzerland;
6
Institute of Plant Sciences, University of Bern, Altenbergrain 21, Bern, Switzerland; 7
Centro de Investigaciones del Mar
y la Atmosfera, Conicet/Universidad de Buenos Aires, C1428EGA, Buenos Aires, Argentina; 8
Department of Plant
Biology, University of Georgia, 2502 Miller Plant Sciences, Athens, GA 30602, USA; 9
Institute of Biochemistry and
Biology, Biodiversity Research/Systematic Botany, University of Potsdam, Maulbeerallee 1, 14469 Potsdam, Germany;
10
Berlin-Brandenburg Institute of Advanced Biodiversity Research (BBIB), Altensteinstr 6, 14195 Berlin, Germany;
Functional Ecology 2015, 29, 615–626 doi: 10.1111/1365-2435.12432
Even phylogenetic patterns do not seem to hold. Sad!

Can we do better?
I think so*.
*or at least, we can create new things that suck in new ways

Reimagine community ecology and macroevolution
Rosindell et al. 2015 Eco Lett
Davies et al.
d problems,
and where
011). Other
mechanisms
g on UNTB
focused on
community
sed Unified
, by adding
o UNTB in
u Zhang
, fitness is
ables us to
aviour with
n would be
build-up of
of UTEM
f individual
nd between
UTEM to
ges-through-
ctions, espe-
to UNTB.
interaction
period to reach their steady-state after which species
abundances, phylogenies and individual finesses were periodi-
cally collected.
1 2 3
2
4 3 5
3
5 4 3
4
1 2 3
2
4 3 4
3
5 4 3
4
1 2 3
2
4 3 3
3
5 4 3
4
0.5 µ
Probability
(1 µ)
Probability
0.5 µ
Probability
FitnessFitness = Fitness
1 2
2
4 3 2
3
5 4 3
4
3 1 2
2
4 3
3
5 4 3
4
3 1 2 3
2
4 3
3
5 4 3
4
BirthDeath
?
Figure 1 A description of one time step in our model for a simple
example where metacommunity size JM = 12. Each circle represents an
individual organism. Species identities are not shown; the colours and

0 50 100 150 200
0
0.2
0.4
0.6
0.8
1.0
stabilizingdifference(1−r)
phylogenetic distance (Mya)
0 50 100 150 200
0
2
4
6
8
10
logfitnessdifference(K)
phylogenetic distance (Mya)
sympatric
allopatric
(a) (b)
geographic history alters the evolutionary trajectory of stabilizing and fitness differences. (a) Stabilizing differences rapidly increase among symp
de), whereas allopatric species pairs (dark shade) show no relationship. (b) Fitness differences, by contrast, increase over evolutionary time in bo
pairs, but are larger on average among allopatric pairs. Stabilizing differences have a maximum of one (electronic supplementary material, equat
the logit-transformed data), whereas fitness differences have no upper limit (electronic supplementary material, equation S2). Because soil moi
izing or fitness differences, each point is a fitted average across soil moisture environments for each species pair. (Online version in colour.
on March 29, 2016http://rspb.royalsocietypublishing.org/Downloaded from
Germain et al. 2016 PRSB
Modernize our concept of co-existence
Intraspecific competition interspecific competition
Facilitates coexistence
Intraspecific competition interspecific competition
Competitive exclusion

io, we can use expressions (4) to predict the
nteraction between any pair of species i and
of phenotype matching, the predicted rate of
ollows:
that phylogeny has no explanatory power). S
trait means evolve through a process of Br
eqn 5a predicts that the overall rate of interac
A
B
C
D
A
B
C
D
Tree shape Genetic drift Stabilizing selection Competition Mutualism
0 16
Pairwise interaction rate
Evolutionary model
A
B
C
D
A B C D
A
B
C
D
A B C D
A
B
C
D
A B C D
A
B
C
D
A B C D
A
B
C
D
A B C D
A
B
C
D
A B C D
A
B
C
D
A B C D
A
B
C
D
A B C D
1
rates between all possible pairs of species within a four species community {A, B, C, D} for two alternative phy
nd one balanced (bottom row) and four different models of evolution/coevolution (columns). The shortest branch l
ons, with longer branches multiples of 10 000 generations as needed to render the trees ultrametric. All evolution
owing parameters: G = 1, N = 1000, r2
zi
¼ r2
zi
¼ 1, a = 0.01, and z0 = 10. For the Ornstein–Uhlenbeck, Mutualism
and h = 10. For the Mutualism model S = 0.00003 and for the Competition model S = À0.00003.
Nuismer and Harmon 2015 Eco Lett
Drury et al. 2016 Sys Bio
Modernize our phylogenetic comparative methods

MST
The scaling of biological processes is a
foundational concept in modern ecology

–5
–4
–3
–2
–1
–2
–1
0
0
50000
100000
150000
200000
–5
–4
–3
–2
–1
–2
–1
0
0.10
–7
1.10
–7
2.10
–7
3.10
–7
–5
–4
–3
–2
–1
–2
–1
0
0
1
2
3
log10
predatormass
log10
predatormass
log10
predatormass
capture
coefffcientb
handlingtimeh
(a) (b)
capture
exponentq
(c)
log10
prey mass
log10
prey mass
log10
prey mass
Figure 1 The generalised allometric functional-response model includes dependencies of the three fundamental functional-response parameters (a) handling time h, (b)
1130 G. Kalinkat et al. Letter
Kalinkat et al. 2013 Eco Lett
Functional response scales with body size

Body Size and Trophic Cascades 361
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
−6
10
−4
10
−2
10
0
10
2
mLpred−1
day−1
Area of capture, a (protists)
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
1
10
3
10
5
10
7
Prey size (protists)
m3
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
−4
10
−2
10
0
Efficiency, e (protists)
predprey−1
10
2
10
4
10
6
10
8
10
−3
10
−1
10
1
Mortality rate, (protists)
day−1
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
−5
10
−3
10
−1
10
1
Handling time, h (protists)
days
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
3
10
5
10
7
10
9
Carrying capacity, K (algae)
cellsmL−1
Body size ( m
3
)
10
0
10
2
10
4
10
6
10
8
10
−2
10
−1
10
0
10
1
Maximum growth rate, r (algae)
day−1
Grazing protists
Carnivorous protists
Protists mixed
Algae
Figure 3: Scaling relationships between model parameters and cell volume for grazing and carnivorous protists and algae. Power law ﬁts
are not statistically distinguishable between grazers and carnivores and so are ﬁt together. See table 1 for parameter values. Gray areas
Dependency of trophic cascade on body size
DeLong et al. 2015 Am Nat

Forster et al. 2012 PNAS
pecies-specific temperature-size responses (% change in mass per °C) expressed as a function of the organism size (dry mass) in aquatic (m
r) and terrestrial environments, including both uni- and multicellular organisms. Terrestrial species have a significant positive regressi
54 × log10DM, R2
= 0.15, df = 53, P 0.01, solid line); aquatic species have a significant negative regression (PCM = −3.90 – 0.53 × log10DM
P 0.01, thick dashed line). Because there is no significant change in the temperature-size response with mass in unicellular species
s given by the thin dashed horizontal line (−1.80%°C−1
).
Temperature size rule

log(R) = log(β0) + βΜ x log(M)
Metabolic rate
Scaling
coefﬁcient
Intercept Body mass

βΜ =3/4
West et al. 1997, 1999 Science
Brown et al. 2004 Ecology

Key relationship in the metabolic theory of ecology
Leads to predictions about:
• Response of physiology to temperature changes
• Biomass production
• Individual growth rates
• Population parameters
• Distribution of traits and lineages across space

Metabolic theory predictive of community structure
0.00.51.0
(
0.10.20.30.40.50.6
Temperature (Celcius)
0.30.60.91.2
Stability
(–1*largestrealeigenvalue)
5 10 15 20 25 30
5 10 15 20 25 30
5 10 15 20 25 30
Consumer:Resourcebiomass
∆RG ∆K 1
∆RG ∆K 1
∆RG ∆K = 1
∆RG ∆K 1
∆T1 ∆T2
(b)
(c)
Figure 3 The effect of temperature on BCR, equilibrium C:R biomass
ratio, and stability. As temperature increases BCR will increase if an
asymmetry causes an increase in resource biomass accumulation or
Gilbert et al. 2014 Eco Lett
NP(g C m−2 year−1)
MP〈Mi
α−1
〉P@20°C(gα
m−2
)
45 94 200 423 896
0.1
1
10
100
1000
Averaged temperature kinetics
MP〈Mi
α−1
〉P
1.11 1.22 1.35 1.49 1.65
0.01
0.1
1
10
100
1
@200gCm–2
year−1(gα
m–2
)
(a)
(b)
ln(y) = 4.52 + 1.74ln(x 200)
R2
= 0.38, P 0.001
ln(y) = 4.52 − 7.86ln(x)
R2
= 0.38, P 0.001
Letter
Biomass
Net primary productivity
MP〈Mi
α−1
〉P@20°C(gα
m−2
)
45 94 200 423 896
0.1
1
10
100
1000
MP〈Mi
α−1
〉P
1.11 1.22 1.35 1.49 1.65
0.01
0.1
1
10
100
1
@200gCm–2
year−1(gα
m–2
)
(a)
(b)
(c)
ln(y) = 4.52 + 1.74ln(x 200)
R2
= 0.38, P 0.001
ln(y) = 4.52 − 7.86ln(x)
R2
= 0.38, P 0.001
Letter
Temperature
Biomass
Barneche et al. 2014 Ecol Lett

Josef Uyeda Rafael Maia Eliot Miller Craig McClain

Metabolic rate
Scaling
coefﬁcient
Intercept Body mass
How does this relationship evolve?

Y
X
Ontogenetic
Same individuals
Different time

Y
X
Y
X
Ontogenetic Static
Same individuals
Different time
Same lineages
Different individuals

Y
X
Y
X
Y
X
Ontogenetic Static Evolutionary
Same individuals
Different time
Same lineages
Different individuals
Different lineages
Lineage means

An evolutionary allometry without any evolution
Y
X

How can we study the evolution of a trait
that we can’t measure?

Macroevolutionary landscape
The structure of population ﬁtness landscapes
through space and time

gent peaks attracted 2.8 lineages on
all but one hosted lineages from
ds. Overall, the number of conver-
peak shifts was significantly greater
by chance (P = 0.01; Fig. 1B), and
count for the exceptional similarity
faunas (18). The number and po-
shifts varied across 100 phylogenies,
er of convergent shifts was similar
able 1). Species traditionally grouped
comorph class (14–16) tended to be
rd the same adaptive peak (fig. S4).
arison of macroevolutionary models
he adaptive landscape plays an im-
shaping parallel diversification. The
accountfor the observed convergence
nd anole faunas was a Simpsonian
0–22), in which lineages experience
rd common peaks on the adaptive
g. S1). Fitted peaks on the anole
respond to trait combinations that
own experimentally to be adaptive
tat partitioning (14) (fig. S4). Al-
ossible that evolutionary constraints
ole in shaping whole-fauna conver-
case of anoles the evidence points to
le for selection. The Anolis radiation
tens of millions of years (14), a time
ich constraints on the production of
unlikely to be maintained, especially
e traits (25). Constraint seems an even
prit considering that diverse radia-
al and South American Anolis, which
ogically different communities, ex-
orphologies not seen in Caribbean
onglysuggestingthatrepeatedGreater
ergence is not due to intrinsic limits
gical variation.
n of adaptive radiations is readily
mple systems over short time scales
nvincing examples at a grander mac-
y scale have so far been lacking.
e case is not yet clear, but our results
the island faunas are far from identical. Most no- cover peaks not reached on smaller islands (1).
Fig. 2. Phenotypic convergence on the macroevolutionary adaptive landscape in island ra-
diations of Greater Antillean Anolis. MCC phylogeny (left panel), painted to depict the estimated
onJune21,2016http://science.sciencemag.org/Downloadedfrom
Mahler et al. 2013 Science

Metabolic rate
Scaling
coefﬁcient
Intercept Body mass
(Somewhat) new models

log(Rj) = Wj,α θ + βΜ,j x log(Mj)
Time spent in each regime
Vector of β0
Lineages evolving around an optimum ~ OU process
Optimum is also evolving across the tree

Reversible Jump Markov Chain Monte Carlo
θ
θθ
Split proposal
θ
θθ
Merge proposal
Automatically detect transition points in data
Compare models with different predictors using Bayes Factors

(Mostly) old data
Trait data from 857 species of vertebrates
Most from White et al. 2006 Biol Lett + some others
Combined previously published phylogenies for mammals,
birds, squamate reptiles, amphibians, and ﬁsh

log(Body mass)
lnBMR
−2 0 2 4 6 8 10 12
−404812
-2 0 2 4 6 8 10 12
-4
0
4
8
12
log(Basalmetabolicrate)

Shifts happen!
Intercept
−4−2024
●
●
●
●
●
●
●
●
●
●
Slope
Root(126)
Salamandroidea(20)
Caudata(4)
Mammalia(364)
Aves(84)
Pleuronectinae(4)
Plethodontidae(34)
Chiroptera(61)
Serpentes(53)
Squamata(83)
0.30.60.9
●
●
●
●
● ●
●
●
● ●
Intercept
InterceptSlope

Transitions between adaptive zones are rare
only 8 shifts leading to clades of 5 taxa
Often associated with major clades/transitions
e.g., Plethodontidae — lungless salamanders
Within each adaptive zone evolution is highly constrained
Lots of phylo signal BETWEEN major groups but little phylo signal WITHIN

What could explain the locations of these shifts?
Genome size?

Genome size?
Increasing genome size decreased β0
but cannot explain away shifts

Genome size?
Curvature in scaling?
regression are extremely significant (P , 3 3 1027
or better), sug-
gesting that both the temperature and quadratic terms are important
predictors of metabolic rate. From the value of bT (the coefficient of
the inverse temperature term) obtained from the quadratic fit, we
calculate an effective activation energy of 21.9 6 3.2 kcal mol21
or
0.95 6 0.14 eV (95% confidence intervals). This value is less than
the free energy of the full hydrolysis of ATP to AMP under standard
cellular conditions (26 kcal mol21
or 1.13 eV; ref. 27), indicating that
the model produces a biologically realistic coefficient.
In addition to temperature, previous studies have attempted to
control for other factors that may affect metabolic rate, such as shared
evolutionary history16,28
, habitat, climate and food type8
. To account
for these potential effects, we analyse the data using phylogenetic
generalized least squares regression29
and by conditioning on catego-
rical variables (Supplementary Information). For both analyses, we
find that thequadraticandtemperature terms remainsignificant, with
some changes in the magnitude of the coefficients (Supplementary
Information). We also find that no single study or group of points is
responsible for the curvature in the data, and that the quadratic and
temperature terms remain significant across a variety of subsets of the
data (Supplementary Information). These results suggest that the
1 2 3 4 5 6
−1
0
1
2
3
Linear
Quadratic
Orca (not included in fit)
Elephant4 (not included in fit)
a
0.90
2/3 and 3/4
Power law
b
log10[B(W)]
LETTERS NATURE|Vol 464|1 April 2010
or better), sug-
or
. To account
nonlinearityof therelationship between basal metabolicrate and mass
on a logarithmic scale is highly robust.
The local scaling exponent, defined as the derivative of the scal-
ing relationship (equation (4)) with respect to log10M, increases
significantly—from 0.57 to 0.87—over the range of the fitted data
(Fig. 1b). This stands in sharp contrast to the constant exponent of a
pure power law, and indicates that the relationship between meta-
bolic rate and mass is quite different for large and small animals. This
finding explains the long-standing disagreement regarding the value
of the scaling exponent, because assuming a power law at the outset
results in linear fits to curved data. Carrying out such fits yields
scaling exponents similar to the slopes of tangent lines at the mean
of the log10M distribution of the underlying data sets (Supplemen-
tary Information). Indeed, performing linear fits over partial mass
ranges confirms this increasing trend and reveals different regions of
the data that are consistent with either 2/3 or 3/4 (Fig. 2). Using the
values of b1 and b2 from the fit of the full model (equation (4)), we
1 2 3 4 5 6
−1
0
1
2
3
Linear
Quadratic
a
0 1 2 3 4 5 6
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
Slope
2/3 and 3/4
Power law
Quadratic
b
log10[B(W)]
log10[M (g)]Kolokotrones et al. 2010

Genome size?
Curvature in scaling?
or better), sug-
or
. To account
1 2 3 4 5 6
−1
0
1
2
3
Linear
Quadratic
a
0.90
2/3 and 3/4
Power law
b
log10[B(W)]
LETTERS NATURE|Vol 464|1 April 2010
or better), sug-
or
. To account
nonlinearityof therelationship between basal metabolicrate and mass
on a logarithmic scale is highly robust.
The local scaling exponent, defined as the derivative of the scal-
ing relationship (equation (4)) with respect to log10M, increases
significantly—from 0.57 to 0.87—over the range of the fitted data
(Fig. 1b). This stands in sharp contrast to the constant exponent of a
pure power law, and indicates that the relationship between meta-
bolic rate and mass is quite different for large and small animals. This
finding explains the long-standing disagreement regarding the value
of the scaling exponent, because assuming a power law at the outset
results in linear fits to curved data. Carrying out such fits yields
scaling exponents similar to the slopes of tangent lines at the mean
of the log10M distribution of the underlying data sets (Supplemen-
tary Information). Indeed, performing linear fits over partial mass
ranges confirms this increasing trend and reveals different regions of
the data that are consistent with either 2/3 or 3/4 (Fig. 2). Using the
values of b1 and b2 from the fit of the full model (equation (4)), we
1 2 3 4 5 6
−1
0
1
2
3
Linear
Quadratic
a
0 1 2 3 4 5 6
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
Slope
2/3 and 3/4
Power law
Quadratic
b
log10[B(W)]
log10[M (g)]Kolokotrones et al. 2010
Matters in some clades (e.g., mammals)
but not a general explanation

What processes cause variation in these traits?
Intercept
−4−2024
●
●
●
●
●
●
●
●
●
●
Slope
Root(126)
Salamandroidea(20)
Caudata(4)
Mammalia(364)
Aves(84)
Pleuronectinae(4)
Plethodontidae(34)
Chiroptera(61)
Serpentes(53)
Squamata(83)
0.30.60.9
●
●
●
●
● ●
●
●
● ●
Intercept
InterceptSlope

How are these predictions changed if scaling evolves?
0.00.51.0
(
0.10.20.30.40.50.6
Temperature (Celcius)
0.30.60.91.2
Stability
(–1*largestrealeigenvalue)
5 10 15 20 25 30
5 10 15 20 25 30
5 10 15 20 25 30
Consumer:Resourcebiomass
∆RG ∆K 1
∆RG ∆K 1
∆RG ∆K = 1
∆RG ∆K 1
∆T1 ∆T2
(b)
(c)
Figure 3 The effect of temperature on BCR, equilibrium C:R biomass
ratio, and stability. As temperature increases BCR will increase if an
asymmetry causes an increase in resource biomass accumulation or
Gilbert et al. 2014 Eco Lett
MP〈Mi
α−1
〉P@20°C(gα
m−2
)
45 94 200 423 896
0.1
1
10
100
1000
MP〈Mi
α−1
〉P
1.11 1.22 1.35 1.49 1.65
0.01
0.1
1
10
100
1
@200gCm–2
year−1(gα
m–2
)
(a)
(b)
ln(y) = 4.52 + 1.74ln(x 200)
R2
= 0.38, P 0.001
ln(y) = 4.52 − 7.86ln(x)
R2
= 0.38, P 0.001
Letter
Biomass
Net primary productivity
MP〈Mi
α−1
〉P@20°C(gα
m−2
)
45 94 200 423 896
0.1
1
10
100
1000
MP〈Mi
α−1
〉P
1.11 1.22 1.35 1.49 1.65
0.01
0.1
1
10
100
1
@200gCm–2
year−1(gα
m–2
)
(a)
(b)
(c)
ln(y) = 4.52 + 1.74ln(x 200)
R2
= 0.38, P 0.001
ln(y) = 4.52 − 7.86ln(x)
R2
= 0.38, P 0.001
Letter
Temperature
Biomass
Barneche et al. 2014 Ecol Lett

Extend this framework to other scaling traits
(Wahlstr€om et al. 2000; Aljetlawi et al. 2004; Vonesh Bolker 2005;
Brose 2010; Vucic-Pestic et al. 2010b; McCoy et al. 2011; Rall et al.
2011) but additionally entails far-reaching and important conse-
quences for population and community ecology.
The allometric scaling of handling time is consistent with prior
studies (Aljetlawi et al. 2004; Vucic-Pestic et al. 2010b; Rall et al.
2011, 2012). Compared to established null models based on the
metabolic theory of ecology (Yodzis Innes 1992; Brown et al.
2004), our results suggest that the power-law exponent of the rela-
tionship between handling time and predator mass (À0.28) is much
shallower than the expected negative ¾ exponent. Moreover, the
power-law increase in handling time with prey mass is also shal-
lower (0.56) than the expected isometric scaling. These shallow scal-
ing relationships of handling time with predator and prey masses
are consistent with the findings from a recent and comprehensive
meta-study on the allometry of feeding rates (Rall et al. 2012).
Together, these results suggest that handling time is constrained by
more complex processes and not solely by metabolism. For
instance, the scaling relationship for predator mass might be biased
by different feeding modes such as sucking or chewing that shift
with increasing body masses. In our data set, liquid-feeding spiders
(mean body mass: 0.036 g; n = 618) and centipedes (0.082 g;
n = 903) are generally smaller than chewing beetles (0.126 g;
n = 1044). Therefore, small liquid feeders that ingest less unpalat-
able parts of their prey such as sclerotised cuticles have relatively
quicker handling times than larger chewers ingesting whole prey
items, which could explain the shallower relationships. On the basis
of a large data base, our results suggest that the assumption of neg-
ative ¾ power-laws should be replaced by shallower scaling relation-
ships for handling time.
The intentional exclusion of the taxonomic information in our
generalised modelling approach is supported by previous work that
has shown how allometric functional-response models can explain a
large part of the variation in empirically observed feeding rates of
taxonomically different predator–prey pairs with a minimal number
of parameters (Rall et al. 2011). Nonetheless, generalised allometric
models can be easily integrated with taxonomic approaches by mak-
ing one or several parameters (e.g. the optimal prey body mass)
dependent on predator taxonomy (Rall et al. 2011). In contrast, tra-
ditional taxonomy-based approaches describe each particular preda-
tor–prey pair with a set of parameters (e.g. Vucic-Pestic et al.
2010b). This traditional approach might produce more precise pre-
dictions (see examples in Fig. 2a-c and Fig. S1 in the Supplementary
Information), but it comes at the cost of using more parameters:
While the generalised model is very efficient in the use of parame-
ters (eight parameters, d.f. = 9), a taxonomic model would have
–5
–4
–3
–2
–1
–2
–1
0
0
50000
100000
150000
200000
–5
–4
–3
–2
–1
–2
–1
0
0.10
–7
1.10
–7
2.10
–7
3.10
–7
–5
–4
–3
–2
–1
–2
–1
0
0
1
2
3
log10
predatormass
log10
predatormass
log10
predatormass
capture
coefffcientb
handlingtimeh
(a) (b)
capture
exponentq
(c)
log10
prey mass
log10
prey mass
log10
prey mass
Figure 1 The generalised allometric functional-response model includes dependencies of the three fundamental functional-response parameters (a) handling time h, (b)
capture coefficient b and (c) the capture exponent q on predator mass and prey mass. These relationships were estimated by fitting functional-response models to feeding
data of terrestrial arthropods (n = 2,564).
© 2013 John Wiley Sons Ltd/CNRS
1130 G. Kalinkat et al. Letter
Body Size and Trophic Cascades 361
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
−6
10
−4
10
−2
10
0
10
2
mLpred−1
day−1
Area of capture, a (protists)
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
1
10
3
10
5
10
7
Prey size (protists)
m3
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
−4
10
−2
10
0
Efficiency, e (protists)
predprey−1
10
2
10
4
10
6
10
8
10
−3
10
−1
10
1
Mortality rate, (protists)
day−1
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
−5
10
−3
10
−1
10
1
Handling time, h (protists)
days
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
3
10
5
10
7
10
9
Carrying capacity, K (algae)
cellsmL−1
Body size ( m
3
)
10
0
10
2
10
4
10
6
10
8
10
−2
10
−1
10
0
10
1
Maximum growth rate, r (algae)
day−1
Grazing protists
Carnivorous protists
Protists mixed
Algae
Figure 3: Scaling relationships between model parameters and cell volume for grazing and carnivorous protists and algae. Power law fits
are not statistically distinguishable between grazers and carnivores and so are fit together. See table 1 for parameter values. Gray areas
indicate 95% confidence intervals.
Sensitivity of the Trophic Cascade
Strength for Protists and Algae
Body size was a good predictor of protist and algae pa-
rameters (fig. 3; table 1). All consumer and resource equi-
librium abundances declined with body size of the pred-
ator (fig. 4). It is the difference in the slopes of these
abundance relationships that drive the body size depen-
dence of interaction strengths, since they are defined as
the ratio of abundances ( and ). For protists, weˆ ˆˆK/R C /C2 2 3
predict the interaction strength between the consumer and
resource (IS12) will increase with predator body size. The
slope of the body size dependence is somewhat shallower
than the canonical prediction given above (fig. 2D). In
contrast to the case with canonical parameters, there is a
very slight dependence of the IS23 on predator body size
in protists (fig. 2E). Because IS12 and IS23 are both depen-
dent on predator body size in protists, there is also a
significant positive relationship between predator body size
This content downloaded from 129.101.137.060 on May 26, 2016 10:49:56 AM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
Fig. 2. Species-specific temperature-size responses (% change in mass per °C) expressed as a function of the organism size (dry mass) in aquatic (marine and
reshwater) and terrestrial environments, including both uni- and multicellular organisms. Terrestrial species have a significant positive regression (PCM =
2 2

MARINE GASTROPOD ENERGETICS
2 4
Log10 shell volume (mm3)
Figure 4. Aggregate relative size-frequency distribu
tions, based on the model relating maximum size to
individual size-frequency distribution, for all assemblag
Figure 5. A, Distributions of average individual mass
and temperature-compensated basal metabolic rate (B0).
B, Proportions of carnivorous individuals for all time
intervals. Horizontal bars represent median values, boxes
enclose the 25th through 75th percentiles, and whiskers
indicate the 2.5th and 97.5th percentiles.
1987), but characterized by the early stages
of benthic ecological restructuring (Aberhan
et al. 2006), appear to be intermediate
between the Triassic and the Late Cretaceous.
These assemblages show a mode similar to
most assemblages in preceding time intervals
but a thicker tail of large individuals, though
the small number of samples in this time
interval and their limited geographic distri
bution (6, most from Morocco) caution
against overinterpretation. The shapes of
modeled size-frequency distributions from
the Late Cretaceous to the Neogene are
Energetics through time
260 SETH FINNEGAN ET AL.
-3.0
A.
I5
CQ
u
■I—
C3
-3.5 -
-4.0
V)
9, e
B ^u
E 2
m 60
B o
'S.J
cd
o
u
(U
Q.
C
aJ
L
-4.5
-5.0
-5.5
-6.0
-6.5
i
t
MMR
1
Shell
Abvss
A A •
B.
v
c.
■•r *
7 V
V
7
,7'
- ^ % Log10 individuals Log10 species
Figure 6. A, Boxplots show the distribution of log10 mean individual metabolic rate (Bavg) for all assemblages in each
time interval. Bars, boxes, and whiskers as in Figure 5. Double-ended arrow marked MMR indicates the interval
over which the Mesozoic Marine Revolution occurred; break indicates a sampling gap of —75 Myr between the Early
Jurassic and the Late Cretaceous. B, C, Bavg plotted against logio of the total number of individuals (B) and species (C)
in each assemblage. Black circles = Early Triassic (w = 6); black diamonds = Middle Triassic (n = 16); black squares =
Late Triassic (n = 58); gray circles = Early Jurassic (n = 9); gray diamonds = Late Cretaceous (n = 56); white circles =
Eocene (n = 64); white diamonds = Neogene (n = 175), white triangles = Recent shallow subtidal (n = 17); white
inverted triangles = Recent slope-abyssal (n = 20).
neogastropods and mesogastropods. Both
of these groups have higher basal metabolic
Middle Triassic, and then rises again between
the Late Triassic and the Early Jurassic. Early
Finnegan et al. 2011 Paleobio
see also Bambach 1993 Paleobio

Synthesizing comparative and field/experimental data
ely to
land-
ealis-
lizing
a are
scape
peaks
rmon
le fit-
tal or
h time
e. Ex-
ution
ds to
ng of
iation
aling.
llom-
of at-
Days
5
MeanFlowerNumber
LA
0.60 0.65 0.70 0.75 0.80 0.85
0
10
20
30
OLS
PGLS
B
Figure 2: The scaling exponent (vLA) between leaf area (LA) and
aboveground biomass mediates the trade-off between time to wilting
and fecundity in wild tomatoes. Each point represents an accession
mean. Accessions with higher vLA (X-axis) took longer to wilt after
the onset of drought (Y-axis in A) but had lower fecundity (Y-axis
in B). Note that both days to wilting and mean flower number are
ht. Fe-
plant
s days
Each
egres-
best-fit
Figures514
515
Figure 1: Wild tomatoes and cultivars are closely-related, yet phenotypically-div516
Lycopersicoides
Juglandifolia
Lycop
ersicon
cultivars
~4.7 my
Muir and Thomas-Huebner 2015 Am Nat

Scaling of biological processes connects organismal
to community to ecosystem ecology
Borrow macroevolutionary concepts and methods
to discover how scaling relationships have evolved
Learn about the constraints that have shaped and will
shape higher levels of organization

The Underpants Gnome Scientiﬁc Method
Phase 1
Understand long-term dynamics of ecological scaling
Phase 2
?
Phase 3
Unite macroevolution and macroevolutionary research

History and future
of ecosystems

Computational Biodiversity Lab | University of British Columbia
mwpennell@gmail.com @mwpennell

Matthew Pennell - Young Investigator Prize Talk

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