Continuous Traits Framework
Camille Magneville
2024-07-26
Source:vignettes/Continuous_traits_framework.Rmd
Continuous_traits_framework.RmdAbout this tutorial
This tutorial explains the workflow used to compute functional space based on continuous traits and it shows how to retrieve species coordinates and species functional distances in the functional space.
DATA This tutorial uses a dataset from one of the 80 CESTES database Jeliazkov & the CESTES consortium (2019)) based on [Villeger et al. 2012] (https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0040679). This data frame contains 45 fish species from the Terminos Lagoon (Gulf of Mexico) gathered into 36 sites considered as assemblages. Each species is described with 16 continuous morphological traits.
When the dataset only gathers continuous traits, the functional space can be computed using one trait for one dimension or using Principal Component Analysis (PCA: convert correlations among samples into a 2D plot). NB Using a PCoA on continuous traits and euclidean distance is the same than using a PCA (clusters made by minimizing the linear distance (PCoA) are the same as those obtained by maximizing linear correlations (PCA)).
1. Load dataset
The species traits data frame has rows corresponding to species and columns corresponding to traits. The different traits are summed up in the following table:
| Trait name | Trait signification |
|---|---|
| logM | log(mass) |
| Ogsf | Oral gape surface |
| OgSh | Oral gape shape |
| OgPo | Oral gape position |
| GrLg | Gill raker length |
| GtLg | Gut length |
| EySz | Eye size |
| EyPo | Eye position |
| BdSh | Body transversal shape |
| BdSf | Body transversal surface |
| PfPo | Pectoral fin position |
| PfSh | Aspect ratio of the pectoral fin |
| CpHt | Caudal peduncle throttling |
| CfSh | Aspect ratio of the caudal fin |
| FsRt | Fins surface ratio |
| FsSf | Fins surface to body size ratio |
To work with mFD with only continuous traits, you must
load two objects:
-
sp_tr: species x traits data frame
# load dataset:
sp_tr <- read.csv(system.file("extdata", "data_cestes_sp_tr.csv",
package = "mFD"), dec = ",", sep = ":")
rownames(sp_tr) <- sp_tr$"Sp"
sp_tr <- sp_tr[ , -1]
# display the table:
knitr::kable(head(sp_tr),
caption = "Species x Traits data frame based on *CESTES* dataset")| logM | OgSf | OgSh | OgPo | EySz | GrLg | GtLg | EyPo | BdSh | BdSf | PfPo | PfSh | CpHt | CfSh | FsRt | FsSf | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Achirus_lineatus | 2.187 | 0.072 | 0.947 | 1.000 | 0.151 | 0.000 | 1.782 | 1.000 | 0.143 | 2.168 | 0.000 | 0.000 | 1.121 | 0.767 | 0.000 | 1.158 |
| Anchoa_mitchilli | 0.706 | 0.283 | 2.054 | 0.508 | 0.474 | 0.381 | 0.688 | 0.584 | 3.292 | 3.974 | 0.773 | 2.708 | 2.493 | 3.108 | 0.504 | 2.618 |
| Archosargus_probatocephalus | 2.674 | 0.082 | 0.754 | 0.221 | 0.282 | 0.035 | 2.591 | 0.652 | 3.091 | 1.679 | 0.666 | 4.740 | 2.584 | 2.393 | 1.526 | 1.504 |
| Archosargus_rhomboidalis | 3.327 | 0.056 | 0.648 | 0.273 | 0.294 | 0.032 | 3.467 | 0.647 | 3.102 | 1.596 | 0.638 | 6.868 | 2.906 | 2.684 | 1.060 | 1.502 |
| Ariopsis_felis | 3.110 | 0.173 | 0.513 | 0.346 | 0.263 | 0.128 | 2.078 | 0.647 | 1.021 | 1.658 | 0.806 | 3.480 | 3.592 | 4.052 | 0.781 | 1.648 |
| Bagre_marinus | 2.170 | 0.248 | 0.519 | 0.489 | 0.357 | 0.142 | 2.154 | 0.613 | 1.016 | 2.087 | 0.662 | 3.674 | 4.205 | 3.460 | 0.625 | 1.678 |
-
asb_sp_w: species x assemblages data frame summarizing biomass recorded in a volume of 4500m3 per site and per species:
# load dataset:
asb_sp_w <- read.csv(system.file("extdata", "data_cestes_asb_sp_w.csv",
package = "mFD"), dec = ",", sep = ":")
rownames(asb_sp_w) <- paste0("site", sep = "_", asb_sp_w$Sites)
asb_sp_w <- asb_sp_w[ , -1]
asb_sp_w$Urobatis_jamaicensis <- as.numeric(asb_sp_w$Urobatis_jamaicensis)
# remove sites 12, 23, 35 because FRic can not be computed on it...
# ... (for a clean example):
asb_sp_w <- asb_sp_w[-c(11, 22, 33), ]
# display the table:
knitr::kable(asb_sp_w[1:7, 1:6],
caption = "Species x Assemblages data frame based on *CESTES* dataset for the first six species and first seven sites")| Achirus_lineatus | Anchoa_mitchilli | Archosargus_probatocephalus | Archosargus_rhomboidalis | Ariopsis_felis | Bagre_marinus | |
|---|---|---|---|---|---|---|
| site_1 | 0 | 0 | 0 | 0 | 169.8 | 66.5 |
| site_2 | 0 | 0 | 0 | 0 | 0.0 | 29.5 |
| site_3 | 0 | 0 | 0 | 0 | 592.4 | 0.0 |
| site_5 | 0 | 0 | 0 | 0 | 0.0 | 0.0 |
| site_6 | 0 | 0 | 0 | 0 | 0.0 | 0.0 |
| site_7 | 0 | 0 | 0 | 0 | 135.4 | 0.0 |
| site_8 | 0 | 0 | 0 | 0 | 0.0 | 0.0 |
2. Compute the functional space
Based on the species-trait data frame or the species-standardized
traits data frame, mFD allows to build a functional space
based on a PCA or using each trait as a dimension. (NB
Using up to the 1.0.3 version of the mFD package does not
allow weighting continuous traits, it will be done in a next version of
the package. You can use the col.w
argument of the PCA function of the FactomineR package.). The function
used to compute functional space with continuous traits is called
mFD::tr.cont.fspace() and is used as follow:
USAGE
mFD::tr.cont.fspace(
sp_tr = sp_tr,
pca = TRUE,
nb_dim = 7,
scaling = "scale_center",
compute_corr = "pearson")It takes as inputs:
the sp_tr data frame
a pca argument that must be set to TRUE if you want to compute a PCA or to FALSE if you want to use each trait as a dimension to construct the multidimensional space
a nb_dim argument referring to the maximum number of dimensions for multidimensional functional spaces. Final number of dimensions depends on the number of positive eigenvalues obtained with PCA if pca = TRUE or the number of traits used if pca = FALSE. NB High value for nb_dim can increase computation time.
a scaling argument allowing traits values to be standardized. They can be standardized in several ways: standardization by the range value of the trait, center-transformation, scale transformation or scale-center transformation can be used. You can also chose not to standardize traits values. NOTE Scaling ensures that trait-based distances and distances in the functional space have the same maximum. Scaling distances implies that the quality of the functional space accounts for congruence in distances rather than their equality
a compute_corr argument which refers to a string value to compute Pearson correlation coefficients between traits using “pearson” or not using “none”.
In this example, we will compute a PCA based on a maximum number of 7 dimensions and get Pearson’s correlation coefficients:
fspace <- mFD::tr.cont.fspace(
sp_tr = sp_tr,
pca = TRUE,
nb_dim = 10,
scaling = "scale_center",
compute_corr = "pearson")If the PCA is computed, the output contains:
- quality metrics for spaces from 2 dimensions to nb_dim dimensions:
NB mean absolute deviation (mad) reflects the actual magnitude of errors that affect distances, hence FD metrics ; mean squared deviation (msd) reflects the potential risk associated with a few species pairs being strongly misplaced in the functional space (Maire et al. (2015)).
fspace$"quality_metrics"## mAD mSD
## 2D 1.83867581 3.380728750
## 3D 1.22034177 1.489235074
## 4D 0.90241642 0.814355528
## 5D 0.59513109 0.354181166
## 6D 0.46267807 0.214071066
## 7D 0.33359921 0.111288894
## 8D 0.23662790 0.055993113
## 9D 0.16252824 0.026415439
## 10D 0.09772059 0.009549359NB The lower the quality metric is, the better the quality of your space is. Here, thanks to mAD and mSD value, we can see that as the number of dimensions increases, the quality increases. However, to decrease computation time, we can chose to work with the 6D space which has good quality of functional space. Generally, you must keep in mind a trade-off between the number of axes and quality of functional space. Increasing the number of functional axes increases computation time.
- eigenvalues, percentage of variance explained and cumulative percentage of variance explained for each axis up to nb_dim dimensions:
fspace$"eigenvalues_percentage_var"## eigenvalue percentage of variance cumulative percentage of variance
## PC1 5.0894430 32.531951 32.53195
## PC2 2.3267315 14.872574 47.40452
## PC3 1.9839001 12.681179 60.08570
## PC4 1.6167089 10.334077 70.41978
## PC5 1.4277215 9.126061 79.54584
## PC6 0.7557779 4.830967 84.37681
## PC7 0.6704457 4.285519 88.66233
## PC8 0.5134516 3.282006 91.94433
## PC9 0.3510937 2.244207 94.18854
## PC10 0.2987544 1.909652 96.09819- a matrix of species coordinates in the functional space:
head(fspace$"sp_faxes_coord")## PC1 PC2 PC3 PC4
## Achirus_lineatus -3.1102450 -4.18756669 0.8212298 -0.7162535
## Anchoa_mitchilli 3.5220130 0.04037005 2.7468533 0.9280388
## Archosargus_probatocephalus 0.5598244 0.56101682 -1.9905123 -0.2138744
## Archosargus_rhomboidalis 0.7557227 1.05395885 -2.3524317 -1.0131106
## Ariopsis_felis 0.7945539 0.63147268 -1.9667765 -0.6958125
## Bagre_marinus 1.1521566 0.25626547 -0.7971292 -0.6188243
## PC5 PC6 PC7 PC8
## Achirus_lineatus 0.1119252 0.8809080 0.22663165 0.52316085
## Anchoa_mitchilli 1.7894441 2.0677051 -0.85219538 0.56621740
## Archosargus_probatocephalus -0.5774869 -0.4797906 -0.33549421 -0.31168020
## Archosargus_rhomboidalis -1.2508715 -0.4855985 0.02667960 -0.01979034
## Ariopsis_felis 0.5466197 -0.5300129 -0.03313655 1.72467762
## Bagre_marinus 0.8995832 -0.3424424 -0.29934540 2.00458491
## PC9 PC10
## Achirus_lineatus -0.211572742 0.5211315
## Anchoa_mitchilli 0.804586482 -0.8717554
## Archosargus_probatocephalus 0.068855803 0.5161352
## Archosargus_rhomboidalis 0.089848798 1.3715056
## Ariopsis_felis -0.450194649 -0.5236044
## Bagre_marinus 0.007347954 0.2391765- a dist object containing species euclidean distances in the functional space (here 5D space and for the first five species):
dist_mat <- as.matrix(fspace$sp_dist_multidim$"6D")
dist_mat[1:5, 1:5]## Achirus_lineatus Anchoa_mitchilli
## Achirus_lineatus 0.000000 8.514492
## Anchoa_mitchilli 8.514492 0.000000
## Archosargus_probatocephalus 6.819349 6.699577
## Archosargus_rhomboidalis 7.503606 7.362973
## Ariopsis_felis 6.958710 6.398155
## Archosargus_probatocephalus
## Achirus_lineatus 6.819349
## Anchoa_mitchilli 6.699577
## Archosargus_probatocephalus 0.000000
## Archosargus_rhomboidalis 1.226627
## Ariopsis_felis 1.248610
## Archosargus_rhomboidalis Ariopsis_felis
## Achirus_lineatus 7.503606 6.958710
## Anchoa_mitchilli 7.362973 6.398155
## Archosargus_probatocephalus 1.226627 1.248610
## Archosargus_rhomboidalis 0.000000 1.913729
## Ariopsis_felis 1.913729 0.000000- a dist object containing species distances based on traits (here for the first five species):
dist_mat <- as.matrix(fspace$sp_dist_init)
dist_mat[1:5, 1:5]## Achirus_lineatus Anchoa_mitchilli
## Achirus_lineatus 0.000000 8.810865
## Anchoa_mitchilli 8.810865 0.000000
## Archosargus_probatocephalus 6.954479 7.010258
## Archosargus_rhomboidalis 7.643421 7.834878
## Ariopsis_felis 7.165968 6.725278
## Archosargus_probatocephalus
## Achirus_lineatus 6.954479
## Anchoa_mitchilli 7.010258
## Archosargus_probatocephalus 0.000000
## Archosargus_rhomboidalis 1.814132
## Ariopsis_felis 2.780871
## Archosargus_rhomboidalis Ariopsis_felis
## Achirus_lineatus 7.643421 7.165968
## Anchoa_mitchilli 7.834878 6.725278
## Archosargus_probatocephalus 1.814132 2.780871
## Archosargus_rhomboidalis 0.000000 3.371347
## Ariopsis_felis 3.371347 0.000000- a correlation matrix containing correlation between traits and their associated pvalue:
fspace$"tr_correl"## logM OgSf OgSh OgPo EySz GrLg GtLg EyPo BdSh BdSf PfPo PfSh
## logM 1.00 -0.05 -0.62 -0.41 0.07 -0.27 0.22 0.48 -0.48 -0.69 -0.35 -0.27
## OgSf -0.05 1.00 0.19 0.04 0.14 0.28 -0.22 0.03 -0.18 -0.05 0.17 -0.07
## OgSh -0.62 0.19 1.00 0.14 0.06 0.35 -0.19 -0.48 0.75 0.57 0.31 0.34
## OgPo -0.41 0.04 0.14 1.00 -0.15 -0.06 -0.11 0.22 -0.05 0.16 -0.30 -0.37
## EySz 0.07 0.14 0.06 -0.15 1.00 0.34 -0.21 -0.14 -0.21 -0.15 0.12 0.41
## GrLg -0.27 0.28 0.35 -0.06 0.34 1.00 0.13 -0.38 0.10 0.16 0.50 0.21
## GtLg 0.22 -0.22 -0.19 -0.11 -0.21 0.13 1.00 -0.18 -0.02 -0.21 0.24 -0.15
## EyPo 0.48 0.03 -0.48 0.22 -0.14 -0.38 -0.18 1.00 -0.62 -0.31 -0.86 -0.65
## BdSh -0.48 -0.18 0.75 -0.05 -0.21 0.10 -0.02 -0.62 1.00 0.50 0.35 0.47
## BdSf -0.69 -0.05 0.57 0.16 -0.15 0.16 -0.21 -0.31 0.50 1.00 0.16 0.05
## PfPo -0.35 0.17 0.31 -0.30 0.12 0.50 0.24 -0.86 0.35 0.16 1.00 0.50
## PfSh -0.27 -0.07 0.34 -0.37 0.41 0.21 -0.15 -0.65 0.47 0.05 0.50 1.00
## CpHt -0.46 -0.07 0.50 -0.05 -0.36 0.12 0.09 -0.61 0.75 0.48 0.41 0.35
## CfSh -0.44 -0.05 0.37 -0.13 -0.09 0.27 0.28 -0.73 0.53 0.35 0.61 0.40
## FsRt 0.08 0.25 -0.21 -0.30 -0.42 -0.06 0.11 0.00 -0.05 0.13 0.15 -0.17
## FsSf 0.32 0.19 -0.13 -0.58 0.29 0.00 -0.28 0.30 -0.19 -0.01 -0.25 0.15
## CpHt CfSh FsRt FsSf
## logM -0.46 -0.44 0.08 0.32
## OgSf -0.07 -0.05 0.25 0.19
## OgSh 0.50 0.37 -0.21 -0.13
## OgPo -0.05 -0.13 -0.30 -0.58
## EySz -0.36 -0.09 -0.42 0.29
## GrLg 0.12 0.27 -0.06 0.00
## GtLg 0.09 0.28 0.11 -0.28
## EyPo -0.61 -0.73 0.00 0.30
## BdSh 0.75 0.53 -0.05 -0.19
## BdSf 0.48 0.35 0.13 -0.01
## PfPo 0.41 0.61 0.15 -0.25
## PfSh 0.35 0.40 -0.17 0.15
## CpHt 1.00 0.81 0.17 -0.22
## CfSh 0.81 1.00 -0.03 -0.25
## FsRt 0.17 -0.03 1.00 0.17
## FsSf -0.22 -0.25 0.17 1.00
##
## n= 45
##
##
## P
## logM OgSf OgSh OgPo EySz GrLg GtLg EyPo BdSh BdSf
## logM 0.7651 0.0000 0.0057 0.6264 0.0738 0.1394 0.0010 0.0009 0.0000
## OgSf 0.7651 0.2153 0.7759 0.3746 0.0632 0.1512 0.8559 0.2328 0.7626
## OgSh 0.0000 0.2153 0.3540 0.7084 0.0196 0.2164 0.0009 0.0000 0.0000
## OgPo 0.0057 0.7759 0.3540 0.3200 0.6850 0.4850 0.1492 0.7320 0.2970
## EySz 0.6264 0.3746 0.7084 0.3200 0.0217 0.1688 0.3552 0.1752 0.3416
## GrLg 0.0738 0.0632 0.0196 0.6850 0.0217 0.4014 0.0092 0.5024 0.3083
## GtLg 0.1394 0.1512 0.2164 0.4850 0.1688 0.4014 0.2431 0.8801 0.1633
## EyPo 0.0010 0.8559 0.0009 0.1492 0.3552 0.0092 0.2431 0.0000 0.0365
## BdSh 0.0009 0.2328 0.0000 0.7320 0.1752 0.5024 0.8801 0.0000 0.0005
## BdSf 0.0000 0.7626 0.0000 0.2970 0.3416 0.3083 0.1633 0.0365 0.0005
## PfPo 0.0198 0.2608 0.0364 0.0465 0.4391 0.0005 0.1170 0.0000 0.0179 0.2825
## PfSh 0.0713 0.6297 0.0237 0.0129 0.0049 0.1765 0.3167 0.0000 0.0010 0.7222
## CpHt 0.0017 0.6657 0.0005 0.7423 0.0137 0.4351 0.5597 0.0000 0.0000 0.0008
## CfSh 0.0027 0.7412 0.0126 0.4075 0.5349 0.0752 0.0648 0.0000 0.0002 0.0168
## FsRt 0.6006 0.1010 0.1606 0.0483 0.0043 0.6867 0.4784 0.9796 0.7473 0.4052
## FsSf 0.0344 0.2210 0.3825 0.0000 0.0554 0.9783 0.0604 0.0428 0.2024 0.9353
## PfPo PfSh CpHt CfSh FsRt FsSf
## logM 0.0198 0.0713 0.0017 0.0027 0.6006 0.0344
## OgSf 0.2608 0.6297 0.6657 0.7412 0.1010 0.2210
## OgSh 0.0364 0.0237 0.0005 0.0126 0.1606 0.3825
## OgPo 0.0465 0.0129 0.7423 0.4075 0.0483 0.0000
## EySz 0.4391 0.0049 0.0137 0.5349 0.0043 0.0554
## GrLg 0.0005 0.1765 0.4351 0.0752 0.6867 0.9783
## GtLg 0.1170 0.3167 0.5597 0.0648 0.4784 0.0604
## EyPo 0.0000 0.0000 0.0000 0.0000 0.9796 0.0428
## BdSh 0.0179 0.0010 0.0000 0.0002 0.7473 0.2024
## BdSf 0.2825 0.7222 0.0008 0.0168 0.4052 0.9353
## PfPo 0.0005 0.0047 0.0000 0.3207 0.1029
## PfSh 0.0005 0.0181 0.0070 0.2514 0.3267
## CpHt 0.0047 0.0181 0.0000 0.2722 0.1433
## CfSh 0.0000 0.0070 0.0000 0.8596 0.0914
## FsRt 0.3207 0.2514 0.2722 0.8596 0.2563
## FsSf 0.1029 0.3267 0.1433 0.0914 0.2563Here we can notice that there is no strong correlation between traits. NB However, if some strong correlation is to be found, then one of the two correlated trait can be remove from the analysis.
If the PCA is not computed, outputs are the same except that mad and msd are not computed and that only one distance object is returned.
3. Plot functional space, compute and illustrate indices
Then, based on the species coordinates matrix, steps are similar as those listed in the mFD General Workflow, from step 5 till the end.
References
Maire et al. (2015) How many dimensions are needed to accurately assess functional diversity? A pragmatic approach for assessing the quality of functional spaces. Global Ecology and Biogeography, 24, 728-740.
Villeger et al. (2012) Low Functional beta Diversity Despite High Taxonomic beta Diversity among Tropical Estuarine Fish Communities. PLoS ONE, 7, e40679.