Functions and data for "A Primer of Ecology with R"

Description

Functions are primarily functions for systems of ordinary differential equations, difference equations, and eigenanalysis and projection of demographic matrices; data are for examples.

Details

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Stevens, M.H.H. (2009) A Primer of Ecology with R Springer, 2nd printing.

See Also

lvcompg, ode

Secondary succession data

Description

Functional group abundances (herbaceous annual, herbaceous perennial, woody) from one of the fields in the Buell-Small long term succession study (http://www.ecostudies.org/bss/). Data are based on visual estimates of percent cover, using annual means of each species, which are then summed for each functional group.

Format

A data frame with 147 observations on the following 3 variables.

AGE

a numeric vector; indicates the age of succession since abandonment from agriculture.

variable

plant functional type; a factor with levels Annual, Perennial, Woody

value

a numeric vector

Source

Data graciously provided by Scott Meiners (Eastern Illinois University, http://www.ecostudies.org/bss/).

References

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

Examples

data(BSsucc)
#lattice::xyplot(value~ AGE, groups=variable, data=BSsucc,
             #type='smooth', span=.3, ylab="Percent Cover",
             #xlab="Age Since Abandonment (y)",
             #auto.key=list(columns=3, space="top", lines=TRUE,
             #points=FALSE))

Data drawn approximately from Collins and Glenn (1991)

Description

Numbers of species which were observed in 1–19 sites.

Format

The format is: num [1:19] 32 16 10 9 8 7 8 6 4 5 ...

Source

Data are approximations of histogram values for a single year of data in:

Collins, S.L. and Glenn, S.M. (1991) Importance of spatial and temporal dynamics in species regional abundance and distribution. Ecology, 72, 654–664.

References

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

Examples

data(CandG)
barplot(CandG, names=1:19)

Closterium Population Data

Description

Data set from an experiment testing whether trophic heterogeneity influences long term population sizes.

Format

A data frame with 144 observations on the following 5 variables.

Nutrients

a factor with levels high low

No.per.ml

a numeric vector

Day

a numeric vector

rep

a factor with levels a b c d

ID

an ordered factor with levels a.low < d.low < c.low < b.low < c.high < a.high < d.high < b.high

Source

Stevens, M. H. H. and Steiner, C. E. (2006) Effects of predation and nutrient enrichment on a food web with edible and inedible prey. Freshwater Biology, 51, 666–671.

References

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

Examples

data(ClostExp)
#lattice::xyplot(log10(No.per.ml) ~ Day|Nutrients, data=ClostExp, groups=rep, type='l')

Lotka-Volterra Competition Games

Description

A pedagogical tool for learning about isoclines and stable equilibria.

Usage

LVCompGames(Alpha = NULL, r1 = 0.1, r2 = 0.1, num = 20, time = 10, step = 1)

Arguments

Value

First generates a plot of isoclines and initial points; the user is then prompted to "Hit <return>" in the console to see the trajectories. These will indicate the rate and path the trajectories, demonstrating, among other things, whether the equilibrium is stable.

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Lotka, A.J. (1956) Elements of Mathematical Biology. Dover Publications, Inc.

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

lvcomp2, lvcompg, clogistic,

Examples

## LVCompGames() # Hit return in the console to see the trajectories.

Simulation of Stochastic Metapopulation Models

Description

Originally focused on creating a community of core-satellite species, this function allows simulation of several metapopulation models, where colonization and extinction rates are stochastic draws from uniform distributions, with specified means and ranges.

Usage

MetaSim(
  Time = 50,
  NSims = 1,
  method = "hanski",
  ci = 0.25,
  e = 0.25,
  phi = 0.75,
  p0 = 0.5,
  D = 0.5
)

Arguments

Details

phi is one half of the relative range of each rate (colonization and extinction). For each time step, each rate is drawn from a uniform distribution, Unif(rate-phi, rate+phi). Thus, the range is 2*phi, and center on the specified mean (ci or e).

Value

Function returns a list with these components.

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Stevens. M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

gotelli, hanski, levins

Examples

out <- MetaSim(NSims=2)
pops <- out$Ns
matplot(out$t, pops, type='l')
title(sub=paste(out$method, "model"))

Population Simulator

Description

Resampling stochastic simulator for a single density-independent population.

Usage

PopSim(Rs, N0, years = 50, sims = 10)

Arguments

Details

Designed to simulate trajectories based on resampled observed N[t+1]/N[t].

Value

Returns a matrix of population sizes for time = t (rows) for each replicated population (columns).

References

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

sparrows

Examples

lambdas <- runif(10, .5, 1.5)
out <- PopSim(Rs=lambdas, years=50, N0=50)
matplot(0:50, out, type='l')
summary(out[51,])

The S-I-R Epidemilogical Disease Model with Births and Deaths

Description

The S-I-R epidemilogical disease model with births and deaths (population dynamics), for use with ode in the deSolve package. This model uses mass action transmission.

Usage

SIRbd(t, y, p)

Arguments

Details

The user does not put these directly into this function, but rather uses ode in the deSolve package.

Value

Returns of list of one component (required by ode).

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Ellner, S.P. and Guckenheimer, J. (2006) Dynamic Models in Biology, Princeton University Press.

Kermack, W.O. and McCormick, W.G. (1927) A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society, Series A, 115, 700–721.

Stevens, M.H.H. (2009) A Primer of Ecology with R, Use R! Series. Springer.

See Also

ross, SIRf, SIRd

Examples

library(deSolve)
N <- 10^6; R <- 0; I <- 1; S <- N - I - R
g <- 1/(13/365); b <- 1/50;
age <- 5; R0 <- 1 + 1/(b*age)
B <- R0 * (g + b) / N
parms <- c(B = B, g = g, b = b, m=b)
years <- seq(0,30, by=.1)
SIRbd.out <- data.frame(ode(c(S=S,I=I,R=R), years, SIRbd, parms, hmax=.01))
matplot(SIRbd.out[,1], sqrt(SIRbd.out[,-1]), type='l',
        lty=1:3, ylab="sqrt(No. of Individuals)", xlab='Years')
legend('right', c('S','I','R'), lty=1:3, col=1:3, bty='n')

The S-I-R Epidemilogical Disease Model

Description

The S-I-R epidemilogical disease model with density-dependent transmission, for use with ode in the deSolve package.

Usage

SIRd(t, y, p)

Arguments

Details

The user does not put these directly into this function, but rather uses ode in the deSolve package.

Value

Returns of list of one component (required by ode).

Author(s)

Hank Stevens <Hank.Stevens@miamioh.edu>

References

Ellner, S.P. and Guckenheimer, J. (2006) Dynamic Models in Biology, Princeton University Press.

Kermack, W.O. and McCormick, W.G. (1927) A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society, Series A, 115, 700–721.

Stevens, M.H.H. (2009) A Primer of Ecology with R, Use R! Series. Springer.

See Also

ross, SIRf, SIRbd

Examples

N <- 10^3; I <- R <- 1; S <- N - I - R
parms <- c(B=.01, g=4)
months <- seq(0, 3, by=0.01)
require(deSolve)
SIR.out <- data.frame( ode(c(S,I,R), months, SIRd, parms) )
matplot(months, SIR.out[,-1], type='l')
legend('right', c('R', 'I', 'S'), lty=3:1, col=3:1, bty='n')

The S-I-R Epidemilogical Disease Model with Frequency Dependent Transmission

Description

The S-I-R epidemilogical disease model with frequency dependent transmission, for use with ode in the deSolve package.

Usage

SIRf(t, y, p)

Arguments

Details

The user does not put these directly into this function, but rather uses ode in the deSolve package.

Value

Returns of list of one component (required by ode).

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Ellner, S.P. and Guckenheimer, J. (2006) Dynamic Models in Biology, Princeton University Press.

Kermack, W.O. and McCormick, W.G. (1927) A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society, Series A, 115, 700–721.

Stevens, M.H.H. (2009) A Primer of Ecology with R, Use R! Series. Springer.

See Also

ross, SIRd, SIRbd, ode

Examples

R <- 0; S <- 1000;  I <- 1000; N <- S+I+R
parmsf <- c(B=1, g=1)
Months <- seq(0, 8, by=0.1)
outf <- ode(c(S,I,R), Months, SIRf, parmsf)
matplot(Months, outf[,-1], type='l', ylab="Prevalence (I/N)")
legend('right', legend=c('S','I','R'), lty=1:3, col=1:3, bty='n')

The S-I-R Epidemilogical Disease Model

Description

The S-I-R epidemiological disease model with births and deaths (population dynamics), for use with ode in the deSolve package. This model uses scaled transmission, where z controls the degree of density- and frequency-dependence.

Usage

SIRmod(t, y, p)

Arguments

Details

The user does not put these directly into this function, but rather uses ode in the deSolve package.

Value

Returns of list of one component (required by ode).

Author(s)

Hank Stevens <Hank.Stevens@miamioh.edu>

References

Ellner, S.P. and Guckenheimer, J. (2006) Dynamic Models in Biology, Princeton University Press.

Kermack, W.O. and McCormick, W.G. (1927) A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society, Series A, 115, 700–721.

Stevens, M.H.H. (2009) A Primer of Ecology with R, Use R! Series. Springer.

See Also

ross, SIRf, SIRd

Examples

library(deSolve)
N <- 10^6; R <- 0; I <- 1; S <- N - I - R
g <- 1/(13/365); b <- 1/50; z <- 0;
age <- 5; R0 <- 1 + 1/(b*age)
B <- R0 * (g + b) / N
parms <- c(B = B, g = g, b = b, mu=b)
years <- seq(0,30, by=.1)
SIR.out <- data.frame(ode(c(S=S,I=I,R=R), years, SIRmod, parms, hmax=.01))
matplot(SIR.out[,1], sqrt(SIR.out[,-1]), type='l',
        lty=1:3, ylab="sqrt(No. of Individuals)", xlab='Years')
legend('right', c('S','I','R'), lty=1:3, col=1:3, bty='n')

Logistic growth with the Allee effect

Description

A function for continuous logistic growth with the Allee effect, for use with ode in the deSolve package.

Usage

alogistic(t, y, p)

Arguments

Details

The user does not put these directly into this function, but rather uses codeode in the deSolve package. The function is based on the logistic growth equation

\frac{dN}{dt} = rN\left(1-\alpha N\right)\left(1 - \frac{a+\tau}{N+\tau}\right)

with a being the threshold population size.

Author(s)

Hank Stevens

References

Stevens. M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

clogistic,dlogistic, thetalogistic, levins

Examples

library(deSolve)
p <- c(r=1,alpha=.01, a=10, tau=.1)
time <- 0:10
initialN <- 11
out <- ode(y=initialN, times=time,
             func=alogistic, parms=p)
plot(time, out[,-1], type='l')

Bipartite network properties

Description

A function to calculate the several properties of randomly constructed bipartite networks. This function installation of packages bipartite, igraph, and rARPACK.

Usage

bip_stability(
  Spp.a = 10:50,
  Spp.p = 5:25,
  C = c(0.05, 0.3),
  IS = NULL,
  quant = FALSE,
  ndd = 1,
  reps = 10
)

Arguments

Details

The interaction strengths are exponentially distributed, with mean of IS (rate = 1/IS). Nestedness is WNODF (Almeida-Neto et al. 2011). It can calculate modularity in two ways, using either the binary adjacency matrix (ones and zeroes, Clauset, Newman and Moore 2004) or a quantitative matrix (Beckett 2016); the latter takes much moore time to calculate, so it uses the binary matrix by default. It also tallies diversity as the total number of species and the connectance as the total number of links divided by the number of possible links.

To calculate resilience, the P by A bipartite matrix is expanded to a (P+A) x (P+A) symmetric matrix so the upper triangular portion are the effects of the animals on the plants, and the lower triangular portion is the effects of the plants on the animals.

The diagonal represents intraspecific density dependence; it is filled with the negative of the largest summed row of interaction strengths in the symmetric matrix. The symmatric matrix is interpreted as a Jacobian matrix. Therefore, resilience is the negative value of the real part of the dominant eigen value of the expanded symmetric matrix.

Value

Returns of list of a matrix with columns for species richness, connectance, nestedness, modularity, and resilience.

Author(s)

Hank Stevens <HankStevens@miamioh.edu>

References

M. Almeida-Neto and W. Ulrich. A straightforward computational approach for measuring nestedness using quantitative matrices. Environmental Modelling and Software, 26(2):173–178, 2011.

S. J. Beckett. Improved community detection in weighted bipartite networks. Royal Society Open Science, 3:140536, 2016.

A. Clauset, M. E. J. Newman, and M. Cristopher. Finding community structrue in very large networks. Physical Review E, 70:066111, 2004.

Examples

# b <- bip_stability(Spp.a = 16:60, Spp.p = 8:30, C=c(.05, 0.5), reps=10, quant=FALSE)
# pairs(b)

A Cat Function

Description

This function allows you to express your love of cats.

Usage

cat_function(love = TRUE)

Arguments

Author(s)

Hilary Parker

Examples

cat_function()

Two-species model of the storage effect

Description

Simulates a fluctuating environment over time, and two species' responses to the environment, after Chesson (1994).

Usage

chesson(
  alpha = c(1.1 * 1e-05, 1e-05),
  d = 0.1,
  years = 10,
  N0 = c(1000, 1e+05),
  w = c(0.6, 1),
  env.var = 1,
  specialization = 1,
  spread = 0.67,
  type = 1
)

Arguments

Details

The argument type controls the value of e^C, the effect of competition on reproduction, where the annual finite rate of increase is R=e^{E-C}. type = 1 causes e^C = \alpha_i N_{J,i}, that is, a species-specific fixed fraction of juveniles that depends on each species response to competition. This is illustrated in a for-loop in Stevens (2009, Ch. 9, Storage Effect, Simulating Dynamics). Any other value for type results in the same negative effect on both species that depends on the number of juveniles and the disturbance rate.

Value

Returns a list of length one, for use with ode in the deSolve package.

Author(s)

Hank Stevens (HankStevens@miamioh.edu)

References

Chesson, P.L. (1994) Multispecies competition in variable environments. Theoretical Population Biology, 45, 227–276.

Stevens. M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

succniche

Examples

out <- chesson(years=50)
layout(matrix(1:4, nc=2))
matplot(out[["time"]], out[["Ns"]], type='l', lty=c(1:3),
        xlab="Time", ylab="N", log="y")
plot(out[["time"]][-1], out[["env"]], type='l',
     xlab="Time", ylab="Environment")
matplot(out[["env"]], out[["Es"]], xlab="Environment",
 ylab="Density-independent reproduction")
matplot(out[["env"]], out[["Rs"]], xlab="Environment",
 ylab="Annual growth rate")

Continuous Logistic Growth

Description

A function for continuous logistic growth, for use with ode in the deSolve package.

Usage

clogistic(times, y, parms)

Arguments

Details

The user does not put these directly into this function, but rather uses ode in the deSolve package.

The function implements the logistic growth equation

\frac{dN}{dt} = rN\left(1-\alpha N\right)

or equivalently

\frac{dN}{dt} = rN\left(\frac{K-N}{K}\right)

Value

Returns of list of one component (required by ode).

Author(s)

Hank Stevens <HankStevens@miamioh.edu>

References

Stevens. M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

dlogistic, thetalogistic, levins, lvcomp2, lvcompg

Examples

library(deSolve)
p <- c(r=1, alpha=.01)
time <- 1:10
initialN <- 10
out <- ode(y=initialN, times=time,
             func=clogistic, parms=p)
plot(time, out[,-1], type='l')

Two-species Competition-colonization Metapopulation Model

Description

This model implements a Levins-type metapopulation model for two species, after Hastings (1980). For use with ode in the deSolve package.

Usage

compcol(t, y, params)

Arguments

Value

Returns a list of length one, for use with ode in the deSolve package.

Author(s)

Hank Stevens <HankStevens@miamioh.edu>

References

Hastings, A. (1980) Disturbance, coexistence, history, and competition for space. Theoretical Population Biology, 18, 363–373.

Stevens. M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

levins, compcolM, succniche

Examples

library(deSolve)
pars <- c(c1 = .3, c2 = 1, m1 = .1, m2 = .1)
pops <- c(.1,.1)
out <- ode(y=pops, t=0:20, fun=compcol, parms = pars)
matplot(out[,1], out[,-1], type='l')

Multi-species Competition-colonization Model, With Habitat Destruction

Description

Multi-species competition colonization model, with habitat destruction, after Nee and May (1992). For use with ode in the deSolve package.

Usage

compcolM(t, y, params)

Arguments

Value

Returns a list of length one, for use with ode in the deSolve package.

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Nee, S. and May, R.M. (1992) Dynamics of metapopulations: habitat destruction and competitive coexistence. Journal of Animal Ecology, 61, 37–40.

Stevens. M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

levins, compcol, succniche

Examples

library(deSolve)
S <- 10
ci <- 2^seq(-5, 5, length=S)
m <- rep(.1, S)
params <- list(ci=ci, m=m, S=S, D=0)
init.N <- rep(0.01, S); t=seq(1, 200, .1)
cc.out <- ode(init.N, t, compcolM, params)
matplot(t, cc.out[, -1], type="l", ylab="Proportion of Habitat", xlab="Years")

Smooth coneflower data

Description

A data set containing size, survival, and flowering in smooth coneflower

Usage

data(coneflower)

Format

A data frame with 136 rows and 5 variables:

logA

natural log of total leaf area in the first year

logAp

natural log of total leaf area in the second year (Ap = A prime)

surv

indicator of survival from year one to year 2 (0,1)

flower_p

indicator of flowering in year 2 (0,1)

Source

Data provided graciously by Rachel Collins (Roanoke College).

Examples

data(coneflower)
ggplot2::qplot(logA, logAp, data=coneflower)

Smooth coneflower new recruits

Description

A data set containing recruit size and survival.

Usage

data(coneflowerrecruits)

Format

A data frame with 36 rows and 3 variables:

area17

total leaf area in the first year

surv18

indicator of survival from year one to year 2 (0,1)

area19

total leaf area in the third year

Smooth coneflower seed data

Description

A data set containing size and seed set of individual coneflowers.

Usage

data(coneflowerseeds)

Format

A data frame with 136 rows and 5 variables:

logAs

natural log of total leaf area in the first year

seeds

number of seeds produced in the first year

Examples

data(coneflowerseeds)
ggplot2::qplot(logAs, seeds, data=coneflowerseeds)

Discrete Logistic Growth

Description

Single species discrete logistic growth – a difference equation. A function for continuous logistic growth, for use with ode in the deSolve package, using method = 'euler' and integer time steps.

Usage

dlogistic(t, y, p)

Arguments

Details

Of the form,

N_{t+1} - N_{t} = r_d N_{t}\left(1 - \alpha N_{t}\right)

Value

Returns of list of one component (required by ode).

Author(s)

Hank Stevens (HankStevens@miamioh.edu)

References

Stevens. M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

clogistic, lvcompg

Examples

library(deSolve)
# MUST use the 'euler' integration method with integer time steps
p <- c(rd=1, alpha=.01)
time <- 0:10
initialN <- 10
out <- ode(y=initialN, times=time,
             func=dlogistic, parms=p, method='euler')
plot(time, out[,-1], type='l')

Discrete Logistic Competition

Description

A function to simulate discrete 2 species Lotka-Volterra competition.

Usage

dlvcomp2(N, alpha, rd = c(1, 1))

Arguments

Value

Returns a vector of length 2, containing N[t+1] for both species.

Author(s)

Hank Stevens (HStevens@muohio.edu)

References

Stevens. M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

dlogistic, lvcomp2, lvcomp3, lvcompg

Examples

alphs <- matrix(c( .01, .005,
                  .008, .01), ncol=2, byrow=TRUE)
t <- 20
N <- matrix(NA, nrow=t+1, ncol=2)
N[1,] <- c(10,10)
for(i in 1:t) N[i+1,] <- dlvcomp2(N[i,], alphs)
matplot(0:t, N, type='l', col=1, ylim=c(0,110))
abline(h=1/alphs[1,1], lty=3)
text(0, 1/alphs[1,1], "K", adj=c(0,0))
legend("right", c(expression("Sp.1 "*(alpha[21]==0.008)),
                  expression("Sp.2 "*(alpha[12]==0.005))), lty=1:2, bty='n')

Propagule Rain Metapopulation Model

Description

A function for the propagule rain or mainland-island metapopulation dynamics, for use with ode in the deSolve package.

Usage

gotelli(t, y, parms)

Arguments

Value

Returns a list of length one, for use with ode in the deSolve package.

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Gotelli, N.J. (1991) Metapopulation models: the rescue effect, the propagule rain, and the core-satellite hypothesis. The American Naturalist, 138, 768–776.

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

gotelli, hanski, lande, MetaSim, clogistic

Examples

## The function is currently defined as
function (t, y, parms)
{
    p <- y[1]
    with(as.list(parms), {
        dp <- ce * (1 - p) - e * p
        return(list(dp))
    })
  }

library(deSolve)
p <- c(ce=.1, e=.01)
time <- 1:10
initialN <- .3
out <- ode(y=initialN, times=time, func=gotelli, parms=p)
plot(time, out[,-1], type='l')

Core-satellite Metapopulation Model

Description

A function for the core-satellite metaapopulation dynamics, for use with ode in the deSolve package.

Usage

hanski(t, y, parms)

Arguments

Value

Returns a list of length one, for use with ode in the deSolve package.

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Hanski, I. (1982) Dynamics of regional distribution: the core and satellite species hypothesis. Oikos, 38, 210–221.

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

gotelli, hanski,lande, MetaSim, clogistic

Examples

prms <- c(ci<- 0.15, e=0.05)
out <- ode(y=.2, times=1:100, func=hanski, parms=prms )
matplot(out[,1], out[,2], type='l', ylab="p", xlab="time")

A Lotka-Volterra Model of Intraguild Predation

Description

A Lotka-Volterra model of intraguild predation, after Holt and Polis (1997). For use with ode in the deSolve package.

Usage

igp(t, y, params)

Arguments

Value

Returns a list of length one which is the vector of the rates of increase (required by ode).

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Holt, R.D. and Polis, G.A. (1997) A theoretical framework for intraguild predation. The American Naturalist, 149, 745–764.

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

lvcompg, scheffer

Examples

library(deSolve)
params <- c(bpb= 0.032, abp=10^-8, bpn=10^-5, anp=10^-4,  mp=1,
             bnb=0.04, abn=10^-8, mn=1,
             r=1, abb=10^-9.5)
t=seq(0, 60, by=.1)
N.init <- c(B = 10^9, N = 10^4, P = 10^3)
igp.out <- ode(N.init, t, igp, params)
matplot(t, log10(igp.out[,-1]+1), type="l",
          ylab="log(Abundance)")
legend('right', c("B", "N", "P"), lty=1:3, col=1:3, lwd=2,
       bty="n")

A Metapopulation Model with Habitat Destruction

Description

A function for the metaapopulation dynamics, for use with ode in the deSolve package.

Usage

lande(t, y, parms)

Arguments

Value

Returns a list of length one, for use with ode in the deSolve package.

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

P. Kareiva and Wennergren, U. (1995) Connecting landscape patterns to ecosystem and population processes. Nature, 373, 299–302.

Lande, R. (1987) Extinction thresholds in demographic models of territorial populations. The American Naturalist, 130, 624–635.

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

gotelli, hanski,levins, MetaSim, clogistic

Examples

## The function is currently defined as
function (t, y, parms)
{
    p <- y[1]
    with(as.list(parms), {
        dp <- ci * p * (1 - D - p) - e * p
        return(list(dp))
    })
  }
library(deSolve)
p <- c(ci=.1, e=.01, D=.5)
time <- 1:10
initialN <- .3
out <- ode(y=initialN, times=time, func=lande, parms=p)
plot(time, out[,-1], type='l')

Classic Metapopulation Model

Description

A function for the classic metaapopulation dynamics, for use with ode in the deSolve package.

Usage

levins(t, y, parms)

Arguments

Value

Returns a list of length one, for use with ode in the deSolve package.

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Levins, R. (1969) Some demographic and genetic consequences of environmental heterogeneity for biological control. Bulletin of the Entomological Society of America, 15, 237–240.

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

gotelli, hanski,lande, MetaSim, clogistic

Examples

## The function is currently defined as
function (t, y, parms)
{
    p <- y[1]
    with(as.list(parms), {
        dp <- ci * p * (1 - p) - e * p
        return(list(dp))
    })
  }
library(deSolve)
p <- c(ci=.1, e=.01)
time <- 1:10
initialN <- .3
out <- ode(y=initialN, times=time, func=levins, parms=p)
plot(time, out[,-1], type='l')

Two Species Lotka-Volterra Competition

Description

System of ordinary differential equations for two species Lotka-Volterra competition. For use with ode in the deSolve package.

Usage

lvcomp2(t, n, parms)

Arguments

Details

The parameters include r1, r2, a11, a12, a21, a22 with the usual meanings. Here the a's are the per capita effects which determine K (a11 = 1/K).

Value

Returns a list of length one which is the rate of increase (required by ode).

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Lotka, A.J. (1956) Elements of Mathematical Biology. Dover Publications, Inc.

Stevens. M.H.H. (2009) A Primer of Theoretical Population Ecology with R. Use R! Series. Springer.

See Also

lvcomp3, lvcompg, clogistic

Examples

## The function is currently defined as
function (t, n, parms)
{
    with(as.list(parms), {
        dn1dt <- r1 * n[1] * (1 - a11 * n[1] - a12 * n[2])
        dn2dt <- r2 * n[2] * (1 - a22 * n[2] - a21 * n[1])
        list(c(dn1dt, dn2dt))
    })
  }
library(deSolve)
parms <- c(r1 = 1, r2 = 0.1, a11 = 0.2, a21 = 0.1, a22 = 0.02, a12 = 0.01)
initialN <- c(1, 1)
out <- ode(y = initialN, times = 1:100, func = lvcomp2, parms = parms)
matplot(out[, 1], out[, -1], type = "l")

Three Species Lotka-Volterra Competition

Description

System of ordinary differential equations for three species Lotka-Volterra competition. For use with ode in the deSolve package.

Usage

lvcomp3(t, n, parms)

Arguments

Details

The parameters include r, a with the usual meanings. Here the a's are the per capita effects which determine K (a11 = 1/K1).

Value

Returns a list of length one which is the rate of increase (required by ode).

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Lotka, A.J. (1956) Elements of Mathematical Biology. Dover Publications, Inc.

Stevens. M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

lvcomp2, lvcompg, clogistic

Examples

## The function is currently defined as
function (t, n, parms)
{
    with(as.list(parms), {
        dn1dt <- r1 * n[1] * (1 - a11 * n[1] - a12 * n[2] - a13 *
            n[3])
        dn2dt <- r2 * n[2] * (1 - a22 * n[2] - a21 * n[1] - a23 *
            n[3])
        dn3dt <- r3 * n[3] * (1 - a33 * n[3] - a31 * n[1] - a32 *
            n[2])
        list(c(dn1dt, dn2dt, dn3dt))
    })
  }

library(deSolve)
parms <- c(r1 = 0.1, r2 = 0.2, r3 = 0.3,
a11 = 0.1, a12 = 0.01, a13 = 0.01,
a21 = 0.01, a22 = 0.15, a23 = 0.01,
a31 = 0.01, a32 = 0.01, a33 = 0.2)
initialN <- c(1, 1, 1)
out <- ode(y = initialN, times = 1:100, func = lvcomp3, parms = parms)
matplot(out[, 1], out[, -1], type = "l")

A General Lotka-Volterra Competition Model

Description

A general Lotka-Volterra competition model, for any number of species. For use with ode in the deSolve package. This function uses a vector and matrix within the list of parameters.

Usage

lvcompg(t, n, parms)

Arguments

Value

Returns a list of length one which is the vector of the rates of increase (required by ode).

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Lotka, A.J. (1956) Elements of Mathematical Biology. Dover Publications, Inc.

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

lvcomp3, clogistic, igp, scheffer

Examples

## Specify the number of species
S <- 10
alpha <- .01
r <- runif(S)*2
a <- matrix(rnorm(S^2, m=alpha, sd=alpha/10), nrow=S, ncol=S)
parms <- list(r,a)
t=seq(0,40, by=.1)
N0 <- runif(S)/(S*alpha)
library(deSolve)
lvout <- ode(N0, t, lvcompg, parms)
matplot(t, lvout[,-1], type="l", ylab="N", log='y')

Moth Species Richness

Description

Data set of moth species richness from Ohio and Indiana, USA.

Format

A data frame with 21 observations on the following 6 variables.

region

a factor with levels NCT WAP for the two collection regions.

site

a factor with levels associated with county names.

area

a numeric vector for the area of each forest fragment

spp

a numeric vector, the number of moth species.

lat

a numeric vector; latitude

long

a numeric vector; longitude

Source

Data proided graciously by Keith Summerville and Thomas Crist; see "A Primer of Ecology with R" for specific references.

References

K. S. Summerville and T. O. Crist. 2003. Determinants of lepidopteran community composition and species diversity in eastern deciduous forests: roles of season, ecoregion and patch size. Oikos, 100:134-148.

K. S. Summerville and T. O. Crist. 2004. Contrasting effects of habitat quantity and quality on moth communities in fragmented landscapes. Ecography, 27:3-12.

Examples

data(moths)
plot(spp ~ area, data=moths)

Function to generate 1/f noise.

Description

Generates 1/f noise with a specified power or amplitude.

Usage

one_over_f(gamma = 1, N = 200)

Arguments

Author(s)

Hank Stevens

References

J. M. Halley. Ecology, evolution and 1/f-noise. Trends in Ecology & Evolution, 11:33-37, 1996. O. L. Petchey, A. Gonzalez, and H. B. Wilson. Effects on population persistence: the interaction between environmental noise colour, intra-specific competition and space. Proceedings of the Royal Society of London Series B, 264:1841-1847, 1997. J. E. Cohen, C. M. Newman, A. E. Cohen, O. L. Petchey, and A. Gonzalez. Spectral mimicry: a method of synthesizing matching time series with different Fourier spectra. Circuits, Systems and Signal Processing, 18:431-442, 1999.

See Also

[spec_mimic()] to rearrange one vector, X, to mimic the spectrum of another vector, Y; [plot_f()] to plot the time series and the spectrogram of the series.

Examples

set.seed(1)
time.series <- one_over_f(gamma=2, N=50)
plot(1:50, time.series, type='l', main="Reddened noise")
time.series <- one_over_f(gamma=0, N=50)
plot(1:50, time.series, type='l', main="White noise")
one_over_f()

Analysis of Jacobian Lotka-Volterra Food Web Matrices

Description

Used primarily to repeat simulations and analyses of Pimm and Lawton (1977), given a Jacobian matrix. Analyses include eigenanalysis, but also measuring average interaction strength (May 1972), average intraspecific negative density dependence, and the strength of the omnivory interaction, if present.

Usage

pimmlawton(mat, N = 1, omni.i = NA, omni.j = NA, omega = NULL)

Arguments

Details

This function simulates a constrained randomization of a Jacobian food web matrix. The matrix it uses mat is of a special form, which assumes that all non-zero values are drawn from a uniform distribution between zero and a value of some specified magnitude, either positive or negative.

Value

Returns a data frame, where each row corresponds to a single random Jacobian matrix, with the following columns.

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

May, R.M. (1973) Stability and Complexity in Model Ecosystems, volume 6 of Monographs in Population Biology. Princeton University Press.

McCann, K., Hastings, A. and Huxel, G.R. (1998) Weak trophic interactions and the balance of nature. Nature, 395, 794–798.

Pimm, S.L and Lawton, J.H. (1997) Number of trophic levels in ecological communities. Nature, 268, 329–331.

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer. 2009.

Examples

### A relevant style of matrix for the first food chain in Pimm and Lawton (1977).
### Note each non-zero element is the appropriate sign, and the maximum magnitude
### specified by Pimm and Lawton (1977).

Aq = matrix(c(
   -1, -10,   0,   0,
  0.1,   0, -10,   0,
    0, 0.1,   0, -10,
    0,   0,  0.1,  0),
  nrow=4, byrow=TRUE)

pimmlawton(Aq, N=1)

out <- pimmlawton(Aq, N=2000)
out <- subset(out, -1/DomEig <150)
hist(-1/out$DomEig, main="Frequencies of Return Time")

plot_f

Description

Function to plot a time series and its periodogram, and calculate the confidence interval of 2 times the spectral power.

Usage

plot_f(z)

Arguments

Author(s)

Hank Stevens

References

J. M. Halley. Ecology, evolution and 1/f-noise. Trends in Ecology & Evolution, 11:33-37, 1996. O. L. Petchey, A. Gonzalez, and H. B. Wilson. Effects on population persistence: the interaction between environmental noise colour, intra-specific competition and space. Proceedings of the Royal Society of London Series B, 264:1841-1847, 1997. J. E. Cohen, C. M. Newman, A. E. Cohen, O. L. Petchey, and A. Gonzalez. Spectral mimicry: a method of synthesizing matching time series with different Fourier spectra. Circuits, Systems and Signal Processing, 18:431-442, 1999.

See Also

[one_over_f()] to generate 1/f noise; [spec_mimic()] to rearrange one vector, X, to mimic the spectrum of another vector; [spectrum()] for the hard work.

Examples

## white noise
plot_f(z=runif(50))

plot_f

The Lotka-Volterra Predator-prey Model

Description

The Lotka-Volterra predator-prey model, for use with ode in the deSolve package.

Usage

predpreyLV(t, y, params)

Arguments

Value

Returns a list of length one, for use with ode in the deSolve package.

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Lotka, A.J. (1956) Elements of Mathematical Biology. Dover Publications, Inc.

Stevens. M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

predpreyRM

Examples

params1 <- c(b=.5, a=.01, s=.2, e=.1)
Time <- seq(0,100, by=.1) # Set time here
LV.out <- ode(c(H0=25,P0=5), Time, predpreyLV, params1)
matplot(Time, (LV.out[,2:3]), type="l", ylab="Population Size")

Rosenzweig-MacArthur Predator-prey Model

Description

An implementation of a predator-prey model, after Rosenzweig and MacArthur (1963). Includes prey density-dependence, and a type-II predator functional response. For use with ode in the deSolve package.

Usage

predpreyRM(t, y, p)

Arguments

Value

Returns a list of length one, for use with ode in the deSolve package.

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Rosenzweig, M.L. and MacArthur, R.H. (1963) Graphical representation and stability conditions of predator-prey interactions. The American Naturalist, 97, 209–223.

Stevens. M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

predpreyLV

Examples

library(deSolve)
pars <- c(b = .8, e = 0.07, s = .2, w = 5, D = 400, alpha = 0.001)
Time <- 50
RM1 <- ode(c(900,120), 1:Time, predpreyRM, pars)
matplot(1:Time, RM1[,-1], type='l')

Weekly deaths from bubonic plague in Bombay in 1905–06

Description

Kermack and McCormick (1927) provided data on the number of plague deaths per week in Bombay in 1905–06 (Bombay is the former name for the Indian coastal city Mumbai. It is the capital of Maharashtra and is one of the largest cities in the world).

Format

A data frame with 32 observations on the following 2 variables.

Week

a numeric vector

CumulativeDeaths

a numeric vector

Source

Data provided kindly by S.P. Ellner (Cornell University)

References

Kermack, W.O. and McCormick, W.G. (1927) A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society, Series A, 115, 700–721.

Examples

data(ross)
str(ross) ; plot(CumulativeDeaths ~ Week, data=ross, type='b')

A resource-based model of alternative stable states

Description

A model of floating vs. submerged plant dominance in shallow aquatic systems, after Scheffeer et al. (2003). For use with ode in the deSolve package. Floating plants are better competitors for light, as long as submerged plants cannot drive down nitrogen levels.

Usage

scheffer(t, y, p)

Arguments

Value

Returns a list of length one which is the vector of the rates of increase (required by ode).

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Scheffer, M., Szabo, S., Gragnani, A., van Nes, E.H., Rinaldi, S., Kautsky, N., Norberg, J., Roijackers, R.M.M. and Franken, R.J.M. (2003) Floating plant dominance as a stable state. Proceeding of the National Academy of Sciences, U.S.A., 100, 4040–4045.

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

lvcompg, igp

Examples

p <- c(N=2.5, as=0.01, af=0.01, b=0.02, qs=0.075, qf=0.005,
       hs=0, hf=0.2, ls=0.05, lf=0.05, rs=0.5, rf=0.5, W=0)
t <- 1:200
Initial <- c(F=10, S=10)
S.out1 <- ode(Initial, t, scheffer, p)
matplot(t, S.out1[,-1], type='l')
legend('right', c("F", "S"), lty=1:2, col=1:2, bty='n')

Song Sparrow Data Set

Description

Song Sparrow (Melospiza melodia) counts in Darrtown, OH, USA. From Sauer, J. R., J.E. Hines, and J. Fallon. 2005. The North American Breeding Bird Survey, Results and Analysis 1966–2004. Version 2005.2. USGS Patuxent Wildlife Research Center, Laurel, MD.

Format

A data frame with 36 observations on the following 3 variables.

Year

a numeric vector

Count

a numeric vector

ObserverNumber

a numeric vector

Source

http://www.pwrc.usgs.gov/BBS/

References

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

PopSim

Examples

data(sparrows)
## maybe
str(sparrows)
plot(Count ~ Year, sparrows)

Function to mimic the power spectrum of an observed time series.

Description

This function rearranges one vector, X, to mimic the spectrum of another vector, Y.

Usage

spec_mimic(X, Y = NULL, gamma = 1)

Arguments

Details

If Y is NULL, this function will use [one_over_f()] to generate a random series with power = gamma.

Author(s)

Hank Stevens

References

J. M. Halley. Ecology, evolution and 1/f-noise. Trends in Ecology & Evolution, 11:33-37, 1996. O. L. Petchey, A. Gonzalez, and H. B. Wilson. Effects on population persistence: the interaction between environmental noise colour, intra-specific competition and space. Proceedings of the Royal Society of London Series B, 264:1841-1847, 1997. J. E. Cohen, C. M. Newman, A. E. Cohen, O. L. Petchey, and A. Gonzalez. Spectral mimicry: a method of synthesizing matching time series with different Fourier spectra. Circuits, Systems and Signal Processing, 18:431-442, 1999.

See Also

[one_over_f()] to generate 1/f noise; [plot_f()] to plot the time series and the spectrogram of the series.

Examples

N = 50
set.seed(1)
X1 <- runif(N)
Y <- one_over_f(gamma=2, N=N)
X2 <- spec_mimic(X1, Y)
series <- cbind(X1, Y, X2)
matplot(1:50, series, type='l')
legend("bottomright", legend=colnames(series), col=1:3, lty=1:3)

A Four-state model of Successional Dynamics

Description

This is the five-state, two-species model of the succession-niche model, after Pacala and Rees (1998). For use with ode in the deSolve package.

Usage

succniche(t, y, params)

Arguments

Value

Returns a list of length one, for use with ode in the deSolve package.

Author(s)

Hank Stevens <HStevens@muohio.edu>

References

Pacala, S.W. and Rees, M. (1998) Models suggesting field experiments to test two hypotheses explaining successional diversity. The American Naturalist, 152, 729–737.

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

levins, compcol, compcolM

Examples

params.suc <- c(a=7, c=0.2, g=.1, m=0.04, D=0)
t=seq(0,50,.1)
init.suc <- c(S=0, E=0.5, M=0.5, R=0.00) # Free space is implicit, F=1-(S+E+M+R).
ccg.out <- data.frame(ode(init.suc, t, succniche, params.suc))
matplot(t, ccg.out[,-1], type="l", ylab="Relative Frequency",
         xlab="Time", ylim=c(0,1) )
legend("right", colnames(ccg.out)[5:2], lty=4:1,  bty="n")

Continuous Theta-Logistic Growth

Description

A function for continuous theta-logistic growth, for use with ode in the deSolve package.

Usage

thetalogistic(times, y, parms)

Arguments

Details

The user does not put these directly into this function, but rather uses ode in the deSolve package. See ode in the deSolve package.

Value

Returns of list of one component (required by ode).

Author(s)

Hank Stevens (HStevens@muohio.edu)

References

Sibly, R.M., Barker, D., Denham, M.C., Hone, J., and Pagel, M. (2005) On the regulation of populations of mammals, birds, fish, and insects. Science, 309, 607–610.

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

clogistic

Examples

library(deSolve)
p <- c(r=1,alpha=.01, theta=.5)
time <- seq(1,10, by=.1)
initialN <- 10
out <- ode(y=initialN, times=time, func=thetalogistic, parms=p)
plot(time, out[,-1], type='l')

Percent cover of six perennial herbaceous plants

Description

Percent cover of six of the most common herbaceous perennial species from the Buell-Small long term succession study (http://www.ecostudies.org/bss/). Data are plot-level visual estimates of percent cover.

Format

A data frame with 15140 observations on the following 8 variables.

X

a numeric vector

Genus

a factor with levels Aster, Euthamia, Solidago

Epithet

a factor with levels canadensis, gigantea, graminifolia, novae-angliae, pilosus, rugosa

FieldName

a factor with levels C3, C4, C5, C6, C7, D1, D2, D3, E1, E2

Age

a numeric vector indicating the number of years of succession, since abandonment from agriculture.

PlotId

a numeric vector

Cover

a numeric vector; percent cover, estimated visually.

Species

a factor with levels A.novae-angliae, A.pilosus, E.graminifolia, S.canadensis, S.gigantea, S.rugosa

Source

Data graciously provided by Scott Meiners (Eastern Illinois University, http://www.ecostudies.org/bss/).

References

Stevens, M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

Examples

data(weeds)
str(weeds);
# lattice::xyplot(Cover ~ Age, data=weeds, groups=Species,
# type=c("a"), auto.key=list(lines=TRUE, points=FALSE, columns=3),
# ylim=c(-1,20))