Leaf-light-project
cong
2021/12/23
1 Background
The big light project puts a LED light into old-growth, secondary and man made forest(rubber tree forest) separetely, which shines at night. We rekon it as a long term disturbance to forest which has continued more than one year. Now we want to know whether this disturbance would effect the understory or not.
1.1 Our hypothesis
- Prolong the light time may effect the nutrition circulation of understory
- LED light attracts insects and insects dead may increase soil nitrogen, then effect the nutrition circulation of understory.
1.2 Place and species I choosed
We choose man made forest, for simulating the street tree and species Colocasia_gigantea and Melastoma_candidum
1.3 method
we punch leaf using leaf-disc to measure leaf nutrition.
2 Data Exploration
the pacakges we’ll use:
library(kableExtra)
library(tidyverse)
#> -- Attaching packages --------------------------------------- tidyverse 1.3.1 --
#> v ggplot2 3.3.5 v purrr 0.3.4
#> v tibble 3.1.6 v dplyr 1.0.7
#> v tidyr 1.2.0 v stringr 1.4.0
#> v readr 2.1.2 v forcats 0.5.1
#> Warning: 程辑包'tidyr'是用R版本4.1.3 来建造的
#> Warning: 程辑包'readr'是用R版本4.1.3 来建造的
#> -- Conflicts ------------------------------------------ tidyverse_conflicts() --
#> x dplyr::filter() masks stats::filter()
#> x dplyr::group_rows() masks kableExtra::group_rows()
#> x dplyr::lag() masks stats::lag()
library(lme4)
#> Warning: 程辑包'lme4'是用R版本4.1.3 来建造的
#> 载入需要的程辑包：Matrix
#> Warning: 程辑包'Matrix'是用R版本4.1.3 来建造的
#>
#> 载入程辑包：'Matrix'
#> The following objects are masked from 'package:tidyr':
#>
#> expand, pack, unpackinput our data
llp <- read_csv("../data-raw/leaf_light_project.csv")
#> Rows: 260 Columns: 11
#> -- Column specification --------------------------------------------------------
#> Delimiter: ","
#> chr (1): species
#> dbl (10): Plot, Distance, angel, individual, leaf ID, disc, disc_area, fresh...
#>
#> i Use `spec()` to retrieve the full column specification for this data.
#> i Specify the column types or set `show_col_types = FALSE` to quiet this message.
llp[1:5,] %>% kbl() %>% kable_styling()| Plot | species | Distance | angel | individual | leaf ID | disc | disc_area | fresh_weight | dry_weight | canopy_openness |
|---|---|---|---|---|---|---|---|---|---|---|
| 5 | Melastoma_candidum | 7.3 | 246 | 1 | 1 | 5 | 10 | 0.0469 | 0.0133 | 0.093571 |
| 5 | Melastoma_candidum | 7.3 | 246 | 1 | 2 | 5 | 10 | 0.0497 | 0.0140 | 0.093571 |
| 5 | Melastoma_candidum | 7.3 | 246 | 1 | 3 | 5 | 10 | 0.0476 | 0.0141 | 0.093571 |
| 5 | Melastoma_candidum | 7.3 | 246 | 1 | 4 | 5 | 10 | 0.0453 | 0.0140 | 0.093571 |
| 5 | Melastoma_candidum | 7.3 | 246 | 1 | 5 | 5 | 10 | 0.0489 | 0.0158 | 0.093571 |
Then we calculate LMA and show our samples location away from the light.
llp1 <- llp |>mutate(LMA = dry_weight/(disc*pi*(0.005)^2))
llp1 |>
mutate(x_loc = Distance*cos(angel*pi/180))|>
mutate(y_loc = Distance*sin(angel*pi/180))|>
ggplot(aes(x_loc, y_loc, size = LMA))+
geom_point(shape =17)+
facet_grid(cols = vars(species))+
theme_bw()
(Notation: coordinate (0,0) is where the light is.)
Next, because we want to know whether light give an effect to understory, so we consider a graph between LMA and Distance away from the light which is on behalf of the gradient of light strength.
llp1 |>
filter(Plot == 2) |>
ggplot(aes(x = Distance, y = LMA))+
geom_point()+
labs(title = "LMA_Colocasia_gigantea")+
theme_bw()
llp1 |>
filter(Plot == 5) |>
ggplot(aes(x = Distance, y = LMA))+
geom_point()+
labs(title = "LMA_Melastoma_candidum")+
theme_bw()
(We see there can be a negative correlation between LMA and Distance, while we can’t simply draw the conclusion based on that, instead we add canopy openness into our consideration. )
llp1|>
ggplot(aes(x = LMA))+
facet_grid(cols = vars(species))+
geom_histogram()
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
3 Data Mining
mod <- lmer(data = llp1, formula = LMA ~ log(Distance)*log(canopy_openness)+(1|species))
summary(mod)
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: LMA ~ log(Distance) * log(canopy_openness) + (1 | species)
#> Data: llp1
#>
#> REML criterion at convergence: 1394.3
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -2.75665 -0.75270 0.02021 0.62920 3.00758
#>
#> Random effects:
#> Groups Name Variance Std.Dev.
#> species (Intercept) 4.657 2.158
#> Residual 12.554 3.543
#> Number of obs: 260, groups: species, 2
#>
#> Fixed effects:
#> Estimate Std. Error t value
#> (Intercept) 22.714 4.139 5.487
#> log(Distance) 11.460 2.393 4.789
#> log(canopy_openness) -1.392 1.713 -0.812
#> log(Distance):log(canopy_openness) 2.836 1.039 2.731
#>
#> Correlation of Fixed Effects:
#> (Intr) lg(Ds) lg(c_)
#> log(Distnc) -0.869
#> lg(cnpy_pn) 0.916 -0.924
#> lg(Dst):(_) -0.870 0.987 -0.9504 stan
4.1 example
library(rstan)
#> Warning: 程辑包'rstan'是用R版本4.1.3 来建造的
library(bayesplot)
#> Warning: 程辑包'bayesplot'是用R版本4.1.3 来建造的
rstan::rstan_options(auto_write = TRUE)
options(mc.cores = parallel::detectCores()) # Run on multiple coresData for Melastoma_candidum
sp1 <- llp1 |>
filter(species == "Melastoma_candidum")
x <- cbind(1,
log(1/(sp1$Distance)^2) |> scale(),
scale(sp1$canopy_openness))
x <- cbind(x, x[,2] * x[,3])
list_d <- list(
N = nrow(sp1),
J = sp1$individual |> unique() |> length(),
K = 4,
ind = sp1$individual,
x = x,
y = log(sp1$LMA))Mathematical model
Main likelihood functions: \[ y_{i,j} \sim \mathcal{N}(\mu_{i,j}, \sigma) \\ \mu_{i,j} = \boldsymbol{X} \cdot \boldsymbol{\beta} + \phi_j\\ \phi_j \sim \mathcal{N}(0, \tau) \]
where,
\(y_{i,j}\) is log(LMA) of leaf disc i of individual j,
\(\sigma\) is the standard deviation of the model,
\(\boldsymbol{X}\) is an \(n \times 4\) matrix with intercepts, distance, canopy_openness and the interaction between distance and canopy_openness,
\(\boldsymbol{\beta}\) is a coefficient vector of size 4 (intercepts, distance, canopy_openness and the interaction between distance and canopy_openness),
\(\phi_j\) is the vayring intercept for individuals,
\(\tau\) is the scaling parameter for individual effects
Prior:
- we usually use weakly informative priors and we don’t use non-informative prirors such as unif(0, 1000).
\[ \boldsymbol{\beta} \sim \mathcal{N}(0, 5) \\ \]
Hyperprior:
- Half-cauchy works best for the scaling parameters for varying intercepts
\[ \boldsymbol{\tau} \sim \text{Half-Caucy}(0, 2.5) \\ \]
In reality, we use a lot of tricks to make the above model works better. For example, we do not try to fit the individual effects directly, but instead, we fit a latent Gaussian variable from which we can recover the individual effects.
\[ \phi_j \sim \mathcal{N}(0, \tau) \]
cab be rewritten as:
\[ \phi_j = \tau \cdot \tilde{\phi_j} \\ \tilde{\phi_j} \sim \mathcal{N}(0, 1) \\ \tau \sim \text{Half-cauchy}(0, 2.5)\\ \]
A Half-cauchy distribution can be also represented using the tangent function and an uniform distribution:
\[ \boldsymbol{\tau} = 2.5 \times tan(\boldsymbol{\tilde{\tau}}) \\ \boldsymbol{\tilde{\tau}} \sim \mathcal{U}(0, \pi / 2) \]
model <- rstan::stan_model("../stan/model.stan")writeLines(readLines("../stan/model.stan"))data{
int<lower=0> N; // number of sample
int<lower=1> J; // number of individual
int<lower=1> K; // number of parameters
matrix[N, K] x; // tree-level predictor
vector[N] y; //log(LMA)
int<lower=1,upper=J> ind[N]; // integer
}
parameters{
matrix[K,1] beta;
vector[J] phi_raw;
real<lower=0,upper=pi()/2> tau_unif;
real<lower=0> sigma;
}
transformed parameters{
real<lower=0> tau;
vector[J] phi;
tau = 2.5 * tan(tau_unif); // implies tau ~ cauchy(0, 2.5)
phi = phi_raw * tau;
}
model {
//vector[N] mu;
//for (n in 1:N) mu[n] = x[n, ] * beta + phi[ind[n]];
phi_raw ~ std_normal();
to_vector(beta) ~ normal(0, 5);
y ~ normal(to_vector(x * beta) + phi[ind], sigma);
}fit <- rstan::sampling(model,
data = list_d,
verbose = TRUE,
iter = 2000,
warmup = 1000,
thin = 1,
chains = 4,
refresh = 200,
seed = 123)
#>
#> CHECKING DATA AND PREPROCESSING FOR MODEL 'model' NOW.
#>
#> COMPILING MODEL 'model' NOW.
#>
#> STARTING SAMPLER FOR MODEL 'model' NOW.summary(fit)$summary
#> mean se_mean sd 2.5% 25%
#> beta[1,1] 3.459415e+00 7.853398e-04 0.030530273 3.400709374 3.439755005
#> beta[2,1] -4.217701e-02 8.895009e-04 0.035601825 -0.112851838 -0.064869256
#> beta[3,1] -6.066213e-04 9.227563e-04 0.037315900 -0.076133762 -0.024549484
#> beta[4,1] -3.083868e-02 6.313788e-04 0.026634990 -0.083572593 -0.048281005
#> phi_raw[1] 6.684914e-01 1.664479e-02 0.713349518 -0.756827727 0.191520685
#> phi_raw[2] 9.094645e-01 9.926824e-03 0.408960234 0.139765019 0.631546170
#> phi_raw[3] 4.588917e-01 1.601212e-02 0.632781780 -0.804461566 0.036797751
#> phi_raw[4] -4.399054e-02 7.877831e-03 0.374580264 -0.780476272 -0.302218183
#> phi_raw[5] 1.169361e-01 8.087798e-03 0.383490651 -0.635332749 -0.131444116
#> phi_raw[6] -1.649391e+00 1.338614e-02 0.569026117 -2.807049285 -2.017514902
#> phi_raw[7] 1.585166e+00 1.751336e-02 0.807104881 0.019132666 1.031307790
#> phi_raw[8] -6.090502e-01 1.182087e-02 0.535483923 -1.642468384 -0.978791784
#> phi_raw[9] 2.194273e-01 1.266569e-02 0.522747700 -0.832486846 -0.128603272
#> phi_raw[10] -4.720144e-01 1.015264e-02 0.447495288 -1.334117775 -0.779435176
#> phi_raw[11] -3.662253e-01 8.371914e-03 0.371679664 -1.097309931 -0.611605487
#> phi_raw[12] 3.018512e-01 8.517681e-03 0.373659135 -0.411958781 0.044866642
#> phi_raw[13] -8.965657e-01 1.173896e-02 0.521534788 -1.920424495 -1.250224968
#> phi_raw[14] 7.402119e-01 9.727350e-03 0.434684793 -0.063503648 0.444242291
#> phi_raw[15] -5.413399e-01 9.301956e-03 0.426498219 -1.398656395 -0.832494995
#> phi_raw[16] -1.083221e+00 1.032768e-02 0.457129601 -1.997108614 -1.394973818
#> phi_raw[17] 1.160439e+00 1.391346e-02 0.625891867 -0.058789727 0.739203055
#> phi_raw[18] 3.529175e-01 9.923761e-03 0.469646899 -0.565044761 0.027482412
#> phi_raw[19] -8.918375e-01 1.301269e-02 0.581157935 -2.005837678 -1.294028332
#> tau_unif 3.937281e-02 2.605414e-04 0.008486024 0.026647742 0.033278082
#> sigma 5.429960e-02 9.485467e-05 0.004509095 0.046222650 0.051225495
#> tau 9.849056e-02 6.526393e-04 0.021258000 0.066635129 0.083225930
#> phi[1] 6.390834e-02 1.647767e-03 0.070519058 -0.077111914 0.018610719
#> phi[2] 8.667453e-02 8.652838e-04 0.037621220 0.014971126 0.061600457
#> phi[3] 4.380325e-02 1.603377e-03 0.062738376 -0.080983231 0.003154367
#> phi[4] -3.961511e-03 7.816415e-04 0.036745247 -0.076656433 -0.028568320
#> phi[5] 1.117928e-02 8.082640e-04 0.037745253 -0.064328086 -0.012582282
#> phi[6] -1.564174e-01 9.781927e-04 0.048742891 -0.254440532 -0.187173361
#> phi[7] 1.504259e-01 1.637569e-03 0.076152419 0.001611483 0.101117362
#> phi[8] -5.776885e-02 1.121579e-03 0.052518027 -0.163906988 -0.091411678
#> phi[9] 2.090914e-02 1.293484e-03 0.052266795 -0.083749701 -0.012662683
#> phi[10] -4.443222e-02 9.716910e-04 0.043447038 -0.128651018 -0.073126835
#> phi[11] -3.442275e-02 7.994778e-04 0.035715209 -0.103112730 -0.057971242
#> phi[12] 2.884252e-02 8.368405e-04 0.036215285 -0.039175742 0.004344796
#> phi[13] -8.478522e-02 1.074608e-03 0.048491380 -0.182592574 -0.115599688
#> phi[14] 7.045599e-02 9.017627e-04 0.040977679 -0.007031062 0.043150119
#> phi[15] -5.125951e-02 8.464533e-04 0.040289229 -0.131300068 -0.077986656
#> phi[16] -1.025267e-01 8.231940e-04 0.040209865 -0.182435842 -0.129081090
#> phi[17] 1.100477e-01 1.262728e-03 0.058846223 -0.005532723 0.071863670
#> phi[18] 3.353886e-02 9.727631e-04 0.045858556 -0.056784222 0.002611720
#> phi[19] -8.486760e-02 1.217299e-03 0.055892865 -0.198489046 -0.121157580
#> lp__ 2.146476e+02 1.592966e-01 4.755898672 204.288106361 211.603486874
#> 50% 75% 97.5% n_eff Rhat
#> beta[1,1] 3.459649e+00 3.47952132 3.518213629 1511.2843 1.0026155
#> beta[2,1] -4.181159e-02 -0.01945860 0.027638929 1601.9602 1.0011173
#> beta[3,1] -9.629045e-04 0.02347595 0.074350187 1635.3615 1.0009074
#> beta[4,1] -3.061634e-02 -0.01365202 0.021578246 1779.6109 1.0019361
#> phi_raw[1] 6.624724e-01 1.13991589 2.070403266 1836.7420 1.0013119
#> phi_raw[2] 9.064038e-01 1.17708614 1.710161574 1697.2332 1.0045413
#> phi_raw[3] 4.635980e-01 0.89105810 1.693875251 1561.7455 1.0026672
#> phi_raw[4] -4.438511e-02 0.21006333 0.673092861 2260.8747 1.0001659
#> phi_raw[5] 1.107323e-01 0.37490918 0.878915948 2248.2724 1.0000986
#> phi_raw[6] -1.631799e+00 -1.26861729 -0.567808107 1806.9813 1.0012613
#> phi_raw[7] 1.576065e+00 2.13892185 3.160146417 2123.8361 1.0002110
#> phi_raw[8] -6.066202e-01 -0.24705222 0.421002589 2052.0780 1.0008602
#> phi_raw[9] 2.175190e-01 0.56672041 1.244796906 1703.4381 1.0017344
#> phi_raw[10] -4.710468e-01 -0.16503121 0.414011422 1942.7596 1.0001207
#> phi_raw[11] -3.633776e-01 -0.11426987 0.334293415 1971.0065 1.0023940
#> phi_raw[12] 3.022662e-01 0.54944489 1.044635670 1924.4580 1.0015757
#> phi_raw[13] -8.859444e-01 -0.54821886 0.097550484 1973.8173 1.0003018
#> phi_raw[14] 7.237264e-01 1.03305239 1.632751505 1996.9160 1.0015596
#> phi_raw[15] -5.215882e-01 -0.25214204 0.246147141 2102.2572 1.0022819
#> phi_raw[16] -1.072930e+00 -0.77015553 -0.232388458 1959.1744 1.0018845
#> phi_raw[17] 1.154933e+00 1.57776754 2.391571348 2023.6173 0.9998111
#> phi_raw[18] 3.409689e-01 0.67028171 1.293775726 2239.7024 1.0001395
#> phi_raw[19] -8.948750e-01 -0.47590199 0.205927140 1994.5937 1.0011467
#> tau_unif 3.805605e-02 0.04393989 0.059602332 1060.8531 1.0017791
#> sigma 5.396330e-02 0.05702135 0.063934316 2259.7551 1.0010920
#> tau 9.518607e-02 0.10992048 0.149182525 1060.9584 1.0017775
#> phi[1] 6.302077e-02 0.10911629 0.204227579 1831.5620 1.0007852
#> phi[2] 8.623714e-02 0.11163314 0.161573105 1890.3778 1.0023479
#> phi[3] 4.379105e-02 0.08493576 0.167979570 1531.0706 1.0020598
#> phi[4] -3.910235e-03 0.02061067 0.068335433 2209.9739 0.9999519
#> phi[5] 1.042480e-02 0.03597433 0.084797721 2180.8118 1.0000415
#> phi[6] -1.546797e-01 -0.12476679 -0.061801998 2482.9831 1.0005970
#> phi[7] 1.500223e-01 0.19858448 0.303725474 2162.5590 1.0010141
#> phi[8] -5.687883e-02 -0.02408947 0.045831163 2192.5898 1.0010408
#> phi[9] 2.099505e-02 0.05464485 0.126876129 1632.7882 1.0017405
#> phi[10] -4.487422e-02 -0.01629578 0.042520795 1999.2358 1.0004984
#> phi[11] -3.444885e-02 -0.01140790 0.034733153 1995.6921 1.0019295
#> phi[12] 2.942737e-02 0.05225277 0.099893093 1872.8302 1.0007509
#> phi[13] -8.452041e-02 -0.05301994 0.009719547 2036.2404 1.0004532
#> phi[14] 6.930699e-02 0.09853478 0.150203556 2064.9530 1.0007749
#> phi[15] -5.006007e-02 -0.02492949 0.026815864 2265.5410 1.0019455
#> phi[16] -1.030092e-01 -0.07524773 -0.023696920 2385.9470 1.0012877
#> phi[17] 1.086331e-01 0.14897601 0.227382207 2171.7872 1.0000436
#> phi[18] 3.309196e-02 0.06381402 0.125281057 2222.4221 1.0001972
#> phi[19] -8.503282e-02 -0.04675622 0.020114280 2108.2302 1.0002783
#> lp__ 2.150419e+02 217.99342919 222.873066075 891.3578 1.004883695% CI
- beta[1,1] is the intercept which is not showing the figure.
beta_name <- paste0("beta[", 2:4, ",1]")
mcmc_areas(fit,
pars = beta_name,
prob = 0.95)
NO EFECT!
Data for Colocasia_gigantea
sp2 <- llp1 |>
filter(species == "Colocasia_gigantea")
x1 <- cbind(1,
log(1/(sp2$Distance) ^2)|> scale(),
scale(sp2$canopy_openness))
x1 <- cbind(x1, x1[,2] * x1[,3])
list_d <- list(
N = nrow(sp2),
J = sp2$individual |> unique() |> length(),
K = 4,
ind = sp2$individual,
x = x1,
y = log(sp2$LMA))model1 <- rstan::stan_model("../stan/model.stan")writeLines(readLines("../stan/model.stan"))data{
int<lower=0> N; // number of sample
int<lower=1> J; // number of individual
int<lower=1> K; // number of parameters
matrix[N, K] x; // tree-level predictor
vector[N] y; //log(LMA)
int<lower=1,upper=J> ind[N]; // integer
}
parameters{
matrix[K,1] beta;
vector[J] phi_raw;
real<lower=0,upper=pi()/2> tau_unif;
real<lower=0> sigma;
}
transformed parameters{
real<lower=0> tau;
vector[J] phi;
tau = 2.5 * tan(tau_unif); // implies tau ~ cauchy(0, 2.5)
phi = phi_raw * tau;
}
model {
//vector[N] mu;
//for (n in 1:N) mu[n] = x[n, ] * beta + phi[ind[n]];
phi_raw ~ std_normal();
to_vector(beta) ~ normal(0, 5);
y ~ normal(to_vector(x * beta) + phi[ind], sigma);
}fit1 <- rstan::sampling(model1,
data = list_d,
verbose = TRUE,
iter = 2000,
warmup = 1000,
thin = 1,
chains = 4,
refresh = 200,
seed = 123)
#>
#> CHECKING DATA AND PREPROCESSING FOR MODEL 'model' NOW.
#>
#> COMPILING MODEL 'model' NOW.
#>
#> STARTING SAMPLER FOR MODEL 'model' NOW.summary(fit1)$summary
#> mean se_mean sd 2.5% 25%
#> beta[1,1] 3.551391519 5.376012e-04 0.017458616 3.515889044 3.540520e+00
#> beta[2,1] -0.104344079 6.332197e-04 0.021320624 -0.145763798 -1.189100e-01
#> beta[3,1] 0.049533548 6.897554e-04 0.022518089 0.005063399 3.432049e-02
#> beta[4,1] -0.011957716 4.417596e-04 0.015659305 -0.042827858 -2.176306e-02
#> phi_raw[1] 0.699591918 1.134201e-02 0.554506126 -0.344208048 3.228900e-01
#> phi_raw[2] 0.324973707 1.094525e-02 0.496455291 -0.669034824 -7.404382e-03
#> phi_raw[3] -0.276551415 1.099761e-02 0.529131297 -1.311322946 -6.275432e-01
#> phi_raw[4] -0.031491326 1.639461e-02 0.814279468 -1.627836474 -5.838141e-01
#> phi_raw[5] -1.260930583 1.169365e-02 0.454407390 -2.177003906 -1.550213e+00
#> phi_raw[6] -0.842655073 1.050027e-02 0.446960304 -1.719985237 -1.144829e+00
#> phi_raw[7] -1.401290254 1.368088e-02 0.549536548 -2.471333746 -1.769725e+00
#> phi_raw[8] -0.587762952 9.320389e-03 0.409373244 -1.399255006 -8.674027e-01
#> phi_raw[9] -0.987648322 1.510734e-02 0.553423986 -2.071983260 -1.364338e+00
#> phi_raw[10] -0.720335117 8.364697e-03 0.400973259 -1.507262293 -9.897081e-01
#> phi_raw[11] 1.423210652 8.321207e-03 0.386608026 0.694826946 1.151029e+00
#> phi_raw[12] -0.871170933 1.268835e-02 0.504646618 -1.870667391 -1.205162e+00
#> phi_raw[13] -0.574040660 1.457756e-02 0.532867874 -1.613431463 -9.394422e-01
#> phi_raw[14] 1.100276083 1.163716e-02 0.492474543 0.160823623 7.684129e-01
#> phi_raw[15] 0.789587370 1.039887e-02 0.455030310 -0.098412285 4.814152e-01
#> phi_raw[16] 0.701940151 7.143924e-03 0.365751211 0.011337286 4.582888e-01
#> phi_raw[17] 0.463558298 7.097726e-03 0.372788861 -0.247654318 2.117034e-01
#> phi_raw[18] -0.202381545 6.966059e-03 0.392731861 -1.002077345 -4.572065e-01
#> phi_raw[19] 0.800195018 7.306029e-03 0.374817060 0.111596427 5.453684e-01
#> phi_raw[20] 0.425647139 7.304931e-03 0.371343955 -0.266293696 1.647563e-01
#> phi_raw[21] -0.376053482 8.013846e-03 0.372671634 -1.116453903 -6.226209e-01
#> phi_raw[22] 2.107829381 1.142668e-02 0.463517075 1.260313296 1.780679e+00
#> phi_raw[23] -0.167484302 8.121748e-03 0.395946777 -0.969485210 -4.294159e-01
#> phi_raw[24] -1.451797879 9.689083e-03 0.467155814 -2.392664165 -1.755272e+00
#> phi_raw[25] 0.844564444 1.037982e-02 0.440084620 -0.004448025 5.434343e-01
#> phi_raw[26] -1.142078744 1.073524e-02 0.465069776 -2.081559034 -1.449243e+00
#> phi_raw[27] -0.747486599 9.226300e-03 0.424151937 -1.583113826 -1.030400e+00
#> phi_raw[28] -0.488616686 9.495459e-03 0.440745336 -1.349014948 -7.839176e-01
#> phi_raw[29] -0.446917001 1.108846e-02 0.476830320 -1.386614536 -7.580102e-01
#> phi_raw[30] -0.035987135 9.283643e-03 0.404899426 -0.848720767 -3.030314e-01
#> phi_raw[31] 0.937098106 7.674587e-03 0.375322700 0.218462458 6.936933e-01
#> phi_raw[32] 0.753998850 9.175108e-03 0.401571505 -0.020811736 4.879268e-01
#> phi_raw[33] 0.104764656 1.021159e-02 0.416396834 -0.724245299 -1.751225e-01
#> phi_raw[34] 1.312013965 1.091468e-02 0.436670304 0.486846505 1.016193e+00
#> phi_raw[35] -0.071820255 1.183941e-02 0.492917271 -1.027714429 -3.991602e-01
#> tau_unif 0.035865228 1.749985e-04 0.005442722 0.026857173 3.196186e-02
#> sigma 0.065802341 7.607081e-05 0.004034621 0.058422581 6.296364e-02
#> tau 0.089704280 4.381377e-04 0.013626510 0.067159082 7.993187e-02
#> phi[1] 0.061552218 1.011627e-03 0.049108081 -0.031837298 2.873364e-02
#> phi[2] 0.028665292 9.893500e-04 0.043873857 -0.058817353 -6.592868e-04
#> phi[3] -0.024344000 1.000612e-03 0.047027668 -0.120054947 -5.530033e-02
#> phi[4] -0.002910694 1.508953e-03 0.073445013 -0.147367923 -5.123449e-02
#> phi[5] -0.111170023 9.337915e-04 0.038526385 -0.188828294 -1.361169e-01
#> phi[6] -0.074240357 9.191357e-04 0.038965652 -0.150572184 -1.003092e-01
#> phi[7] -0.123578764 1.219170e-03 0.047566629 -0.220606181 -1.541196e-01
#> phi[8] -0.051755348 8.100312e-04 0.036080936 -0.124326755 -7.625771e-02
#> phi[9] -0.086989103 1.280728e-03 0.048444826 -0.181720182 -1.197135e-01
#> phi[10] -0.063448750 6.883092e-04 0.034770411 -0.131325887 -8.653713e-02
#> phi[11] 0.125483589 5.803671e-04 0.031119527 0.063153599 1.048662e-01
#> phi[12] -0.076731071 1.077715e-03 0.044231162 -0.162946927 -1.065451e-01
#> phi[13] -0.050521048 1.283719e-03 0.047267252 -0.141126407 -8.298963e-02
#> phi[14] 0.097214427 1.041188e-03 0.042970052 0.014464036 6.817264e-02
#> phi[15] 0.069713155 9.311865e-04 0.040038990 -0.009170628 4.277125e-02
#> phi[16] 0.061842649 6.017047e-04 0.031375940 0.001008979 4.145421e-02
#> phi[17] 0.040949209 6.276722e-04 0.032662980 -0.022447435 1.872365e-02
#> phi[18] -0.017893271 6.228139e-04 0.034578471 -0.087360093 -4.055644e-02
#> phi[19] 0.070695505 6.033602e-04 0.032297511 0.009103373 4.887955e-02
#> phi[20] 0.037632516 6.321466e-04 0.032463594 -0.024207936 1.475622e-02
#> phi[21] -0.033169926 7.021059e-04 0.032765218 -0.095389574 -5.564626e-02
#> phi[22] 0.185848026 7.344018e-04 0.035332189 0.118240693 1.621001e-01
#> phi[23] -0.014709036 7.250784e-04 0.034907468 -0.081832127 -3.807411e-02
#> phi[24] -0.128015610 7.877454e-04 0.039069762 -0.202763650 -1.543972e-01
#> phi[25] 0.074420141 8.678444e-04 0.038233493 -0.000467207 4.897980e-02
#> phi[26] -0.100631753 9.063127e-04 0.039511143 -0.179724619 -1.276242e-01
#> phi[27] -0.065809688 8.143920e-04 0.036827690 -0.137879899 -9.080363e-02
#> phi[28] -0.042916399 8.497280e-04 0.038708566 -0.115735128 -6.863808e-02
#> phi[29] -0.039341766 1.009394e-03 0.042301199 -0.123201547 -6.735023e-02
#> phi[30] -0.003068622 8.342816e-04 0.035851598 -0.074894255 -2.660556e-02
#> phi[31] 0.082681179 6.247334e-04 0.031880270 0.019928568 6.240795e-02
#> phi[32] 0.066465465 7.737133e-04 0.034688259 -0.001890577 4.363748e-02
#> phi[33] 0.009391427 9.196422e-04 0.037102860 -0.064644177 -1.539377e-02
#> phi[34] 0.115645161 8.520530e-04 0.036413590 0.043854374 9.195582e-02
#> phi[35] -0.006410288 1.054748e-03 0.043691692 -0.092460251 -3.499123e-02
#> lp__ 343.901596991 2.253899e-01 6.255869133 331.058639324 3.397765e+02
#> 50% 75% 97.5% n_eff Rhat
#> beta[1,1] 3.551545462 3.562483350 3.585804476 1054.6278 1.0078589
#> beta[2,1] -0.104395643 -0.089768192 -0.062071174 1133.6813 1.0026273
#> beta[3,1] 0.049525615 0.064747643 0.093790999 1065.7928 1.0072752
#> beta[4,1] -0.012089802 -0.001825354 0.019510556 1256.5304 1.0042267
#> phi_raw[1] 0.684743722 1.082478246 1.806472417 2390.1900 1.0014333
#> phi_raw[2] 0.323226257 0.650949892 1.308272661 2057.3529 1.0015732
#> phi_raw[3] -0.272575385 0.079326022 0.760381238 2314.8883 1.0007752
#> phi_raw[4] -0.029697091 0.518391464 1.508359207 2466.8607 0.9998896
#> phi_raw[5] -1.245784809 -0.962668385 -0.383661755 1510.0465 1.0013994
#> phi_raw[6] -0.844685729 -0.540184736 0.021581422 1811.9132 1.0026648
#> phi_raw[7] -1.401743510 -1.015808466 -0.378670600 1613.4846 1.0029138
#> phi_raw[8] -0.587112865 -0.309532121 0.199629948 1929.1715 1.0009372
#> phi_raw[9] -0.992957607 -0.614267765 0.073474809 1341.9619 1.0031924
#> phi_raw[10] -0.724845399 -0.451141925 0.067170248 2297.8960 0.9997452
#> phi_raw[11] 1.421857210 1.663180065 2.208475500 2158.5847 1.0024199
#> phi_raw[12] -0.868457893 -0.538670703 0.111098601 1581.8480 1.0010537
#> phi_raw[13] -0.582594116 -0.207539989 0.445106426 1336.1938 1.0023518
#> phi_raw[14] 1.086393116 1.429569950 2.068511921 1790.9107 1.0016765
#> phi_raw[15] 0.798996527 1.087336408 1.689657209 1914.7328 1.0014335
#> phi_raw[16] 0.690299324 0.932893639 1.459278156 2621.1865 1.0003134
#> phi_raw[17] 0.450590034 0.709015002 1.236264538 2758.5913 1.0016859
#> phi_raw[18] -0.201646020 0.063398224 0.564653376 3178.4694 1.0014050
#> phi_raw[19] 0.786098130 1.048703381 1.580783864 2631.9398 1.0022241
#> phi_raw[20] 0.419813530 0.667653829 1.165705803 2584.1664 1.0012897
#> phi_raw[21] -0.374635436 -0.124693897 0.368604969 2162.5724 1.0034795
#> phi_raw[22] 2.079637833 2.417525004 3.053682976 1645.4743 1.0042987
#> phi_raw[23] -0.158527103 0.104935740 0.604269713 2376.7011 1.0005125
#> phi_raw[24] -1.454866821 -1.134621013 -0.512741763 2324.6534 1.0010043
#> phi_raw[25] 0.840303327 1.141872327 1.737889989 1797.5971 1.0024357
#> phi_raw[26] -1.116071296 -0.822599315 -0.272177201 1876.7777 1.0007335
#> phi_raw[27] -0.743177616 -0.454419435 0.059316672 2113.4295 1.0021117
#> phi_raw[28] -0.484550675 -0.192561562 0.348929809 2154.4851 1.0027136
#> phi_raw[29] -0.438925844 -0.136918373 0.492191011 1849.2056 1.0034898
#> phi_raw[30] -0.028808816 0.224304125 0.750907752 1902.2058 1.0019136
#> phi_raw[31] 0.919116696 1.175754646 1.714965888 2391.6612 1.0015739
#> phi_raw[32] 0.751770623 1.017446621 1.542726559 1915.5935 1.0041195
#> phi_raw[33] 0.114181511 0.380665171 0.926508236 1662.7535 1.0018845
#> phi_raw[34] 1.304575658 1.599714090 2.178363483 1600.6083 1.0065140
#> phi_raw[35] -0.070665396 0.253463753 0.908981748 1733.3555 1.0012128
#> tau_unif 0.035252324 0.039141107 0.048233650 967.3051 1.0040803
#> sigma 0.065733866 0.068497441 0.073908730 2812.9979 1.0007337
#> tau 0.088167335 0.097902768 0.120677723 967.2709 1.0040818
#> phi[1] 0.060244038 0.094677734 0.159414027 2356.4859 1.0006652
#> phi[2] 0.028696827 0.057398187 0.115010678 1966.5805 1.0013949
#> phi[3] -0.023486377 0.007052944 0.068332899 2208.8976 1.0009820
#> phi[4] -0.002739357 0.046576339 0.137141293 2369.0439 0.9999203
#> phi[5] -0.110278473 -0.085558629 -0.034872792 1702.2239 1.0034667
#> phi[6] -0.073731490 -0.047983394 0.002111177 1797.2340 1.0043579
#> phi[7] -0.123795476 -0.091803383 -0.035543238 1522.2164 1.0046599
#> phi[8] -0.051704096 -0.027595019 0.017401900 1984.0475 1.0010526
#> phi[9] -0.087063140 -0.054805179 0.006824878 1430.8062 1.0030148
#> phi[10] -0.063954103 -0.040518690 0.006165732 2551.8346 0.9997969
#> phi[11] 0.125728806 0.146539483 0.186679175 2875.1489 1.0009080
#> phi[12] -0.077056643 -0.047723681 0.009646001 1684.4132 1.0011615
#> phi[13] -0.051272244 -0.018573033 0.040848238 1355.7541 1.0027629
#> phi[14] 0.095688985 0.126358997 0.183060628 1703.2308 1.0010971
#> phi[15] 0.069841883 0.095863684 0.148208824 1848.8125 1.0012016
#> phi[16] 0.061239591 0.082613245 0.124070971 2719.1091 0.9999606
#> phi[17] 0.039990740 0.063104776 0.105030641 2707.9823 1.0013847
#> phi[18] -0.017985947 0.005781485 0.049669546 3082.4429 1.0016751
#> phi[19] 0.070233159 0.091728942 0.137082473 2865.3971 1.0012106
#> phi[20] 0.037552467 0.059206843 0.102915411 2637.2880 1.0010851
#> phi[21] -0.033456801 -0.011141177 0.031712282 2177.8143 1.0039086
#> phi[22] 0.185867245 0.209800766 0.254462958 2314.5875 1.0023651
#> phi[23] -0.014184347 0.009026518 0.053100806 2317.7511 1.0005492
#> phi[24] -0.128143370 -0.102178885 -0.051025492 2459.8564 1.0003827
#> phi[25] 0.074024515 0.099213663 0.151458572 1940.9047 1.0023656
#> phi[26] -0.099654583 -0.073738215 -0.024611373 1900.5666 1.0004700
#> phi[27] -0.065556165 -0.041110320 0.005725060 2044.9465 1.0020240
#> phi[28] -0.042541503 -0.017499160 0.032945274 2075.1731 1.0030915
#> phi[29] -0.039117325 -0.012095313 0.044393338 1756.2414 1.0039358
#> phi[30] -0.002559186 0.020382431 0.068860357 1846.6802 1.0020050
#> phi[31] 0.081693565 0.104024215 0.146253575 2604.0815 1.0007208
#> phi[32] 0.066197558 0.089348542 0.135034991 2010.0408 1.0030812
#> phi[33] 0.010007552 0.034043178 0.080988712 1627.7100 1.0018832
#> phi[34] 0.115541826 0.139269577 0.189050774 1826.3911 1.0061915
#> phi[35] -0.006193792 0.022690490 0.079580074 1715.9313 1.0009852
#> lp__ 344.087949600 348.326915839 355.203139067 770.3826 1.0042396beta_name <- paste0("beta[", 2:4, ",1]")
mcmc_areas(fit1,
pars = beta_name,
prob = 0.95)
So we can see for species Colocasia_gigantea the regression coefficients of distance and canopy openness are significant.
5 Table the results
For species one “Melastoma_candidum”, coefficients table.
test <- summary(fit)$summary[2:4,] |> as_tibble()
quantile_interval <- paste0("[",round(test$`2.5%`,4),", ", round(test$`97.5%`,4),"]")
table_sp1 <- data.frame(
"Parameters" = c(
"ALAN's effect",
"Daylight's effect",
"interaction"),
"mean_value" = round(test$mean,4),
quantile_interval
)
table_sp1 %>%
kbl(caption = "Coefficients table of species Melastoma_candidum") %>%column_spec(3,bold = ifelse(test$`2.5%`*test$`97.5%`>0, "T","F"))%>%
kable_classic(full_width = F, html_font = "Cambria")| Parameters | mean_value | quantile_interval |
|---|---|---|
| ALAN’s effect | -0.0422 | [-0.1129, 0.0276] |
| Daylight’s effect | -0.0006 | [-0.0761, 0.0744] |
| interaction | -0.0308 | [-0.0836, 0.0216] |
For species “Colocasia_gigantea”, coefficients table.
test1 <- summary(fit1)$summary[2:4,] |> as_tibble()
quantile_interval <- paste0("[",round(test1$`2.5%`,4),", ", round(test1$`97.5%`,4),"]")
table_sp2 <- data.frame(
"Parameters" = c(
"ALAN's effect",
"Daylight's effect",
"interaction"),
"mean_value" = round(test1$mean,4),
quantile_interval
)
table_sp2 %>%
kbl(caption = "Coefficients table of species Colocasia_gigantea") %>%column_spec(3,bold = ifelse(test1$`2.5%`*test1$`97.5%`>0, "T","F"))%>%
kable_classic(full_width = F, html_font = "Cambria")| Parameters | mean_value | quantile_interval |
|---|---|---|
| ALAN’s effect | -0.1043 | [-0.1458, -0.0621] |
| Daylight’s effect | 0.0495 | [0.0051, 0.0938] |
| interaction | -0.0120 | [-0.0428, 0.0195] |
#Put together
rbind(table_sp1,table_sp2)|>
kbl( caption = "Coefficients table") %>%
kable_paper("striped", full_width = F) %>%
column_spec(3,bold =c(ifelse(test$`2.5%`*test$`97.5%`>0, "T","F"), ifelse(test1$`2.5%`*test1$`97.5%`>0, "T","F"))) %>%
pack_rows("Melastoma_candidum", 1, 3) %>%
pack_rows("Colocasia_gigantea", 4, 6)| Parameters | mean_value | quantile_interval |
|---|---|---|
| Melastoma_candidum | ||
| ALAN’s effect | -0.0422 | [-0.1129, 0.0276] |
| Daylight’s effect | -0.0006 | [-0.0761, 0.0744] |
| interaction | -0.0308 | [-0.0836, 0.0216] |
| Colocasia_gigantea | ||
| ALAN’s effect | -0.1043 | [-0.1458, -0.0621] |
| Daylight’s effect | 0.0495 | [0.0051, 0.0938] |
| interaction | -0.0120 | [-0.0428, 0.0195] |