Last updated: 2022-01-17

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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 espartal denso mat. claro mat. denso mat. medio
   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

	df	AIC
mni$lme </td> <td style="text-align:right;"> 15 </td> <td style="text-align:right;"> 319.8728 </td> </tr> <tr> <td style="text-align:left;"> mfull$lme	23	334.4627
mi$lme	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

A. parametric coefficients	Estimate	Std. Error	t-value	p-value
(Intercept)	2.1133	0.0893	23.6583	< 0.0001
treatQP	-0.3109	0.1287	-2.4157	0.0162
rangomat. claro	0.2813	0.1236	2.2766	0.0234
rangomat. denso	0.2007	0.1242	1.6162	0.1069
rangomat. medio	0.2099	0.1241	1.6909	0.0917
treatQP:rangomat. claro	0.0214	0.1781	0.1201	0.9045
treatQP:rangomat. denso	0.0671	0.1788	0.3751	0.7078
treatQP:rangomat. medio	0.0943	0.1785	0.5283	0.5976
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):rangoespartal denso	2.7565	4.0000	7.5048	< 0.0001
s(meses):rangomat. claro	0.0000	4.0000	0.0000	0.9918
s(meses):rangomat. denso	0.0000	4.0000	0.0000	0.5012
s(meses):rangomat. medio	0.0000	4.0000	0.0000	0.7363

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

	df	AIC
mni$lme </td> <td style="text-align:right;"> 16 </td> <td style="text-align:right;"> 312.3255 </td> </tr> <tr> <td style="text-align:left;"> mi$lme	18	326.0420
mfull$lme	24	329.8890

# 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

A. parametric coefficients	Estimate	Std. Error	t-value	p-value
(Intercept)	-0.1894	0.1138	-1.6634	0.0971
treatQP	-0.3762	0.1620	-2.3218	0.0208
rangomat. claro	0.7181	0.1590	4.5167	< 0.0001
rangomat. denso	0.4363	0.1597	2.7329	0.0066
rangomat. medio	0.4576	0.1596	2.8665	0.0044
treatQP:rangomat. claro	0.2180	0.2258	0.9652	0.3351
treatQP:rangomat. denso	0.3415	0.2266	1.5075	0.1325
treatQP:rangomat. medio	0.4197	0.2264	1.8538	0.0646
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):rangoespartal denso	3.0818	4.0000	20.0725	< 0.0001
s(meses):rangomat. claro	0.0000	4.0000	0.0000	0.5747
s(meses):rangomat. denso	1.8420	4.0000	2.6999	0.0022
s(meses):rangomat. medio	0.0000	4.0000	0.0000	0.5277

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

	df	AIC
mni$lme </td> <td style="text-align:right;"> 16 </td> <td style="text-align:right;"> 553.3551 </td> </tr> <tr> <td style="text-align:left;"> mfull$lme	24	569.3552
mi$lme	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

A. parametric coefficients	Estimate	Std. Error	t-value	p-value
(Intercept)	3.3643	0.1385	24.2926	< 0.0001
treatQP	-0.0363	0.1959	-0.1855	0.8530
rangomat. claro	-0.6656	0.1960	-3.3959	0.0008
rangomat. denso	-0.1238	0.1959	-0.6320	0.5278
rangomat. medio	-0.0805	0.1958	-0.4109	0.6814
treatQP:rangomat. claro	0.0529	0.2772	0.1909	0.8487
treatQP:rangomat. denso	-0.0637	0.2771	-0.2299	0.8183
treatQP:rangomat. medio	-0.0284	0.2770	-0.1025	0.9184
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):rangoespartal denso	3.8968	4.0000	33.2093	< 0.0001
s(meses):rangomat. claro	0.0000	4.0000	0.0000	0.1724
s(meses):rangomat. denso	3.8000	4.0000	25.9436	< 0.0001
s(meses):rangomat. medio	1.9142	4.0000	1.1067	0.0882

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

	df	AIC
mni$lme </td> <td style="text-align:right;"> 16 </td> <td style="text-align:right;"> 903.7188 </td> </tr> <tr> <td style="text-align:left;"> mfull$lme	24	919.8059
mi$lme	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

A. parametric coefficients	Estimate	Std. Error	t-value	p-value
(Intercept)	6.9438	0.1776	39.1092	< 0.0001
treatQP	-0.2177	0.2505	-0.8691	0.3854
rangomat. claro	-1.8986	0.2648	-7.1699	< 0.0001
rangomat. denso	-0.6566	0.2539	-2.5857	0.0101
rangomat. medio	-0.7835	0.2550	-3.0727	0.0023
treatQP:rangomat. claro	0.2753	0.3724	0.7391	0.4603
treatQP:rangomat. denso	0.0413	0.3558	0.1162	0.9076
treatQP:rangomat. medio	0.0687	0.3597	0.1911	0.8485
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):rangoespartal denso	3.7961	4.0000	19.4941	< 0.0001
s(meses):rangomat. claro	0.0000	4.0000	0.0000	0.7831
s(meses):rangomat. denso	3.7580	4.0000	22.1492	< 0.0001
s(meses):rangomat. medio	0.0000	4.0000	0.0000	0.7361

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):rangoespartal denso	2.756	4	7.50	< 0.001
Richness	s(meses):rangomat. claro	0.000	4	0.00	0.992
Richness	s(meses):rangomat. denso	0.000	4	0.00	0.501
Richness	s(meses):rangomat. medio	0.000	4	0.00	0.736
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):rangoespartal denso	3.082	4	20.07	< 0.001
Shannon	s(meses):rangomat. claro	0.000	4	0.00	0.575
Shannon	s(meses):rangomat. denso	1.842	4	2.70	0.002
Shannon	s(meses):rangomat. medio	0.000	4	0.00	0.528
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):rangoespartal denso	3.897	4	33.21	< 0.001
Cobertura total	s(meses):rangomat. claro	0.000	4	0.00	0.172
Cobertura total	s(meses):rangomat. denso	3.800	4	25.94	< 0.001
Cobertura total	s(meses):rangomat. medio	1.914	4	1.11	0.088
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):rangoespartal denso	3.796	4	19.49	< 0.001
Fitovolumen	s(meses):rangomat. claro	0.000	4	0.00	0.783
Fitovolumen	s(meses):rangomat. denso	3.758	4	22.15	< 0.001
Fitovolumen	s(meses):rangomat. medio	0.000	4	0.00	0.736

Parametrics terms

Variable	param. terms	df	F	p.value
Richness	treat	1	5.836	0.016
Richness	rango	3	1.880	0.132
Richness	treat:rango	3	0.116	0.951
Shannon	treat	1	5.391	0.021
Shannon	rango	3	6.971	< 0.001
Shannon	treat:rango	3	1.302	0.273
Cobertura total	treat	1	0.034	0.853
Cobertura total	rango	3	4.781	0.003
Cobertura total	treat:rango	3	0.063	0.979
Fitovolumen	treat	1	0.755	0.385
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

Temporal evolution of veg. parameters by rangos (Spanish)

Antonio J. Pérez-Luque

2022-01-17

Introdución y Objetivos

Análisis estadístico

Riqueza

Modelo

Model validation

Diversidad

Modelo

Model validation

Cobertura

Modelo

Model validation

Fitovolumen

Modelo

Model validation

Overall

	df	AIC
mni\(lme </td> <td style="text-align:right;"> 15 </td> <td style="text-align:right;"> 319.8728 </td> </tr> <tr> <td style="text-align:left;"> mfull\)lme	23	334.4627
mi$lme	17	336.0228