| Title: | Fitting and Plotting Tools for the Maximum Entropy Theory of Ecology (METE) |
|---|---|
| Description: | Fit and plot macroecological patterns predicted by the Maximum Entropy Theory of Ecology (METE). |
| Authors: | Andy Rominger, Cory Merow |
| Maintainer: | Cory Merow <[email protected]> |
| License: | GPL-2 |
| Version: | 1.2 |
| Built: | 2025-02-05 04:11:09 UTC |
| Source: | https://github.com/cmerow/meter |
Fits and plots macroecological patterns predicted by the Maximum Entropy Theory of Ecology (METE)
| Package: | meteR |
| Type: | Package |
| Version: | 1.0 |
| Date: | 2014-01-04 |
| License: | GPL-2 |
Andy Rominger, Cory Merow, John Harte
Maintainer: Cory Merow [email protected]
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.
A dataset containing the community abundace data for plant species, as well as the locations of plots with respect to one another
anboanbo
A data frame with 121 rows and 4 variables:
plot coordinate
plot coordinate
species ID
number of individuals
A dataset containing the community abundace data for individuals, as well as their body mass.
artharth
A data frame with 547 rows and 3 variables:
species ID
number of individuals
biomass
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.
Compute METE SAR by downscaling from some larger area A0 to a smaller areas.
downscaleSAR(x, A, A0, EAR = FALSE)downscaleSAR(x, A, A0, EAR = FALSE)
x |
an object of class meteESF |
A |
numerical vector of areas (<= |
A0 |
total study area |
EAR |
logical. TRUE computes the endemics area relatinship |
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
.
an object of class sar inheriting from data.frame with
columns A and S giving area and species richness, respectively
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
meteESF, meteSAR, empiricalSAR, upscaleSAR
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')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')
ebar calculates the relationship between average metabolic rate of a species and that species' abundance. Also known as the Damuth relationship
ebar(x)ebar(x)
x |
an object of class meteESF. |
See examples.
An object of class meteRelaT. The object contains a list with the following elements.
predpredicted relationship
obsobserved relationship
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
meteDist, sad.meteESF, metePsi
data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) damuth <- ebar(esf1)data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) damuth <- ebar(esf1)
computes observed SAR or EAR from raw data
empiricalSAR(spp, abund, row, col, x, y, Amin, A0, EAR = FALSE)empiricalSAR(spp, abund, row, col, x, y, Amin, A0, EAR = FALSE)
spp |
vector of species identities |
abund |
numberic vector abundances associated with each record |
row |
identity of row in a gridded landscape associated with each record, or desired number of rows to divide the landcape into |
col |
identity of column in a gridded landscape associated with each recod, or desired number of columns to divide the landcape into |
x |
the x-coordinate of an individual if recorded |
y |
the y-coordinate of an individual if recorded |
Amin |
the smallest area, either the anchor area for upscaling or the desired area to downscale to |
A0 |
the largest area, either the area to upscale to or the total area from which to downscale |
EAR |
logical, should the EAR or SAR be computed |
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
an object of class sar inheriting from data.frame with
columns A and S giving area and species richness, respectively
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
meteESF, meteSAR, downscaleSAR, upscaleSAR
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)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)
gsneESF Calculates the “ecosystem structure
function” using a higher taxon (e.g. genera) as an additional constraint
gsneESF(gen, spp, abund, power, G0 = NULL, S0 = NULL, N0 = NULL, E0 = NULL, minE)gsneESF(gen, spp, abund, power, G0 = NULL, S0 = NULL, N0 = NULL, E0 = NULL, minE)
gen |
A vector of genera names |
spp |
A vector of species names |
abund |
A vector of abundances |
power |
A vector of metabolic rates |
G0 |
Total number of genera |
S0 |
Total number of species |
N0 |
Total number of individuals |
E0 |
Total metabolic rate; defaults to N0*1e6 if not specified or
calculated from |
minE |
Minimum possible metabolic rate |
Use follows that of meteESF
An object of class meteESF with elements
dataThe data used to construct the ESF
eminThe minimum metabolic rate used to rescale metabolic rates
LaVector of Lagrange multipliers
La.infoTermination information from optimization procedure
state.varState variables used to constrain entropy maximization
ZNormalization constant for ESF
Andy Rominger <[email protected]>, Cory Merow
meteESF
ipd.meteESF calculates the distribution Psi(e | N0, S0, E0),
the distribution of metabolic rates across all individuals in a commmunity
ipd(x, ...) ## S3 method for class 'meteESF' ipd(x, ...)ipd(x, ...) ## S3 method for class 'meteESF' ipd(x, ...)
x |
an object of class meteESF. |
... |
additiona arguments to be passed to methods |
See examples.
An object of class meteDist. The object contains a list with the following elements.
The data used to construct the prediction
density funciton
cumulative density function
quantile funtion
random number generator
Vector of Lagrange multipliers
State variables used to constrain entropy maximization
Specifies the type of distribution is 'sad'
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
meteDist, sad.meteESF, metePsi
data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) ipd1 <- ipd(esf1)data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) ipd1 <- ipd(esf1)
logLik.meteDist computes log-likelihood of a meteDist object
## S3 method for class 'meteDist' logLik(object, ...)## S3 method for class 'meteDist' logLik(object, ...)
object |
a |
... |
arguments to be passed |
Degrees of freedom are assumed to be equal to the number of Lagrange multpliers needed to specify the METE prediction. See Examples for usage.
object of class logLik
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
sad, ssad, ipd, sipd
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)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)
logLikZ.meteDist computes a log-likelihood z-score by simulation from a
fitted METE distribution
logLikZ(x, ...) ## S3 method for class 'meteDist' logLikZ(x, nrep = 999, return.sim = FALSE, ...)logLikZ(x, ...) ## S3 method for class 'meteDist' logLikZ(x, nrep = 999, return.sim = FALSE, ...)
x |
a |
... |
arguments to be passed to methods |
nrep |
number of simulations from the fitted METE distribution |
return.sim |
logical; return the simulated liklihood values |
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).
list with elements
The z-score
nrep Simulated values (scaled by mean and sd as is the z-score) if return.sim=TRUE, NULL otherwise
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
mseZ.meteDist
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')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')
meteESF calculate the rank distribution of a meteDist object
meteDist2Rank(x)meteDist2Rank(x)
x |
|
Extracts the predicted rank distribution from a meteDist object.
This is effectively the quantile function of the distribution. Used, e.g.,
in plot.meteDist
A vector of predicted quantiles, typically used to compare against data as in plot.meteDist
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) sad1 <- sad(esf1) meteDist2Rank(sad1)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 Calculates the “ecosystem structure
function” which forms the core of the Maximum Entropy Theory of
Ecology
meteESF(spp, abund, power, S0 = NULL, N0 = NULL, E0 = NULL, minE)meteESF(spp, abund, power, S0 = NULL, N0 = NULL, E0 = NULL, minE)
spp |
A vector of species names |
abund |
A vector of abundances |
power |
A vector of metabolic rates |
S0 |
Total number of species |
N0 |
Total number of individuals |
E0 |
Total metabolic rate; defaults to N0*1e6 if not specified or
calculated from |
minE |
Minimum possible metabolic rate |
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
An object of class meteESF with elements
dataThe data used to construct the ESF
eminThe minimum metabolic rate used to rescale metabolic rates
LaVector of Lagrange multipliers
La.infoTermination information from optimization procedure
state.varState variables used to constrain entropy maximization
ZNormalization constant for ESF
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
metePi
## 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## 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
meteNu is a low level function to calculate the value of
(the distribution of metabolic rates/power across all species in a commmunity) at the given value of e; vectorized in e.
meteNu(e, la1, la2, Z, S0, N0, E0)meteNu(e, la1, la2, Z, S0, N0, E0)
e |
the value (metabolic rate/power) at which to calculate |
la1, la2
|
Lagrange multipliers |
Z |
partition function |
S0 |
Total number of species |
N0 |
Total number of individuals |
E0 |
Total metabolic rate |
Typically only used in spd.meteESF and not called by the user.
numeric vector of length equal to length of e
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
spd.mete
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'])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'])
metePhi returns the species abundance distribution
(Phi(n)) predicted by METE; vectorized in n
metePhi(n, la1, la2, Z, S0, N0, E0)metePhi(n, la1, la2, Z, S0, N0, E0)
n |
the value (number of individuals) at which to calculate
|
la1, la2
|
Lagrange multipliers |
Z |
partition function |
S0 |
Total number of species |
N0 |
Total number of individuals |
E0 |
Total metabolic rate |
See Examples
numeric
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
sad.mete
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$state.var['E0'])esf1=meteESF(spp=arth$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'])
metePi is a low level function that returns the spatial species abundance
distribution predicted by METE; vectorized in n
metePi(n, la, n0)metePi(n, la, n0)
n |
A vector giving abundances of each entry |
la |
The spatial Lagrange multiplier returned by |
n0 |
Total abundance in area A0 |
See Examples
a numeric vector giving the probability of each entry in n
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
metePi
metePi(0:10, 0.01, 100)metePi(0:10, 0.01, 100)
metePsi is a low level function to calculate the value of
(the distribution of metabolic rates/power across all individuals in a commmunity) at the given value of e; vectorized in e.
metePsi(e, la1, la2, Z, S0, N0, E0)metePsi(e, la1, la2, Z, S0, N0, E0)
e |
the value (metabolic rate/power) at which to calculate |
la1, la2
|
Lagrange multipliers |
Z |
partition function |
S0 |
Total number of species |
N0 |
Total number of individuals |
E0 |
Total metabolic rate |
Typically only used in ipd.meteESF and not called by the user.
numeric vector of length equal to length of e
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
ipd.mete
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'])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'])
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
meteSAR(spp, abund, row, col, x, y, S0 = NULL, N0 = NULL, Amin, A0, upscale = FALSE, EAR = FALSE)meteSAR(spp, abund, row, col, x, y, S0 = NULL, N0 = NULL, Amin, A0, upscale = FALSE, EAR = FALSE)
spp |
vector of species identities |
abund |
numberic vector abundances associated with each record |
row |
identity of row in a gridded landscape associated with each record, or desired number of rows to divide the landcape into |
col |
identity of column in a gridded landscape associated with each recod, or desired number of columns to divide the landcape into |
x |
the x-coordinate of an individual if recorded |
y |
the y-coordinate of an individual if recorded |
S0 |
total number of species |
N0 |
total abundance |
Amin |
the smallest area, either the anchor area for upscaling or the desired area to downscale to |
A0 |
the largest area, either the area to upscale to or the total area from which to downscale |
upscale |
logical, should upscaling or downscaling be carried out |
EAR |
logical, should the EAR or SAR be computed |
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).
an object of class meteRelat with elements
predpredicted relationship; an object of class sar
obsobserved relationship; an object of classsar
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
sad, meteESF, metePi
## 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)## 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 calculates the “spatial structure
function” (analogous to the ecosystem structure function). From
the SSF the spatial abundance distribution can be calculated.
meteSSF(spp, sppID, abund, row, col, x, y, n0 = sum(abund), A, A0)meteSSF(spp, sppID, abund, row, col, x, y, n0 = sum(abund), A, A0)
spp |
A vector of species names |
sppID |
A character giving the name of the desired species (as it appears in ‘spp’) |
abund |
A vector of abundances |
row |
A vector of row IDs for each observation |
col |
A vector of column IDs for each observation |
x |
A vector of x coordinates for each observation |
y |
A vector of y coordinates for each observation |
n0 |
Total abundance in area A0 |
A |
The area at which abundances were recorded |
A0 |
Total study area |
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
An object of class meteSSF with elements
dataThe data used to construct the SSF
LaVector of Lagrange multipliers
La.infoTermination information from optimization procedure
state.varState variables used to constrain entropy maximization
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
metePi
data(anbo) ## calculate SSF Pi pi1 <- meteSSF(anbo$spp, 'crcr', anbo$count, row=anbo$row, col=anbo$column, A=1, A0=16) pi1data(anbo) ## calculate SSF Pi pi1 <- meteSSF(anbo$spp, 'crcr', anbo$count, row=anbo$row, col=anbo$column, A=1, A0=16) pi1
Distribution of metabolic rates over individuals within a species of abundance n0
meteTheta(e, n, la2)meteTheta(e, n, la2)
e |
Metabolic rate |
n |
Number of individuals in species |
la2 |
Lagrange multiplier (lambda_2) as obtained from |
numeric vector of length equal to lengthof e
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
metePsi, ipd
Other Theta: sipd
mse.meteDist computes mean squared error for rank or cdf between METE prediction and data
mse(x, ...) ## S3 method for class 'meteDist' mse(x, type = c("rank", "cumulative"), relative = TRUE, log = FALSE, ...)mse(x, ...) ## S3 method for class 'meteDist' mse(x, type = c("rank", "cumulative"), relative = TRUE, log = FALSE, ...)
x |
a |
... |
arguments to be passed to methods |
type |
'rank' or 'cumulative' |
relative |
logical; if true use relative MSE |
log |
logical; if TRUE calculate MSE on logged distirbution. If FALSE use arithmetic scale. |
See Examples.
numeric; the value of the mean squared error.
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
mseZ.meteDist
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)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)
mseZ.meteDist Compute z-score of mean squared error
mseZ(x, ...) ## S3 method for class 'meteDist' mseZ(x, nrep, return.sim = TRUE, type = c("rank", "cumulative"), relative = TRUE, log = FALSE, ...)mseZ(x, ...) ## S3 method for class 'meteDist' mseZ(x, nrep, return.sim = TRUE, type = c("rank", "cumulative"), relative = TRUE, log = FALSE, ...)
x |
a |
... |
arguments to be passed to methods |
nrep |
number of simulations from the fitted METE distribution |
return.sim |
logical; return the simulated liklihood values |
type |
either "rank" or "cumulative" |
relative |
logical; if true use relative MSE |
log |
logical; if TRUE calculate MSE on logged distirbution. If FALSE use arithmetic scale |
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.
list with elements
The z-score
nrep Simulated values
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
logLikZ
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)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 abundance-metabolic rate relationship with flexibility to adjust plotting parameters
## S3 method for class 'damuth' plot(x, add = FALSE, ...)## S3 method for class 'damuth' plot(x, add = FALSE, ...)
x |
an object of class damuth |
add |
logical; should new |
... |
arguments passed to |
see examples
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
empiricalSAR, downscaleSAR, upscaleSAR, meteSAR
data(arth) esf1 <- meteESF(arth$spp, arth$count, arth$mass^0.75) ebar1 <- ebar(esf1) plot(ebar1)data(arth) esf1 <- meteESF(arth$spp, arth$count, arth$mass^0.75) ebar1 <- ebar(esf1) plot(ebar1)
plot.meteDist plots both the theoretical prediction and data for a
meteDist object using either a rank or cumulative distribution plot
## S3 method for class 'meteDist' plot(x, ptype = c("cdf", "rad"), th.col = "red", lower.tail = TRUE, add.legend = TRUE, add.line = FALSE, ...)## S3 method for class 'meteDist' plot(x, ptype = c("cdf", "rad"), th.col = "red", lower.tail = TRUE, add.legend = TRUE, add.line = FALSE, ...)
x |
a |
ptype |
type of plot; either "cdf" or "rad" |
th.col |
line color of theoretical prediction |
lower.tail |
logical; choose TRUE to highlight differences between data and theory at low abundance; choose FALSE to highlight differences at high abundance. |
add.legend |
logical; add a legend |
add.line |
add the curve for a fitted model to the existing plot |
... |
arguments to be passed to |
plot.meteDist automatically extracts the prediction and data (if used
in meteESF) from the meteDist object. Additional plotting
arguments can be passed to ....
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
sad, ipd, ssad, sipd, print.meteDist
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')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.meteRelat plots both the theoretical prediction and data for a
meteRelat object
## S3 method for class 'meteRelat' plot(x, add.legend = TRUE, th.col = "red", ...)## S3 method for class 'meteRelat' plot(x, add.legend = TRUE, th.col = "red", ...)
x |
a |
add.legend |
logical; add a legend |
th.col |
line color of theoretical prediction |
... |
arguments to be passed to |
plot.meteRelat automatically extracts the prediction and data (if used
in meteESF) from the meteDist object. Additional plotting
arguments can be passed to ....
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
meteSAR
data(anbo) anbo.sar <- meteSAR(anbo$spp, anbo$count, anbo$row, anbo$col, Amin=1, A0=16) plot(anbo.sar)data(anbo) anbo.sar <- meteSAR(anbo$spp, anbo$count, anbo$row, anbo$col, Amin=1, A0=16) plot(anbo.sar)
Plot species or endemics area relationship with flexibility to adjust plotting parameters
## S3 method for class 'sar' plot(x, add = FALSE, ...)## S3 method for class 'sar' plot(x, add = FALSE, ...)
x |
an object of class SAR made with |
add |
logical; should new |
... |
arguments passed to |
see examples
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
empiricalSAR, downscaleSAR, upscaleSAR, meteSAR
data(anbo) anbo.obs.sar <- empiricalSAR(anbo$spp, anbo$count, anbo$row, anbo$col, Amin=1, A0=16) plot(anbo.obs.sar)data(anbo) anbo.obs.sar <- empiricalSAR(anbo$spp, anbo$count, anbo$row, anbo$col, Amin=1, A0=16) plot(anbo.obs.sar)
predict predicts the probabilities for given combinations of abundance and energ from the “ecosystem structure
function”
predictESF(esf, abund, power)predictESF(esf, abund, power)
esf |
A fitted object of class |
abund |
A vector of abundances |
power |
A vector of metabolic rates |
Uses a fitted object of class meteESF and user supplied values of abundance and power to predict values of the ESF
a data.frame with abundance, power, and the predicted value of the ESF
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
meteESF
## 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))## 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))
S3 method for class damuth
## S3 method for class 'damuth' print(x, ...)## S3 method for class 'damuth' print(x, ...)
x |
an object of class |
... |
arguments to be passed to methods |
See Examples
Returns the object silently
Andy Rominger <[email protected]>, Cory Merow
data(arth) esf1 <- meteESF(arth$spp, arth$count, arth$mass^0.75) ebar1 <- ebar(esf1) print(ebar1)data(arth) esf1 <- meteESF(arth$spp, arth$count, arth$mass^0.75) ebar1 <- ebar(esf1) print(ebar1)
meteDist objectsS3 method for class meteDist
## S3 method for class 'meteDist' print(x, ...)## S3 method for class 'meteDist' print(x, ...)
x |
a |
... |
arguments to be passed |
Prints state variables and lagrange multipliers
The meteDist object is returned invisibly
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) ipd1 <- ipd(esf1) ipd1data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) ipd1 <- ipd(esf1) ipd1
print.meteESF prints an object of class meteESF
## S3 method for class 'meteESF' print(x, ...)## S3 method for class 'meteESF' print(x, ...)
x |
an object of class |
... |
arguments to be passed |
See Examples
x silently
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) print(esf1) esf1 # alternatively...data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) print(esf1) esf1 # alternatively...
meteRelat objectsS3 method for class meteRelat
## S3 method for class 'meteRelat' print(x, ...)## S3 method for class 'meteRelat' print(x, ...)
x |
an object of class meteRelat |
... |
arguments to be passed to methods |
x silently
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
S3 method for class sar
## S3 method for class 'sar' print(x, ...)## S3 method for class 'sar' print(x, ...)
x |
an object of class |
... |
arguments to be passed to methods |
See Examples
Returns the object silently
Andy Rominger <[email protected]>, Cory Merow
data(anbo) anbo.sar <- meteSAR(anbo$spp, anbo$count, anbo$row, anbo$col, Amin=1, A0=16) print(anbo.sar) anbo.sar # alternativelydata(anbo) anbo.sar <- meteSAR(anbo$spp, anbo$count, anbo$row, anbo$col, Amin=1, A0=16) print(anbo.sar) anbo.sar # alternatively
residuals.meteDist computes residuals between METE predictions and
data of a meteDist object
## S3 method for class 'meteDist' residuals(object, type = c("rank", "cumulative"), relative = TRUE, log = FALSE, ...)## S3 method for class 'meteDist' residuals(object, type = c("rank", "cumulative"), relative = TRUE, log = FALSE, ...)
object |
a |
type |
'rank' or 'cumulative' |
relative |
logical; if true use relative MSE |
log |
logical; if TRUE calculate MSE on logged distirbution. If FALSE use arithmetic scale. |
... |
arguments to be passed to methods |
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).
a numeic vector giving residuals for each data point
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
mse.meteDist
data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) sad1 <- sad(esf1) residuals(sad1)data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) sad1 <- sad(esf1) residuals(sad1)
residuals.meteRelat computes residuals between METE predictions and
data of a meteDist object
## S3 method for class 'meteRelat' residuals(object, ...)## S3 method for class 'meteRelat' residuals(object, ...)
object |
a |
... |
arguments to be passed |
See Examples. Typically not called directly by the user and rather used for
calculating the mean square error with mse.meteRelat.
a numeic vector giving residuals for each data point
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
mse.meteDist
data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) ebar1 <- ebar(esf1) residuals(ebar1)data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) ebar1 <- ebar(esf1) residuals(ebar1)
sad.mete returns the species abundance distribution
predicted by METE ()
sad(x) ## S3 method for class 'meteESF' sad(x)sad(x) ## S3 method for class 'meteESF' sad(x)
x |
an object of class mete. |
See Examples.
An object of class meteDist. The object contains a list with the following elements.
The data used to construct the prediction
density funciton
cumulative density function
quantile funtion
random number generator
Vector of Lagrange multipliers
State variables used to constrain entropy maximization
Specifies the type of distribution is 'sad'
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
metePhi
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))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))
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
sipd(x, ...) ## S3 method for class 'meteESF' sipd(x, sppID, n, ...)sipd(x, ...) ## S3 method for class 'meteESF' sipd(x, sppID, n, ...)
x |
An object of class meteESF (i.e. the fitted distribution |
... |
arguments to be passed to methods |
sppID |
the name or index of the species of interest as listed in the |
n |
integer. Alternatively can extract METE prediction by indicating number of individuals in the species |
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.
An object of class meteDist. The object contains a list with the following elements.
The data used to construct the prediction
density funciton
cumulative density function
quantile funtion
random number generator
Vector of Lagrange multipliers
State variables used to constrain entropy maximization
Specifies the type of distribution is 'sad'
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
sad.meteESF, ipd.meteESF, metePsi
Other Theta: meteTheta
data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) sipd1 <- sipd(esf1, sppID=5) sipd1data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) sipd1 <- sipd(esf1, sppID=5) sipd1
spd.meteESF calculates the distribution nu(e | N0, S0, E0),
the distribution of average metabolic rates across for each species in a commmunity
spd(x) ## S3 method for class 'meteESF' spd(x)spd(x) ## S3 method for class 'meteESF' spd(x)
x |
an object of class meteESF. |
See examples.
An object of class meteDist. The object contains a list with the following elements.
The data used to construct the prediction
density funciton
cumulative density function
quantile funtion
random number generator
Vector of Lagrange multipliers
State variables used to constrain entropy maximization
Specifies the type of distribution is 'sad'
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
meteDist, sad.meteESF, metePsi
data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) spd1 <- spd(esf1)data(arth) esf1 <- meteESF(spp=arth$spp, abund=arth$count, power=arth$mass^(.75), minE=min(arth$mass^(.75))) spd1 <- spd(esf1)
ssad(x) ## S3 method for class 'meteSSF' ssad(x)ssad(x) ## S3 method for class 'meteSSF' ssad(x)
x |
An objects of class meteSSF; i.e. the spatial structure function |
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
data(anbo) pi1 <- meteSSF(anbo$spp, 'crcr', anbo$count, row=anbo$row, col=anbo$col, A=1, A0=16) plot(ssad(pi1))data(anbo) pi1 <- meteSSF(anbo$spp, 'crcr', anbo$count, row=anbo$row, col=anbo$col, A=1, A0=16) plot(ssad(pi1))
Based on information at an anchor scale (A0)
calcuate predicted species area relationship at larger scales
upscaleSAR(x, A0, Aup, EAR = FALSE)upscaleSAR(x, A0, Aup, EAR = FALSE)
x |
an object of class meteESF |
A0 |
the anchor scale at which community data are availible. |
Aup |
the larges area to which to upscale |
EAR |
logical. TRUE computes the endemics area relatinship; currently not supported |
Currently only doublings of area are supported and only
the SAR (not EAR) is supported. Upscaling works by iteratively
solving for the constraints ( and at larger scales)
that would lead to the observed data at the anchor scale. See
references for more details on this approach.
an object of class sar inheriting from data.frame with
columns A and S giving area and species richness, respectively
Andy Rominger <[email protected]>, Cory Merow
Harte, J. 2011. Maximum entropy and ecology: a theory of abundance, distribution, and energetics. Oxford University Press.
meteESF, meteSAR, empiricalSAR, downscaleSAR
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')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')