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Calcular la Disparidad y Variabilidad proporcional.

Vamos a utilizar unos índices que nos permiten estimar la variabilidad temporal de las series temporales. En concreto:

  • D = disparity index, que habla de las diferencias entre pares consecutivos (en nuestro caso años)
  • PV = proportional variability, informa acerca de la diferencia proporcional entre todos los años en una misma serie temporal.

Mas información sobre estos índices: (Fernández‐Martínez et al. 2018; Fernández‐Martínez and Peñuelas 2021; Heath and Borowski 2013)

  • A partir de estos índices, la idea es identificar el comportamiento de la serie temporal y ver donde están ocurriendo mas cambios en el nivel de infestación
coplas2019 <- read_csv(here::here("data/coplas2019sn.csv")) %>% 
    filter(sp_abrev != "ppinea") 

df <- coplas2019 %>% 
  filter(! %>% 
  dplyr::select(code, especie, `1993`:`2019`) %>% 
  pivot_longer(names_to = "year", values_to = "infestacion", `1993`:`2019`) 

# disparity index 
disparity <- function(x, k) { 
  # x es el vector con la serie temporal 
  # k es una cte que se añade para evitar problemas de 
  # indeterminación
  x <- x[!] # remove NA 
  n <- length(x) # length time series 
  f <- NA
  for (i in (1:(n-1))){ 
    f[i] = abs(log((x[i+1] + k) / (x[i] + k)))} 
  D <- sum(f) / (n-1) 

# Proportional Variability See 
pvIndex <- function (x){
  x <- x[!] # remove NA 
  n <- length(x) # length time series 
  pairs <- combn(x,2)
  min.z <- apply(pairs, MARGIN = 2, min)
  max.z <- apply(pairs, MARGIN = 2, max)
  z <- 1-(min.z/max.z)
  z[is.nan(z)] <- 1 # this solve problems of NaN
  PV <- 2*sum(z) / (n*(n-1))
parcelas <- unique(df$code)

df.disparity <- c() 

for (i in 1:length(parcelas)) { 
  aux <- df %>% filter(code == parcelas[i])
  D_parcela <- disparity(aux$infestacion, k=.1)
  PV_parcela <- pvIndex(aux$infestacion)
  out <- data.frame(code = parcelas[i], 
                    D = D_parcela,
                    PV = PV_parcela)
  df.disparity <- rbind(df.disparity, out)

dispar <- coplas2019 %>% 
    code, elev_mean, especie, sp_abrev) %>% 

dispar$especie <- fct_relevel(dispar$especie,  
         "P. halepensis", "P. pinaster",
         "P. nigra", "P. sylvestris")


plot_comparaD <- ggstatsplot::ggbetweenstats(
  data = dispar,
  x = especie,
  y = D,
  ylab = "Disparity") +
  ggplot2::scale_color_manual(values = colores_pinos)

Version Author Date
53bcfcc Antonio J Perez-Luque 2021-05-19
b9f3a00 Antonio J Perez-Luque 2021-05-18
null device 

Tal como observamos en el gráfico anterior, vemos que existe una mayor disparidad en las parcelas de P. sylvestris que en el resto. Esto, parece indicar, que en esta parcelas es donde estamos observando mayores diferencias entre años (“dientes de sierra más grandes”). Las parcelas de P. halepensis son las que menos disparidad presentan. En las parcelas de

Proportional Varibility

plot_comparaPV <- ggstatsplot::ggbetweenstats(
  data = dispar,
  x = especie,
  y = PV,
  ylab = "Proportional Variability") +
  ggplot2::scale_color_manual(values = colores_pinos)

Version Author Date
53bcfcc Antonio J Perez-Luque 2021-05-19
b9f3a00 Antonio J Perez-Luque 2021-05-18
null device 

No observamos diferencias entre las especies para el indice PV, esto es, a lo largo de la serie temporal la variabilidad no es diferente entre especies.


  • Realizamos un modelo de la PV y la elevación.
  • Utilizamos la regresion beta
# Corrección para que no llegue al 1 ni al 0. See 
n.obs <- sum(!$PV))
dispar$PVm <- ((dispar$PV * (n.obs -1)) + 0.5)/n.obs

model.pv <- betareg(PVm ~ elev_mean, data=dispar)

betareg(formula = PVm ~ elev_mean, data = dispar)

Standardized weighted residuals 2:
    Min      1Q  Median      3Q     Max 
-2.7974 -0.6566 -0.1471  0.4957  4.8832 

Coefficients (mean model with logit link):
              Estimate Std. Error z value Pr(>|z|)    
(Intercept)  1.825e+00  9.862e-02  18.501  < 2e-16 ***
elev_mean   -3.449e-04  6.527e-05  -5.285 1.26e-07 ***

Phi coefficients (precision model with identity link):
      Estimate Std. Error z value Pr(>|z|)    
(phi)   5.7438     0.2524   22.76   <2e-16 ***
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Type of estimator: ML (maximum likelihood)
Log-likelihood: 623.4 on 3 Df
Pseudo R-squared: 0.02583
Number of iterations: 13 (BFGS) + 2 (Fisher scoring) 
  • Aunque parece haber una relación, el modelo es muy poco explicativo (insginifcante, diría)
ggplot(dispar, aes(x=elev_mean, y=PVm)) +
  geom_point(size=1, color="gray") +
  geom_line(aes(y = predict(model.pv, dispar)), color = "blue") +
  theme_bw() +
  theme(panel.grid = element_blank()) +
  xlab("Elevacion") + 
  ylab("Proportional Variability")

Version Author Date
b9f3a00 Antonio J Perez-Luque 2021-05-18
Fernández‐Martínez, Marcos, and Josep Peñuelas. 2021. “Measuring Temporal Patterns in Ecology: The Case of Mast Seeding.” Ecology and Evolution, March, ece3.7291.
Fernández‐Martínez, Marcos, Sara Vicca, Ivan A. Janssens, Jofre Carnicer, Javier Martín‐Vide, and Josep Peñuelas. 2018. “The Consecutive Disparity Index, D : A Measure of Temporal Variability in Ecological Studies.” Ecosphere 9 (12): e02527.
Heath, Joel P., and Peter Borowski. 2013. “Quantifying Proportional Variability.” Edited by Shu-Dong Zhang. PLoS ONE 8 (12): e84074.

R version 4.0.2 (2020-06-22)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Catalina 10.15.3

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib

[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] betareg_3.1-4     DHARMa_0.3.3.0    ggstatsplot_0.7.2 ggpubr_0.4.0     
 [5] flextable_0.6.3   here_1.0.1        forcats_0.5.1     stringr_1.4.0    
 [9] dplyr_1.0.4       purrr_0.3.4       readr_1.4.0       tidyr_1.1.2      
[13] tibble_3.0.6      ggplot2_3.3.3     tidyverse_1.3.0   workflowr_1.6.2  

loaded via a namespace (and not attached):
  [1] readxl_1.3.1              uuid_0.1-4               
  [3] pairwiseComparisons_3.1.3 backports_1.2.1          
  [5] systemfonts_1.0.0         plyr_1.8.6               
  [7] splines_4.0.2             gmp_0.6-2                
  [9] kSamples_1.2-9            ipmisc_5.0.2             
 [11] TH.data_1.0-10            rstantools_2.1.1         
 [13] digest_0.6.27             SuppDists_1.1-9.5        
 [15] foreach_1.5.1             htmltools_0.5.1.1        
 [17] magrittr_2.0.1            memoise_2.0.0            
 [19] paletteer_1.3.0           openxlsx_4.2.3           
 [21] modelr_0.1.8              officer_0.3.16           
 [23] sandwich_3.0-0            colorspace_2.0-0         
 [25] rvest_0.3.6               ggrepel_0.9.1            
 [27] haven_2.3.1               xfun_0.20                
 [29] crayon_1.4.1              jsonlite_1.7.2           
 [31] lme4_1.1-26               zeallot_0.1.0            
 [33] iterators_1.0.13          survival_3.2-7           
 [35] zoo_1.8-8                 glue_1.4.2               
 [37] gtable_0.3.0              emmeans_1.5.4            
 [39] MatrixModels_0.4-1        statsExpressions_1.0.1   
 [41] car_3.0-10                Rmpfr_0.8-2              
 [43] abind_1.4-5               scales_1.1.1             
 [45] mvtnorm_1.1-1             DBI_1.1.1                
 [47] rstatix_0.6.0             PMCMRplus_1.9.0          
 [49] Rcpp_1.0.6                xtable_1.8-4             
 [51] performance_0.7.2         foreign_0.8-81           
 [53] Formula_1.2-4             stats4_4.0.2             
 [55] httr_1.4.2                modeltools_0.2-23        
 [57] ellipsis_0.3.1            farver_2.0.3             
 [59] flexmix_2.3-17            pkgconfig_2.0.3          
 [61] reshape_0.8.8             nnet_7.3-15              
 [63] multcompView_0.1-8        sass_0.3.1               
 [65] dbplyr_2.1.0              labeling_0.4.2           
 [67] effectsize_0.4.4-1        tidyselect_1.1.0         
 [69] rlang_0.4.10              later_1.1.0.1            
 [71] ggcorrplot_0.1.3          munsell_0.5.0            
 [73] cellranger_1.1.0          tools_4.0.2              
 [75] cachem_1.0.4              cli_2.3.0                
 [77] generics_0.1.0            broom_0.7.4              
 [79] evaluate_0.14             fastmap_1.1.0            
 [81] BWStest_0.2.2             yaml_2.2.1               
 [83] rematch2_2.1.2            knitr_1.31               
 [85] fs_1.5.0                  zip_2.1.1                
 [87] nlme_3.1-152              WRS2_1.1-1               
 [89] pbapply_1.4-3             whisker_0.4              
 [91] xml2_1.3.2                correlation_0.6.1        
 [93] compiler_4.0.2            rstudioapi_0.13          
 [95] curl_4.3                  ggsignif_0.6.0           
 [97] reprex_1.0.0              statmod_1.4.35           
 [99] bslib_0.2.4               stringi_1.5.3            
[101] highr_0.8                 parameters_0.13.0        
[103] gdtools_0.2.3             lattice_0.20-41          
[105] Matrix_1.3-2              nloptr_1.2.2.2           
[107] vctrs_0.3.6               pillar_1.4.7             
[109] lifecycle_1.0.0           mc2d_0.1-18              
[111] lmtest_0.9-38             jquerylib_0.1.3          
[113] estimability_1.3          data.table_1.13.6        
[115] insight_0.14.0            httpuv_1.5.5             
[117] patchwork_1.1.1           R6_2.5.0                 
[119] promises_1.2.0.1          rio_0.5.16               
[121] BayesFactor_0.9.12-4.2    codetools_0.2-18         
[123] boot_1.3-26               MASS_7.3-53              
[125] gtools_3.8.2              assertthat_0.2.1         
[127] rprojroot_2.0.2           withr_2.4.1              
[129] multcomp_1.4-16           bayestestR_0.9.0         
[131] parallel_4.0.2            hms_1.0.0                
[133] grid_4.0.2                minqa_1.2.4              
[135] coda_0.19-4               rmarkdown_2.6.6          
[137] carData_3.0-4             git2r_0.28.0             
[139] lubridate_1.7.10          base64enc_0.1-3