Structural Distributions

VOR distribution

VOR <- veg.s.stack %>%
  filter(response == "Visual Obstruction Reading")

MASS::fitdistr(VOR$value, "normal")$estimate [[1]]
## [1] 2.667521
MASS::fitdistr(VOR$value, "Gamma")$estimate [[1]]
## [1] 6.92051
VORndist <- tibble(
                  response = "VOR", 
                  dist = "normal",
                  X = seq(0, 5, 0.025),
                  value = dnorm(X, mean = MASS::fitdistr(VOR$value, "normal")$estimate [[1]], 
                                sd = MASS::fitdistr(VOR$value, "normal")$estimate [[2]]))

VORgdist <- tibble(
                  response = "VOR", 
                  dist = "gamma",
                  X = seq(0, 5, 0.025),
                  value = dgamma(X, shape = MASS::fitdistr(VOR$value, "Gamma")$estimate [[1]], 
                                 rate = MASS::fitdistr(VOR$value, "Gamma")$estimate [[2]]))
VORdist <- rbind(VORndist, VORgdist)

VORdist.gg <- 
  VOR %>%
  ggplot(aes(x=value)) + theme_bw() + 
  geom_histogram(aes(y=..density..),      
                 binwidth=.5,
                 colour="black", fill="lightgreen") +
  geom_density(alpha=.2, fill="#FF6666")+
  geom_line(data=VORdist, 
            aes(x = X, y = value, color = dist))

VORdist.gg

#vor is gamma dist

litter distribution

Litter <- veg.s.stack %>%
  filter(substr(response, 1,1) == "C")

MASS::fitdistr(Litter$value, "normal")$estimate [[1]]
## [1] 16.72692
MASS::fitdistr(Litter$value, "Gamma")$estimate [[1]]
## [1] 6.290656
litndist <- tibble(
                  response = "Litter",
                  dist = "normal",
                  X = seq(0, 40, 0.1),
                  value = dnorm(X, mean = MASS::fitdistr(Litter$value, "normal")$estimate [[1]],
                                sd = MASS::fitdistr(Litter$value, "normal")$estimate [[2]]))

litgdist <- tibble(
                  response = "Litter", 
                  dist = "gamma", 
                  X = seq(0, 40, 0.1),
                  value = dgamma(X, shape = MASS::fitdistr(Litter$value, "Gamma")$estimate [[1]], 
                                 rate = MASS::fitdistr(Litter$value, "Gamma")$estimate [[2]]))

litdist <-rbind(litndist, litgdist)


Litdist.gg <- 
  Litter %>%
  ggplot(aes(x=value)) + theme_bw() + 
  geom_histogram(aes(y=..density..),      
                 binwidth=1.5,
                 colour="black", fill="lightgreen") +
  geom_density(alpha=.2, fill="#FF6666")+
  geom_line(data=litdist, 
            aes(x = X, y = value, color = dist))

Litdist.gg

#litter is gamma dist

Compositional Distributions

POPR distribution

POPR <- veg.c.stack %>%
  filter(substr(response, 1,1) == "K")
POPR$value <- POPR$value + 0.001

MASS::fitdistr(POPR$value, "normal")$estimate [[1]]
## [1] 35.99331
MASS::fitdistr(POPR$value, "Gamma")$estimate [[1]]
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
## [1] 6.097191
POPRndist <- tibble(
  response = "Kentucky bluegrass",
  dist = "normal",
  X = seq(0, 70, 0.1),
  value = dnorm(X, mean = MASS::fitdistr(POPR$value, "normal")$estimate [[1]],
                sd = MASS::fitdistr(POPR$value, "normal")$estimate [[2]]))

POPRgdist <- tibble(
  response = "Kentucky bluegrass", 
  dist = "gamma", 
  X = seq(0, 70, 0.1),
  value = dgamma(X, shape = MASS::fitdistr(POPR$value, "Gamma")$estimate [[1]], 
                 rate = MASS::fitdistr(POPR$value, "Gamma")$estimate [[2]]))
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
POPRdist <-rbind(POPRndist, POPRgdist)


POPRdist.gg <- 
  POPR %>%
  ggplot(aes(x=value)) + theme_bw() + 
  geom_histogram(aes(y=..density..),      
                 binwidth=1.5,
                 colour="black", fill="lightgreen") +
  geom_density(alpha=.2, fill="#FF6666")+
  geom_line(data=POPRdist, 
            aes(x = X, y = value, color = dist))

 POPRdist.gg

#POPR is normal dist

BRIN dist

BRIN <- veg.c.stack %>%
  filter(substr(response, 1,2) == "sm")
  BRIN$value <- BRIN$value + 0.001
 
MASS::fitdistr(BRIN$value, "normal")$estimate [[1]]
## [1] 16.4916
MASS::fitdistr(BRIN$value, "Gamma")#$estimate [[1]]
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
##      shape         rate   
##   0.81997402   0.04972084 
##  (0.06554454) (0.00535391)
BRINndist <- tibble(
  response = "smooth brome",
  dist = "normal",
  X = seq(0, 70, 0.1),
  value = dnorm(X, mean = MASS::fitdistr(BRIN$value, "normal")$estimate [[1]],
                sd = MASS::fitdistr(BRIN$value, "normal")$estimate [[2]]))

BRINgdist <- tibble(
  response = "smooth brome", 
  dist = "gamma", 
  X = seq(0, 70, 0.1),
  value = dgamma(X, shape = MASS::fitdistr(BRIN$value, "Gamma")$estimate [[1]], 
                 rate = MASS::fitdistr(BRIN$value, "Gamma")$estimate [[2]]))
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
BRINdist <-rbind(BRINndist, BRINgdist)


BRINdist.gg <- 
  BRIN %>%
  ggplot(aes(x=value)) + theme_bw() + 
  geom_histogram(aes(y=..density..),      
                 binwidth=1.5,
                 colour="black", fill="lightgreen") +
  geom_density(alpha=.2, fill="#FF6666")+
  geom_line(data=BRINdist, 
            aes(x = X, y = value, color = dist))

 BRINdist.gg

#BRIN is normal

NatC3 dist

NatC3 <- veg.c.stack %>%
  filter(response == "native C3")
NatC3$value <- NatC3$value + 0.001

MASS::fitdistr(NatC3$value, "normal")$estimate [[1]]
## [1] 8.179205
MASS::fitdistr(NatC3$value, "Gamma")$estimate [[1]]
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
## [1] 0.4956497
NatC3ndist <- tibble(
  response = "native C3",
  dist = "normal",
  X = seq(0, 70, 0.1),
  value = dnorm(X, mean = MASS::fitdistr(NatC3$value, "normal")$estimate [[1]],
                sd = MASS::fitdistr(NatC3$value, "normal")$estimate [[2]]))

NatC3gdist <- tibble(
  response = "native C3", 
  dist = "gamma", 
  X = seq(0, 70, 0.1),
  value = dgamma(X, shape = MASS::fitdistr(NatC3$value, "Gamma")$estimate [[1]], 
                 rate = MASS::fitdistr(NatC3$value, "Gamma")$estimate [[2]]))
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
NatC3dist <-rbind(NatC3ndist, NatC3gdist)

NatC3dist.gg <- 
  NatC3 %>%
  ggplot(aes(x=value)) + theme_bw() + 
  geom_histogram(aes(y=..density..),      
                 binwidth=1.5,
                 colour="black", fill="lightgreen") +
  geom_density(alpha=.2, fill="#FF6666")+
  geom_line(data=NatC3dist, 
            aes(x = X, y = value, color = dist))

NatC3dist.gg

# natC3 is normal

natC4 dist

NatC4 <- veg.c.stack %>%
  filter(response == "native C4")
NatC4$value <- NatC4$value + 0.001

MASS::fitdistr(NatC4$value, "normal")#$estimate [[1]]
##      mean         sd    
##   2.3411709   3.7237528 
##  (0.2434293) (0.1721305)
MASS::fitdistr(NatC4$value, "Gamma")#$estimate [[1]]
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
##      shape         rate   
##   0.24429224   0.10434627 
##  (0.01755392) (0.01570550)
NatC4ndist <- tibble(
  response = "native C4",
  dist = "normal",
  X = seq(0,28, 0.1),
  value = dnorm(X, mean = MASS::fitdistr(NatC4$value, "normal")$estimate [[1]],
                sd = MASS::fitdistr(NatC4$value, "normal")$estimate [[2]]))

NatC4gdist <- tibble(
  response = "native C4", 
  dist = "gamma", 
  X = seq(0, 28, 0.1),
  value = dgamma(X, shape = MASS::fitdistr(NatC4$value, "Gamma")$estimate [[1]], 
                 rate = MASS::fitdistr(NatC4$value, "Gamma")$estimate [[2]]))
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
NatC4dist <-rbind(NatC4ndist, NatC4gdist)


NatC4dist.gg <- 
  NatC4 %>%
  ggplot(aes(x=value)) + theme_bw() + 
  geom_histogram(aes(y=..density..),      
                 binwidth=1.5,
                 colour="black", fill="lightgreen") +
  geom_density(alpha=.2, fill="#FF6666")+
  geom_line(data=NatC4dist, 
            aes(x = X, y = value, color = dist))

NatC4dist.gg

#natC4 is normal

NatLeg dist

NatLeg <- veg.c.stack %>%
  filter(response == "native legume")
NatLeg$value <- NatLeg$value + 0.001

MASS::fitdistr(NatLeg$value, "normal")#$estimate [[1]]
##      mean         sd    
##   4.3287778   4.4964038 
##  (0.2939391) (0.2078463)
MASS::fitdistr(NatLeg$value, "Gamma")#$estimate [[1]]
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
##      shape         rate   
##   0.56365791   0.13021191 
##  (0.04350173) (0.01514999)
NatLegndist <- tibble(
  response = "native legume",
  dist = "normal",
  X = seq(0,28, 0.1),
  value = dnorm(X, mean = MASS::fitdistr(NatLeg$value, "normal")$estimate [[1]],
                sd = MASS::fitdistr(NatLeg$value, "normal")$estimate [[2]]))

NatLeggdist <- tibble(
  response = "native legume", 
  dist = "gamma", 
  X = seq(0, 28, 0.1),
  value = dgamma(X, shape = MASS::fitdistr(NatLeg$value, "Gamma")$estimate [[1]], 
                 rate = MASS::fitdistr(NatLeg$value, "Gamma")$estimate [[2]]))
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
NatLegdist <-rbind(NatLegndist, NatLeggdist)

NatLegdist.gg <- 
  NatLeg %>%
  ggplot(aes(x=value)) + theme_bw() + 
  geom_histogram(aes(y=..density..),      
                 binwidth=1.5,
                 colour="black", fill="lightgreen") +
  geom_density(alpha=.2, fill="#FF6666")+
  geom_line(data=NatLegdist, 
            aes(x = X, y = value, color = dist))

NatLegdist.gg

#natleg is normal

intleg dist

IntLeg <- veg.c.stack %>%
  filter(response == "introduced legume")
IntLeg$value <- IntLeg$value + 0.001

MASS::fitdistr(IntLeg$value, "normal")#$estimate [[1]]
##      mean         sd    
##   2.4715128   3.2913812 
##  (0.2151643) (0.1521442)
MASS::fitdistr(IntLeg$value, "Gamma")#$estimate [[1]]
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
##      shape         rate   
##   0.33371507   0.13502489 
##  (0.02457127) (0.01822881)
IntLegndist <- tibble(
  response = "introduced legume",
  dist = "normal",
  X = seq(0,28, 0.1),
  value = dnorm(X, mean = MASS::fitdistr(IntLeg$value, "normal")$estimate [[1]],
                sd = MASS::fitdistr(IntLeg$value, "normal")$estimate [[2]]))

IntLeggdist <- tibble(
  response = "introduced legume", 
  dist = "gamma", 
  X = seq(0, 28, 0.1),
  value = dgamma(X, shape = MASS::fitdistr(IntLeg$value, "Gamma")$estimate [[1]], 
                 rate = MASS::fitdistr(IntLeg$value, "Gamma")$estimate [[2]]))
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
IntLegdist <-rbind(IntLegndist, IntLeggdist)

IntLegdist.gg <- 
  IntLeg %>%
  ggplot(aes(x=value)) + theme_bw() + 
  geom_histogram(aes(y=..density..),      
                 binwidth=1.5,
                 colour="black", fill="lightgreen") +
  geom_density(alpha=.2, fill="#FF6666")+
  geom_line(data=IntLegdist, 
            aes(x = X, y = value, color = dist))

IntLegdist.gg

#intleg is normal

NatFrb dist

NatFrb <- veg.c.stack %>%
  filter(response == "native forb")
NatFrb$value <- NatFrb$value + 0.001

MASS::fitdistr(NatFrb$value, "normal")#$estimate [[1]]
##       mean          sd    
##   15.9061282    9.0303983 
##  ( 0.5903356) ( 0.4174303)
MASS::fitdistr(NatFrb$value, "Gamma")#$estimate [[1]]
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
##      shape       rate   
##   2.1001491   0.1320178 
##  (0.1808497) (0.0128332)
NatFrbndist <- tibble(
  response = "native forb",
  dist = "normal",
  X = seq(0,50, 0.1),
  value = dnorm(X, mean = MASS::fitdistr(NatFrb$value, "normal")$estimate [[1]],
                sd = MASS::fitdistr(NatFrb$value, "normal")$estimate [[2]]))

NatFrbgdist <- tibble(
  response = "native forb", 
  dist = "gamma", 
  X = seq(0, 50, 0.1),
  value = dgamma(X, shape = MASS::fitdistr(NatFrb$value, "Gamma")$estimate [[1]], 
                 rate = MASS::fitdistr(NatFrb$value, "Gamma")$estimate [[2]]))
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
NatFrbdist <-rbind(NatFrbndist, NatFrbgdist)

NatFrbdist.gg <- 
  NatFrb %>%
  ggplot(aes(x=value)) + theme_bw() + 
  geom_histogram(aes(y=..density..),      
                 binwidth=1.5,
                 colour="black", fill="lightgreen") +
  geom_density(alpha=.2, fill="#FF6666")+
  geom_line(data=NatFrbdist, 
            aes(x = X, y = value, color = dist))

NatFrbdist.gg

#natfrb is normal

intfrb dist

IntFrb <- veg.c.stack %>%
  filter(response == "introduced forb")
IntFrb$value <- IntFrb$value + 0.001

MASS::fitdistr(IntFrb$value, "normal")#$estimate [[1]]
##      mean         sd    
##   2.5629658   3.0110704 
##  (0.1968398) (0.1391868)
MASS::fitdistr(IntFrb$value, "Gamma")#$estimate [[1]]
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
##      shape         rate   
##   0.43904264   0.17130274 
##  (0.03310944) (0.02127196)
IntFrbndist <- tibble(
  response = "introduced forb",
  dist = "normal",
  X = seq(0,20, 0.1),
  value = dnorm(X, mean = MASS::fitdistr(IntFrb$value, "normal")$estimate [[1]],
                sd = MASS::fitdistr(IntFrb$value, "normal")$estimate [[2]]))

IntFrbgdist <- tibble(
  response = "introduced forb", 
  dist = "gamma", 
  X = seq(0, 20, 0.1),
  value = dgamma(X, shape = MASS::fitdistr(IntFrb$value, "Gamma")$estimate [[1]], 
                 rate = MASS::fitdistr(IntFrb$value, "Gamma")$estimate [[2]]))
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
IntFrbdist <-rbind(IntFrbndist, IntFrbgdist)

IntFrbdist.gg <- 
  IntFrb %>%
  ggplot(aes(x=value)) + theme_bw() + 
  geom_histogram(aes(y=..density..),      
                 binwidth=1.5,
                 colour="black", fill="lightgreen") +
  geom_density(alpha=.2, fill="#FF6666")+
  geom_line(data=IntFrbdist, 
            aes(x = X, y = value, color = dist))

IntFrbdist.gg

#intfrb is normal

natwdy dist

NatWdy <- veg.c.stack %>%
  filter(response == "native woody")
NatWdy$value <- NatWdy$value + 0.001

MASS::fitdistr(NatWdy$value, "normal")#$estimate [[1]]
##      mean         sd    
##   7.3988632   4.9351300 
##  (0.3226195) (0.2281265)
MASS::fitdistr(NatWdy$value, "Gamma")#$estimate [[1]]
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
##      shape         rate   
##   0.82834544   0.11195573 
##  (0.06628468) (0.01203771)
NatWdyndist <- tibble(
  response = "native woody",
  dist = "normal",
  X = seq(0,30, 0.1),
  value = dnorm(X, mean = MASS::fitdistr(NatWdy$value, "normal")$estimate [[1]],
                sd = MASS::fitdistr(NatWdy$value, "normal")$estimate [[2]]))

NatWdygdist <- tibble(
  response = "native woody", 
  dist = "gamma", 
  X = seq(0, 30, 0.1),
  value = dgamma(X, shape = MASS::fitdistr(NatWdy$value, "Gamma")$estimate [[1]], 
                 rate = MASS::fitdistr(NatWdy$value, "Gamma")$estimate [[2]]))
## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced

## Warning in densfun(x, parm[1], parm[2], ...): NaNs produced
NatWdydist <-rbind(NatWdyndist, NatWdygdist)

NatWdydist.gg <- 
  NatWdy %>%
  ggplot(aes(x=value)) + theme_bw() + 
  geom_histogram(aes(y=..density..),      
                 binwidth=1.5,
                 colour="black", fill="lightgreen") +
  geom_density(alpha=.2, fill="#FF6666")+
  geom_line(data=NatWdydist, 
            aes(x = X, y = value, color = dist))

NatWdydist.gg

#natwdy is normal