Last updated: 2022-01-18

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Introdución y Objetivos

  • Analizar la evolución de los parámetros de vegetación a lo largo del tiempo, entre dos tratamientos: Herbivorísmo pírico (HP) y Quemas Prescritas (QP), considerando los diferentes rangos

  • Usamos solamente datos de la quema de Otoño

  • Diseño:

    • tratamiento: HP y QP
    • rangos
    • 6 fechas de muestreo
    • 32 plots por tratamiento
     rango
treat Matorral claro Matorral denso Matorral medio Espartal denso
   HP             48             48             48             48
   QP             48             48             48             48

Análisis estadístico

  • Se utilizaron Modelos Mixtos Aditivos Generalizados (GAMM) para evaluar los efectos del tratamiento (Quemas Prescritos vs. Herbivorismo Pírico) sobre la evolución de la cobertura vegetal, el fitovolumen y los índices de diversidad (Shannon, Riqueza).

Riqueza

Modelo

f <- as.formula(
  riq ~ 
    s(meses, by = interaction(treat, rango), k = 5, bs = "cs") +
    s(meses, by = treat, k = 5, bs = "cs") + 
    s(meses, by = rango, k = 5, bs = "cs") + 
    treat * rango
)

fi <- as.formula(
  riq ~ 
    s(meses, by = interaction(treat, rango), k = 5, bs = "cs") +
    treat * rango
)

fni <- as.formula(
  riq ~ 
    s(meses, by = treat, k = 5, bs = "cs") + 
    s(meses, by = rango, k = 5, bs = "cs") + 
    treat * rango
)


mfull <- gamm(f,
          random = list(quadrat = ~1), 
          data = veg, 
          family = poisson,
          method = "ML")

 Maximum number of PQL iterations:  20 
mi <- gamm(fi,
          random = list(quadrat = ~1), 
          data = veg, 
          family = poisson,
          method = "ML")

 Maximum number of PQL iterations:  20 
mni <- gamm(fni,
          random = list(quadrat = ~1), 
          data = veg, 
          family = poisson,
          method = "ML")

 Maximum number of PQL iterations:  20
  • Seleccionamos los suavizados, y elegimos el modelo con menor AIC
model df AIC
mni 15 319.8728
mfull 23 334.4627
mi 17 336.0228 
# Distribution of Model Family

Predicted Distribution of Residuals

 Distribution Probability
       normal         66%
      tweedie         34%

Predicted Distribution of Response

               Distribution Probability
              beta-binomial         59%
          negative binomial         12%
 neg. binomial (zero-infl.)          9%

Model validation

Version Author Date
e845f96 ajpelu 2022-01-17
A. parametric coefficients Estimate Std. Error t-value p-value
(Intercept) 2.3946 0.0854 28.0294 < 0.0001
treatQP -0.2895 0.1234 -2.3454 0.0195
rangoMatorral denso -0.0806 0.1214 -0.6637 0.5073
rangoMatorral medio -0.0714 0.1214 -0.5883 0.5567
rangoEspartal denso -0.2813 0.1236 -2.2766 0.0234
treatQP:rangoMatorral denso 0.0457 0.1752 0.2607 0.7945
treatQP:rangoMatorral medio 0.0729 0.1749 0.4169 0.6770
treatQP:rangoEspartal denso -0.0214 0.1781 -0.1201 0.9045
B. smooth terms edf Ref.df F-value p-value
s(meses):treatHP 1.6005 4.0000 4.1012 0.0001
s(meses):treatQP 3.4564 4.0000 6.4054 < 0.0001
s(meses):rangoMatorral claro 0.0000 4.0000 0.0000 0.9918
s(meses):rangoMatorral denso 0.0000 4.0000 0.0000 0.5012
s(meses):rangoMatorral medio 0.0000 4.0000 0.0000 0.7363
s(meses):rangoEspartal denso 2.7565 4.0000 7.5048 < 0.0001

Diversidad

Modelo

f <- as.formula(
  shan ~ 
    s(meses, by = interaction(treat, rango), k = 5, bs = "cs") +
    s(meses, by = treat, k = 5, bs = "cs") + 
    s(meses, by = rango, k = 5, bs = "cs") + 
    treat * rango
)

fi <- as.formula(
  shan ~ 
    s(meses, by = interaction(treat, rango), k = 5, bs = "cs") +
    treat * rango
)

fni <- as.formula(
  shan ~ 
    s(meses, by = treat, k = 5, bs = "cs") + 
    s(meses, by = rango, k = 5, bs = "cs") + 
    treat * rango
)


mfull <- gamm(f,
          random = list(quadrat = ~1), 
          data = veg, 
          family = tw,
          method = "ML")

 Maximum number of PQL iterations:  20 
mi <- gamm(fi,
          random = list(quadrat = ~1), 
          data = veg, 
          family = tw,
          method = "ML")

 Maximum number of PQL iterations:  20 
mni <- gamm(fni,
          random = list(quadrat = ~1), 
          data = veg, 
          family = tw,
          method = "ML")

 Maximum number of PQL iterations:  20
  • Seleccionamos los suavizados, y elegimos el modelo con menor AIC
model df AIC
mni 16 312.3255
mi 18 326.0420
mfull 24 329.8889 
# Distribution of Model Family

Predicted Distribution of Residuals

 Distribution Probability
       normal         62%
      tweedie         19%
         beta         12%

Predicted Distribution of Response

 Distribution Probability
      tweedie         47%
      weibull         25%
         beta         12%

Model validation

Version Author Date
e845f96 ajpelu 2022-01-17
A. parametric coefficients Estimate Std. Error t-value p-value
(Intercept) 0.5287 0.1110 4.7639 < 0.0001
treatQP -0.1583 0.1573 -1.0059 0.3151
rangoMatorral denso -0.2817 0.1576 -1.7872 0.0747
rangoMatorral medio -0.2605 0.1576 -1.6529 0.0992
rangoEspartal denso -0.7181 0.1590 -4.5166 < 0.0001
treatQP:rangoMatorral denso 0.1236 0.2233 0.5535 0.5803
treatQP:rangoMatorral medio 0.2017 0.2231 0.9042 0.3665
treatQP:rangoEspartal denso -0.2180 0.2258 -0.9652 0.3351
B. smooth terms edf Ref.df F-value p-value
s(meses):treatHP 2.3165 4.0000 2.1678 0.0131
s(meses):treatQP 2.2922 4.0000 3.6264 0.0006
s(meses):rangoMatorral claro 0.0000 4.0000 0.0000 0.5747
s(meses):rangoMatorral denso 1.8420 4.0000 2.6999 0.0022
s(meses):rangoMatorral medio 0.0000 4.0000 0.0000 0.5277
s(meses):rangoEspartal denso 3.0818 4.0000 20.0725 < 0.0001

Cobertura

Modelo

f <- as.formula(
  cob ~ 
    s(meses, by = interaction(treat, rango), k = 5, bs = "cs") +
    s(meses, by = treat, k = 5, bs = "cs") + 
    s(meses, by = rango, k = 5, bs = "cs") + 
    treat * rango
)

fi <- as.formula(
  cob ~ 
    s(meses, by = interaction(treat, rango), k = 5, bs = "cs") +
    treat * rango
)

fni <- as.formula(
  cob ~ 
    s(meses, by = treat, k = 5, bs = "cs") + 
    s(meses, by = rango, k = 5, bs = "cs") + 
    treat * rango
)


mfull <- gamm(f,
          random = list(quadrat = ~1), 
          data = veg, 
          family = nb,
          method = "ML")

 Maximum number of PQL iterations:  20 
mi <- gamm(fi,
          random = list(quadrat = ~1), 
          data = veg, 
          family = nb,
          method = "ML")

 Maximum number of PQL iterations:  20 
mni <- gamm(fni,
          random = list(quadrat = ~1), 
          data = veg, 
          family = nb,
          method = "ML")

 Maximum number of PQL iterations:  20
  • Seleccionamos los suavizados, y elegimos el modelo con menor AIC
model df AIC
mni 16 553.3551
mfull 24 569.3556
mi 18 604.5710 
# Distribution of Model Family

Predicted Distribution of Residuals

 Distribution Probability
       normal         69%
      tweedie         28%
         beta          3%

Predicted Distribution of Response

               Distribution Probability
 neg. binomial (zero-infl.)         91%
              beta-binomial          9%

Model validation

Version Author Date
e845f96 ajpelu 2022-01-17
A. parametric coefficients Estimate Std. Error t-value p-value
(Intercept) 2.6987 0.1387 19.4558 < 0.0001
treatQP 0.0166 0.1962 0.0846 0.9326
rangoMatorral denso 0.5418 0.1960 2.7644 0.0060
rangoMatorral medio 0.5852 0.1960 2.9861 0.0030
rangoEspartal denso 0.6656 0.1960 3.3959 0.0008
treatQP:rangoMatorral denso -0.1166 0.2773 -0.4206 0.6743
treatQP:rangoMatorral medio -0.0813 0.2772 -0.2934 0.7694
treatQP:rangoEspartal denso -0.0529 0.2772 -0.1909 0.8487
B. smooth terms edf Ref.df F-value p-value
s(meses):treatHP 3.2434 4.0000 5.4764 < 0.0001
s(meses):treatQP 3.7914 4.0000 21.8033 < 0.0001
s(meses):rangoMatorral claro 0.0000 4.0000 0.0000 0.1724
s(meses):rangoMatorral denso 3.8000 4.0000 25.9436 < 0.0001
s(meses):rangoMatorral medio 1.9142 4.0000 1.1067 0.0882
s(meses):rangoEspartal denso 3.8968 4.0000 33.2093 < 0.0001

Fitovolumen

Modelo

f <- as.formula(
  fitovol ~ 
    s(meses, by = interaction(treat, rango), k = 5, bs = "cs") +
    s(meses, by = treat, k = 5, bs = "cs") + 
    s(meses, by = rango, k = 5, bs = "cs") + 
    treat * rango
)

fi <- as.formula(
  fitovol ~ 
    s(meses, by = interaction(treat, rango), k = 5, bs = "cs") +
    treat * rango
)

fni <- as.formula(
  fitovol ~ 
    s(meses, by = treat, k = 5, bs = "cs") + 
    s(meses, by = rango, k = 5, bs = "cs") + 
    treat * rango
)


mfull <- gamm(f,
          random = list(quadrat = ~1), 
          data = veg, 
          family = tw,
          method = "ML")

 Maximum number of PQL iterations:  20 
mi <- gamm(fi,
          random = list(quadrat = ~1), 
          data = veg, 
          family = tw,
          method = "ML")

 Maximum number of PQL iterations:  20 
mni <- gamm(fni,
          random = list(quadrat = ~1), 
          data = veg, 
          family = tw,
          method = "ML")

 Maximum number of PQL iterations:  20
  • Seleccionamos los suavizados, y elegimos el modelo con menor AIC
model df AIC
mni 16 903.7188
mfull 24 919.8060
mi 18 958.6921 
# Distribution of Model Family

Predicted Distribution of Residuals

 Distribution Probability
       normal         53%
      tweedie         47%

Predicted Distribution of Response

 Distribution Probability
    lognormal         31%
      tweedie         22%
            F         16%

Model validation

Version Author Date
e845f96 ajpelu 2022-01-17
A. parametric coefficients Estimate Std. Error t-value p-value
(Intercept) 5.0453 0.1969 25.6224 < 0.0001
treatQP 0.0576 0.2773 0.2076 0.8357
rangoMatorral denso 1.2420 0.2682 4.6310 < 0.0001
rangoMatorral medio 1.1151 0.2685 4.1532 < 0.0001
rangoEspartal denso 1.8986 0.2648 7.1699 < 0.0001
treatQP:rangoMatorral denso -0.2339 0.3765 -0.6212 0.5348
treatQP:rangoMatorral medio -0.2065 0.3794 -0.5443 0.5866
treatQP:rangoEspartal denso -0.2753 0.3724 -0.7391 0.4603
B. smooth terms edf Ref.df F-value p-value
s(meses):treatHP 3.5747 4.0000 29.5108 < 0.0001
s(meses):treatQP 3.7773 4.0000 42.6866 < 0.0001
s(meses):rangoMatorral claro 0.0000 4.0000 0.0000 0.7831
s(meses):rangoMatorral denso 3.7580 4.0000 22.1492 < 0.0001
s(meses):rangoMatorral medio 0.0000 4.0000 0.0000 0.7361
s(meses):rangoEspartal denso 3.7961 4.0000 19.4941 < 0.0001

Overall

  • Smooth terms
    Variable term edf ref.df F p
    Richness s(meses):treatHP 1.601 4 4.10 < 0.001
    Richness s(meses):treatQP 3.456 4 6.40 < 0.001
    Richness s(meses):rangoMatorral claro 0.000 4 0.00 0.992
    Richness s(meses):rangoMatorral denso 0.000 4 0.00 0.501
    Richness s(meses):rangoMatorral medio 0.000 4 0.00 0.736
    Richness s(meses):rangoEspartal denso 2.756 4 7.50 < 0.001
    Shannon s(meses):treatHP 2.317 4 2.17 0.013
    Shannon s(meses):treatQP 2.292 4 3.63 0.001
    Shannon s(meses):rangoMatorral claro 0.000 4 0.00 0.575
    Shannon s(meses):rangoMatorral denso 1.842 4 2.70 0.002
    Shannon s(meses):rangoMatorral medio 0.000 4 0.00 0.528
    Shannon s(meses):rangoEspartal denso 3.082 4 20.07 < 0.001
    Cobertura total s(meses):treatHP 3.243 4 5.48 < 0.001
    Cobertura total s(meses):treatQP 3.791 4 21.80 < 0.001
    Cobertura total s(meses):rangoMatorral claro 0.000 4 0.00 0.172
    Cobertura total s(meses):rangoMatorral denso 3.800 4 25.94 < 0.001
    Cobertura total s(meses):rangoMatorral medio 1.914 4 1.11 0.088
    Cobertura total s(meses):rangoEspartal denso 3.897 4 33.21 < 0.001
    Fitovolumen s(meses):treatHP 3.575 4 29.51 < 0.001
    Fitovolumen s(meses):treatQP 3.777 4 42.69 < 0.001
    Fitovolumen s(meses):rangoMatorral claro 0.000 4 0.00 0.783
    Fitovolumen s(meses):rangoMatorral denso 3.758 4 22.15 < 0.001
    Fitovolumen s(meses):rangoMatorral medio 0.000 4 0.00 0.736
    Fitovolumen s(meses):rangoEspartal denso 3.796 4 19.49 < 0.001
  • Parametrics terms
Variable param. terms df F p.value
Richness treat 1 5.501 0.02
Richness rango 3 1.880 0.132
Richness treat:rango 3 0.116 0.951
Shannon treat 1 1.012 0.315
Shannon rango 3 6.971 < 0.001
Shannon treat:rango 3 1.302 0.273
Cobertura total treat 1 0.007 0.933
Cobertura total rango 3 4.781 0.003
Cobertura total treat:rango 3 0.063 0.979
Fitovolumen treat 1 0.043 0.836
Fitovolumen rango 3 17.379 < 0.001
Fitovolumen treat:rango 3 0.207 0.892
Variable R2 AIC Model distribution
Richness 0.262 319.87 Poisson
Shannon 0.384 312.33 Tweedie
Cobertura total 0.698 553.36 Negative Binomial
Fitovol 0.839 903.72 Tweedie 

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

locale:
[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] emmeans_1.5.4     plotrix_3.8-1     gtsummary_1.4.2   patchwork_1.1.1  
 [5] performance_0.8.0 broom_0.7.9       tidymv_3.2.1      kableExtra_1.3.1 
 [9] itsadug_2.4       plotfunctions_1.4 gratia_0.6.0      mgcv_1.8-33      
[13] nlme_3.1-152      janitor_2.1.0     here_1.0.1        forcats_0.5.1    
[17] stringr_1.4.0     dplyr_1.0.6       purrr_0.3.4       readr_1.4.0      
[21] tidyr_1.1.3       tibble_3.1.2      ggplot2_3.3.5     tidyverse_1.3.1  
[25] workflowr_1.7.0  

loaded via a namespace (and not attached):
 [1] TH.data_1.0-10      colorspace_2.0-2    ellipsis_0.3.2     
 [4] rprojroot_2.0.2     estimability_1.3    snakecase_0.11.0   
 [7] fs_1.5.0            rstudioapi_0.13     farver_2.1.0       
[10] fansi_0.4.2         mvtnorm_1.1-1       lubridate_1.7.10   
[13] xml2_1.3.2          codetools_0.2-18    splines_4.0.2      
[16] knitr_1.31          jsonlite_1.7.2      gt_0.3.0           
[19] dbplyr_2.1.1        compiler_4.0.2      httr_1.4.2         
[22] backports_1.2.1     assertthat_0.2.1    Matrix_1.3-2       
[25] fastmap_1.1.0       cli_2.5.0           later_1.1.0.1      
[28] htmltools_0.5.2     tools_4.0.2         coda_0.19-4        
[31] gtable_0.3.0        glue_1.4.2          Rcpp_1.0.7         
[34] cellranger_1.1.0    jquerylib_0.1.3     vctrs_0.3.8        
[37] broom.helpers_1.4.0 insight_0.14.4      xfun_0.23          
[40] ps_1.5.0            rvest_1.0.0         lifecycle_1.0.1    
[43] getPass_0.2-2       MASS_7.3-53         zoo_1.8-8          
[46] scales_1.1.1.9000   ragg_1.1.1          hms_1.0.0          
[49] promises_1.2.0.1    sandwich_3.0-0      yaml_2.2.1         
[52] mvnfast_0.2.7       sass_0.3.1          stringi_1.7.4      
[55] highr_0.8           bayestestR_0.9.0    randomForest_4.6-14
[58] systemfonts_1.0.0   rlang_0.4.12        pkgconfig_2.0.3    
[61] evaluate_0.14       lattice_0.20-41     labeling_0.4.2     
[64] processx_3.5.1      tidyselect_1.1.1    magrittr_2.0.1     
[67] R6_2.5.1            generics_0.1.0      multcomp_1.4-16    
[70] DBI_1.1.1           pillar_1.6.1        haven_2.3.1        
[73] whisker_0.4         withr_2.4.1         survival_3.2-7     
[76] modelr_0.1.8        crayon_1.4.1        utf8_1.1.4         
[79] rmarkdown_2.8       grid_4.0.2          readxl_1.3.1       
[82] callr_3.7.0         git2r_0.28.0        reprex_2.0.0       
[85] digest_0.6.27       webshot_0.5.2       xtable_1.8-4       
[88] httpuv_1.5.5        textshaping_0.3.2   munsell_0.5.0      
[91] tweedie_2.3.3       viridisLite_0.4.0   bslib_0.2.4