Supplementary Information for the manuscript: Leaf habit affects the distribution of drought sensitivity but not water transport efficiency in the tropics
German Vargas G.1,2,*, Norbert Kunert3,4,5, William M. Hammond6, Z. Carter Berry7, Leland K. Weden8, Chris M.
Smith-Martin9, Brett T. Wolfe4,10, Laura Toro1, Ariadna Mondragón-Botero1, Jesús N. Pinto-Ledezma11, Naomi B. Schwartz12, María Uriarte9, Lawren Sack13, Kristina J. Anderson-Teixeira3,4 and Jennifer S. Powers1,11
1Department of Plant and Microbial Biology, University of Minnesota, St. Paul, MN 55108, USA.
2School of Biological Sciences, The University of Utah, Salt Lake City, UT 84112, USA.
3Conservation Ecology Center, Smithsonian National Zoo and Conservation Biology Institute, Front Royal, VA 22630, USA.
4Forest Global Earth Observatory, Smithsonian Tropical Research Institute, Panama, Republic of Panama.
5Department of Integrative Biology and Biodiversity Research, Institute of Botany, University of Natural Resources and Life Sciences Vienna, Vienna A-1190, Austria.
6Agronomy Department, Institute of Food and Agricultural Sciences, University of Florida, Gainesville, FL 32611, USA.
7Department of Biology, Wake Forest University, Winston-Salem, NC 27109, USA.
8Department of Environmental Systems Science, ETH Zürich, Zürich, Switzerland.
9Department of Ecology, Evolution and Environmental Biology, Columbia University, New York, NY 10027, USA.
10School of Renewable Natural Resources, Louisiana State University Agricultural Center, Baton Rouge, LA 70803, USA.
11Department of Ecology, Evolution and Behavior, University of Minnesota, St. Paul, MN 55108, USA.
12Department of Geography, University of British Columbia, Vancouver, BC V6T 1Z2, Canada.
13Department of Ecology and Evolution, University of California Los Angeles, Los Angeles, CA 90095, USA.
* Correspondence to: [email protected]
Table S1. Correlation matrix table among five climatic predictors: aridity index (AI), dry season length (DSL), maximum climatic water deficit (MCWD), seasonality index (S), and mean annual rainfall (MAR). Values represent the Pearson’s product moment correlation coefficient.
Median climatic affiliations:
AI DSL MCWD S MAR
AI 1.00 -0.78 0.80 -0.60 0.91
DSL -0.78 1.00 -0.92 0.71 -0.93
MCWD 0.80 -0.92 1.00 -0.82 0.86
S -0.60 0.71 -0.82 1.00 -0.64
MAR 0.91 -0.93 0.86 -0.64 1.00
Extreme climatic affiliations:
AI DSL MCWD S MAR
AI 1.00 -0.90 0.89 -0.71 0.95
DSL -0.90 1.00 0.80 0.68 -0.95
MCWD 0.89 -0.80 1.00 -0.74 0.90
S -0.71 0.68 -0.74 1.00 -0.72
MAR 0.95 -0.95 0.90 -0.72 1.00
Trait sampling climate:
AI DSL MCWD S MAR
AI 1.00 -0.87 0.79 -0.58 0.94
DSL -0.87 1.00 -0.84 0.61 -0.93
MCWD 0.79 -0.84 1.00 -0.79 0.82
S -0.58 0.61 -0.79 1.00 -0.56
MAR 0.94 -0.93 0.82 -0.56 1.00
Fig. S1. Regression coefficient (β) values on the effect of aridity index (AI) and rainfall seasonality index (S) on three plant hydraulic traits: stem-specific hydraulic conductivity (KS), leaf water potential at turgor loss point (TLP), and the water potential at 50% loss of conductivity or 50 % accumulation of embolism events in the xylem (P50), obtained by fitting two Bayesian multilevel models: one using data from all observations and one using observations coming from stem data only. For each dataset, we fitted three models: using the extreme climatic affiliation values (extreme), using the median climatic affiliations values (median), and using the climatic values obtained from the trait sampling localities (site). Each point represents the median with its associated 95% high-density credible interval (HDI) for deciduous (D) and evergreen (E) plant species. The shaded gray band represents the region of practical equivalence based on the variability of the response variable in question as [-0.1*sdY, 0.1*sdY], The asterisks indicate whether 99% of the MCMC distribution falls outside the ROPE, which suggests strong evidence that the climatic predictor affects trait variation. Numbers represent the percentual overlap in the β posterior distributions among datasets.
* *
47.4 64.3
* *
45.6 73.8
*
63 36.5
57.6 64.3
*
53.5 73.8
71 36.5 site
AI
site S median
AI
median S extreme
AI
extreme S
D E D E
−0.5 0.0 0.5
−0.5 0.0 0.5
−0.5 0.0 0.5
βcoefficient
P50
*
*
* *
site AI
site S median
AI
median S extreme
AI
extreme S
D E D E
−0.2 0.0 0.2 0.4
−0.2 0.0 0.2 0.4
−0.2 0.0 0.2 0.4 TLP
40.6 73.5
39.1 81.4
* *
54.5 76.7
* *
54.5 73.5
59.7 81.4
71.9 76.7 site
AI
site S median
AI
median S extreme
AI
extreme S
D E D E
−0.5 0.0 0.5
−0.5 0.0 0.5
−0.5 0.0 0.5 Ks
Stem data only a No a Yes
Fig. S2. Scatter plots showing the univariate effects of aridity index (AI), rainfall seasonality (S), mean annual rainfall (MAR), dry season length (DSL), and maximum climatic water deficit (MCWD) on the water potential at leaf turgor loss (ΨTLP) for evergreen (green) and drought-deciduous (yellow) tropical plants. Regression coefficients (β) were obtained by fitting independent phylogenetic Bayesian multilevel linear models using as climatic predictors the median climatic affiliation values (AImed, Smed, MARmed, DSLmed, MCWDmed), the extreme climatic affiliation values (AImin, Smax, MARmin, DSLmax, MCWDmin), and the trait sampling localities climate (AIsite, Ssite, MARsite, DSLsite, MCWDsite). Regression lines and their associated 95% high-density credible intervals indicate strong evidence (β ≠ 0) of a given climatic predictor's effect on ΨTLP.
−4.0
−3.0
−2.0
−1.0
0 1 2 3
AIsite
−4.0
−3.0
−2.0
−1.0
0.0 0.5 1.0 1.5
Ssite
−4.0
−3.0
−2.0
−1.0
0 1000 2000 3000 4000 5000 MARsite(mm yr−1)
−4.0
−3.0
−2.0
−1.0
0 4 8 12
DSLsite(Months)
−4.0
−3.0
−2.0
−1.0
−900 −600 −300 0 MCWDsite(mm yr−1)
−4.0
−3.0
−2.0
−1.0
0 1 2 3
AImed
−4.0
−3.0
−2.0
−1.0
0.0 0.5 1.0 1.5
Smed
−4.0
−3.0
−2.0
−1.0
0 1000 2000 3000 4000 5000 MARmed(mm yr−1)
−4.0
−3.0
−2.0
−1.0
0 4 8 12
DSLmed(Months)
−4.0
−3.0
−2.0
−1.0
−900 −600 −300 0 MCWDmed(mm yr−1)
−4.0
−3.0
−2.0
−1.0
0 1 2 3
AImin
−4.0
−3.0
−2.0
−1.0
0.0 0.5 1.0 1.5
Smax
−4.0
−3.0
−2.0
−1.0
0 1000 2000 3000 4000 5000 MARmin(mm yr−1)
−4.0
−3.0
−2.0
−1.0
0 4 8 12
DSLmax(Months)
−4.0
−3.0
−2.0
−1.0
−900 −600 −300 0 MCWDmin(mm yr−1) ΨTLP(MPa)
Fig. S3. Scatter plots showing the univariate effects of aridity index (AI), rainfall seasonality (S), mean annual rainfall (MAR), dry season length (DSL), and maximum climatic water deficit (MCWD) on the water potential at 50% loss of conductivity or 50 % accumulation of embolism events in the xylem (ΨP50) for evergreen (green) and drought-deciduous (yellow) tropical plants. Regression coefficients (β) were obtained by fitting independent phylogenetic Bayesian multilevel linear models using as climatic predictors the median climatic affiliation values (AImed, Smed, MARmed, DSLmed, MCWDmed), the extreme climatic affiliation values (AImin, Smax, MARmin, DSLmax, MCWDmin), and the trait sampling localities climate (AIsite, Ssite, MARsite, DSLsite, MCWDsite).
Regression lines and their associated 95% high-density credible intervals indicate strong evidence (β ≠ 0) of a given climatic predictor's effect on ΨP50.
−10.0
−5.0 0.0
0 1 2 3
AIsite
−10.0
−5.0 0.0
0.0 0.5 1.0 1.5
Ssite
−10.0
−5.0 0.0
0 10002000300040005000 MARsite(mm yr−1)
−10.0
−5.0 0.0
0 4 8 12
DSLsite(Months)
−10.0
−5.0 0.0
−900 −600 −300 0 MCWDsite(mm yr−1)
−10.0
−5.0 0.0
0 1 2 3
AImed
−10.0
−5.0 0.0
0.0 0.5 1.0 1.5
Smed
−10.0
−5.0 0.0
0 10002000300040005000 MARmed(mm yr−1)
−10.0
−5.0 0.0
0 4 8 12
DSLmed(Months)
−10.0
−5.0 0.0
−900 −600 −300 0 MCWDmed(mm yr−1)
−10.0
−5.0 0.0
0 1 2 3
AImin
−10.0
−5.0 0.0
0.0 0.5 1.0 1.5
Smax
−10.0
−5.0 0.0
0 10002000300040005000 MARmin(mm yr−1)
−10.0
−5.0 0.0
0 4 8 12
DSLmax(Months)
−10.0
−5.0 0.0
−900 −600 −300 0 MCWDmin(mm yr−1) ΨP50(MPa)
Fig. S4. Scatter plots showing the univariate effects of aridity index (AI), rainfall seasonality (S), mean annual rainfall (MAR), dry season length (DSL), and maximum climatic water deficit (MCWD) on xylem-specific hydraulic conductivity (KS) for evergreen (green) and drought-deciduous (yellow) tropical plants. Regression coefficients (β) were obtained by fitting independent phylogenetic Bayesian multilevel linear models using as climatic predictors the median climatic affiliation values (AImed, Smed, MARmed, DSLmed, MCWDmed), the extreme climatic affiliation values (AImin, Smax, MARmin, DSLmax, MCWDmin), and the trait sampling localities climate (AIsite, Ssite, MARsite, DSLsite, MCWDsite). Regression lines and their associated 95% high-density credible intervals indicate strong evidence (β ≠ 0) of a given climatic predictor's effect on KS.
−2.0 0.0 2.0 4.0
0 1 2 3
AIsite
−2.0 0.0 2.0 4.0
0.0 0.5 1.0 1.5
Ssite
−2.0 0.0 2.0 4.0
0 10002000300040005000 MARsite(mm yr−1)
−2.0 0.0 2.0 4.0
0 4 8 12
DSLsite(Months)
−2.0 0.0 2.0 4.0
−900 −600 −300 0 MCWDsite(mm yr−1)
−2.0 0.0 2.0 4.0
0 1 2 3
AImed
−2.0 0.0 2.0 4.0
0.0 0.5 1.0 1.5
Smed
−2.0 0.0 2.0 4.0
0 10002000300040005000 MARmed(mm yr−1)
−2.0 0.0 2.0 4.0
0 4 8 12
DSLmed(Months)
−2.0 0.0 2.0 4.0
−900 −600 −300 0 MCWDmed(mm yr−1)
−2.0 0.0 2.0 4.0
0 1 2 3
AImin
−2.0 0.0 2.0 4.0
0.0 0.5 1.0 1.5
Smax
−2.0 0.0 2.0 4.0
0 10002000300040005000 MARmin(mm yr−1)
−2.0 0.0 2.0 4.0
0 4 8 12
DSLmax(Months)
−2.0 0.0 2.0 4.0
−900 −600 −300 0 MCWDmin(mm yr−1) ln(Ks)(kgm−2 s−1 MPa−1 )
Fig. S5. Regression coefficient (β) values from univariate Bayesian multilevel models of the effect of aridity index (AI), dry season length (DSL), mean annual rainfall (MAR), maximum climatic water deficit (MCWD), and rainfall seasonality index (S) on two plant hydraulic traits: stem-specific hydraulic conductivity (KS) and the water potential at 50% loss of conductivity or 50 % accumulation of embolism events in the xylem (P50). For each climatic predictor, we show coefficients from two models: one using data from all observations and one using observations coming from stem data only. For each dataset, we fitted three models: using the extreme climatic affiliation values (extreme), using the median climatic affiliations values (median), and using the climatic values obtained from the trait sampling localities (site). Each point represents the median with its associated 95% high-density credible interval (HDI) for deciduous (D) and evergreen (E) plant species. The shaded gray band represents the region of practical equivalence based on the variability of the response variable in question as [-0.1*sdY, 0.1*sdY], The asterisks indicate whether 99% of the MCMC distribution falls outside the ROPE, which suggests strong evidence that the climatic predictor affects trait variation. Numbers represent the percentual overlap in the β posterior distributions among datasets.
*
56.1 70.1
* *
62.7 81.8
* *
76 62.4
*
54.9 71.6
60.8 79.2
* *
75 75.7
*
56.8 70.2
* *
63.1 80.7
*
72.6 67.1
63.8 73.3
65.2 77.6
77.5 88.6
68.6 80.1
69.4 70
*
84.1 67.5 site
AI
site DSL
site MAR
site MCWD
site S median
AI
median DSL
median MAR
median MCWD
median S extreme
AI
extreme DSL
extreme MAR
extreme MCWD
extreme S
D E D E D E D E D E
−0.5 0.0 0.5
−0.5 0.0 0.5
−0.5 0.0 0.5
βcoefficient
P50
46.4 83.4
47 87
**
58.2 83.6
36.4 78.7
48.3 79.4
**
64.9 83.9
44.1 79.4
42.1 81.9
**
58 82.2
58.9 84.9
56.2 82.2
68.5 81.5
61.6 86.2
70.3 83.2
76.9 81.5 site
AI
site DSL
site MAR
site MCWD
site S median
AI
median DSL
median MAR
median MCWD
median S extreme
AI
extreme DSL
extreme MAR
extreme MCWD
extreme S
D E D E D E D E D E
−0.5 0.0 0.5
−0.5 0.0 0.5
−0.5 0.0 0.5
βcoefficient
Ks
Stem data only a No a Yes
Fig. S6. Quantile regression coefficient (β) values from Bayesian multilevel models on the effect of aridity index (AI), and rainfall seasonality index (S) on two plant hydraulic traits: stem-specific hydraulic conductivity (KS) and the water potential at 50% loss of conductivity or 50 % accumulation of embolism events in the xylem (P50). For each climatic predictor, we show coefficients from two models: one using data from all observations and one using observations coming from stem data only. For each dataset, we fitted two models: using the median climatic affiliations values (median), and using the climatic values obtained from the trait sampling localities (site). Each point represents the median with its associated 95% high-density credible interval (HDI) for deciduous and evergreen plant species. The shaded gray band represents the region of practical equivalence based on the variability of the response variable in question as [-0.1*sdY, 0.1*sdY], The asterisks indicate
whether 99% of the MCMC distribution falls outside the ROPE, which suggests strong evidence that the climatic predictor affects trait variation. Numbers represent the percentual overlap in the β posterior distributions among datasets.
* * * * *
43.3 44.1 48.9 53.9 55
62.6 69.5 71.9 72.2 72.3
* * * * * * * * * *
69.4 71.3 79.7 82.8 84.5
*
47.3 47.3 53.2 64.9 81.6
51.6 53.5 57.2 62.2 62.7
75.6 78.3 79.8 81.6 79.8
* * *
69.4 71.3 79.7 82.8 84.5
47.3 47.3 53.2 64.9 81.6 site
AI Deciduous
site AI Evergreen
site S Deciduous
site S Evergreen median
AI Deciduous
median AI Evergreen
median S Deciduous
median S Evergreen
0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9
−0.5 0.0 0.5 1.0
−0.5 0.0 0.5 βcoefficient 1.0 P50
43.3 44.1 48.9 53.9 55
* * * * * *
62.6 69.5 71.9 72.2 72.3
69.4 71.3 79.7 82.8 84.5
47.3 47.3 53.2 64.9 81.6
51.6 53.5 57.2 62.2 62.7
75.6 78.3 79.8 81.6 79.8
69.4 71.3 79.7 82.8 84.5
47.3 47.3 53.2 64.9 81.6 site
AI Deciduous
site AI Evergreen
site S Deciduous
site S Evergreen median
AI Deciduous
median AI Evergreen
median S Deciduous
median S Evergreen
0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9
−0.5 0.0 0.5 1.0
−0.5 0.0 0.5 βcoefficient 1.0 Ks
Stem data only a No a Yes
Fig. S7. Quantile regression coefficient (β) values from Bayesian multilevel models on the effect of aridity index (AI), and rainfall seasonality index (S) on the water potential at leaf turgor loss point (ΨTLP). We fitted two models: using the median climatic affiliations values (median), and using the climatic values obtained from the trait sampling localities (site). Each point represents the median with its associated 95% high-density credible interval (HDI) for deciduous and evergreen plant species. The shaded gray band represents the region of practical equivalence based on the variability of the response variable in question as [-0.1*sdY, 0.1*sdY], The asterisks indicate whether 99% of the MCMC distribution falls outside the ROPE, which suggests strong evidence that the climatic predictor affects trait variation.
*
* * * * *
* * * * *
* * * * *
site AI Deciduous
site AI Evergreen
site S Deciduous
site S Evergreen median
AI Deciduous
median AI Evergreen
median S Deciduous
median S Evergreen
0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9
−0.50
−0.25 0.00 0.25 0.50
−0.50
−0.25 0.00 0.25
β co e ff ic ie n t
0.50Fig. S8. Group level effects on model variance for the different levels method within species (σmethod:sp), species associated uncertainty (σsp), and species phylogenetic relatedness (σphy). The circles represent the median estimate, and the error bars represent the 50% (thick) and 95% (thin) credible intervals.
σphy
σsp
σmethod:sp
0.0 0.4 0.8 1.2
Group level effects
AImed & Smed
σphy
σsp
σmethod:sp
0.0 0.4 0.8 1.2
Group level effects
AImin & Smax
σphy
σsp
σmethod:sp
0.0 0.4 0.8 1.2
Group level effects
AIsite & Ssite a) Ks
σphy σsp
σmethod:sp
0.0 0.4 0.8 1.2
Group level effects
σphy σsp
σmethod:sp
0.0 0.4 0.8 1.2
Group level effects
σphy σsp
σmethod:sp
0.0 0.4 0.8 1.2
Group level effects
b) TLP
σphy
σsp
σmethod:sp
0.0 0.4 0.8 1.2
MCMC draws
Group level effects
σphy
σsp
σmethod:sp
0.0 0.4 0.8 1.2
MCMC draws
Group level effects
σphy
σsp
σmethod:sp
0.0 0.4 0.8 1.2
MCMC draws
Group level effects
c) P50
Fig. S9. Boxplots of AI and S values as obtained from species BIEN-derived occurrence records for evergreen and drought-deciduous plant species. Each panel represents the climatic affiliations using the median, maximum, and minimum. Statistical results from a Student t-test comparing values among evergreen and drought-deciduous species. The horizontal line represents the median, the box is defined by the 25th and 75th percentiles, and the whiskers are the maximum values.
t=8.238; d.f.=772; p<0.001
0 1 2 3 4
AI
Median
t=2.149; d.f.=772; p<0.05
0 2 4 6
Maximum
t=7.905; d.f.=772; p<0.001
0.0 0.5 1.0 1.5 2.0
Minimum
t=−7.766; d.f.=772; p<0.001
0.0 0.2 0.4 0.6
Deciduous Evergreen
S
t=−8.239; d.f.=772; p<0.001
0.0 0.5 1.0 1.5
Deciduous Evergreen
t=−1.722; d.f.=772; p>0.05
0.0 0.2 0.4
Deciduous Evergreen
Fig. S10. Posterior median estimates with their associated 95% high-density credible interval of plant hydraulic trait values for drought-deciduous and evergreen pan-tropical plants. Panels depict values for xylem specific hydraulic conductivity (KS), the water potential at leaf turgor loss (ΨTLP), and the water potential at 50 % KS loss or 50 % accumulation of embolism events in the xylem (ΨP50). Each panel represents a model with the linear combination of climate predictors using species’ median climatic affiliation values (AImed and Smed), the values linked to the driest and more seasonal environment where the species occurs (AImin and Smax), and the climatic values obtained from the trait sampling localities (AIsite and Ssite).
−0.5 0.0 0.5 1.0 1.5
Deciduous Evergreen KS(kgm−2 s−1 Mpa−1 ) AImed & Smed
−0.5 0.0 0.5 1.0 1.5
Deciduous Evergreen KS(kgm−2 s−1 Mpa−1 ) AImin & Smax
−0.5 0.0 0.5 1.0 1.5
Deciduous Evergreen KS(kgm−2 s−1 Mpa−1 ) AIsite & Ssite
−2.5
−2.0
−1.5
−1.0
Deciduous Evergreen ΨTLP(Mpa)
AImed & Smed
−2.5
−2.0
−1.5
−1.0
Deciduous Evergreen ΨTLP(Mpa)
AImin & Smax
−2.5
−2.0
−1.5
−1.0
Deciduous Evergreen ΨTLP(Mpa)
AIsite & Ssite
−5
−4
−3
−2
−1
Deciduous Evergreen ΨP50(Mpa)
AImed & Smed
−5
−4
−3
−2
−1
Deciduous Evergreen ΨP50(Mpa)
AImin & Smax
−5
−4
−3
−2
−1
Deciduous Evergreen ΨP50(Mpa)
AIsite & Ssite
Fig. S11. Sampling site climate as a function of the species’ climatic affiliation for the aridity index (AI), the seasonality index (S), mean annual rainfall (MAR), dry season length (DSL), and maximum climatic water deficit (MCWD). Each dot represents an observation of any of the three hydraulic traits in this study at a given sampling site. Straight lines and uncertainties represent the mean response and the 95% high-density interval from a multilevel Bayesian model with species as a random intercept, while the dashed line is the 1:1 relationship. This data shows that in most cases, species were sampled in either wetter or drier regions, less seasonal or more seasonal than their median climatic affiliation.
−2 0 2 4
−2 0 2 4
AI
MedianA I
Site−2 0 2 4
−2 0 2 4
S
MedianS
Site−2 0 2 4
−2 0 2 4
MAR
MedianM A R
Site−2
−1 0 1 2 3
−2 −1 0 1 2 3
DSL
MedianD S L
Site−4
−2 0 2
−4 −2 0 2
MCWD
MedianM C W D
SiteLeaf habit
Deciduous EvergreenNotes S1. Reconciliation of species nomenclature conflicts.
We reconciled nomenclature conflicts with the Iplantcollaborative database
(http://tnrs.iplantcollaborative.org/TNRSapp.html, accessed June 15th, 2020). The database scored the species name from 0 to 1. When the scores were below 1, names were checked both in the Tropicos
(http://www.tropicos.org, accessed July 23rd, 2020) and The Plant List (http://www.theplantlist.org/, accessed July 23rd, 2020) databases. When we encountered discrepancies among databases, the names used in Tropicos were preferred. In case a name was not found in either The Plant List or the Tropicos databases, the whole genus was inspected to find similar names. When two accepted names were valid for a species, we refer to the local botanical authorities in the country where trait data collection took place.
Notes S2. Phylogenetic Bayesian multilevel model to explain plant hydraulic traits variation as a function of aridity and seasonality.
We fitted three intependendent models for each plant hydraulic trait (y), in which we assumed trait variation of the i-th observation follows a normal distribution with a mean (μ) and error (σe) that follows a t distribution. Therefore, trait μ is assumed to be the sum of the linear combination of the effects (β) by the climate predictors (AI and S) and leaf habit (LH). In these models, we assigned species-specific intercepts (αsp) and another species-specific intercept associated with the species phylogeny. The residual variation of αsp (σsp) follows a gamma distribution and αphy assumes that residual trait variation (σphy) is correlated as indicated by a phylogenetic distance matrix (D). By having two independent intercepts associated with species (αsp and αphy), we assumed that trait variation at the species level is not explained by species phylogenetic relatedness and can be explained by multiple sources not considered in this model (e.g., within-species differences). We used the same model for fitting the quantile regression analysis, but we changed the associated distribution of the
response variable from normal to following a Laplace distribution. This change was done in order to account for unequal variation across quantiles in the response of plant hydraulic traits to the climatic predictors. In all models, the posterior distributions were obtained by sampling using a Hamiltonian Monte-Carlo algorithm over four Markov-chains Monte-Carlo (MCMC) with 15000 iterations and a burn-in period of 3000 iterations, as follows.
Likelihood:
yi⇠N(µi,se)
µi=a+asp[i]+aphy[i]+b1AIi+b2Si+b3LHi+b4AIi:LHi+b5Si:LHi
Priors:
asp[i]⇠N(0,ssp) ssp⇠G(2,0.2) aphy[i]⇠N 0,sphy
sphy⇠ 2 66 64
0 Dsp1 sp2 0
... ··· ...
Dsp1 spn ··· ··· 0 3 77 75
b1,b2,b3,b4and b5⇠N(0,se) a⇠N(0,se)
se⇠t(4,0,5)
1
