Transform data using I-splines

Description

Evaluates the I-splines for all variables of a data frame, as performed in Zeta.msgdm.

Usage

Ispline(dat, order.ispline = 2, kn.ispline = 1, rescale = 0)

Arguments

Value

Ispline returns a data frame with the same number of rows as dat and

ncol(dat) * (order.ispline + kn.ispline) columns.

References

Ramsay, J. O. (1988). Monotone regression splines in action. Statistical Science, 425-441.

Ferrier, S., Manion, G., Elith, J., & Richardson, K. (2007). Using generalized dissimilarity modelling to analyse and predict patterns of beta diversity in regional biodiversity assessment. Diversity and Distributions, 13(3), 252-264.

See Also

Zeta.msgdm

Examples

utils::data(bird.env.coarse)
data.env <- bird.env.coarse[,3:9]
data.env.splines <- Ispline(data.env)

Marion Island Environmental Dataset

Description

Geographic coordinates, altitude and island side (East, West) at 12 plots (4 transects and 3 altitudes) on Marion Island.

Usage

data(Marion.env)

Format

A data frame with 12 rows (plots) and 4 columns (variables).

Details

The data set contains the following variables:

• x: x-position in meters in UTM 37 projection

• y: y-position in meters in UTM 37 projection

• Altitude: mean elevation

• Side: cardinal (East or West) side of the island

Location: Marion Island – 46° 53' 34.2" S, 37 degrees 45' 02.3" E

Data owner: Melodie A. McGeoch

References

Nyakatya, M.J. & McGeoch, M.A. (2008). Temperature variation across Marion Island associated with a keystone plant species (Azorella selago Hook. (Apiaceae)). Polar Biology, 31, 139-151.

McGeoch, M.A., Le Roux, P.C., Hugo, E.A. & Nyakatya, M.J. (2008). Spatial variation in the terrestrial biotic system. The Prince Edward Islands: Land-Sea Interactions in a Changing World (ed. by S.L. Chown and P.W. Froneman), pp. 245-276. African SunMedia, Stellenbosch.

Marion Island Species Presence-Absence Dataset

Description

Inventory of springtails and mite species presence-absence in 12 plots (4 transects and 3 altitudes) on Marion Island.

Usage

data(Marion.species)

Format

A data frame with 12 rows (plots) and 33 columns (species).

Details

The data set contains the following variables:

• x: x-position in meters in UTM 37 South projection

• y: y-position in meters in UTM 37 South projection

• columns 3-24: mite species presence absence

• columns 25-33: springtail species presence absence

Location: Marion Island – 46° 53' 34.2" S, 37 degrees 45' 02.3" E

Data owner: Melodie A. McGeoch

References

Nyakatya, M.J. & McGeoch, M.A. (2008). Temperature variation across Marion Island associated with a keystone plant species (Azorella selago Hook. (Apiaceae)). Polar Biology, 31, 139-151.

McGeoch, M.A., Le Roux, P.C., Hugo, E.A. & Nyakatya, M.J. (2008). Spatial variation in the terrestrial biotic system. The Prince Edward Islands: Land-Sea Interactions in a Changing World (ed. by S.L. Chown and P.W. Froneman), pp. 245-276. African SunMedia, Stellenbosch.

Plots I-splines for Multi-Site Generalised Dissimilarity Modelling

Description

Plots I-splines computed by Return.ispline, or calls Return.ispline if the outputs from
Zeta.msgdm are provided before plotting.

Usage

Plot.ispline(
  isplines = NULL,
  msgdm,
  data.env,
  distance = FALSE,
  biotic = 0,
  pch = NULL,
  lty = NULL,
  legend = TRUE,
  lwd = 1,
  cex = 1,
  num.quantiles = 11
)

Arguments

Value

Plot.ispline returns a data frame with the same number of rows as dat and ncol(dat) *
(order.ispline + kn.ispline) columns.

References

Ramsay, J. O. (1988). Monotone regression splines in action. Statistical Science, 425-441.

Ferrier, S., Manion, G., Elith, J., & Richardson, K. (2007). Using generalized dissimilarity modelling to analyse and predict patterns of beta diversity in regional biodiversity assessment. Diversity and Distributions, 13(3), 252-264.

See Also

Zeta.msgdm

Examples

utils::data(Marion.species)
xy.marion <- Marion.species[1:2]
data.spec.marion <- Marion.species[3:33]

utils::data(Marion.env)
data.env.marion <- Marion.env[3]

zeta.ispline <- Zeta.msgdm(data.spec.marion, data.env.marion, xy.marion, sam = 100,
    order = 3, normalize = "Jaccard", reg.type = "ispline")
zeta.ispline
zeta.ispline.r <- Return.ispline(zeta.ispline, data.env.marion, distance = TRUE)
zeta.ispline.r

dev.new()
Plot.ispline(isplines = zeta.ispline.r, distance = TRUE)

dev.new()
Plot.ispline(msgdm = zeta.ispline, data.env = data.env.marion, distance = TRUE)

Zeta distance-decay plotting

Description

Plots the output of the function Zeta.ddecay.

Usage

Plot.zeta.ddecay(zeta.ddecay)

Arguments

Value

A plot of the zeta distance-decay with distance on the x-axis and the value of zeta on the y-axis.

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

See Also

Zeta.decline.mc, Zeta.order.mc, Zeta.decline.ex, Zeta.order.ex, Zeta.ddecay,

Zeta.ddecays

Examples

utils::data(bird.spec.coarse)
xy.bird <- bird.spec.coarse[,1:2]
data.spec.bird <- bird.spec.coarse[,3:193]

dev.new()
zeta.ddecay.bird <- Zeta.ddecay(xy.bird, data.spec.bird, sam = 100, order = 3,
    confint.level = 0.95,plot=FALSE)
Plot.zeta.ddecay(zeta.ddecay.bird)

##########

utils::data(Marion.species)
xy.marion <- Marion.species[,1:2]
data.spec.marion <- Marion.species[,3:33]

zeta.ddecay.marion <- Zeta.ddecay(xy.marion, data.spec.marion, sam = 100, order = 3,
    confint.level = 0.95, trsf = "log", normalize = "Jaccard",plot=FALSE)
dev.new()
Plot.zeta.ddecay(zeta.ddecay.marion)

Zeta distance-decay plotting for multiple orders

Description

Plots the output of the function Zeta.ddecays.

Usage

Plot.zeta.ddecays(zeta.ddecays)

Arguments

Value

A plot of the zeta distance-decay with the orders on the x-axis and the slope of the linear distance-decays on the y-axis.

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

See Also

Zeta.decline.mc, Zeta.order.mc, Zeta.decline.ex, Zeta.order.ex, Zeta.ddecays,

Zeta.ddecay, Plot.zeta.ddecay

Examples

utils::data(bird.spec.coarse)
xy.bird <- bird.spec.coarse[,1:2]
data.spec.bird <- bird.spec.coarse[,3:193]

dev.new()
zeta.ddecays.bird <- Zeta.ddecays(xy.bird, data.spec.bird, sam = 100, orders = 2:5,
    plot = FALSE, confint.level = 0.95)
Plot.zeta.ddecays(zeta.ddecays.bird)

##########

utils::data(Marion.species)
xy.marion <- Marion.species[,1:2]
data.spec.marion <- Marion.species[,3:33]

dev.new()
zeta.ddecays.marion <- Zeta.ddecays(xy.marion, data.spec.marion, sam = 100,
   orders = 2:5, plot = FALSE, confint.level = 0.95)
Plot.zeta.ddecays(zeta.ddecays.marion)

Zeta diversity decline plotting

Description

Plots the output of the functions Zeta.decline.mc and Zeta.decline.ex.

Usage

Plot.zeta.decline(zeta, sd.plot = TRUE, arrange.plots = TRUE)

Arguments

Value

A plot of the zeta decline with 4 subplots displaying (i) the raw decline, (ii) the ratios of the zeta values (computed as \zeta_i / \zeta_{i-1}), (iii) the fit in a log plot and (iv) the fit in a log-log plot.

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

See Also

Zeta.decline.mc, Zeta.order.mc, Zeta.decline.ex, Zeta.order.ex

Examples

utils::data(bird.spec.coarse)
xy.bird <- bird.spec.coarse[1:2]
data.spec.bird <- bird.spec.coarse[3:193]

dev.new(width = 12, height = 4)
zeta.bird <- Zeta.decline.mc(data.spec.bird, orders = 1:5, sam=100, plot = FALSE)
Plot.zeta.decline(zeta.bird)

##########

utils::data(Marion.species)
xy.marion <- Marion.species[1:2]
data.spec.marion <- Marion.species[3:33]

dev.new(width = 12, height = 4)
zeta.marion <- Zeta.decline.ex(data.spec.marion, orders = 1:5, plot = FALSE)
Plot.zeta.decline(zeta.marion)

Plotting of zeta diversity scaling with sample grain dependency based on the minimum distance between sites

Description

Plots the output of the function Zeta.scale.min.dist.

Usage

Plot.zeta.scale.min.dist(
  zeta.scale.irreg,
  size.init = 1,
  add = FALSE,
  ylim = NULL,
  col = "black"
)

Arguments

Value

A plot of the zeta diversity scaling with the mapping grain m (the number of sites combined to generate data at a coarser grain) on the x-axis and the value of zeta on the y-axis.

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

Scheiner S.M., Chiarucci A., Fox G.A., Helmus M.R., McGlinn D.J. & Willig M.R. (2011). The underpinnings of the relationship of species richness with space and time. Ecological Monographs, 81, 195-213.

See Also

Zeta.decline.mc, Zeta.order.mc, Zeta.decline.ex, Zeta.order.ex,

Zeta.scale.min.dist, rescale.regular, Zeta.scale.regular, rescale.regular,

Plot.zeta.scale.regular

Examples

utils::data(Marion.species)
xy.marion <- Marion.species[,1:2]
data.spec.marion <- Marion.species[,3:33]

zeta.scale.irreg.species <- Zeta.scale.min.dist(xy.marion, data.spec.marion, m = 1:3,
    order = 3, reorder = 3, sam = 50, normalize = "Jaccard",plot=FALSE)
dev.new()
Plot.zeta.scale.min.dist(zeta.scale.irreg.species)

Plotting of zeta diversity scaling with sample grain using hierarchical increases in grain size

Description

Plots the output of the function Zeta.scale.regular.

Usage

Plot.zeta.scale.regular(
  zeta.scale.reg,
  size.init = 1,
  add = FALSE,
  ylim = NULL,
  col = "black"
)

Arguments

Value

A plot of the zeta diversity scaling with the mapping grain n x n (the number of sites combined to generate data at a coarser grain) on the x-axis and the value of zeta on the y-axis.

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

Scheiner S.M., Chiarucci A., Fox G.A., Helmus M.R., McGlinn D.J. & Willig M.R. (2011). The underpinnings of the relationship of species richness with space and time. Ecological Monographs, 81, 195-213.

See Also

Zeta.decline.mc, Zeta.order.mc, Zeta.decline.ex, Zeta.order.ex,

Zeta.scale.regular, Zeta.scale.min.dist, rescale.regular,

Plot.zeta.scale.min.dist

Examples

utils::data(bird.spec.fine)
xy.bird <- bird.spec.fine[1:400,1:2]
data.spec.bird <- bird.spec.fine[1:400,3:192]

##sam = 25 is used here for fast execution, but a higher value is advised
zeta.scale.reg <- Zeta.scale.regular(xy.bird, data.spec.bird, n = 1:3, order = 3,
    sam = 25, normalize = "Jaccard",plot=FALSE)
dev.new()
Plot.zeta.scale.regular(zeta.scale.reg)

Predict zeta values for new environmental and distance data

Description

Predict the zeta values for new environmental and distance data from the models returned by Zeta.msgdm.

Usage

Predict.msgdm(model.msgdm, reg.type, newdata, type = "response")

Arguments

Value

Predict.msgdm returns a vector of predicted zeta values.

References

Ramsay, J. O. (1988). Monotone regression splines in action. Statistical Science, 425-441.

Ferrier, S., Manion, G., Elith, J., & Richardson, K. (2007). Using generalized dissimilarity modelling to analyse and predict patterns of beta diversity in regional biodiversity assessment. Diversity and Distributions, 13(3), 252-264.

See Also

Zeta.msgdm

Examples

utils::data(bird.spec.fine)
xy.bird <- bird.spec.fine[1:500,1:2]
data.spec.bird <- bird.spec.fine[1:500,3:192]
utils::data(bird.env.fine)
data.env.bird1 <- bird.env.fine[1:500,3:9] ##training data
data.env.bird2 <- bird.env.fine[501:604,3:9] ##data to predict on

##glm
zeta.glm <- Zeta.msgdm(data.spec.bird, data.env.bird1, sam = 100, order = 3, 
                         reg.type = "glm")
newdata <- data.frame(matrix(NA,100,ncol(data.env.bird1)))
names(newdata) <- names(data.env.bird1)
for(z in 1:100){
  samp <- sample(1:104, 3, replace = FALSE)
  newdata[z,] <- apply(apply(data.env.bird2[samp,], 2,
                             stats::dist), 2, mean)
}
##rescale the data like during MS-GDM
newdata <- newdata/matrix(rep(zeta.glm$rescale.factor,100),
                          100,length(zeta.glm$rescale.factor),byrow=TRUE)
new.zeta.glm <- Predict.msgdm(model.msgdm = zeta.glm$model, reg.type = "glm",
                              newdata = newdata)

##I-splines
zeta.ispline <- Zeta.msgdm(data.spec.bird, data.env.bird1, sam = 100, order = 3,
                           reg.type = "ispline", normalize = "Jaccard")
data.env.bird.splines <- Ispline(data.env.bird2)
newdata <- data.frame(matrix(NA,100,ncol(data.env.bird.splines$splines)))
names(newdata) <- names(data.env.bird.splines$splines)
for(z in 1:100){
  samp <- sample(1:104, 3, replace = FALSE)
  newdata[z,] <- apply(apply(data.env.bird.splines$splines[samp,], 2, stats::dist),
                       2, mean)
}

##rescale the data like during MS-GDM
newdata <- newdata/matrix(rep(zeta.ispline$rescale.factor,100),
                          100,length(zeta.ispline$rescale.factor),byrow=TRUE)
new.zeta.ispline <- Predict.msgdm(model.msgdm = zeta.ispline$model, reg.type = "ispline",
                                  newdata = newdata)

Perform an I-spline regression

Description

Evaluates the I-splines for all variables of a data frame of predictor variables, and perform a generalised linear regression with constraint on the parameters.

Usage

Reg.ispline(
  response,
  predictor,
  order.ispline = 2,
  kn.ispline = 1,
  family = stats::gaussian(),
  method.glm = "glm.fit.cons",
  cons = 1,
  cons.inter = 1,
  control = list(),
  Plot = TRUE,
  lty = NULL,
  lwd = 1
)

Arguments

Details

Reg.ispline performs a non-linear regression using a combination of GLM and I-splines. It can, for example, be used to compare regression outputs when using MS-GDM with I-splines on environmental variables and biotic variables as in Zetya.msgdm to the same regression approach without environmental variables.

Value

Reg.ispline returns a list of the following elements:

.

.

References

Ramsay, J. O. (1988). Monotone regression splines in action. Statistical Science, 425-441.

See Also

Zeta.msgdm,Ispline

Examples

utils::data(Marion.species)
xy.marion <- Marion.species[1:2]

data.spec.marion <- Marion.species[3:33]

##random other communities
data.spec.marion2a <- data.spec.marion
data.spec.marion2a[which(data.spec.marion2a==1,arr.ind=TRUE)] <- 0
for(i in 1:ncol(data.spec.marion2a))
  data.spec.marion2a[sample(nrow(data.spec.marion2a),8),i] <- 1
data.spec.marion2b <- data.spec.marion
data.spec.marion2b[which(data.spec.marion2b==1,arr.ind=TRUE)] <- 0
for(i in 1:ncol(data.spec.marion2b))
data.spec.marion2b[sample(nrow(data.spec.marion2b),8),i] <- 1

dat.spec.tot <- list(data.spec.marion,data.spec.marion2a,data.spec.marion2b)
zeta.tot <- Zeta.order.mc.mult(data.spec=dat.spec.tot,order=3,sam=200)
zeta.splines <- Ispline(zeta.tot$zeta.val[,2:3])
data.tot <- data.frame(zeta.val=zeta.tot$zeta.val[,1],zeta.splines$splines)

dev.new()
Reg.ispline(response = zeta.tot$zeta.val[,1], predictor = zeta.tot$zeta.val[,2:3], 
                         lwd=2, cons=1)

Computing splines coordinates from I-spline-based multi-site generalised dissimilarity modelling

Description

Stores the coordinates of the I-splines resulting from Zeta.msgdm for plotting.

Usage

Return.ispline(msgdm, data.env, distance = FALSE, biotic = 0)

Arguments

Details

Return.ispline allows to store the same number of coordinates for all I-splines, to average replicates and obtain confidence intervals.

Value

Return.ispline returns a list containing the following components used to plot the I-splines:

See Also

Zeta.msgdm, Ispline

Examples

utils::data(Marion.species)
xy.marion <- Marion.species[1:2]
data.spec.marion <- Marion.species[3:33]

utils::data(Marion.env)
data.env.marion <- Marion.env[3]

zeta.ispline <- Zeta.msgdm(data.spec.marion, data.env.marion, xy.marion, sam = 100,
    order = 3, normalize = "Jaccard", reg.type = "ispline")
zeta.ispline
zeta.ispline.r <- Return.ispline(zeta.ispline, data.env.marion, distance = TRUE)
zeta.ispline.r

dev.new()
Plot.ispline(isplines = zeta.ispline.r, distance = TRUE)

dev.new()
Plot.ispline(msgdm = zeta.ispline, data.env = data.env.marion, distance = TRUE)

Zeta distance decay for a specific number of assemblages or sites

Description

Computes the distance decay of zeta diversity for a specific order (number of assemblages or sites), using either a generalised linear model with possible constraint on the coefficients, a generalised additive model, or a shape constrained additive model.

Usage

Zeta.ddecay(
  xy,
  data.spec,
  order = 2,
  sam = 1000,
  distance.type = "Euclidean",
  dist.custom = NULL,
  method = "mean",
  reg.type = "glm",
  family = stats::gaussian(),
  method.glm = "glm.fit.cons",
  cons = -1,
  cons.inter = 1,
  confint.level = 0.95,
  kn = -1,
  bs = "mpd",
  trsf = "NULL",
  cutoff = NULL,
  rescale = FALSE,
  normalize = FALSE,
  empty.row = "remove",
  plot = TRUE
)

Arguments

Value

Zeta.ddecay returns a list containing the following components:

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

See Also

Zeta.decline.mc, Zeta.order.mc, Zeta.decline.ex, Zeta.order.ex, Zeta.ddecays,

Plot.zeta.ddecay

Examples

utils::data(bird.spec.coarse)
xy.bird <- bird.spec.coarse[,1:2]
data.spec.bird <- bird.spec.coarse[,3:193]

dev.new()
zeta.ddecay.bird <- Zeta.ddecay(xy.bird, data.spec.bird, sam = 100, order = 3,
    method.glm = "glm.fit2", confint.level = 0.95)
    
dev.new()
zeta.ddecay.bird <- Zeta.ddecay(data.spec=data.spec.bird, distance.type = "custom",
    dist.custom = as.matrix(dist(xy.bird)), cutoff = 800000, sam = 100, order = 3,
    reg.type = "gam", confint.level = 0.95)

##########

utils::data(Marion.species)
xy.marion <- Marion.species[,1:2]
data.spec.marion <- Marion.species[,3:33]

dev.new()
zeta.ddecay.marion <- Zeta.ddecay(xy.marion, data.spec.marion, sam = 100, order = 3,
    method.glm = "glm.fit2", confint.level = 0.95, trsf = "log", normalize = "Jaccard")

Zeta distance decay for a range of numbers of assemblages or sites

Description

Computes the distance decay of zeta diversity for a range of orders (number of assemblages or sites), using generalised linear models.

Usage

Zeta.ddecays(
  xy,
  data.spec,
  orders = 2:10,
  sam = 1000,
  family = stats::gaussian(),
  distance.type = "Euclidean",
  dist.custom = NULL,
  method = "mean",
  confint.level = 0.95,
  trsf = "NULL",
  cutoff = NULL,
  rescale = FALSE,
  normalize = FALSE,
  plot = TRUE
)

Arguments

Value

Zeta.ddecays returns a list containing the following components:

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

See Also

Zeta.decline.mc, Zeta.order.mc, Zeta.decline.ex, Zeta.order.ex, Zeta.ddecay

Examples

utils::data(bird.spec.coarse)
xy.bird <- bird.spec.coarse[,1:2]
data.spec.bird <- bird.spec.coarse[,3:193]

dev.new()
zeta.ddecays.bird <- Zeta.ddecays(xy.bird, data.spec.bird, sam = 100, orders = 2:5,
    plot = TRUE, confint.level = 0.95)

##########

utils::data(Marion.species)
xy.marion <- Marion.species[,1:2]
data.spec.marion <- Marion.species[,3:33]

dev.new()
zeta.ddecays.marion <- Zeta.ddecays(xy.marion, data.spec.marion, sam = 100,
   orders = 2:5, plot = TRUE, confint.level = 0.95)

Expectation of zeta diversity decline

Description

Computes the expectation of zeta diversity, the number of species shared by multiple assemblages for a range of orders (number of assemblages or sites), using a formula based on the occupancy of the species, and fits the decline to an exponential and a power law relationship.

Usage

Zeta.decline.ex(
  data.spec,
  orders = 1:10,
  sd.correct = TRUE,
  confint.level = 0.95,
  sd.plot = TRUE,
  rescale = FALSE,
  empty.row = "empty",
  plot = TRUE
)

Arguments

Details

Zeta.decline.ex is much faster than Zeta.decline.mc to compute the exact value of zeta diversity when the number of species is lower than C^N_{i}, where N is the total number of sites and i is the order of zeta.

sd.correct should be set to TRUE if the assemblages represent a subsample of the whole system. It can be set to FALSE if the sampling is exhaustive, for example in case of a continuous regular grid covering the whole study area.

The exponential and the power law fit are performed using linear regressions on log-transformed data (only the zeta values are log-transformed for the exponential fit, and both the orders and the zeta values are log-transformed for the power law fit).

Value

Zeta.decline.ex returns a list containing the following components:

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

McGeoch M. A., Latombe G., Andrew N. R., Nakagawa S., Nipperess D. A., Roige M., Marzinelli E. M., Campbell A. H., Verges A., Thomas T., Steinberg P. D., Selwood K. E., Henriksen M. V. & Hui C. (2019). Measuring continuous compositional change using decline and decay in zeta diversity. Ecology, 100(11), e02832.

See Also

Zeta.decline.mc, Zeta.order.mc, Zeta.order.ex, Plot.zeta.decline

Examples

utils::data(bird.spec.coarse)
data.spec.bird <- bird.spec.coarse[,3:193]

dev.new(width = 12, height = 4)
zeta.bird <- Zeta.decline.ex(data.spec.bird, orders = 1:5)
zeta.bird

##########

utils::data(Marion.species)
xy.marion <- Marion.species[,1:2]
data.spec.marion <- Marion.species[,3:33]

dev.new(width = 12, height = 4)
zeta.marion <- Zeta.decline.ex(data.spec.marion, orders = 1:5)
zeta.marion

Zeta diversity decline using Monte Carlo sampling

Description

Computes zeta diversity, the number of species shared by multiple assemblages, for a range of orders (number of assemblages or sites), using combinations of sampled sites, and fits the decline to an exponential and a power law relationship.

Usage

Zeta.decline.mc(
  data.spec,
  xy = NULL,
  orders = 1:10,
  sam = 1000,
  sd.correct = TRUE,
  sd.correct.adapt = FALSE,
  confint.level = 0.95,
  sd.plot = TRUE,
  rescale = FALSE,
  normalize = FALSE,
  NON = FALSE,
  FPO = NULL,
  DIR = FALSE,
  empty.row = "empty",
  plot = TRUE,
  silent = TRUE
)

Arguments

Details

If the number of combinations of sites is lower than the value of the parameter sam, all the combinations are used and an exact solution is computed. In that case, using the number of site combinations as the denominator may be appropriate to compute the standard deviation, if all sites were sampled and the zeta values. This can be adjusted with parameters sd.correct and sd.correct.adapt.

Zeta.decline.mc is faster than Zeta.decline.ex to compute the exact value of zeta diversity when the number of species is higher than C^N_{i}, where N is the total number of sites and i is the order of zeta.

The exponential and the power law fit are performed using linear regressions on log-transformed data (only the zeta values are log-transformed for the exponential fit, and both the orders and the zeta values are log-transformed for the power law fit).

Zeta.decline.mc enables accomodating richness heterogeneity by setting normalize =
"Jaccard", normalize = "Sorensen" or normalize = "Simpson". This cannot be performed by
Zeta.decline.ex.

Value

Zeta.decline.mc returns a list containing the following components:

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

See Also

Zeta.decline.ex, Zeta.order.ex, Zeta.order.mc, Plot.zeta.decline

Examples

utils::data(bird.spec.coarse)
xy.bird <- bird.spec.coarse[,1:2]
data.spec.bird <- bird.spec.coarse[,3:193]

dev.new(width = 12, height = 4)
zeta.bird <- Zeta.decline.mc(data.spec.bird, xy.bird, orders = 1:5, sam = 100,
   NON = TRUE)
zeta.bird

##########

utils::data(Marion.species)
xy.marion <- Marion.species[,1:2]
data.spec.marion <- Marion.species[,3:33]

dev.new(width = 12, height = 4)
zeta.marion <- Zeta.decline.mc(data.spec.marion, orders = 1:5, sam = 100,
     normalize = "Jaccard")
zeta.marion

Multi-site generalised dissimilarity modelling for a set of environmental variables and distances

Description

Computes a regression model of zeta diversity for a given order (number of assemblages or sites) against a set of environmental variables and distances between sites. The different regression models available are generalised linear models, generalised linear models with negative constraints, generalised additive models, shape constrained additive models, and I-splines.

Usage

Zeta.msgdm(
  data.spec,
  data.env,
  xy = NULL,
  data.spec.pred = NULL,
  order = 1,
  sam = 1000,
  reg.type = "ispline",
  family = NULL,
  method.glm = "glm.fit.cons",
  cons = -1,
  cons.inter = NULL,
  confint.level = 0.95,
  bs = "mpd",
  kn = -1,
  order.ispline = 2,
  kn.ispline = 1,
  distance.type = "Euclidean",
  dist.custom = NULL,
  rescale = FALSE,
  rescale.pred = TRUE,
  method = "mean",
  normalize = "Simpson",
  silent = FALSE,
  empty.row = 0,
  control = list(),
  glm.init = FALSE
)

Arguments

Details

The environmental variables can be numeric or factorial.

If order = 1, the variables are used as such in the regression, and factorial variables must be dummy for the output of the regression to be interpretable.

For numeric variables, if order>1 the pairwise difference between sites is computed and combined according to method. For factorial variables, the distance corresponds to the number of unique values over the number of assemblages of sites specified by order.

If xy = NULL, Zeta.msgdm only uses environmental variables in the regression. Otherwise, it also computes and uses euclidian distance (average or maximum distance between multiple sites, depending on the parameters method) as an explanatory variable.

If rescale.pred = TRUE, zeta is regressed against the differences of values of the environmental variables divided by the maximum difference for each variable, to be rescaled between 0 and 1. If !is.null(xy), distances between sites are also divided by the maximum distance. If order = 1, the variables are transformed by first subtracting their minimum value, and dividing by the difference of their maximum and minimum values.

If reg.type = "ispline", the variables are rescaled between 0 and 1 prior to computing the I-splines by subtracting their minimum value, and dividing by the difference of their maximum and minimum values.

Value

Zeta.msgdm returns a list whose component vary depending on the regression technique. The list can contain the following components:

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

Ferrier, S., Manion, G., Elith, J., & Richardson, K. (2007). Using generalized dissimilarity modelling to analyse and predict patterns of beta diversity in regional biodiversity assessment. Diversity and Distributions, 13(3), 252-264.

See Also

Zeta.decline.mc, Zeta.order.mc, Zeta.decline.ex, Zeta.order.ex, Predict.msgdm,

Ispline

Examples

utils::data(bird.spec.coarse)
xy.bird <- bird.spec.coarse[1:2]
data.spec.bird <- bird.spec.coarse[3:193]
utils::data(bird.env.coarse)
data.env.bird <- bird.env.coarse[,3:9]

zeta.glm <- Zeta.msgdm(data.spec.bird, data.env.bird, sam = 100, order = 3,
                               reg.type = "glm")
zeta.glm
dev.new()
graphics::plot(zeta.glm$model)

zeta.ngls <- Zeta.msgdm(data.spec.bird, data.env.bird, xy.bird, sam = 100, order = 3,
    reg.type = "ngls", rescale = TRUE)
zeta.ngls

##########

utils::data(Marion.species)
xy.marion <- Marion.species[1:2]
data.spec.marion <- Marion.species[3:33]
utils::data(Marion.env)
data.env.marion <- Marion.env[3]

zeta.gam <- Zeta.msgdm(data.spec.marion, data.env.marion, sam = 100, order = 3,
    reg.type = "gam")
zeta.gam
dev.new()
graphics::plot(zeta.gam$model)

zeta.ispline <- Zeta.msgdm(data.spec.marion, data.env.marion, xy.marion, sam = 100,
    order = 3, normalize = "Jaccard", reg.type = "ispline")
zeta.ispline

zeta.ispline.r <- Return.ispline(zeta.ispline, data.env.marion, distance = TRUE)
zeta.ispline.r

dev.new()
Plot.ispline(isplines = zeta.ispline.r, distance = TRUE)

dev.new()
Plot.ispline(msgdm = zeta.ispline, data.env = data.env.marion, distance = TRUE)

Expectation of zeta diversity for a specific number of assemblages or sites

Description

Computes the expectation of zeta diversity, the number of species shared by multiple assemblages, for a specific order (number of assemblages or sites) using a formula based on the occupancy of the species.

Usage

Zeta.order.ex(
  data.spec,
  order = 1,
  sd.correct = TRUE,
  rescale = FALSE,
  empty.row = "empty"
)

Arguments

Details

Zeta.order.ex is much faster than Zeta.order.mc to compute the exact value of zeta diversity when the number of species is lower than C^N_{i}, where N is the total number of sites and i is the order of zeta.

sd.correct should be set to TRUE if the assemblages represent a subsample of the whole system. It can be set to FALSE if the sampling is exhaustive, for example in case of a continuous regular grid covering the whole study area.

Value

zeta.order.ex returns a list containing the following components:

References

Hui C. & McGeoch M.A. (2014). zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

McGeoch M. A., Latombe G., Andrew N. R., Nakagawa S., Nipperess D. A., Roige M., Marzinelli E. M., Campbell A. H., Verges A., Thomas T., Steinberg P. D., Selwood K. E., Henriksen M. V. & Hui C. (2019). Measuring continuous compositional change using decline and decay in zeta diversity. Ecology, 100(11), e02832.

See Also

Zeta.order.mc, Zeta.decline.ex, Zeta.decline.mc

Examples

utils::data(bird.spec.coarse)
data.spec.bird <- bird.spec.coarse[,3:193]

zeta.bird <- Zeta.order.ex(data.spec.bird, order = 3)
zeta.bird

##########

utils::data(Marion.species)
data.spec.marion <- Marion.species[,3:33]

zeta.marion <- Zeta.order.ex(data.spec.marion, order = 3)
zeta.marion

Zeta diversity for a specific number of assemblages or sites using Monte Carlo sampling

Description

Computes zeta diversity, the number of species shared by multiple assemblages, for a specific order (number of assemblages or sites).

Usage

Zeta.order.mc(
  data.spec,
  xy = NULL,
  order = 1,
  sam = 1000,
  sd.correct = TRUE,
  sd.correct.adapt = FALSE,
  rescale = FALSE,
  normalize = FALSE,
  NON = FALSE,
  FPO = NULL,
  DIR = FALSE,
  empty.row = "empty",
  silent = TRUE
)

Arguments

Details

If the number of combinations of sites is lower than the value of the parameter sam, all the combinations are used and an exact solution is computed. In that case, using the number of site combinations as the denominator may be appropriate to compute the standard deviation, if all sites were sampled and the zeta values. This can be adjusted with parameters sd.correct and sd.correct.adapt.

Zeta.order.mc is faster than Zeta.order.ex to compute the exact value of zeta diversity when the number of species is higher than C^N_{i}, where N is the total number of sites and i is the order of zeta.

Zeta.order.mc enables accomodating richness heterogeneity by setting normalize = "Jaccard", normalize = "Sorensen" or normalize = "Simpson". This cannot be performed by
Zeta.order.ex.

Value

Zeta.order.mc returns a list containing the following components:

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

See Also

Zeta.decline.mc

Examples

utils::data(bird.spec.coarse)
xy.bird <- bird.spec.coarse[,1:2]
data.spec.bird <- bird.spec.coarse[,3:193]

zeta.bird <- Zeta.order.mc(data.spec.bird, order = 3, sam=100)
zeta.bird

##########

utils::data(Marion.species)
xy.marion <- Marion.species[,1:2]
data.spec.marion <- Marion.species[,3:33]

zeta.marion <- Zeta.order.mc(data.spec.marion, xy.marion, order = 3, sam = 100,
   NON = TRUE)
zeta.marion

Number of species in common between a specific number of assemblages or sites using Monte Carlo sampling, for multiple combinations and several groups of taxa

Description

Computes the number of species shared by multiple assemblages, for a specific order (number of assemblages or sites), for multiple combinations and several groups of taxa.

Usage

Zeta.order.mc.mult(
  data.spec,
  xy = NULL,
  order = 1,
  sam = 1000,
  sd.correct = TRUE,
  sd.correct.adapt = FALSE,
  rescale = FALSE,
  normalize = FALSE,
  NON = FALSE,
  FPO = NULL,
  DIR = FALSE,
  empty.row = "empty",
  silent = TRUE
)

Arguments

Details

Contrary to Zeta.order.mc, the number of species shared by the different combinations of assemblages are not averaged, but returned as is. This is useful to then compare local zeta diversity for different groups of taxa.

As for Zeta.order.mc, if the number of combinations of sites is lower than the value of the parameter sam, all the combinations are used and an exact solution is computed. In that case, using the number of site combinations as the denominator may be appropriate to compute the standard deviation, if all sites were sampled and the zeta values. This can be adjusted with parameters sd.correct and sd.correct.adapt.

Value

Zeta.order.mc.mult returns a list containing the following components:

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

See Also

Zeta.decline.mc

Examples

utils::data(Marion.species)
xy.marion <- Marion.species[1:2]

data.spec.marion <- Marion.species[3:33]

##random other communities
data.spec.marion2a <- data.spec.marion
data.spec.marion2a[which(data.spec.marion2a==1,arr.ind=TRUE)] <- 0
for(i in 1:ncol(data.spec.marion2a))
  data.spec.marion2a[sample(nrow(data.spec.marion2a),8),i] <- 1
data.spec.marion2b <- data.spec.marion
data.spec.marion2b[which(data.spec.marion2b==1,arr.ind=TRUE)] <- 0
for(i in 1:ncol(data.spec.marion2b))
data.spec.marion2b[sample(nrow(data.spec.marion2b),8),i] <- 1

dat.spec.tot <- list(data.spec.marion,data.spec.marion2a,data.spec.marion2b)
zeta.tot <- Zeta.order.mc.mult(data.spec=dat.spec.tot,order=3,sam=200)

Sensitivity analysis for the sample size of zeta

Description

Computes zeta diversity for a given order (number of assemblages or sites) for a range of sample sizes, to assess the sensitivity to this parameter.

Usage

Zeta.sam.sensitivity(
  data.spec,
  xy = NULL,
  order = 1,
  sam.seq,
  reps = 20,
  sd.correct = TRUE,
  sd.correct.adapt = FALSE,
  rescale = FALSE,
  normalize = FALSE,
  NON = FALSE,
  FPO = NULL,
  DIR = FALSE,
  display = TRUE,
  plot = TRUE,
  notch = TRUE
)

Arguments

Details

Note that the execution of Zeta.sam.sensitivity can be quite lengthy, because of the number of replicates needed.

Value

Zeta.sam.sensitivity returns a matrix with (sam.max-sam.min)/sam.incr columns and reps rows.

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

See Also

Zeta.decline.mc, Zeta.order.mc, Zeta.decline.ex, Zeta.order.ex

Zeta diversity scaling with sample grain dependency based on the minimum distance between sites

Description

Computes zeta diversity scaling with sample grain for a specific order (number of assemblages or sites), increasing grain by sequentially adding sites based on the minimum distance between them.

Usage

Zeta.scale.min.dist(
  xy,
  data.spec,
  m,
  order = 1,
  reorder = 100,
  shuffle = TRUE,
  sam = 1000,
  method = "mean",
  rescale = FALSE,
  normalize = FALSE,
  plot = TRUE,
  sd = TRUE,
  distance.type = "Euclidean",
  dist.custom = NULL,
  zeta.type = "exact"
)

Arguments

Details

The nearest neighbouring sites (plots, quadrates, or areas of varying shapes) are grouped as spatial clusters of 2, 3, 4, etc. sites, based on the minimum distance between them. Since the procedure is based on the relative distance between sites, the site order can have an impact on the output. The procedure is therefore performed 'reorder' times, for which sites are randomly reordered each time, and the mean zeta is computed. This function is suitable for both regularly and irregularly spaced sites, contiguous or non contiguous (sensu Scheiner et al., 2011). For regularly spaced sites, the use of Zeta.scale.regular is recommended.

Value

zeta.scale.min.dist returns a list containing the following components:

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

Scheiner S.M., Chiarucci A., Fox G.A., Helmus M.R., McGlinn D.J. & Willig M.R. (2011). The underpinnings of the relationship of species richness with space and time. Ecological Monographs, 81, 195-213.

See Also

Zeta.decline.mc, Zeta.order.mc, Zeta.decline.ex, Zeta.order.ex,

Zeta.scale.regular, rescale.regular

Examples

utils::data(Marion.species)
xy.marion <- Marion.species[,1:2]
data.spec.marion <- Marion.species[,3:33]

dev.new()
zeta.scale.irreg.species <- Zeta.scale.min.dist(xy.marion, data.spec.marion, m = 1:3,
    order = 3, reorder = 3, sam = 50, normalize = "Jaccard")

Zeta diversity scaling with sample grain using hierarchical increases in grain size

Description

Computes zeta diversity scaling with sample grain for a specific order (number of assemblages or sites), increasing grain by hierarchically nesting of regularly spaced sites.

Usage

Zeta.scale.regular(
  xy,
  data.spec,
  n,
  order = 1,
  sam = 1000,
  method = "mean",
  rescale = FALSE,
  normalize = FALSE,
  plot = TRUE,
  zeta.type = "exact"
)

Arguments

Details

The sites (plots or quadrates) are incrementally aggregated as nearest neighbouring groups of 4, 9, etc. sites, using a nested approach, starting from the lowest x and y, to increase the grain. The sites can be spatially contiguous or discontiguous, as long as they are regularly spaced (see Scheiner et al., 2011). If the total number of sites is not a multiple of n[i] x n[i], the extra sites are discarded.

Value

Zeta.scale.regular returns a list containing the following components:

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

Scheiner S.M., Chiarucci A., Fox G.A., Helmus M.R., McGlinn D.J. & Willig M.R. (2011). The underpinnings of the relationship of species richness with space and time. Ecological Monographs, 81, 195-213.

See Also

Zeta.decline.mc, Zeta.order.mc, Zeta.decline.ex, Zeta.order.ex

Zeta.scale.min.dist, rescale.regular, rescale.min.dist

Examples

utils::data(bird.spec.fine)
xy.bird <- bird.spec.fine[1:400,1:2]
data.spec.bird <- bird.spec.fine[1:400,3:192]

dev.new()
##sam = 25 is used here for fast execution, but a higher value is advised
zeta.scale.reg <- Zeta.scale.regular(xy.bird, data.spec.bird, n = 1:3, order = 3,
    sam = 25, normalize = "Jaccard", zeta.type="monte carlo")

Variation partitioning for zeta diversity

Description

Variation partitioning of zeta diversity for a specific order (number of assemblages or sites) over distance and environmental variables.

Usage

Zeta.varpart(
  msgdm.mod,
  num.part = 2,
  reg.type = "glm",
  family = stats::gaussian(),
  method.glm = "glm.fit.cons",
  cons = -1,
  cons.inter = 1,
  kn = -1,
  bs = "mpd"
)

Arguments

Details

Note that, for a given regression, the variation explained is computed as 1-(RSS/TSS)*(v-1)/(v-p-1), where RSS is the residual sum of squares and TSS is the total sum of squares, v is the number of variables used in the regression (which is greater than the original number of variables for I-splines) and p is the number of samples. 1-(RSS/TSS) corresponds to the classical R-squared for linear regression only, and results for non-linear regressions should be interpreted with caution.

The environmental variables can be numeric or factorial, and order must be greater than 1.

For numeric variables, the pairwise difference between sites is computed and combined according to method. For factorial variables, the distance corresponds to the number of unique values over the number of assemblages of sites specified by order.

Zeta is regressed against the differences of values of the environmental variables divided by the maximum difference for each variable, to be rescaled between 0 and 1. If !is.null(xy), distances between sites are also divided by the maximum distance.

Value

Zeta.varpart returns a data frame with one column containing the variation explained by each component a (the variation explained by distance alone), b (the variation explained by either distance or the environment), c (the variation explained by the environment alone) and d (the unexplained variation).

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

Borcard, D., Legendre, P. & Drapeau, P. (1992). Partialling out the spatial component of ecological variation. Ecology 73, 1045-1055.

Legendre, P. & Legendre, L.F. (2012). Numerical ecology, 3rd English edition. Elsevier Science BV, Amsterdam.

See Also

Zeta.decline.mc, Zeta.order.mc, Zeta.decline.ex, Zeta.order.ex, Zeta.msgdm, pie.neg

Examples

utils::data(bird.spec.coarse)
xy.bird <- bird.spec.coarse[,1:2]
data.spec.bird <- bird.spec.coarse[,3:193]
utils::data(bird.env.coarse)
data.env.bird <- bird.env.coarse[,3:9]

zeta.bird <- Zeta.msgdm(data.spec.bird, data.env.bird, xy.bird, sam = 100, order = 3)
zeta.varpart.bird <- Zeta.varpart(zeta.bird, method.glm = "glm.fit2")
zeta.varpart.bird
dev.new()
pie.neg(zeta.varpart.bird[4:7,1], density = c(4, 0, 8, -1),
    angle = c(90, 0, 0, 0),
    labels = c("distance", "undistinguishable", "environment", "unexplained"),
    radius = 0.9)

##########

utils::data(Marion.species)
xy.marion <- Marion.species[,1:2]
data.spec.marion <- Marion.species[,3:33]
utils::data(Marion.env)
data.env.marion <- Marion.env[3:4]

zeta.marion <- Zeta.msgdm(data.spec.marion, data.env.marion, xy.marion, sam = 100,
    order = 3, normalize = "Jaccard")
zeta.varpart.marion <- Zeta.varpart(zeta.marion, method.glm = "glm.fit2")
zeta.varpart.marion
dev.new()
pie.neg(zeta.varpart.marion[4:7,1], density = c(4, 0, 8, -1),
    angle = c(90, 0, 0, 0),
    labels = c("distance", "undistinguishable", "environment", "unexplained"),
    radius = 0.9)

South-East Australia Environmental Dataset at Coarse Scale

Description

Projected coordinates and environmental variables in 123, 100 x 100 km sites.

Usage

data(bird.env.coarse)

Format

A data frame with 123 rows (sites) and 9 columns (xy coordinates and environmental variables).

Details

The data set contains the following variables:

• x: x-position in meters in UTM 53 South projection

• y: y-position in meters in UTM 53 South projection

• Natural: Proportion of area of conservation and natural environments

• Irrigated: Proportion of area of production from irrigated agriculture and plantations

• Water: Proportion of area of water features

• Elevation: Elevation

• ApP: Area per person

• Temp: Temperature

• Precip: Precipitation

Location: Australia – 51° 27' 2.27" S, 135° 21' 35.19" E

Data owners: ABARES, Australian Bureau of Statistics,GEBCO, WorldClim

References

http://data.daff.gov.au/anrdl/metadata_files/pa_luav4g9abl07811a00.xml

http://www.gebco.net/

http://www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/1270.0.55.0072011?

http://www.worldclim.org/

Hijmans, R.J., Cameron, S.E., Parra, J.L., Jones, P.G. & Jarvis, A. (2005) Very high resolution interpolated climate surfaces for global land areas. International journal of climatology, 25, 1965-1978.

South-East Australia Environmental Dataset at Fine Scale

Description

Projected coordinates and environmental variables in 604, 25 x 25 km contiguous sites.

Usage

data(bird.env.fine)

Format

A data frame with 604 rows (sites) and 9 columns (xy coordinates and environmental variables).

Details

The data set contains the following variables:

• x: x-position in meters in UTM 53 South projection

• y: y-position in meters in UTM 53 South projection

• Natural: Proportion of area of conservation and natural environments

• Irrigated: Proportion of area of production from irrigated agriculture and plantations

• Water: Proportion of area of water features

• Elevation: Elevation

• ApP: Area per person

• Temp: Temperature

• Precip: Precipitation

Location: Australia – 50° 33' 5.03" S, 135° 21' 10.40" E

Data owners: ABARES, Australian Bureau of Statistics,GEBCO, WorldClim

References

http://data.daff.gov.au/anrdl/metadata_files/pa_luav4g9abl07811a00.xml

http://www.gebco.net/

http://www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/1270.0.55.0072011?

http://www.worldclim.org/

Hijmans, R.J., Cameron, S.E., Parra, J.L., Jones, P.G. & Jarvis, A. (2005) Very high resolution interpolated climate surfaces for global land areas. International journal of climatology, 25, 1965-1978.

Australia Bird Atlas Species Occurrence Dataset at Coarse Scale over South-East Australia

Description

Inventory of bird species occurrence in 123, 100 x 100 km sites.

Usage

data(bird.spec.coarse)

Format

A data frame with 123 rows (sites) and 193 columns (xy coordinates and species).

Details

• x: x-position in meters in UTM 53 South projection

• y: y-position in meters in UTM 53 South projection

• columns 3-193: bird species occurrence

The original bird occurrence data were arranged into a continuous grid covering South-East Australia. Only cells whose richness was within 10 percents of real estimated richness are included here, so that the data corresponds to presence-absence data.

Location: Australia – 51° 27' 2.27" S, 135° 21' 35.19" E

Data owner: BirdLife Australia

References

Barrett, G., Silcocks, A., Barry, S., Cunningham, R. & Poulter, R. (2003) The new atlas of Australian birds. Royal Australasian Ornithologists Union, Melbourne, 1-824.

Australia Bird Atlas Species Occurrence Dataset at Fine Scale over South-East Australia

Description

Inventory of bird species occurrence in 604, 25 x 25 km sites.

Usage

data(bird.spec.fine)

Format

A data frame with 604 rows (sites) and 193 columns (xy coordinates and species).

Details

• x: x-position in meters in UTM 53 South projection

• y: y-position in meters in UTM 53 South projection

• columns 3-192: bird species occurrence

Location: Australia – 50° 33' 5.03" S, 135° 21' 10.40" E

Data owner: BirdLife Australia

The original bird occurrence data were arranged into a continuous grid covering South-East Australia. Only cells whose richness was within 10 percents of real estimated richness are included here, so that the data corresponds to presence-absence data.

References

Barrett, G., Silcocks, A., Barry, S., Cunningham, R. & Poulter, R. (2003) The new atlas of Australian birds. Royal Australasian Ornithologists Union, Melbourne, 1-824.

Fitting Generalized Linear Models with constraint on the coefficients signs

Description

glm.cons is an adaptation of function glm2 from package {glm2} in which the least squares estimation is replaced by a regression with signs constraint on the coefficients using function nnnpls from package {nnls}.

Usage

glm.cons(
  formula,
  family = stats::gaussian(),
  data,
  weights,
  subset,
  na.action,
  start = NULL,
  etastart,
  mustart,
  offset,
  control = list(...),
  model = TRUE,
  method = "glm.fit.cons",
  cons = -1,
  cons.inter = 1,
  x = FALSE,
  y = TRUE,
  contrasts = NULL,
  ...
)

Arguments

Value

The value returned by glm.cons has exactly the same structure as the value returned by glm and glm.2.

References

Marschner, I.C. (2011) glm2: Fitting generalized linear models with convergence problems. The R Journal, 3(2), 12-15.

See Also

glm, glm2

Examples

## Dobson (1990) Page 93: Randomized Controlled Trial :
counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3)
print(d.AD <- data.frame(treatment, outcome, counts))
glm.D93 <- glm.cons(counts ~ outcome + treatment, family = poisson())
glm.D93.ngl <- glm.cons(counts ~ outcome + treatment, family = poisson(),
   method="glm.fit.cons")
summary(glm.D93)
summary(glm.D93.ngl)

Generalized Linear Models fitting method with negative coefficients constraint

Description

glm.fit.cons is an adaptation of function glm.fit2 from package {glm2} in which the least squares estimation is replaced by a non-positive regression using function nnnpls from package {nnls}.

Usage

glm.fit.cons(
  x,
  y,
  weights = rep(1, nobs),
  cons = -1,
  cons.inter = 1,
  start = NULL,
  etastart = NULL,
  mustart = NULL,
  offset = rep(0, nobs),
  family = stats::gaussian(),
  control = list(),
  intercept = TRUE
)

Arguments

Value

The value returned by glm.fit.cons has exactly the same structure as the value returned by glm.fit and glm.fit2.

References

Marschner, I.C. (2011) glm2: Fitting generalized linear models with convergence problems. The R Journal, 3(2), 12-15.

See Also

glm.fit, glm.fit2

Examples

## Dobson (1990) Page 93: Randomized Controlled Trial :
counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3)
print(d.AD <- data.frame(treatment, outcome, counts))
glm.D93 <- glm.cons(counts ~ outcome + treatment, family = poisson())
glm.D93.ngl <- glm.cons(counts ~ outcome + treatment, family = poisson(),
   method="glm.fit.cons")
summary(glm.D93)
summary(glm.D93.ngl)

Pie Chart, considering negative values as zeros

Description

Plots a pie chart, considering negative values as zeros, for the purpose of illustrating variation partitioning.

Usage

pie.neg(
  x,
  labels = names(x),
  edges = 200,
  radius = 0.8,
  clockwise = FALSE,
  init.angle = if (clockwise) 90 else 0,
  density = NULL,
  angle = 45,
  col = NULL,
  border = NULL,
  lty = NULL,
  main = NULL,
  warning = TRUE,
  ...
)

Arguments

Details

This function is identical to the function pie from package graphics, except that it considers all negative values as zeros, to allow for plotting variation partitioning outputs. The original pie function from package graphics returns an error when negative values are present. However, variation partitioning can return negative values, which can then be treated as zeros (Legendre & Legendre, 2008). This function allows direct use of the results from Zeta.varpart without editing the data.

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988). The new S language. Wadsworth & Brooks/Cole.

Cleveland, W. S. (1985). The elements of graphing data. Wadsworth: Monterey, CA, USA.

Legendre, P. & Legendre, L.F. (2012). Numerical ecology, 3rd English edition. Elsevier Science BV, Amsterdam.

See Also

pie, Zeta.varpart

Examples

pie.neg(rep(1, 24), col = rainbow(24), radius = 0.9)

Rescaling of data based on the minimum distance between sites

Description

Combines sites based on the minimum distance between them.

Usage

rescale.min.dist(
  xy,
  data.spec,
  data.env = NULL,
  m,
  distance.type = "Euclidean",
  dist.custom = NULL,
  method = "mean",
  shuffle = FALSE
)

Arguments

Details

The nearest neighbouring sites (plots, quadrates, or areas of varying shapes) are grouped as spatial clusters of 2, 3, 4, etc. sites, based on the minimum distance between them. Since the procedure is based on the relative distance between sites, the site order can have an impact on the output. This function is suitable for both regularly and irregularly spaced sites, contiguous or non contiguous. For regularly spaced sites, the use of rescale.regular is recommended.

Value

rescale.min.dist returns a data frame with the rescaled data.

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

Scheiner S.M., Chiarucci A., Fox G.A., Helmus M.R., McGlinn D.J. & Willig M.R. (2011). The underpinnings of the relationship of species richness with space and time. Ecological Monographs, 81, 195-213.

See Also

Zeta.decline.mc, Zeta.order.mc, Zeta.decline.ex, Zeta.order.ex,

Zeta.scale.min.dist, Zeta.scale.regular, rescale.regular

Examples

utils::data(Marion.species)
xy.marion <- Marion.species[,1:2]
data.spec.marion <- Marion.species[,3:33]

data.rescale <- rescale.min.dist(xy.marion, data.spec.marion, m=2)

Rescaling of data following a hierarchical increase in grain size

Description

Increases grain by hierarchically nesting regularly spaced sites.

Usage

rescale.regular(xy, data.spec, data.env = NULL, method = "mean", n)

Arguments

Details

The sites (plots or quadrates) are aggregated as nearest neighbouring groups of n x n sites, using a nested approach, starting from the lowest x and y, to increase the grain. The sites can be spatially contiguous or discontiguous, as long as they are regularly spaced. This function is not suitable for irregularly spaced sites. If the total number of sites is not a multiple of n x n, the extra sites are discarded.

Value

rescale.regular returns a data frame with the rescaled data.

References

Hui C. & McGeoch M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. The American Naturalist, 184, 684-694.

Scheiner S.M., Chiarucci A., Fox G.A., Helmus M.R., McGlinn D.J. & Willig M.R. (2011). The underpinnings of the relationship of species richness with space and time. Ecological Monographs, 81, 195-213.

See Also

Zeta.decline.mc, Zeta.order.mc, Zeta.decline.ex, Zeta.order.ex, Zeta.scale.regular, Zeta.scale.min.dist, rescale.min.dist

Examples

xy.bird <- bird.spec.fine[1:2]
data.spec.bird <- bird.spec.fine[3:192]

data.rescale <- rescale.regular(xy.bird, data.spec.bird, n = 4)