Ecology Lab
Wilkes University 2014
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Lab 1: Kirby Park Tree Diversity
Background
Ecological edges are formed then two contrasting habitats are
adjacent. Forest-field edges are excellent study locations to
study edge effects – changes in ecological conditions that occur
at the edge.
Lab Objectives:
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
Familiarize students with data collection methods
Familiarize students with data analysis including
o Species accumulation curves
o T-test and Mann-Whitney U tests
o Graphical presentation of medians and quantiles
o Graphical presentation of species accumulation curves
Lab Length: 2 weeks
Equipment:
Field notebook, dbh tape, min 10 m measuring tape
Week 1
At arbitrary starting point count trees within an 8 m radius
circle. All trees are identified to species and dbh measured.
One track of plots are located along the forest edge and another
parallel track is located just to the interior but not
overlapping with the edge track. Six plot of edge and interior
are sampled.
Week 2
Students develop a hypotheses and predictions related to the
data collected. These hypotheses should account for edge and
interior environments and
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
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H1: Tree density
H2: Tree sizes
H3: Species richness
2
H1:
Prediction 1:
Graph:
Analysis:
H2:
Prediction 2:
Graph:
Analysis:
H3:
Prediction 3:
Graph:
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Analysis:
Caveats



was sampling adequate for species richness assessment?
o Species Accumulation curves
What is the distribution of the data?
o Histograms
Statistical Inference
Reporting:
Inference:
Lab Report
Write up a lab report, in first person with





Short abstract
Introduction that explains your hypotheses and predictions
Methods that explain how do did it
o include tools and accuracy of measurements
o how sample sites were determined (systematic, random,
arbitrary)
Results that simply give the outcomes
o Start generally (sample sizes, distributions)
o Refer to figures
o Give results of statistics
Discussion that ties it all together
o discusses the problems and solution
o maybe more interesting questions that came up
o Alternative hypothesis should also be stated
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
Literature Cited
5
Lab 2: Phylogenetic analysis of ecological
traits
Background:
Phylogenetics is the recovery of evolutionary history by
reconstructing the relative topology branching points as well as
providing the number of changes that have occurred between
groups. These data are required to determine if traits are a
homoplasy, synapomorphy, or symplesiomorphy.
Lab Objectives:



Familiarize students phylogenetic methods
Familiarize students with character maps
Familiarize students with phylogenetic-friendly data sets
The data
Use GenBank http://www.ncbi.nlm.nih.gov/genbank/
The analysis
Please use http://www.phylogeny.fr/
The critters
Assigned in class
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Lab 3: Human Demography:
Cemetery Data
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Lab 4: Population Growth
Part 1 Deterministic models: exponential
growth
# intrinsic reproductive rate
r <- 0.1
# let's simulate 80 years
t <- 1:80 # 50 years
#start with 1 female
n_01 <- 1
# set the equation
n_t <- n_01*exp(r*t)
# see the numbers
n_t
#let's plot
plot(t, n_t, type="o", ylim=c(0,1000))
#increase the starting pop to 10
n_010 <- 10
n_t2 <- n_010*exp(r*t)
#add these data to the plot
lines(t, n_t2, type="o", col="red", pch=17 )
#increase the starting pop to 100
n_0100 <- 100
n_t3 <- n_0100*exp(r*t)
#add these data to the plot
lines(t, n_t3, type="o", col="blue", pch=16)
Export this graph to Word
1. Write a short statement on what you did
2. What a short statement on the effect of changing the starting
population on population dynamics
Since many journals do not print color graphs, consider using different line
types (e.g., solid, dash, dot) by using lty=X and X is 1,2,3, etc.
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Part 1.2 The effect of changing r, the intrinsic
population growth rate
# run simulation for 80 generations
t <- 1:80
#start population with 10
n_0 <- 10
# start with r = -0.1
r <- -0.01
#run "simulation"
n_t1 <- n_0*exp(r*t)
#plot
plot(t, n_t1, type="o", ylim=c(0,100))
#let's change r to 0
r2 <- 0
#run simulation
n_t2 <- n_0*exp(r2*t)
#add to plot
lines(t, n_t2, type="o", col="green", pch=17)
#lets change r to 0.01
r3 <- 0.01
#run simulation
n_t3 <- n_0*exp(r3*t)
#add line to plot
lines(t, n_t3, type="o", col="blue", pch=17)
#lets change r to 0.025
r4 <- 0.025
#run simulation
n_t4 <- n_0*exp(r4*t)
#add line to plot
lines(t, n_t4, type="o", col="red", pch=17)
#lets change r to 0.05
r5 <- 0.05
#run simulation
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n_t5 <- n_0*exp(r5*t)
#add line to plot
lines(t, n_t5, type="o", col="orange", pch=17)
#lets change r to 0.06
r6 <- 0.06
#run simulation
n_t6 <- n_0*exp(r6*t)
#add line to plot
lines(t, n_t6, type="o", col="purple", pch=17)
Export this graph to Word
1. Write a short statement on what you did
2. What a short statement on the effect of changing r on population
dynamics
Part 2. Deterministic models: Logistic
Growth
Part 2.1 Altering carrying capacity
# run simulations for 100 generations
t <- 1:100
#let's keep r fixed
r <- 0.1
#let's keep the initial populations fixed at 10
n_0 <- 10
# let's be nice and have a large carrying capacity
k <- 10000
#do the calculation
#be careful with the parentheses!!!!
n_t <- k/(1+((k-n_0)/n_0)*exp(-r*t))
#plot the result
plot(t, n_t, type="o", ylim=c(0,11000))
# add a horizontal line to show carrying capacity
abline(h=10000)
#let's be less nice and reduce the carrying capacity to 4000
10
k2 <- 4000
#rerun
n_t2 <- k2/(1+((k2-n_0)/n_0)*exp(-r*t))
lines(t, n_t2, type="o", col="orange")
abline(h=4000, col="orange")
#let's put the squeeze on and reduce carrying capacity to 2000
k3 <- 2000
n_t3 <- k3/(1+((k3-n_0)/n_0)*exp(-r*t))
lines(t, n_t3, type="o", col="blue")
abline(h=2000, col="blue")
#let's put the squeeze on and reduce carrying capacity to 1000
k4 <- 1000
n_t4 <- k4/(1+((k4-n_0)/n_0)*exp(-r*t))
lines(t, n_t4, type="o", col="red")
abline(h=1000, col="red")
Export this graph to Word
1. Write a short statement on what you did
2. What a short statement on the effect of changing K on population
dynamics
Part 2.2 The effect of changing r in a logistic model
# run simulations for 100 generations
t <- 1:200
#let's keep the initial populations fixed at 10
n_0 <- 10
#let's keep the carrying capacity fixed at 4000
k <- 4000
#lower r
r1 <- 0.05
n_t1 <- k/(1+((k-n_0)/n_0)*exp(-r1*t))
plot(t, n_t1, type="o")
abline(h=4000)
#increase r
r2 <- 0.075
n_t2 <- k/(1+((k-n_0)/n_0)*exp(-r2*t))
lines(t, n_t2, type="o", col="purple")
#increase r again
r3 <- 0.1
n_t3 <- k/(1+((k-n_0)/n_0)*exp(-r3*t))
lines(t, n_t3, type="o", col="red")
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Export this graph to Word
1. Write a short statement on what you did
2. What a short statement on the effect of changing r on population
dynamic
Part 2.3 Growth rates in a logistic model
k <- 1000
n <- 1:1000
r <- 0.1
growth.rate <- n*r*((k-n)/(k))
plot(n,growth.rate)
abline(v=k/2)
Export this graph to Word
1. Write a short statement on what you did
2. Interpret the graph
3. What does the vertical line
Part 3 Population Lags
1. Go to http://www.cbs.umn.edu/populus/installer and download Populus
2. Click on Model -> Single species dynamics -> Density-dependent growth
3. You can do everything we just did in R in this Window (you probably
want to kill me now)
4. Under model click Lagged Logistic
5. Make the lag (tao) = 1, increase r from 0.1 to 1 (note the line
relative to K)
6. With r=0.3, increase tao from 0 to 5
Export this graph to Word
1. Write a short statement on what you did
2. Interpret the modifications you made. A paragraph for steps 5 and 6
Part 4: Stochastic Models
######################
#
#
thanks to Peter Houk (peterhouk@gmail.com)
#
#########################
t<-100; alpha<-0.01; F<-0.6; N0<-80; r0 <- 1
r<-c(r0, numeric(t))
for (i in 1:t)
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r[i+1]<- {
runif(1,0.2,1.8)
}
N<-c(N0, numeric(t))
for (i in 1:t) {
N[i+1]<(N[i]+r[i]*N[i]*(1-(N[i]*alpha))-F*N[i])
}
plot(0:t, N, type="l", xlab="time", ylab="fish population")
# Now repeat 100 times and some CI bands
t<-100
bevholt<-function(alpha=0.01, r0=1.2, F=0.6, N0=80, t=100) {
r<-c(r0, numeric(t))
for (i in 1:t) r[i+1]<- {
runif(1,0.4,1.4)
}
N<-c(N0, numeric(t))
for (i in 1:t) N[i+1]<- {
(N[i]+r[i]*N[i]*(1-(N[i]*alpha))-F*N[i])
}
return(N)
}
pop.sim<-bevholt()
plot(0:t, pop.sim, type="l", xlab="time", ylab="fish population")
sims<-replicate(10, {
output<-matrix(bevholt(), nrow=101)
},
simplify=TRUE)
matplot(0:t, sims, type="l")
mean_sim<-apply(sims, 1, mean)
plot(0:t, mean_sim, type="l", ylim=c(15,80))
lower_ci<-mean_sim-apply(sims, 1, sd)
upper_ci<-mean_sim+apply(sims, 1, sd)
lines(lower_ci, lty='dashed')
lines(upper_ci, lty='dashed')
#################################
# Peter Solymos solymos@ualberta.ca
#################################
K <- 10000 # carrying capacity
r <- 0.3
# reproductive potential
sigma <- 0.2 # error
T <- 50
# generations
N0 <- 10
# starting pop
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N <- numeric(T) # make sure N is a number
N[1] <- N0 # set the starting pop to N0
for(i in 2:T) {
N[i] <- exp(r * (1 - N[i - 1]/K) + log(N[i - 1]) + rnorm(1, 0, sigma))
}
plot(N, type="b")
# Wrapped in a function, you get:
Ricker <- function(r, K, sigma, T, N0) {
N <- numeric(T)
N[1] <- N0
for(i in 2:T) {
N[i] <- exp(r * (1 - N[i - 1]/K) + log(N[i - 1]) + rnorm(1, 0,
sigma))
}
N
}
set.seed(1234)
NN <- replicate(10, Ricker(r=0.3, K=10^4, sigma=0.2, T=50, N0=10))
matplot(NN, type="l", col=1, lty=1)
lines(rowMeans(NN), col=2, lwd=2)
abline(h=K, col=4, lty=2)
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Lab 5: Age/Stage Structured
Population Models
Background
The previous exercise counts the individuals in the population
and treats all equally but we know
Part 1: Matrices and Matrix operations
A matrix is an array of numbers arranged into rows and columns. The
dimensions of a matrix are usually expressed as row by column, such as 5 x 6
for a matrix with 5 rows and 6 columns. Typically, matrices are indicated by
uppercase letters, early in the alphabet.
Elements make up the matrix and have a particular row and column location
A vector is a column of elements or you can think of it as a matrix with one
column and several vectors. A vector has a particular length, which is the
number of elements. A vector can be thought of as a M x 1 matrix.
A scalar is a matrix composed of a single element.
Exercise
In R, create a 3 x 4 matrix. How many elements?
## generate data
a <- c(1:12)
a
A <- matrix(a, nrow=3, ncol=4)
A
# write the matrix in the space below
# but what happens if you say?
B <- matrix(a, nrow=3, ncol=4)
## indexing
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B[2,2]
# returns what?
A[2,2]
# returns what?
A[,1]
#returns what?
A[3,]
#returns what?
A[,]
#Returns what?
###Multiplying a matrix times a scalar
A * 5
#returns what?
5 * A
#returns what?
#### multiplying a matrix times a vector
# make a vector
B <- c(10,20,30)
A * B
#returns what?
B * A
#returns what?
### matrix multiplication
b <- c(1:12)
B <- matrix(b, nrow=4, ncol=3)
B
A %*% B
#Returns what?
B %*% A
#returns what?
Part 2: Exploring populations with Matrices
X <- c(0.5, 0.5, 0, 0, 2.4, 0, 0.8, 0, 1, 0, 0, 0.5, 0, 0, 0, 0)
dim(X) <- c(4, 4)
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X
p <- c(20, 10, 40, 30)
p
X %*% p
P <- numeric(40)
P
dim(P) <- c(4, 10)
P[, 1] <- p
for (i in 1:9) { P[, i + 1] <- X %*% P[, i]}
matplot(1:10, t(P), type = "b", main = "Population projection",
xlab = "Year", ylab = "Individuals")
###########################################################################
#
#
#
Marc Taylor <marchtaylor@gmail.com>
#
#####################################################################
# you will need the library popbio for this exercise
# go to Packages -> Install and you will be asked to select a mirror; select
PA1
#now activate popbio by typing
library(popbio)
# you only need to install once but you need to activate popbio everytime
###################################################################
#
#
SMALL MAMMAL
#
##################################################################
# data for the Leslie matrix
mydata <- c(0.5, 0.6666, 0, 1.0, 0, 0.3333, 0.75, 0, 0)
# create the matrix
L=matrix(mydata, nrow=3, ncol=3)
#view it
L
# this is different from the last exam because these data were produced "by
column"
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# where our first example produced the matrix "by row"
# run for 10 generations
time=10
#starting population structure
No=c(2,0,0)
POP=c(No)
Nt=No
# here we loop (repeat the command) for 10 generations
for (i in 1:time){
Nt = drop(L %*% Nt)
POP=rbind(POP,Nt)
}
# now plot the data (which we also need to loop
plot(0:time,POP[,1], type="l", ylim=range(POP), ylab="numbers", xlab="time")
for (i in 2:length(POP[1,])){
lines(0:time,POP[,i],col=i)
}
#add a legend to the plot
legend(0.5*time,max(POP),
c(paste("class",(1:length(No)))),
lwd=1,
col=c(1:length(No)))
###Eigenvalues (info on pop trajectory and distribution)
sum(POP[(time),])/sum(POP[(time-1),]) # the rate of population change between
the last two iterations
x=eigen(L)
x
#dominant eigen value
abs(x$values)
#The stable population distribution is specified by the 1st vector. The
proportion of each element of the vector sum equals the corresponding class
proportions.
abs(x$vectors[,1]/sum(x$vectors[,1]))
sensitivity(L, zero=F)
elasticity(L)
lambda(L)
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