Analyses with the Maximum Entropy Theory of Ecology (METE)

Description

Fits and plots macroecological patterns predicted by the Maximum Entropy Theory of Ecology (METE)

Details

Author(s)

Andy Rominger, Cory Merow, John Harte

Maintainer: Cory Merow cory.merow@gmail.com

References

Harte, J., Zillio, T., Conlisk, E. & Smith, A. (2008). Maximum entropy and the state-variable approach to macroecology. Ecology, 89, 2700-2711.

Harte, J. (2008). From Spatial Pattern in the Distribution and Abundance of Species to a Unified Theory of Ecology: The Role of Maximum Entropy Methods. Applied Optimization pp. 243-272. Applied Optimization. Springer Berlin Heidelberg, Berlin, Heidelberg.

Harte, J., Smith, A.B. & Storch, D. (2009). Biodiversity scales from plots to biomes with a universal species-area curve. Ecology Letters, 12, 789-797.

Harte, J. (2011). Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press, Oxford, UK.

Community abundance data for a desert grassland (anza borrego)

Description

A dataset containing the community abundace data for plant species, as well as the locations of plots with respect to one another

Usage

anbo

Format

A data frame with 121 rows and 4 variables:

row

plot coordinate

column

plot coordinate

spp

species ID

count

number of individuals

Arthropod community abundance data

Description

A dataset containing the community abundace data for individuals, as well as their body mass.

Usage

arth

Format

A data frame with 547 rows and 3 variables:

spp

species ID

count

number of individuals

mass

biomass

Source

Gruner, D. S. 2007. Geological age, ecosystem development, and local resource constraints on arthropod community structure in the Hawaiian Islands. Biological Journal of the Linnean Society, 90: 551–570.

Downscale the species area relationship (SAR) or endemics area relationship (EAR)

Description

Compute METE SAR by downscaling from some larger area A0 to a smaller areas.

Usage

downscaleSAR(x, A, A0, EAR = FALSE)

Arguments

Details

Downscaling is done non-iteratively (i.e. the SAD and SSAD are calculated based on state variables at the anchor scale A0) thus unlike the upscaling SAR function, downscaling can be computed for any arbitrary scale \leq A_0.

Value

an object of class sar inheriting from data.frame with columns A and S giving area and species richness, respectively

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

meteESF, meteSAR, empiricalSAR, upscaleSAR

Examples

data(anbo)
anbo.esf <- meteESF(spp=anbo$spp, abund=anbo$count)
anbo.thr.downscale <- downscaleSAR(anbo.esf, 2^(seq(-3, 4, length=7)), 16)
plot(anbo.thr.downscale)

## theoretical SARs from state variables only
thr.downscale <- downscaleSAR(meteESF(S0=40, N0=400), 2^seq(-1,4,by=1), 16)
thr.downscaleEAR <- downscaleSAR(meteESF(S0=40, N0=400), 2^seq(-1, 4, by=1), 16, EAR=TRUE)
plot(thr.downscale, ylim=c(0, 40), col='red')
plot(thr.downscaleEAR, add=TRUE, col='blue')

Relationship between mean metabolic rate (\bar{\epsilon}) and abundance

Description

ebar calculates the relationship between average metabolic rate of a species and that species' abundance. Also known as the Damuth relationship

Usage

ebar(x)

Arguments

Details

See examples.

Value

An object of class meteRelaT. The object contains a list with the following elements.

pred

predicted relationship

obs

observed relationship

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

meteDist, sad.meteESF, metePsi

Examples

data(arth)
esf1 <- meteESF(spp=arth$spp,
               abund=arth$count,
               power=arth$mass^(.75),
               minE=min(arth$mass^(.75)))
damuth <- ebar(esf1)

Empirical SAR or EAR

Description

computes observed SAR or EAR from raw data

Usage

empiricalSAR(spp, abund, row, col, x, y, Amin, A0, EAR = FALSE)

Arguments

Details

Currently only doublings of area are supported. There are several options for specifying areas. Either row and col or x and y must be provided for each data entry (i.e. the length of row and col or x and y must equal the length of spp and abund). If x and y are provided then the landscape is gridded either by specifying Amin (the size of the smallest grid cell) or by providing the number or desired rows and columns via the row and col arguments. If only row and col are provided these are taken to be the row and column identities of each data entry

Value

an object of class sar inheriting from data.frame with columns A and S giving area and species richness, respectively

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

meteESF, meteSAR, downscaleSAR, upscaleSAR

Examples

data(anbo)
anbo.obs.sar <- empiricalSAR(anbo$spp, anbo$count, anbo$row, anbo$col, Amin=1, A0=16)
plot(anbo.obs.sar)
anbo.obs.ear <- empiricalSAR(anbo$spp, anbo$count, anbo$row, anbo$col, Amin=1, A0=16, EAR=TRUE)
plot(anbo.obs.ear)

## empirical SAR from simulated x, y data
anbo$x <- runif(nrow(anbo), 0, 1) + anbo$column
anbo$y <- runif(nrow(anbo), 0, 1) + anbo$row
meteSAR(anbo$spp, anbo$count, x=anbo$x, y=anbo$y, row=4, col=4)

Individual Power Distribution

Description

ipd.meteESF calculates the distribution Psi(e | N0, S0, E0), the distribution of metabolic rates across all individuals in a commmunity

Usage

ipd(x, ...)

## S3 method for class 'meteESF'
ipd(x, ...)

Arguments

Details

See examples.

Value

An object of class meteDist. The object contains a list with the following elements.

data

The data used to construct the prediction

d

density funciton

p

cumulative density function

q

quantile funtion

r

random number generator

La

Vector of Lagrange multipliers

state.var

State variables used to constrain entropy maximization

type

Specifies the type of distribution is 'sad'

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

meteDist, sad.meteESF, metePsi

Examples

data(arth)
esf1 <- meteESF(spp=arth$spp,
               abund=arth$count,
               power=arth$mass^(.75),
               minE=min(arth$mass^(.75)))
ipd1 <- ipd(esf1)

Compute log-likelihood of a meteDist object

Description

logLik.meteDist computes log-likelihood of a meteDist object

Usage

## S3 method for class 'meteDist'
logLik(object, ...)

Arguments

Details

Degrees of freedom are assumed to be equal to the number of Lagrange multpliers needed to specify the METE prediction. See Examples for usage.

Value

object of class logLik

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

sad, ssad, ipd, sipd

Examples

data(arth)
## object holding ecosystem structure function
esf1 <- meteESF(spp=arth$spp,
                abund=arth$count,
                power=arth$mass^(.75),
                minE=min(arth$mass^(.75)))
## calculate individual power distribution and its likelihood
ipd1 <- ipd(esf1)
logLik(ipd1)

Compute log-likelihood z-score

Description

logLikZ.meteDist computes a log-likelihood z-score by simulation from a fitted METE distribution

Usage

logLikZ(x, ...)

## S3 method for class 'meteDist'
logLikZ(x, nrep = 999, return.sim = FALSE, ...)

Arguments

Details

logLikZ.meteDist simulates from a fitted METE distribution (e.g. a species abundance distribution or individual power distribution) and calculates the likelihood of these simulated data sets. The distribution of these values is compared against the likelihood of the data to obtain a z-score, specifically z = ((logLik_obs - mean(logLik_sim)) / sd(logLik_sim))^2. This value is squared so that it will be approximately Chi-squared distributed and a goodness of fit test naturally arrises as 1 - pchisq(z, df=1).

Value

list with elements

z

The z-score

sim

nrep Simulated values (scaled by mean and sd as is the z-score) if return.sim=TRUE, NULL otherwise

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

mseZ.meteDist

Examples

data(arth)
## object holding ecosystem structure function
esf1 <- meteESF(spp=arth$spp,
                abund=arth$count,
                power=arth$mass^(.75),
                minE=min(arth$mass^(.75)))
## calculate individual power distribution
ipd1 <- ipd(esf1)
## calculate z-score, keeping all simulated log likelihoods for plotting
llz <- logLikZ(ipd1, nrep=100, return.sim=TRUE)

plot(density(llz$sim),xlim=range(c(llz$sim,llz$obs)),
     xlab='scaled log(likelihood)^2',col='red')
abline(v=llz$z,lty=2)
legend('top',legend=c('data','simulated'),col=c('black','red'),
      lty=c(1,1),bty='n')

meteDist2Rank

Description

meteESF calculate the rank distribution of a meteDist object

Usage

meteDist2Rank(x)

Arguments

Details

Extracts the predicted rank distribution from a meteDist object. This is effectively the quantile function of the distribution. Used, e.g., in plot.meteDist

Value

A vector of predicted quantiles, typically used to compare against data as in plot.meteDist

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

Examples

data(arth)
esf1 <- meteESF(spp=arth$spp,
                abund=arth$count,
                power=arth$mass^(.75),
                minE=min(arth$mass^(.75)))
sad1 <- sad(esf1)
meteDist2Rank(sad1)

meteESF

Description

meteESF Calculates the “ecosystem structure function” R(n,\epsilon) which forms the core of the Maximum Entropy Theory of Ecology

Usage

meteESF(spp, abund, power, S0 = NULL, N0 = NULL, E0 = NULL, minE)

Arguments

Details

Uses either data or state variables to calculate the Ecosystem Structure Function (ESF). power nor E0 need not be specified; if missing an arbitrarily large value is assigned to E0 (N0*1e5) such that it will minimally affect estimation of Lagrange multipliers. Consider using sensitivity analysis to confirm this assumption. Examples show different ways of combining data and state variables to specify constraints

Value

An object of class meteESF with elements

data

The data used to construct the ESF

emin

The minimum metabolic rate used to rescale metabolic rates

La

Vector of Lagrange multipliers

La.info

Termination information from optimization procedure

state.var

State variables used to constrain entropy maximization

Z

Normalization constant for ESF

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

metePi

Examples

## case where complete data availible
esf1 <- meteESF(spp=arth$spp,
                abund=arth$count,
                power=arth$mass^(.75),
                minE=min(arth$mass^(.75)))
esf1

## excluding metabolic rate data
esf2 <- meteESF(spp=arth$spp,
                abund=arth$count)
esf2

## using state variables only
esf3 <- meteESF(S0=50, N0=500, E0=5000)
esf3
esf4 <- meteESF(S0=50, N0=500)
esf4

Equation of the PMF for the METE species metabolic rate distribution

Description

meteNu is a low level function to calculate the value of \nu(e | N_0, S_0, E_0) (the distribution of metabolic rates/power across all species in a commmunity) at the given value of e; vectorized in e.

Usage

meteNu(e, la1, la2, Z, S0, N0, E0)

Arguments

Details

Typically only used in spd.meteESF and not called by the user.

Value

numeric vector of length equal to length of e

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

spd.mete

Examples

data(arth)
esf1 <- meteESF(spp=arth$spp,
                abund=arth$count,
                power=arth$mass^(.75),
                minE=min(arth$mass^(.75)))
meteNu(1:10,
       esf1$La[1],esf1$La[2],
       esf1$Z,esf1$state.var['S0'],
       esf1$state.var['N0'],
       esf1$state.var['E0'])

Equation of the METE species abundance distribution

Description

metePhi returns the species abundance distribution (Phi(n)) predicted by METE; vectorized in n

Usage

metePhi(n, la1, la2, Z, S0, N0, E0)

Arguments

Details

See Examples

Value

numeric

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

sad.mete

Examples

esf1=meteESF(spp=arth$spp,
              abund=arth$count,
              power=arth$mass^(.75),
              minE=min(arth$mass^(.75)))
metePhi(min(arth$mass^(.75)),
       esf1$La[1],esf1$La[2],
       esf1$Z,esf1$state.var['S0'],
       esf1$state.var['N0'],
       esf1$state.var['E0'])

Equation of the PMF of the METE spatial species abundance distribution

Description

metePi is a low level function that returns the spatial species abundance distribution Pi(n) predicted by METE; vectorized in n

Usage

metePi(n, la, n0)

Arguments

Details

See Examples

Value

a numeric vector giving the probability of each entry in n

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

metePi

Examples

metePi(0:10, 0.01, 100)

Equation of the PMF for the METE individual metabolic rate distribution

Description

metePsi is a low level function to calculate the value of \Psi(e | N_0, S_0, E_0) (the distribution of metabolic rates/power across all individuals in a commmunity) at the given value of e; vectorized in e.

Usage

metePsi(e, la1, la2, Z, S0, N0, E0)

Arguments

Details

Typically only used in ipd.meteESF and not called by the user.

Value

numeric vector of length equal to length of e

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

ipd.mete

Examples

data(arth)
esf1 <- meteESF(spp=arth$spp,
                abund=arth$count,
                power=arth$mass^(.75),
                minE=min(arth$mass^(.75)))
metePsi(1:10,
        esf1$La[1],esf1$La[2],
        esf1$Z,esf1$state.var['S0'],
        esf1$state.var['N0'],
        esf1$state.var['E0'])

Compute METE species area relationship (SAR)

Description

Uses raw data or state variables to calculate METE SAR and EAR (endemics area relatiohsip) as well as compute the observed SAR or EAR from data, if provided

Usage

meteSAR(spp, abund, row, col, x, y, S0 = NULL, N0 = NULL, Amin, A0,
  upscale = FALSE, EAR = FALSE)

Arguments

Details

Currently only doublings of area are supported. Predictions and comparison to data can be made via several options. If spp and abund are not provided then only theoretical predictions are returned without emperical SAR or EAR results. In this case areas can either be specified by providing Amin and A0 from which a vector of doubling areas is computed, or my providing row, col and A0 in which case row and col are taken to be the number of desired rows and columns used to construct a grid across the landscape. If data are provided in the form of spp and abund then either row and col or x and y must be provided for each data entry (i.e. the length of row and col or x and y must equal the length of spp and abund). If x and y are provided then the landscape is gridded either by specifying Amin (the size of the smallest grid cell) or by providing the number or desired rows and columns via the row and col arguments.

SARs and EARs can be predicted either interatively or non-iteratively. In the non-iterative case the SAD and SSAD (which are used to calculate the SAR or EAR prediction) are derived from state variables at one anchor scale. In the iterative approach state variables are re-calculated at each scale. Currently downscaling and upscaling are done differently ( downscaling is only implemented in the non-iterative approach, whereas upscaling is only implemented in the iterative approach). The reason is largely historical (downscaling as originally done non-iteratively while upscaling was first proposed in an iterative framework). Future implementations in meteR will allow for both iterative and non-iterative approaches to upscaling and downscaling. While iterative and non-iterative methods lead to slightly different predictions these are small in comparison to typical ranges of state variables (see Harte 2011).

Value

an object of class meteRelat with elements

pred

predicted relationship; an object of class sar

obs

observed relationship; an object of classsar

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

sad, meteESF, metePi

Examples

## Not run: 
data(anbo)

## using row and col from anbo dataset
anbo.sar1 <- meteSAR(anbo$spp, anbo$count, anbo$row, anbo$col, Amin=1, A0=16)
plot(anbo.sar1)

## using simulated x, y data
anbo.sar2 <- meteSAR(anbo$spp, anbo$count, x=anbo$x, y=anbo$y, row=4, col=4)
plot(anbo.sar2)

## using just state variable
thr.sar <- meteSAR(Amin=1, A0=16, S0=50, N0=500)

## End(Not run)

meteSSF

Description

meteSSF calculates the “spatial structure function” \Pi(n) (analogous to the ecosystem structure function). From the SSF the spatial abundance distribution can be calculated.

Usage

meteSSF(spp, sppID, abund, row, col, x, y, n0 = sum(abund), A, A0)

Arguments

Details

Uses either data or state variables to calculate the Spatial Structure Function (SSF). Uses internal code to determine when computation-saving approximations can be safely made

Value

An object of class meteSSF with elements

data

The data used to construct the SSF

La

Vector of Lagrange multipliers

La.info

Termination information from optimization procedure

state.var

State variables used to constrain entropy maximization

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

metePi

Examples

data(anbo)
## calculate SSF Pi
pi1 <- meteSSF(anbo$spp, 'crcr', anbo$count, row=anbo$row, col=anbo$column, A=1, A0=16)
pi1

Equation of the PMF for the METE Intra-specific metabolic rate distribution

Description

Distribution of metabolic rates over individuals within a species of abundance n0

Usage

meteTheta(e, n, la2)

Arguments

Value

numeric vector of length equal to lengthof e

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

metePsi, ipd

Other Theta: sipd, sipd.meteESF

Computes mean squared error for rank or cdf

Description

mse.meteDist computes mean squared error for rank or cdf between METE prediction and data

Usage

mse(x, ...)

## S3 method for class 'meteDist'
mse(x, type = c("rank", "cumulative"), relative = TRUE,
  log = FALSE, ...)

Arguments

Details

See Examples.

Value

numeric; the value of the mean squared error.

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

mseZ.meteDist

Examples

data(arth)
esf1 <- meteESF(spp=arth$spp,
                abund=arth$count,
                power=arth$mass^(.75),
                minE=min(arth$mass^(.75)))
sad1 <- sad(esf1)
mse(sad1, type='rank', relative=FALSE)
ebar1 <- ebar(esf1)
mse(ebar1)

Compute z-score of mean squared error

Description

mseZ.meteDist Compute z-score of mean squared error

Usage

mseZ(x, ...)

## S3 method for class 'meteDist'
mseZ(x, nrep, return.sim = TRUE, type = c("rank",
  "cumulative"), relative = TRUE, log = FALSE, ...)

Arguments

Details

mseZ.meteDist simulates from a fitted METE distribution (e.g. a species abundance distribution or individual power distribution) and calculates the MSE between the simulated data sets and the METE prediction. The distribution of these values is compared against the MSE of the data to obtain a z-score in the same was as logLikZ; see that help document for more details.

Value

list with elements

z

The z-score

sim

nrep Simulated values

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

logLikZ

Examples

esf1=meteESF(spp=arth$spp,
              abund=arth$count,
              power=arth$mass^(4/3),
              minE=min(arth$mass^(4/3)))
sad1=sad(esf1)
mseZ(sad1, nrep=100, type='rank',return.sim=TRUE)

Plot the relationship between abundance and metabolic rate, i.e. objects of class damuth

Description

Plot abundance-metabolic rate relationship with flexibility to adjust plotting parameters

Usage

## S3 method for class 'damuth'
plot(x, add = FALSE, ...)

Arguments

Details

see examples

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

empiricalSAR, downscaleSAR, upscaleSAR, meteSAR

Examples

data(arth)
esf1 <- meteESF(arth$spp, arth$count, arth$mass^0.75)
ebar1 <- ebar(esf1)
plot(ebar1)

Plot METE distributions and associated data

Description

plot.meteDist plots both the theoretical prediction and data for a meteDist object using either a rank or cumulative distribution plot

Usage

## S3 method for class 'meteDist'
plot(x, ptype = c("cdf", "rad"), th.col = "red",
  lower.tail = TRUE, add.legend = TRUE, add.line = FALSE, ...)

Arguments

Details

plot.meteDist automatically extracts the prediction and data (if used in meteESF) from the meteDist object. Additional plotting arguments can be passed to ....

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

sad, ipd, ssad, sipd, print.meteDist

Examples

data(arth)
esf1 <- meteESF(spp=arth$spp,
               abund=arth$count,
               power=arth$mass^(.75),
               minE=min(arth$mass^(.75)))
ipd1 <- ipd(esf1)
plot(ipd1)
plot(ipd1, ptype='rad')

Plot predicted METE relationships and associated observed relationship seen in data

Description

plot.meteRelat plots both the theoretical prediction and data for a meteRelat object

Usage

## S3 method for class 'meteRelat'
plot(x, add.legend = TRUE, th.col = "red", ...)

Arguments

Details

plot.meteRelat automatically extracts the prediction and data (if used in meteESF) from the meteDist object. Additional plotting arguments can be passed to ....

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

meteSAR

Examples

data(anbo)
anbo.sar <- meteSAR(anbo$spp, anbo$count, anbo$row, anbo$col, Amin=1, A0=16)
plot(anbo.sar)

Plot the species abundance distribution (SAR), i.e. objects of class sar

Description

Plot species or endemics area relationship with flexibility to adjust plotting parameters

Usage

## S3 method for class 'sar'
plot(x, add = FALSE, ...)

Arguments

Details

see examples

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

empiricalSAR, downscaleSAR, upscaleSAR, meteSAR

Examples

data(anbo)
anbo.obs.sar <- empiricalSAR(anbo$spp, anbo$count, anbo$row, anbo$col, Amin=1, A0=16)
plot(anbo.obs.sar)

predictESF

Description

predict predicts the probabilities for given combinations of abundance and energ from the “ecosystem structure function” R(n,\epsilon)

Usage

predictESF(esf, abund, power)

Arguments

Details

Uses a fitted object of class meteESF and user supplied values of abundance and power to predict values of the ESF

Value

a data.frame with abundance, power, and the predicted value of the ESF

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

meteESF

Examples

## case where complete data availible
esf1 <- meteESF(spp=arth$spp,
                abund=arth$count,
                power=arth$mass^(.75),
                minE=min(arth$mass^(.75)))
predictESF(esf1,
           abund=c(10,3),
           power=c(.01,3))

print.damuth

Description

S3 method for class damuth

Usage

## S3 method for class 'damuth'
print(x, ...)

Arguments

Details

See Examples

Value

Returns the object silently

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

Examples

data(arth)
esf1 <- meteESF(arth$spp, arth$count, arth$mass^0.75)
ebar1 <- ebar(esf1)
print(ebar1)

Print summaries of meteDist objects

Description

S3 method for class meteDist

Usage

## S3 method for class 'meteDist'
print(x, ...)

Arguments

Details

Prints state variables and lagrange multipliers

Value

The meteDist object is returned invisibly

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

Examples

data(arth)
esf1 <- meteESF(spp=arth$spp,
                abund=arth$count,
                power=arth$mass^(.75),
                minE=min(arth$mass^(.75)))
ipd1 <- ipd(esf1)
ipd1

print.meteESF

Description

print.meteESF prints an object of class meteESF

Usage

## S3 method for class 'meteESF'
print(x, ...)

Arguments

Details

See Examples

Value

x silently

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

Examples

data(arth)
esf1 <- meteESF(spp=arth$spp,
                abund=arth$count,
                power=arth$mass^(.75),
                minE=min(arth$mass^(.75)))
print(esf1)
esf1 # alternatively...

Print summaries of meteRelat objects

Description

S3 method for class meteRelat

Usage

## S3 method for class 'meteRelat'
print(x, ...)

Arguments

Value

x silently

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

print.sar

Description

S3 method for class sar

Usage

## S3 method for class 'sar'
print(x, ...)

Arguments

Details

See Examples

Value

Returns the object silently

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

Examples

data(anbo)
anbo.sar <- meteSAR(anbo$spp, anbo$count, anbo$row, anbo$col, Amin=1, A0=16)
print(anbo.sar)
anbo.sar # alternatively

Compute residuals between METE predictions and data of a meteDist object

Description

residuals.meteDist computes residuals between METE predictions and data of a meteDist object

Usage

## S3 method for class 'meteDist'
residuals(object, type = c("rank", "cumulative"),
  relative = TRUE, log = FALSE, ...)

Arguments

Details

See Examples. Typically not called directly by the user and rather used for calculating the mean square error with mse.meteDist. If type='rank' returned value will be of length equal to number of observations (e.g. number of species in case of SAD) but if type='cumulative' returned value will be of length equal to number of unique ovservations (e.g. number of unique abundances in case of SAR).

Value

a numeic vector giving residuals for each data point

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

mse.meteDist

Examples

data(arth)
esf1 <- meteESF(spp=arth$spp,
                abund=arth$count,
                power=arth$mass^(.75),
                minE=min(arth$mass^(.75)))
sad1 <- sad(esf1)
residuals(sad1)

Compute residuals between METE predictions and date of a meteRelat object

Description

residuals.meteRelat computes residuals between METE predictions and data of a meteDist object

Usage

## S3 method for class 'meteRelat'
residuals(object, ...)

Arguments

Details

See Examples. Typically not called directly by the user and rather used for calculating the mean square error with mse.meteRelat.

Value

a numeic vector giving residuals for each data point

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

mse.meteDist

Examples

data(arth)
esf1 <- meteESF(spp=arth$spp,
                abund=arth$count,
                power=arth$mass^(.75),
                minE=min(arth$mass^(.75)))
ebar1 <- ebar(esf1)
residuals(ebar1)

METE species abundance distribution

Description

sad.mete returns the species abundance distribution predicted by METE (\Phi(n))

Usage

sad(x)

## S3 method for class 'meteESF'
sad(x)

Arguments

Details

See Examples.

Value

An object of class meteDist. The object contains a list with the following elements.

data

The data used to construct the prediction

d

density funciton

p

cumulative density function

q

quantile funtion

r

random number generator

La

Vector of Lagrange multipliers

state.var

State variables used to constrain entropy maximization

type

Specifies the type of distribution is 'sad'

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

metePhi

Examples

data(arth)
esf1 <- meteESF(spp=arth$spp,
                abund=arth$count,
                power=arth$mass^(.75),
                minE=min(arth$mass^(.75)))
sad1 <- sad(esf1)
sad1
sad1$r(20)
sad1$q(seq(0,1,length=10))

Generic method to obtain the species-level individual power distribution (SIPD)

Description

Extract species level individual power distribution from ESF object and return object inheriting from meteDist. This distribution (Theta) describes the distribution of metabolic rates across the individuals of a species with n individuls

Usage

sipd(x, ...)

## S3 method for class 'meteESF'
sipd(x, sppID, n, ...)

Arguments

Details

If n is provided then only the theoretical prediction is returned (because data from multiple species could map to the same n). Thus if data and prediction are desired use sppID.

Value

An object of class meteDist. The object contains a list with the following elements.

data

The data used to construct the prediction

d

density funciton

p

cumulative density function

q

quantile funtion

r

random number generator

La

Vector of Lagrange multipliers

state.var

State variables used to constrain entropy maximization

type

Specifies the type of distribution is 'sad'

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

sad.meteESF, ipd.meteESF, metePsi

Other Theta: meteTheta

Examples

data(arth)
esf1 <- meteESF(spp=arth$spp,
                abund=arth$count,
                power=arth$mass^(.75),
                minE=min(arth$mass^(.75)))
sipd1 <- sipd(esf1, sppID=5)
sipd1

Species Power Distribution

Description

spd.meteESF calculates the distribution nu(e | N0, S0, E0), the distribution of average metabolic rates across for each species in a commmunity

Usage

spd(x)

## S3 method for class 'meteESF'
spd(x)

Arguments

Details

See examples.

Value

An object of class meteDist. The object contains a list with the following elements.

data

The data used to construct the prediction

d

density funciton

p

cumulative density function

q

quantile funtion

r

random number generator

La

Vector of Lagrange multipliers

state.var

State variables used to constrain entropy maximization

type

Specifies the type of distribution is 'sad'

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

meteDist, sad.meteESF, metePsi

Examples

data(arth)
esf1 <- meteESF(spp=arth$spp,
               abund=arth$count,
               power=arth$mass^(.75),
               minE=min(arth$mass^(.75)))
spd1 <- spd(esf1)

Species Spatial Abundance Distribution

Description

Species Spatial Abundance Distribution

Usage

ssad(x)

## S3 method for class 'meteSSF'
ssad(x)

Arguments

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

Examples

data(anbo)
pi1 <- meteSSF(anbo$spp, 'crcr', anbo$count, row=anbo$row, col=anbo$col, A=1, A0=16)
plot(ssad(pi1))

upscale SAR

Description

Based on information at an anchor scale (A0) calcuate predicted species area relationship at larger scales

Usage

upscaleSAR(x, A0, Aup, EAR = FALSE)

Arguments

Details

Currently only doublings of area are supported and only the SAR (not EAR) is supported. Upscaling works by iteratively solving for the constraints (S and N at larger scales) that would lead to the observed data at the anchor scale. See references for more details on this approach.

Value

an object of class sar inheriting from data.frame with columns A and S giving area and species richness, respectively

Author(s)

Andy Rominger <ajrominger@gmail.com>, Cory Merow

References

Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.

See Also

meteESF, meteSAR, empiricalSAR, downscaleSAR

Examples

data(anbo)
anbo.sar <- meteSAR(anbo$spp, anbo$count, anbo$row, anbo$col, Amin=1, A0=16)
anbo.sar
plot(anbo.sar, xlim=c(1, 2^10), ylim=c(3, 50), log='xy')

## get upscaled SAR and add to plot
anbo.esf <- meteESF(spp=anbo$spp, abund=anbo$count) # need ESF for upscaling
anbo.sarUP <- upscaleSAR(anbo.esf, 16, 2^10)
plot(anbo.sarUP, add=TRUE, col='blue')