Cumulative Precipitation
Figure 1.
Animal Gains
HREC Animal Gains
## Warning: package 'bindrcpp' was built under R version 3.4.3
##
## Error: Pasture
## Df Sum Sq Mean Sq F value Pr(>F)
## Year 1 1.0685 1.0685 3.615 0.308
## Residuals 1 0.2956 0.2956
##
## Error: Within
## Df Sum Sq Mean Sq F value Pr(>F)
## Year 1 1.43 1.4334 3.827 0.0523 .
## Residuals 150 56.19 0.3746
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Error: Pasture
## Df Sum Sq Mean Sq F value Pr(>F)
## Year 1 0.05488 0.05488 0.199 0.733
## Residuals 1 0.27568 0.27568
##
## Error: Within
## Df Sum Sq Mean Sq F value Pr(>F)
## Year 1 0.274 0.27376 29.95 5.51e-08 ***
## Residuals 1090 9.965 0.00914
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Simultaneous Tests for General Linear Hypotheses
##
## Fit: lmer(formula = avgDday ~ Year + 0 + (1 | Pasture), data = HrecCows)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## Year2016 == 0 0.64285 0.08488 7.574 < 1e-10 ***
## Year2017 == 0 0.45370 0.08556 5.303 2.28e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)
## Computing profile confidence intervals ...
## Warning in optwrap(optimizer, par = thopt, fn = mkdevfun(rho, 0L), lower
## = fitted@lower): convergence code 3 from bobyqa: bobyqa -- a trust region
## step failed to reduce q
## 2.5 % 97.5 %
## .sig01 0.0000000 0.2764354
## .sigma 0.5470750 0.6856556
## Year2016 0.4706808 0.8205275
## Year2017 0.2786964 0.6300638
##
## Simultaneous Tests for General Linear Hypotheses
##
## Fit: lmer(formula = avgDday ~ Year + 0 + (1 | Pasture), data = HrecSheep)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## Year2016 == 0 0.25761 0.01255 20.52 <1e-10 ***
## Year2017 == 0 0.28930 0.01263 22.90 <1e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)
## Computing profile confidence intervals ...
## 2.5 % 97.5 %
## .sig01 0.007734052 0.05092279
## .sigma 0.091696304 0.09972491
## Year2016 0.229388738 0.28582508
## Year2017 0.261004367 0.31759827
Only showing the Cow and sheep results
HREC Gains Boxplot
CGREC Animal Gains
##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = avgDday ~ Treatment + (1 | Pasture), data = CgrecCows)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## SpringOnly - NoFire == 0 1.18656 0.46610 2.546 0.0293 *
## SpringSummer - NoFire == 0 1.23397 0.46566 2.650 0.0219 *
## SpringSummer - SpringOnly == 0 0.04741 0.46587 0.102 0.9943
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)
##
## Simultaneous Tests for General Linear Hypotheses
##
## Fit: lmer(formula = avgDday ~ Treatment + 0 + (1 | Pasture), data = CgrecCows)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## TreatmentNoFire == 0 -0.5045 0.3294 -1.531 0.3316
## TreatmentSpringSummer == 0 0.7294 0.3291 2.216 0.0779 .
## TreatmentSpringOnly == 0 0.6820 0.3297 2.068 0.1114
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)
## Computing profile confidence intervals ...
## 2.5 % 97.5 %
## .sig01 0.38818804 0.8997925
## .sigma 0.42223219 0.5003632
## TreatmentNoFire -1.11142191 0.1024986
## TreatmentSpringOnly 0.07450877 1.2894870
## TreatmentSpringSummer 0.12298592 1.3357239
No difference in the calves, but both burn treatments are different than the no burn treatment.
Figure 2
comparison of the three models (continued below)
| Fecal.HREC.null |
4 |
1975 |
1990 |
-983.3 |
1967 |
NA |
NA |
| Fecal.HREC.p |
5 |
1934 |
1954 |
-962.1 |
1924 |
42.44 |
1 |
| Fecal.HREC.pt |
6 |
1927 |
1950 |
-957.3 |
1915 |
9.628 |
1 |
| Fecal.HREC.null |
NA |
| Fecal.HREC.p |
7.292e-11 |
| Fecal.HREC.pt |
0.001916 |
null vs model with patch and treatment (continued below)
| Fecal.HREC.null |
4 |
1975 |
1990 |
-983.3 |
1967 |
NA |
NA |
| Fecal.HREC.pt |
6 |
1927 |
1950 |
-957.3 |
1915 |
52.07 |
2 |
| Fecal.HREC.null |
NA |
| Fecal.HREC.pt |
4.941e-12 |
null vs model with patch (continued below)
| Fecal.HREC.null |
4 |
1975 |
1990 |
-983.3 |
1967 |
NA |
NA |
| Fecal.HREC.p |
5 |
1934 |
1954 |
-962.1 |
1924 |
42.44 |
1 |
| Fecal.HREC.null |
NA |
| Fecal.HREC.p |
7.292e-11 |
## Data: subset(ProGO, REC == "HREC")
## Models:
## Fecal.HREC.pt: Fecal ~ Patch + Treatment + (1 | Pasture/Month)
## Fecal.HREC.INT: Fecal ~ Patch * Treatment + (1 | Pasture/Month)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## Fecal.HREC.pt 6 1926.6 1950.3 -957.29 1914.6
## Fecal.HREC.INT 7 1925.8 1953.6 -955.92 1911.8 2.7382 1 0.09798
##
## Fecal.HREC.pt
## Fecal.HREC.INT .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: Fecal ~ Patch + Treatment + (1 | Pasture/Month)
## Data: subset(ProGO, REC == "HREC")
##
## AIC BIC logLik deviance df.resid
## 1926.6 1950.3 -957.3 1914.6 381
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8643 -0.6093 -0.1039 0.4130 5.4006
##
## Random effects:
## Groups Name Variance Std.Dev.
## Month:Pasture (Intercept) 9.807e-01 9.903e-01
## Pasture (Intercept) 1.280e-13 3.578e-07
## Residual 7.755e+00 2.785e+00
## Number of obs: 387, groups: Month:Pasture, 18; Pasture, 6
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 4.0490 0.4590 8.821
## PatchU -2.2314 0.3307 -6.748
## TreatmentSheep 2.2983 0.5463 4.207
##
## Correlation of Fixed Effects:
## (Intr) PatchU
## PatchU -0.544
## TreatmntShp -0.591 0.000
## Computing profile confidence intervals ...
## Warning in zeta(shiftpar, start = opt[seqpar1][-w]): slightly lower
## deviances (diff=-2.27374e-13) detected
## Warning in nextpar(mat, cc, i, delta, lowcut, upcut): Last two rows have
## identical or NA .zeta values: using minstep
## Warning in nextpar(mat, cc, i, delta, lowcut, upcut): Last two rows have
## identical or NA .zeta values: using minstep
## Warning in zetafun(np, ns): slightly lower deviances (diff=-2.27374e-13)
## detected
## Warning in FUN(X[[i]], ...): non-monotonic profile for .sig02
## Warning in confint.thpr(pp, level = level, zeta = zeta): bad spline fit
## for .sig02: falling back to linear interpolation
## 2.5 % 97.5 %
## .sig01 0.6117623 1.5615556
## .sig02 0.0000000 0.9250144
## .sigma 2.5953345 2.9985164
## (Intercept) 3.1236080 4.9747728
## PatchU -2.8814333 -1.5816383
## TreatmentSheep 1.1584913 3.4335414
Fecal.CGREC.null <- lmer(Fecal ~ 1 + (1|Pasture/Month),
data=subset(ProGO, REC=="CGREC"), REML=FALSE)
Fecal.CGREC.p <- lmer(Fecal ~ Patch + (1|Pasture/Month),
data=subset(ProGO, REC=="CGREC"), REML=FALSE)
Fecal.CGREC.pt <- lmer(Fecal ~ Patch + Treatment + (1|Pasture/Month),
data=subset(ProGO, REC=="CGREC"), REML=FALSE)
anova(Fecal.CGREC.null, Fecal.CGREC.p, Fecal.CGREC.pt) %>%
pander(caption="comparison of the three models")
comparison of the three models (continued below)
| Fecal.CGREC.null |
4 |
2765 |
2784 |
-1379 |
2757 |
NA |
NA |
| Fecal.CGREC.p |
5 |
2589 |
2613 |
-1290 |
2579 |
177.7 |
1 |
| Fecal.CGREC.pt |
6 |
2587 |
2614 |
-1287 |
2575 |
4.955 |
1 |
| Fecal.CGREC.null |
NA |
| Fecal.CGREC.p |
1.539e-40 |
| Fecal.CGREC.pt |
0.02602 |
anova(Fecal.CGREC.null,Fecal.CGREC.pt) %>%
pander(caption="null vs patch and treatment")
null vs patch and treatment (continued below)
| Fecal.CGREC.null |
4 |
2765 |
2784 |
-1379 |
2757 |
NA |
NA |
| Fecal.CGREC.pt |
6 |
2587 |
2614 |
-1287 |
2575 |
182.7 |
2 |
| Fecal.CGREC.null |
NA |
| Fecal.CGREC.pt |
2.171e-40 |
anova(Fecal.CGREC.null, Fecal.CGREC.p) %>%
pander(caption="null vs patch only")
null vs patch only (continued below)
| Fecal.CGREC.null |
4 |
2765 |
2784 |
-1379 |
2757 |
NA |
NA |
| Fecal.CGREC.p |
5 |
2589 |
2613 |
-1290 |
2579 |
177.7 |
1 |
| Fecal.CGREC.null |
NA |
| Fecal.CGREC.p |
1.539e-40 |
anova(Fecal.CGREC.pt, Fecal.CGREC.p) %>%
pander(caption="patch and treatment vs patch only")
patch and treatment vs patch only (continued below)
| Fecal.CGREC.p |
5 |
2589 |
2613 |
-1290 |
2579 |
NA |
NA |
| Fecal.CGREC.pt |
6 |
2587 |
2614 |
-1287 |
2575 |
4.955 |
1 |
| Fecal.CGREC.p |
NA |
| Fecal.CGREC.pt |
0.02602 |
Fecal.CGREC.INT <- lmer(Fecal ~ Patch * Treatment + (1|Pasture/Month),
data=subset(ProGO, REC=="CGREC"), REML=FALSE)
anova(Fecal.CGREC.pt, Fecal.CGREC.INT)
## Data: subset(ProGO, REC == "CGREC")
## Models:
## Fecal.CGREC.pt: Fecal ~ Patch + Treatment + (1 | Pasture/Month)
## Fecal.CGREC.INT: Fecal ~ Patch * Treatment + (1 | Pasture/Month)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## Fecal.CGREC.pt 6 2586.5 2614.3 -1287.3 2574.5
## Fecal.CGREC.INT 7 2588.5 2620.9 -1287.3 2574.5 0.0021 1 0.9638
summary(Fecal.CGREC.pt)
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: Fecal ~ Patch + Treatment + (1 | Pasture/Month)
## Data: subset(ProGO, REC == "CGREC")
##
## AIC BIC logLik deviance df.resid
## 2586.5 2614.3 -1287.3 2574.5 751
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2632 -0.5794 -0.2970 0.3760 7.7836
##
## Random effects:
## Groups Name Variance Std.Dev.
## Month:Pasture (Intercept) 0.07048 0.2655
## Pasture (Intercept) 0.00000 0.0000
## Residual 1.71050 1.3079
## Number of obs: 757, groups: Month:Pasture, 24; Pasture, 8
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.6878 0.1515 17.737
## PatchU -1.8529 0.1295 -14.311
## TreatmentSpring Only -0.3385 0.1448 -2.337
##
## Correlation of Fixed Effects:
## (Intr) PatchU
## PatchU -0.743
## TrtmntSprnO -0.515 0.062
confint(Fecal.CGREC.pt)
## Computing profile confidence intervals ...
## 2.5 % 97.5 %
## .sig01 0.1380031 0.42457752
## .sig02 0.0000000 0.19460993
## .sigma 1.2436480 1.37779835
## (Intercept) 2.3886292 2.98842573
## PatchU -2.1069856 -1.59878928
## TreatmentSpring Only -0.6353726 -0.04389973
summary(Fecal.CGREC.p)
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: Fecal ~ Patch + (1 | Pasture/Month)
## Data: subset(ProGO, REC == "CGREC")
##
## AIC BIC logLik deviance df.resid
## 2589.5 2612.6 -1289.7 2579.5 752
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.3702 -0.5547 -0.3021 0.3328 7.8266
##
## Random effects:
## Groups Name Variance Std.Dev.
## Month:Pasture (Intercept) 9.851e-02 3.139e-01
## Pasture (Intercept) 1.996e-47 4.468e-24
## Residual 1.711e+00 1.308e+00
## Number of obs: 757, groups: Month:Pasture, 24; Pasture, 8
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.5087 0.1344 18.67
## PatchU -1.8380 0.1293 -14.21
##
## Correlation of Fixed Effects:
## (Intr)
## PatchU -0.804
confint(Fecal.CGREC.p)
## Computing profile confidence intervals ...
## Warning in zeta(shiftpar, start = opt[seqpar1][-w]): slightly lower
## deviances (diff=-4.54747e-13) detected
## Warning in nextpar(mat, cc, i, delta, lowcut, upcut): Last two rows have
## identical or NA .zeta values: using minstep
## Warning in nextpar(mat, cc, i, delta, lowcut, upcut): Last two rows have
## identical or NA .zeta values: using minstep
## Warning in zetafun(np, ns): slightly lower deviances (diff=-4.54747e-13)
## detected
## Warning in FUN(X[[i]], ...): non-monotonic profile for .sig02
## Warning in confint.thpr(pp, level = level, zeta = zeta): bad spline fit
## for .sig02: falling back to linear interpolation
## 2.5 % 97.5 %
## .sig01 0.1818811 0.4831699
## .sig02 0.0000000 0.2972714
## .sigma 1.2437317 1.3779110
## (Intercept) 2.2444090 2.7746637
## PatchU -2.0919826 -1.5838729
Protein
Pro.HREC.null <- lmer(PROTEIN ~ 1 + (1|Pasture/Month),
data=subset(ProGO, REC=="HREC"), REML=FALSE)
Pro.HREC.p <- lmer(PROTEIN ~ Patch + (1|Pasture/Month),
data=subset(ProGO, REC=="HREC"), REML=FALSE)
Pro.HREC.pt <- lmer(PROTEIN ~ Patch + Treatment + (1|Pasture/Month),
data=subset(ProGO, REC=="HREC"), REML=FALSE)
anova(Pro.HREC.null, Pro.HREC.p, Pro.HREC.pt) %>%
pander(caption="comparison of the three models")
comparison of the three models (continued below)
| Pro.HREC.null |
4 |
1708 |
1724 |
-850.1 |
1700 |
NA |
NA |
| Pro.HREC.p |
5 |
1707 |
1727 |
-848.5 |
1697 |
3.169 |
1 |
| Pro.HREC.pt |
6 |
1703 |
1726 |
-845.3 |
1691 |
6.373 |
1 |
| Pro.HREC.null |
NA |
| Pro.HREC.p |
0.07505 |
| Pro.HREC.pt |
0.01158 |
#Not different than the null model
anova(Pro.HREC.null, Pro.HREC.p) %>%
pander(caption="null vs patch only")
null vs patch only (continued below)
| Pro.HREC.null |
4 |
1708 |
1724 |
-850.1 |
1700 |
NA |
NA |
| Pro.HREC.p |
5 |
1707 |
1727 |
-848.5 |
1697 |
3.169 |
1 |
| Pro.HREC.null |
NA |
| Pro.HREC.p |
0.07505 |
anova(Pro.HREC.null, Pro.HREC.pt) %>%
pander(caption="null vs patch and treatment")
null vs patch and treatment (continued below)
| Pro.HREC.null |
4 |
1708 |
1724 |
-850.1 |
1700 |
NA |
NA |
| Pro.HREC.pt |
6 |
1703 |
1726 |
-845.3 |
1691 |
9.542 |
2 |
| Pro.HREC.null |
NA |
| Pro.HREC.pt |
0.00847 |
anova(Pro.HREC.p, Pro.HREC.pt) %>%
pander(caption="patch vs patch and treatment")
patch vs patch and treatment
| Pro.HREC.p |
5 |
1707 |
1727 |
-848.5 |
1697 |
NA |
NA |
NA |
| Pro.HREC.pt |
6 |
1703 |
1726 |
-845.3 |
1691 |
6.373 |
1 |
0.01158 |
Pro.HREC.INT <- lmer(PROTEIN ~ Patch * Treatment + (1|Pasture/Month),
data=subset(ProGO, REC=="HREC"), REML=FALSE)
anova(Pro.HREC.pt, Pro.HREC.INT)
## Data: subset(ProGO, REC == "HREC")
## Models:
## Pro.HREC.pt: PROTEIN ~ Patch + Treatment + (1 | Pasture/Month)
## Pro.HREC.INT: PROTEIN ~ Patch * Treatment + (1 | Pasture/Month)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## Pro.HREC.pt 6 1702.6 1726.3 -845.28 1690.6
## Pro.HREC.INT 7 1704.4 1732.1 -845.19 1690.4 0.1761 1 0.6748
summary(Pro.HREC.pt)
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: PROTEIN ~ Patch + Treatment + (1 | Pasture/Month)
## Data: subset(ProGO, REC == "HREC")
##
## AIC BIC logLik deviance df.resid
## 1702.6 1726.3 -845.3 1690.6 381
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4975 -0.6211 -0.1070 0.4765 5.3782
##
## Random effects:
## Groups Name Variance Std.Dev.
## Month:Pasture (Intercept) 0.26903 0.5187
## Pasture (Intercept) 0.07008 0.2647
## Residual 4.41918 2.1022
## Number of obs: 387, groups: Month:Pasture, 18; Pasture, 6
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 10.0808 0.3335 30.226
## PatchU -0.4386 0.2496 -1.757
## TreatmentSheep -1.3074 0.3904 -3.349
##
## Correlation of Fixed Effects:
## (Intr) PatchU
## PatchU -0.566
## TreatmntShp -0.581 0.000
confint(Pro.HREC.pt) #no protein difference at patch, sheep lower than cattle
## Computing profile confidence intervals ...
## 2.5 % 97.5 %
## .sig01 0.1687074 0.94355440
## .sig02 0.0000000 0.87170367
## .sigma 1.9592320 2.26340034
## (Intercept) 9.3657468 10.79909521
## PatchU -0.9291927 0.05209052
## TreatmentSheep -2.2147505 -0.40692034
fixef(Pro.HREC.pt)
## (Intercept) PatchU TreatmentSheep
## 10.080797 -0.438619 -1.307373
summary(Pro.HREC.p)
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: PROTEIN ~ Patch + (1 | Pasture/Month)
## Data: subset(ProGO, REC == "HREC")
##
## AIC BIC logLik deviance df.resid
## 1706.9 1726.7 -848.5 1696.9 382
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4440 -0.6055 -0.1066 0.4862 5.4384
##
## Random effects:
## Groups Name Variance Std.Dev.
## Month:Pasture (Intercept) 0.2690 0.5186
## Pasture (Intercept) 0.4964 0.7046
## Residual 4.4199 2.1024
## Number of obs: 387, groups: Month:Pasture, 18; Pasture, 6
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 9.4290 0.3805 24.782
## PatchU -0.4456 0.2497 -1.784
##
## Correlation of Fixed Effects:
## (Intr)
## PatchU -0.496
confint(Pro.HREC.p)
## Computing profile confidence intervals ...
## 2.5 % 97.5 %
## .sig01 0.1671093 0.99173263
## .sig02 0.1691537 1.57480330
## .sigma 1.9593667 2.26360723
## (Intercept) 8.5959614 10.26074984
## PatchU -0.9363244 0.04522755
Pro.CGREC.null <- lmer(PROTEIN ~ 1 + (1|Pasture/Month),
data=subset(ProGO, REC=="CGREC"), REML=FALSE)
Pro.CGREC.p <- lmer(PROTEIN ~ Patch + (1|Pasture/Month),
data=subset(ProGO, REC=="CGREC"), REML=FALSE)
Pro.CGREC.pt <- lmer(PROTEIN ~ Patch + Treatment + (1|Pasture/Month),
data=subset(ProGO, REC=="CGREC"), REML=FALSE)
anova(Pro.CGREC.null, Pro.CGREC.p, Pro.CGREC.pt) %>%
pander(caption="comparison of the three models")
comparison of the three models (continued below)
| Pro.CGREC.null |
4 |
3383 |
3402 |
-1688 |
3375 |
NA |
NA |
| Pro.CGREC.p |
5 |
3160 |
3183 |
-1575 |
3150 |
225.1 |
1 |
| Pro.CGREC.pt |
6 |
3162 |
3190 |
-1575 |
3150 |
0.0004245 |
1 |
| Pro.CGREC.null |
NA |
| Pro.CGREC.p |
6.906e-51 |
| Pro.CGREC.pt |
0.9836 |
#.P IS THE BETTER MODEL
anova(Pro.CGREC.null, Pro.CGREC.p) %>%
pander(caption=" null vs patch")
null vs patch (continued below)
| Pro.CGREC.null |
4 |
3383 |
3402 |
-1688 |
3375 |
NA |
NA |
| Pro.CGREC.p |
5 |
3160 |
3183 |
-1575 |
3150 |
225.1 |
1 |
| Pro.CGREC.null |
NA |
| Pro.CGREC.p |
6.906e-51 |
anova(Pro.CGREC.null, Pro.CGREC.pt) %>%
pander(caption="null vs patch and treatment")
null vs patch and treatment (continued below)
| Pro.CGREC.null |
4 |
3383 |
3402 |
-1688 |
3375 |
NA |
NA |
| Pro.CGREC.pt |
6 |
3162 |
3190 |
-1575 |
3150 |
225.1 |
2 |
| Pro.CGREC.null |
NA |
| Pro.CGREC.pt |
1.304e-49 |
anova(Pro.CGREC.p, Pro.CGREC.pt) %>%
pander(caption="patch vs patch and treatment")
patch vs patch and treatment (continued below)
| Pro.CGREC.p |
5 |
3160 |
3183 |
-1575 |
3150 |
NA |
NA |
| Pro.CGREC.pt |
6 |
3162 |
3190 |
-1575 |
3150 |
0.0004245 |
1 |
| Pro.CGREC.p |
NA |
| Pro.CGREC.pt |
0.9836 |
Pro.CGREC.INT <- lmer(PROTEIN ~ Patch * Treatment + (1|Pasture/Month),
data=subset(ProGO, REC=="CGREC"), REML=FALSE)
anova(Pro.CGREC.pt, Pro.CGREC.INT)
## Data: subset(ProGO, REC == "CGREC")
## Models:
## Pro.CGREC.pt: PROTEIN ~ Patch + Treatment + (1 | Pasture/Month)
## Pro.CGREC.INT: PROTEIN ~ Patch * Treatment + (1 | Pasture/Month)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## Pro.CGREC.pt 6 3162.0 3189.7 -1575.0 3150.0
## Pro.CGREC.INT 7 3137.5 3169.9 -1561.8 3123.5 26.428 1 2.735e-07
##
## Pro.CGREC.pt
## Pro.CGREC.INT ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(Pro.CGREC.pt)
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: PROTEIN ~ Patch + Treatment + (1 | Pasture/Month)
## Data: subset(ProGO, REC == "CGREC")
##
## AIC BIC logLik deviance df.resid
## 3162.0 3189.7 -1575.0 3150.0 751
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1770 -0.6828 -0.1490 0.5190 4.9338
##
## Random effects:
## Groups Name Variance Std.Dev.
## Month:Pasture (Intercept) 0.377739 0.6146
## Pasture (Intercept) 0.008836 0.0940
## Residual 3.583823 1.8931
## Number of obs: 757, groups: Month:Pasture, 24; Pasture, 8
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 12.188125 0.263938 46.178
## PatchU -3.040369 0.187688 -16.199
## TreatmentSpring Only 0.006072 0.294560 0.021
##
## Correlation of Fixed Effects:
## (Intr) PatchU
## PatchU -0.619
## TrtmntSprnO -0.581 0.045
confint(Pro.CGREC.pt)
## Computing profile confidence intervals ...
## 2.5 % 97.5 %
## .sig01 0.3918434 0.9030728
## .sig02 0.0000000 0.6318090
## .sigma 1.8002131 1.9942528
## (Intercept) 11.6337283 12.7277087
## PatchU -3.4089867 -2.6718668
## TreatmentSpring Only -0.6397023 0.6672886
fixef(Pro.CGREC.pt)
## (Intercept) PatchU TreatmentSpring Only
## 12.188124924 -3.040368577 0.006071581
summary(Pro.CGREC.p)
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: PROTEIN ~ Patch + (1 | Pasture/Month)
## Data: subset(ProGO, REC == "CGREC")
##
## AIC BIC logLik deviance df.resid
## 3160.0 3183.1 -1575.0 3150.0 752
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1774 -0.6825 -0.1494 0.5193 4.9335
##
## Random effects:
## Groups Name Variance Std.Dev.
## Month:Pasture (Intercept) 0.377738 0.61460
## Pasture (Intercept) 0.008784 0.09372
## Residual 3.583837 1.89310
## Number of obs: 757, groups: Month:Pasture, 24; Pasture, 8
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 12.1913 0.2148 56.75
## PatchU -3.0405 0.1875 -16.22
##
## Correlation of Fixed Effects:
## (Intr)
## PatchU -0.729
confint(Pro.CGREC.p) #p or pt give basically the same CI for protein; pt accounts for # treatment
## Computing profile confidence intervals ...
## 2.5 % 97.5 %
## .sig01 0.3918435 0.9030232
## .sig02 0.0000000 0.6317193
## .sigma 1.8002166 1.9942563
## (Intercept) 11.7528694 12.6227237
## PatchU -3.4087572 -2.6724256
#Pro.CGREC.F <- lmer(PROTEIN ~ Patch + Treatment + (1|Month) + (1|Pasture),
# data=subset(ProGO, REC=="CGREC"), REML=FALSE)
# summary(Pro.CGREC.F)
# confint(Pro.CGREC.F)
Biomass
Bio.HREC.null <- lmer(Biomass ~ 1 + (1|Pasture/Month),
data=subset(ProGO, REC=="HREC"), REML=FALSE)
Bio.HREC.p <- lmer(Biomass ~ Patch + (1|Pasture/Month),
data=subset(ProGO, REC=="HREC"), REML=FALSE)
Bio.HREC.pt <- lmer(Biomass ~ Patch + Treatment + (1|Pasture/Month),
data=subset(ProGO, REC=="HREC"), REML=FALSE)
anova(Bio.HREC.null, Bio.HREC.p, Bio.HREC.pt) %>%
pander(caption="comparison of the three models")
comparison of the three models (continued below)
| Bio.HREC.null |
4 |
3011 |
3027 |
-1501 |
3003 |
NA |
NA |
| Bio.HREC.p |
5 |
2974 |
2994 |
-1482 |
2964 |
39.05 |
1 |
| Bio.HREC.pt |
6 |
2976 |
2999 |
-1482 |
2964 |
0.2868 |
1 |
| Bio.HREC.null |
NA |
| Bio.HREC.p |
4.139e-10 |
| Bio.HREC.pt |
0.5923 |
#.P AND PT ARE ABOUT THE SAME
anova(Bio.HREC.null, Bio.HREC.p) %>%
pander(caption="null vs patch")
null vs patch (continued below)
| Bio.HREC.null |
4 |
3011 |
3027 |
-1501 |
3003 |
NA |
NA |
| Bio.HREC.p |
5 |
2974 |
2994 |
-1482 |
2964 |
39.05 |
1 |
| Bio.HREC.null |
NA |
| Bio.HREC.p |
4.139e-10 |
anova(Bio.HREC.null, Bio.HREC.p, Bio.HREC.pt) %>%
pander(caption="null vs patch and treatment")
null vs patch and treatment (continued below)
| Bio.HREC.null |
4 |
3011 |
3027 |
-1501 |
3003 |
NA |
NA |
| Bio.HREC.p |
5 |
2974 |
2994 |
-1482 |
2964 |
39.05 |
1 |
| Bio.HREC.pt |
6 |
2976 |
2999 |
-1482 |
2964 |
0.2868 |
1 |
| Bio.HREC.null |
NA |
| Bio.HREC.p |
4.139e-10 |
| Bio.HREC.pt |
0.5923 |
Bio.HREC.INT <- lmer(Biomass ~ Patch * Treatment + (1|Pasture/Month),
data=subset(ProGO, REC=="HREC"), REML=FALSE)
anova(Bio.HREC.pt, Bio.HREC.INT)
## Data: subset(ProGO, REC == "HREC")
## Models:
## Bio.HREC.pt: Biomass ~ Patch + Treatment + (1 | Pasture/Month)
## Bio.HREC.INT: Biomass ~ Patch * Treatment + (1 | Pasture/Month)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## Bio.HREC.pt 6 2975.6 2999.3 -1481.8 2963.6
## Bio.HREC.INT 7 2967.0 2994.7 -1476.5 2953.0 10.565 1 0.001152 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(Bio.HREC.pt)
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: Biomass ~ Patch + Treatment + (1 | Pasture/Month)
## Data: subset(ProGO, REC == "HREC")
##
## AIC BIC logLik deviance df.resid
## 2975.6 2999.3 -1481.8 2963.6 381
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8403 -0.7404 -0.1928 0.5383 2.9856
##
## Random effects:
## Groups Name Variance Std.Dev.
## Month:Pasture (Intercept) 4.832 2.198
## Pasture (Intercept) 15.985 3.998
## Residual 117.168 10.824
## Number of obs: 387, groups: Month:Pasture, 18; Pasture, 6
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 15.572 2.721 5.723
## PatchU 8.250 1.286 6.416
## TreatmentSheep 1.949 3.598 0.542
##
## Correlation of Fixed Effects:
## (Intr) PatchU
## PatchU -0.357
## TreatmntShp -0.660 0.000
confint(Bio.HREC.pt) #PATCH SIG, TREATMENT NOT
## Computing profile confidence intervals ...
## 2.5 % 97.5 %
## .sig01 0.000000 4.522105
## .sig02 1.760247 8.627888
## .sigma 10.088122 11.654854
## (Intercept) 9.450430 21.690614
## PatchU 5.723598 10.777187
## TreatmentSheep -6.375216 10.303160
summary(Bio.HREC.p)
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: Biomass ~ Patch + (1 | Pasture/Month)
## Data: subset(ProGO, REC == "HREC")
##
## AIC BIC logLik deviance df.resid
## 2973.9 2993.7 -1481.9 2963.9 382
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8305 -0.7365 -0.1879 0.5464 2.9937
##
## Random effects:
## Groups Name Variance Std.Dev.
## Month:Pasture (Intercept) 4.832 2.198
## Pasture (Intercept) 16.898 4.111
## Residual 117.172 10.825
## Number of obs: 387, groups: Month:Pasture, 18; Pasture, 6
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 16.545 2.082 7.948
## PatchU 8.250 1.286 6.416
##
## Correlation of Fixed Effects:
## (Intr)
## PatchU -0.467
confint(Bio.HREC.p) #PATCH IS SIGNIFICANT
## Computing profile confidence intervals ...
## 2.5 % 97.5 %
## .sig01 0.000000 4.522122
## .sig02 1.867843 8.843722
## .sigma 10.088254 11.655059
## (Intercept) 11.969645 21.132414
## PatchU 5.723341 10.777057
Bio.CGREC.null <- lmer(Biomass ~ 1 + (1|Pasture/Month),
data=subset(ProGO, REC=="CGREC"), REML=FALSE)
Bio.CGREC.p <- lmer(Biomass ~ Patch + (1|Pasture/Month),
data=subset(ProGO, REC=="CGREC"), REML=FALSE)
Bio.CGREC.pt <- lmer(Biomass ~ Patch + Treatment + (1|Pasture/Month),
data=subset(ProGO, REC=="CGREC"), REML=FALSE)
anova(Bio.CGREC.null, Bio.CGREC.p, Bio.CGREC.pt) %>%
pander(caption="comparison of the three models")
comparison of the three models (continued below)
| Bio.CGREC.null |
4 |
5499 |
5517 |
-2745 |
5491 |
NA |
NA |
| Bio.CGREC.p |
5 |
5429 |
5453 |
-2710 |
5419 |
71.18 |
1 |
| Bio.CGREC.pt |
6 |
5430 |
5458 |
-2709 |
5418 |
1.298 |
1 |
| Bio.CGREC.null |
NA |
| Bio.CGREC.p |
3.255e-17 |
| Bio.CGREC.pt |
0.2546 |
#.P IS THE BETTER MODEL
anova(Bio.CGREC.null, Bio.CGREC.p) %>%
pander(caption="null vs patch")
null vs patch (continued below)
| Bio.CGREC.null |
4 |
5499 |
5517 |
-2745 |
5491 |
NA |
NA |
| Bio.CGREC.p |
5 |
5429 |
5453 |
-2710 |
5419 |
71.18 |
1 |
| Bio.CGREC.null |
NA |
| Bio.CGREC.p |
3.255e-17 |
anova(Bio.CGREC.null, Bio.CGREC.pt) %>%
pander(caption="null vs patch and treatment")
null vs patch and treatment (continued below)
| Bio.CGREC.null |
4 |
5499 |
5517 |
-2745 |
5491 |
NA |
NA |
| Bio.CGREC.pt |
6 |
5430 |
5458 |
-2709 |
5418 |
72.48 |
2 |
| Bio.CGREC.null |
NA |
| Bio.CGREC.pt |
1.823e-16 |
Bio.CGREC.INT <- lmer(Biomass ~ Patch * Treatment + (1|Pasture/Month),
data=subset(ProGO, REC=="CGREC"), REML=FALSE)
anova(Bio.CGREC.pt, Bio.CGREC.INT)
## Data: subset(ProGO, REC == "CGREC")
## Models:
## Bio.CGREC.pt: Biomass ~ Patch + Treatment + (1 | Pasture/Month)
## Bio.CGREC.INT: Biomass ~ Patch * Treatment + (1 | Pasture/Month)
## Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
## Bio.CGREC.pt 6 5430.2 5457.9 -2709.1 5418.2
## Bio.CGREC.INT 7 5427.3 5459.7 -2706.7 5413.3 4.8385 1 0.02783 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(Bio.CGREC.pt)
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: Biomass ~ Patch + Treatment + (1 | Pasture/Month)
## Data: subset(ProGO, REC == "CGREC")
##
## AIC BIC logLik deviance df.resid
## 5430.2 5457.9 -2709.1 5418.2 751
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1457 -0.6682 -0.1832 0.4933 4.8393
##
## Random effects:
## Groups Name Variance Std.Dev.
## Month:Pasture (Intercept) 5.292e+00 2.301e+00
## Pasture (Intercept) 2.978e-13 5.457e-07
## Residual 7.237e+01 8.507e+00
## Number of obs: 757, groups: Month:Pasture, 24; Pasture, 8
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 15.4692 1.0799 14.325
## PatchU 7.3321 0.8429 8.698
## TreatmentSpring Only 1.3027 1.1283 1.155
##
## Correlation of Fixed Effects:
## (Intr) PatchU
## PatchU -0.679
## TrtmntSprnO -0.552 0.053
confint(Bio.CGREC.pt)
## Computing profile confidence intervals ...
## Warning in nextpar(mat, cc, i, delta, lowcut, upcut): Last two rows have
## identical or NA .zeta values: using minstep
## Warning in nextpar(mat, cc, i, delta, lowcut, upcut): Last two rows have
## identical or NA .zeta values: using minstep
## Warning in FUN(X[[i]], ...): non-monotonic profile for .sig02
## Warning in confint.thpr(pp, level = level, zeta = zeta): bad spline fit
## for .sig02: falling back to linear interpolation
## 2.5 % 97.5 %
## .sig01 1.438861 3.448834
## .sig02 0.000000 2.144707
## .sigma 8.089442 8.961712
## (Intercept) 13.316869 17.611006
## PatchU 5.677675 8.986246
## TreatmentSpring Only -1.057132 3.662826
fixef(Bio.CGREC.pt)
## (Intercept) PatchU TreatmentSpring Only
## 15.469173 7.332050 1.302719
summary(Bio.CGREC.p)
## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: Biomass ~ Patch + (1 | Pasture/Month)
## Data: subset(ProGO, REC == "CGREC")
##
## AIC BIC logLik deviance df.resid
## 5429.5 5452.6 -2709.7 5419.5 752
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1674 -0.6667 -0.1902 0.5015 4.8265
##
## Random effects:
## Groups Name Variance Std.Dev.
## Month:Pasture (Intercept) 5.712 2.390
## Pasture (Intercept) 0.000 0.000
## Residual 72.370 8.507
## Number of obs: 757, groups: Month:Pasture, 24; Pasture, 8
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 16.1534 0.9105 17.741
## PatchU 7.2843 0.8419 8.652
##
## Correlation of Fixed Effects:
## (Intr)
## PatchU -0.772
confint(Bio.CGREC.p)
## Computing profile confidence intervals ...
## 2.5 % 97.5 %
## .sig01 1.455832 3.561241
## .sig02 0.000000 2.395668
## .sigma 8.089484 8.961780
## (Intercept) 14.325825 17.954553
## PatchU 5.631343 8.936701
Figure
