(O) O = b

PHYLOGENETIC COMPARATIVE
METHODS IN (MACRO)ECOLOGY
José Alexandre Felizola Diniz-Filho
Thiago Fernando L V B Rangel
Departamento de Ecologia, ICB,
Universidade Federal de Goiás, BRASIL
traits
Ecophylogenetics
Assemblages
PHYLOGENETIC DIVERSITY
-“Amount” of phylogenetic information in a clade
-Species are not equally “important” (in a conservation context)
2005
THE OVERALL REASONING OF
PHYLOGENETIC DIVERSITY
ORIGINALITY
Vane-Wright: index 1/ n
May index: 1 / Soma(branchs)
Count
2
Originality (O)
0.50
Vane Wright
2
3
3
2
1
0.50
0.33
0.33
0.50
1.00
May
Count
7
Originality (O)
0.14
7
10
10
0.14
0.10
0.10
8
1
0.125 1.00
Count
1
Originality (O)
0.25
O = b/T
Age of the Most Recent
Common Ancestor
(MRCA)
1
1
1
0.25
0.25
0.25
2
4
0.50 1.00
Count
1
Originality (O)
0.06
O = bK/  bk = 15
Age of MRCA
1
1
1
0.06
0.06
0.06
2
4
0.13 0.26
FIRST METRICS FOR PD
GD = 1 -  (1 – pk) (Crozier 1992)
where pk is a measure of genetic distances, ranging from 0 to 1
PD =  bk (Faith 1992)
where bk is the branch lenght
Dan Faith
A
1
B
C
D
E
F
A
1
B
C
D
E
F
Diversidade filogenética total
Faith’s PD =  bk = 15
A
B
C
D
E
F
Local A
PD = 7
A
B
C
D
E
F
Local B
PD = 11
A
B
C
D
E
F
Local
A
B
S PDL / PDT
3
46.7 %
3
73.3 %
This is a community matrix in which
each column contain 1 for the
species present and 0 elsewhere
> library(picante)
> pd.result <- pd(comm, phy, include.root = TRUE)
COMPARING AND USING PD METRICS
Faith’s PD
Total Taxonomic Diversity
Average Taxonomic Divesrity
Mean root distance
Levi Carina
Terribile
128 spp of snakes in >17000 cells in Brazilian Cerrado
Lioph
Lioph
Erythr
Lioph
Lioph
Lioph
Lioph
Lystro
Lystro
Xenod
Wagle
Philod
Philod
Philod
Pseud
Clelia
Clelia
Clelia
Boirun
Pseud
Pseud
Phimo
Rhach
Oxyrh
Oxyrh
Tham
Gome
Apost
Apost
Apost
Apost
Phalo
Phalo
Phalo
Psom
Helico
Helico
Helico
Pseud
Hydro
Sibyn
Atract
Atract
Imand
Lepto
Dipsa
Xenop
Echin
Chiron
Chiron
Chiron
Lepto
Simop
Drymo
Dryma
Spilot
Mastig
Oxybe
Tantil
Micru
Micru
Micru
Micru
Micru
Bothro
Bothro
Bothro
Bothro
Bothro
Bothro
Bothro
Crotal
Eunec
Epicra
Corall
Boa
c
Aniliu
Liotyp
Typhl
Lepto
PD and Evolutionary Models
PD and Extinction
PHYLOGENETIC SPECIES VARIABILITY (PSV)
Matthew Helmus
Phylogenetic
species
covariance
among
The phylogenetic variability of species observed in a
give place is given by
where C is the covariance among species, scaled to range between 0
and 1 (phylogenetic correlation). If there is no phylogenetic structure,
then R = I , so that
The PSV is given dividing the observed variability by the maximum
expected in the absence of phylogenetic structure,
so that
Covariancia
1.00
0.75
0.00
0.00
0.75
1.00
0.00
0.00
0.00
0.00
1.00
0.90
0.00
0.00
0.90
1.00
0.275
PSV = 1 – mean of R = 0.725
A
B
C
D
E
F
A
A
B
C
D
E
F
B
0
1
3
3
3
4
A
A
B
C
D
E
F
Soma
PSV
PSV(local)
C
0
3
3
3
4
B
1.00
0.75
0.25
0.25
0.25
0.00
4.00
0.867
0.4167
D
0
1
2
4
C
1.00
0.25
0.25
0.25
0.00
E
0
2
4
D
1.00
0.75
0.50
0.00
F
0
4
E
1.00
0.50
0.00
0
F
1.00
0.00
1.00
Phylogenetic species
richness
Phylogenetic species
evenness
PD and PSV
Riqueza ( S = 4536 mammals)
Case: 2939
S_pd_spp
x2: -5.9 y2: -0.3
S_pd_spp: 161
210
200
190
180
170
160
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
PD
Case: 3031
PD_spp
x2: -5.3 y2: -1.7
PD_spp: 3361
5,600
5,400
5,200
5,000
4,800
4,600
4,400
4,200
4,000
3,800
3,600
3,400
3,200
3,000
2,800
2,600
2,400
2,200
2,000
1,800
1,600
1,400
1,200
1,000
800
600
400
200
PSV
Case: 166
PSV
x2: 0.5 y2: 3.5
PSV: 0.497
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
5,500
0.85
0.8
5,000
0.75
0.7
4,500
0.65
4,000
0.6
0.55
0.5
PSV
PD_spp
3,500
3,000
0.45
0.4
2,500
0.35
2,000
0.3
0.25
1,500
0.2
1,000
0.15
0.1
500
0.05
0
0
20
40
60
80
100
120
S_pd_spp
140
160
180
200
0
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210
S_pd_spp
Case: 2871
Longitude: -6.3
Residuals
Latitude: -0.9
Residuals: -340.056
PHYLOBETADIVERSITY
A
1
B
C
D
E
F
Diversidade filogenética total
PD =  bk = 15
F
E
D
Local 1
D, E, F,
C
Local 2
A, B, C, D, E
B
A
F
E
D
Local 1
D, E, F,
C
Local 2
A, B, C, D, E
B
A
Jaccard = 2 / (2 + 1 + 3) = 0.333
A
1
B
C
D
E
F
Diversidade filogenética total
PD =  bk = 15
Diversidade filogenética
compartilhada
PD (A)=  bk(A) = 4
F
E
D
Local 1
D, E, F,
C
Local 2
A, B, C, D, E
B
A
Jaccard = 2 / (2 + 1 + 3) = 0.333
“Jaccard” PD = 4 / 15 = 0.267
F
E
D
Local 1
D, E, F,
C
Local 2
A, B, C, E, F
B
A
Jaccard = 2 / (2 + 1 + 3) = 0.333
A
1
B
C
D
E
F
Diversidade filogenética total
PD =  bk = 15
Diversidade filogenética
compartilhada
PD (A)=  bk(A) = 8
F
E
D
Local 1
D, E, F,
C
Local 2
A, B, C, E, F
B
A
Jaccard = 2 / (2 + 1 + 3) = 0.333
“Jaccard” PD = 8 / 15 = 0.533
Functions in PICANTE
>phylosor(comum,phy)
>pcd(comum,phy)
Generates a pairwise matrix
among communities, so you
have to use clustering or
ordination
methods
to
visualize this....
Calculate PHYLOSOR for
each focal cell or assemblage,
in respect to neighbours, and
map it....
COMMUNITY PHYLOGENETICS
Campbell Webb
David Acklerly
Mark McPeek
Michael Donoghue
Data from Leandro Duarte,
UFRGS
INITIAL REASONING...
Interpreting PD in comparison to
random samples
MORE COMPLEX INTERPRETATIONS
Phylogenetic scales,
spatial scales and
evolutionary models...
METHODS
“Net Relatedness Index”
(NRI)
NRI > 0
NRI = -(MS – MR) / sd(MR)
(Distância média entre as
espécies da comunidade é
menor do que o esperado por
combinações de espécies ao
acaso)
Onde
“Phylogenetic Clustering”
MS = distância média entre as n
espécies da comunidade local;
MR = média de MS para n espécies
selecionadas ao acaso na filogenia,
replicadas k vezes (simulação)
sd (MR) = desvio padrão das
médias nas aleatorizações
NRI
NRI < 0
(Distância média entre as espécies da
comunidade é maior do que o
esperado por combinações de
espécies ao acaso)
“Phylogenetic Overdispersion”
A
A
B
C
D
E
F
A
B
C
D
E
F
B
0
1
3
3
3
4
C
D
0
3
3
3
4
0
1
2
4
E
F
0
2
4
0
4
0
1
C
D
E
C
0
1
2
D
1
0
2
E
2
2
0
MS = (1 + 2 + 2) / 3 = 1.667
Amostrando 3 espécies
ao acaso...
A
B
C
D
E
F
A
1
A
B
C
D
E
F
B
0
1
3
3
3
4
C
0
3
3
3
4
D
0
1
2
4
E
0
2
4
F
0
4
0
MR(1) = (3 + 4 + 4) / 3 = 3.667
Repeat1000 vezes!!!!!
3.67
0.6
3.67
1.67
3.67
Random
3.33
0.5
3.00
2.67
3.33
2.33
0.4
2.67
Overdispersion
2.00
Clustering
2.00
f
3.00
0.3
3.67
3.33
2.67
2.33
0.2
3.67
95%
3.33
3.00
0.1
2.33
1.67
3.33
3.33
3.67
0.0
-3
-2
3.33
-1
0
1
2
3
Z
3.67
2.00
2.00
3.00
2.91
0.67
Mean of MS = 2.92 ± 0.6
NRI = -(1.667 – 2.92) / 0 .6 = 2.08
A
B
C
D
E
F
C
0
1
3
3
3
4
1
D
0
3
3
3
4
E
0
1
2
4
C
F
0
2
4
0
4
D
0
E
C
0
1
2
D
1
0
2
E
2
2
0
MS = (1 + 2 + 2) / 3 = 1.667
0.6
0.5
0.4
f
A
A
B
C
D
E
F
B
0.3
0.2
0.1
0.0
-3
-2
-1
0
1
2
3
Z
NRI = 2.08
NTI
0.6
Random
0.5
f
Overdispersion
0.4
Clustering
0.3
0.2
0.1
0.0
-3
-2
-1
0
1
2
3
Z
-What if the distribution of randomized distances is not
normal? The NRI (as an index) is not very accurate...
-The best is simple to report the P-value as a count of
observed distances in comparison with random
distribution
local
Nexus file
ntaxa
mpd.obs
mpd.rand.me
an
mpd.rand.sd
mpd.obs.rank
mpd.obs.z
mpd.obs.p
PSVs
1
19
25.275
22.519
1.610
94.000
1.712
0.940
0.743
2
20
25.305
22.531
1.618
94.000
1.715
0.940
0.744
3
19
25.275
22.519
1.610
94.000
1.712
0.940
0.743
4
19
25.275
22.519
1.610
94.000
1.712
0.940
0.743
5
19
25.275
22.519
1.610
94.000
1.712
0.940
0.743
6
19
25.275
22.519
1.610
94.000
1.712
0.940
0.743
7
18
25.098
22.497
1.603
96.000
1.623
0.960
0.738
8
18
25.098
22.497
1.603
96.000
1.623
0.960
0.738
9
18
25.098
22.497
1.603
96.000
1.623
0.960
0.738
10
16
24.117
22.388
1.677
81.000
1.031
0.810
0.709
11
20
25.305
22.531
1.618
94.000
1.715
0.940
0.744
12
20
25.305
22.531
1.618
94.000
1.715
0.940
0.744
13
20
25.305
22.531
1.618
94.000
1.715
0.940
0.744
14
20
25.305
22.531
1.618
94.000
1.715
0.940
0.744
15
19
25.275
22.519
1.610
94.000
1.712
0.940
0.743
16
19
25.275
22.519
1.610
94.000
1.712
0.940
0.743
17
19
25.275
22.519
1.610
94.000
1.712
0.940
0.743
18
19
25.275
22.519
1.610
94.000
1.712
0.940
0.743
19
18
25.098
22.497
1.603
96.000
1.623
0.960
0.738
Use the distances
> serpcom20 <-read.table("serp_com20.txt",header=TRUE)
> serptree <- read.nexus("Serpentes_Cerrado.nex")
> serpdis <-cophenetic(serptree)
>nri20 <-ses.mpd(serpcom_tot,serpdist,abundance.weight=FALSE,runs=99)
> psv20 <-psv(serpcom20,serptree)
Use the
newick
PSV
How to define the regional pool?
Nathan Swenson
Kissling
Svenning
BACK TO TRAITS...
traits
Ecophylogenetics
Assemblages
Phylogenetic signal...
Library(SYNCSA)
comunidade<-as.matrix(read.table("primcomun.txt",header=T,row.names="site"))
comunidade
distancia<-as.matrix(read.table("primdist.txt",header=T))
distancia
ambiente<-as.matrix(read.table("primenv.txt",header=T,row.names=letters[1:10]))
ambiente
atributos<-as.matrix(read.table("PRIMLOG.txt",header=T,row.names="spp"))
atributos
require(SYNCSA)
# Para calcular as correlações propostas pelo artigo do Pillar e Duarte 2010
syncsa(comunidade,atributos,distancia,ambiente)
syncsa(comunidade,atributos,distancia,ambiente,scale=F)
# Para calcular a matriz P (phylogeny-weighted species composition)
matrix.p(comunidade,distancia)
# Para calcular os PCPS
require(ape)
matriz<-matrix.p(comunidade,distancia)
distancia_P<-vegdist(matriz$matrix.P,method="euclidean")
pcoa(distancia_P)
MACROECOLOGY
Diversification (r)
1. Geographical
variation in
diversification rates
TROP
TEMP
Historical
explanations
2. Variation in initial
conditions
AGE
John Wiens
Michael Donoghue
Spatial patterns of species richness and
mean root distance in Australian birds
(Hawkins et al. 2005, J.Biogeogr.32: 1035-1042)
Richness
(Sibley & Alhquist 1990)
MRD
PATH MODEL (Australia)
AET
0.507
0.851
0.246
NDVI
Richness
0.505
-0.237
Z(RD)
History
SFD = 0.043
Fo = 0.0
RMSEA = 0
P(H0) = 0.474
Spatial patterns in species richness and mean root distance in New
World birds (Hawkins et al. 2006, J.Biogeogr. 33: 770-780)
“Phylogenetic deconstruction” (sensu Marquet et al. 2004) of spatial patterns of
richness in New World birds (Hawkins et al. 2006, J.Biogeogr. 33: 770-780)
Derived groups
r2 = 0.712
Niche conservatism
Basal groups
r2 = 0.986
Richness in world birds follows the same
pattern…(Hawkins et al., Am.Nat, 2007)
Local LTT
PHYLOGENETIC UNCERTAINTY
All we discussed up to now is assuming that phylogeny is
known without error, which is obviously not true,
because...
1) There are uncertainty about TOPOLOGY (politomies is only part of the
problem);
2) We are not sure about BRACH LENGHTS (models of molecular
evolution, methods for calibration, and so on);
3) We do not have data for all species, so we have MISSING SPECIES
(especially when working at broad scales; few exceptions with supertrees,
but they have usually lots of uncertainty due to the other sources)
Criticism by Abouheif...
Clade A
Clade B
Our solution for macroecology in PAM dealing (mainly)
with uncertainty source 3 (“missing species”)
Richard Field –
PAM tutorial
Most Derived Consensus Clade
(MDCC)
Phylogenetic Unknown
Taxa (PUT)
((A:2.35, B:3.76): 2.0,C:2.6);
2.35
A
2.0
3.76
2.6
B
C
((A:2.35, B:3.76)MDCC1: 2.0,C:2.6);
2.35
Most Derived
Consensus Clade 1
A
2.0
3.76
2.6
B
C
((A:2.35, B:3.76)MDCC1:2.0,C:2.6)MDCC2;
Most Derived
Consensus Clade 1
2.35
A
2.0
3.76
2.6
B
C
Most Derived
Consensus Clade 2
Tab space
(D);
(E, F);
→
→
MDCC1
MDCC2
((A:2.35, B:3.76)MDCC1: 2.0,C:2.6);
2.35
A
2.0
D
3.76
E
F
2.6
C
B
(((A:2.35,(B:1.76,D:2.3):1.87):2.12):2.3,
(((E:2.4,F:1.2):2.1),C:4.3):2.2);
A
D
B
E
F
C
A random
solution...
Original tree
4
A
AB
4
4
ABCD
B
C
0
8
8
0
16 16
16 16
B
A
B
C
C 16 16
D 16 16
4
CD
4
4
A
D
0
8
D
8
0
Species to be added (PUTs)
4
A
AB
4
4
ABCD
B
C
4
CD
4
4
D
Species
P1
P2
P3
P4
P5
Insertion
AB
CD
ABCD
B
C
A
3
1
P1
AB
3
2
1
3
2
1
P4
P3
6
ABCD
B
C
2
2
1
CD
1
1
1
1
P5
P2
D
1
P1
AB
3
2
1
3
2
1
B
P4
P3
6
ABCD
These remain constant
A
3
C
2
2
1
CD
1
4
1
4
P5
P2
D
A
B
A
B
C
D
0
8
8
0
16 16
16 16
P1 P 2 P3 P 4 P5
6
8
16
8
12
12
8
2
16
16
C 16 16 0 8 16
D 16 16 8 0 16
P1 6 8 16 16 0
4
8
16
16
16
12
16
16
8
4
8
16
P 2 16 8 4 8 16
P3 12 12 16 16 12
P 4 8 2 16 16 8
0
16
16
16
0
12
16
12
0
2
16
16
2
16
16
0
P5 16 16
4
8
16
PSR Curve
1
PSR = 0.177 ± 0.035
0.95
0.9
0.85
Uncertainty in
eigenvalues
0.8
0.75
0.7
0.65
0.6
R2
0.55
0.5
0.45
0.4
0.35
Uncertainty in R2
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0.2
0.4
0.6
Acum Lambda (%)
0.8
1
Frequency
PSR Values
11
10
9
8
7
6
5
4
3
2
1
0
Mean PSR: 0.177 ± 0.035
0.139
0.154
0.168
0.183
0.197
0.871
0.892
Coefficient of Determination (r²)
0.912
Frequency
PSR
13
12
11
10
9
8
7
6
5
4
3
2
1
0
PVR Regression
Mean r²: 0.899 ± 0.048
0.83
0.851
PHYLOGE
NY
PUTs STATISTICS
MaxLik
1 bootsptrap1
1 bootsptrap2
1
MaxLik
1 bootstrap_n
MaxLik
2 bootstrap
MaxLik
2 bootstrap
...
MaxLik
49 bootstrap
MaxLik
49 bootstrap
MaxLik
50 bootstrap
MaxLik
50 bootstrap
Bayes
1 bootstrap
Bayes
1 bootstrap
Bayes
2 bootstrap
Bayes
2 bootstrap
...
bootstrap
Bayes
49 bootstrap
Bayes
49 bootstrap
Bayes
50 bootstrap
Bayes
50 bootstrap
K
1.170
0.791
1.237
1.242
0.575
0.925
1.440
0.555
1.154
0.588
1.435
0.632
0.832
0.475
0.714
1.113
1.361
0.700
1.183
Error of
statistics
within PUT
and Phylogeny
Variation among
PUTs allocation
within Phylogeny
Variation among
Phylogenies
NESTED ANOVA
Hierarchical (Nested) Analysis of Variance (ANOVA):
Distance Class: 1 [<.001 - 20]
Moran's I (Grand Mean): 0.881
Groups (PUTs)
Degrees of Freedom: 49
Mean Squares: 4.84565
Variance Component (Raw): 0.09427
Variance Component (%): 0.41656
Coefficient of Variation: 0.34835
F: 36.6987
P: 0
PAM
Phylogenetic Structure
- Descriptive Statistics
- Lineage through time (LTT) plots
Phylogenetic Signal
- Moran’s I and correlograms
- Blomberg’s K
- Pagel’s Lambda
Correlated Evolution
- Autoregressive model
- Phylogenetic Eigenvector Regression
- Partial Phylogenetic Regression
- Phylogenetic Generalized Least Squares
Phylogenetic Diversity and Community Phylogenetics
- Phylogenetic Species Variability (PSV)
- NRI
- Shared Jaccard (Phylobetadiversity)
- Phylogenetically-Weighted Species Composition