Electronic Supplementary Material (ESM): Online Resource 1
Online Resource 1. Summary of experimental manipulations of prey for field mesocosm
experiment, and arena area for laboratory experiment.
Predator interference alters foraging behavior of a generalist predatory arthropod
List of Authors. –
Jason M. Schmidt1, *, Thomas O. Crist1, Kerri Wrinn1 and Ann L. Rypstra2
1
Department of Zoology, Miami University, Oxford, OH, 45056, USA
2
Department of Zoology, Miami University, Hamilton, OH, 45011, USA
*Corresponding author present address and contact information:
Jason M Schmidt PhD
Assistant Professor | Biocontrol lab
UGA Entomology | Coastal Plain Experimental Station
2360 Rainwater Rd, Tifton, GA 31793
Ph: (229) 386-7251 |Email: jschmid2@uga.edu
http://www.ent.uga.edu/personnel/Schmidt/index.html
Electronic Supplementary Material (ESM): Online Resource 1
Online Resource 1. Summary of experimental manipulations of prey for field mesocosm
experiment, and arena area for laboratory experiment.
Total number of prey added organized by prey order. Seven 1.5m2 samples were suction
sampled from the grassy border surrounding the soybean fields located at the Ecology
Research Center, Butler County. This addition of prey to mesocosms was approximately
an increase in density of prey by 2316 m-2. Standard deviation was calculated on the
mean number of insects of the seven samples.
Prey order
Number of
prey added
Std. dev.
Coleoptera
11
1.17
Collembola
1235
167.62
135
7.87
Hemiptera
19
2.04
Homoptera
335
18.56
2
0.52
Diptera
Orthopera
Electronic Supplementary Material (ESM): Online Resource 1
Online Resource 1. Summary of experimental manipulations of prey for field mesocosm
experiment, and arena area for laboratory experiment.
Description of procedure.
We used a caged laboratory approach to estimate the magnitude of interference between
these predators. The table below represents container sizes used for different densities to
approximately hold the search surface area each spider, Pardosa milvina, was exposed to
constant. Pardosa are numerically abundant and can reach 50 spiders m-2 when trophic
resources and habitat structure are provided (Marshall et al. 2002). Furthermore, spiders
in the genus Pardosa occur at much higher densities (600 spiders m-2) in other systems
(Finke and Denno 2002). In addition, because we provided preferred habitat structure
(Schmidt and Rypstra 2010), this makes the experimental conditions more realistic in
light of being conducted in small laboratory containers.
Spider
abundance
treatment
1
2
4
8
Diameter of
container (cm)
Area to spider
ratio (cm2/spider)
9.5
14.0
20.5
25.5
70.8
76.9
82.4
63.8
References
Finke DL, Denno RF (2002) Intraguild predation diminished in complex-structured
vegetation: Implications for prey suppression. Ecology 83: 643–652.
Marshall S, Pavuk D and Rypstra AL (2002) A comparative study of phenology and daily
activity patterns in the wolf spiders Pardosa milvina and Hogna helluo in soybean
agroecosystems in southwestern Ohio (Araneae, Lycosidae). Journal of
Arachnology 30: 503–510.
Schmidt JM and Rypstra AL (2010) Opportunistic predator prefers habitat complexity
that exposes prey while reducing cannibalism and intraguild encounters. Oecologia
164: 899–910.
Electronic Supplementary Material (ESM): Online Resource 2
Online Resource 2. Description of R code programming used to estimate functional response
parameters.
Predator interference alters foraging behavior of a generalist predatory arthropod
List of Authors. –
Jason M. Schmidt1, *, Thomas O. Crist1, Kerri Wrinn1 and Ann L. Rypstra2
1
Department of Zoology, Miami University, Oxford, OH, 45056, USA
2
Department of Zoology, Miami University, Hamilton, OH, 45011, USA
*Corresponding author present address and contact information:
Jason M Schmidt PhD
Assistant Professor | Biocontrol lab
UGA Entomology | Coastal Plain Experimental Station
2360 Rainwater Rd, Tifton, GA 31793
Ph: (229) 386-7251 |Email: jschmid2@uga.edu
http://www.ent.uga.edu/personnel/Schmidt/index.html
Electronic Supplementary Material (ESM): Online Resource 2
Online Resource 2. Description of R code programming used to estimate functional response
parameters.
#
#
#
#
#
#
#
#
#
#
#
#
#
#
Use numerical integration of instantaneous functional responses (fun.resp)
and maximum likelihood estimation of sums of squares (sum.sq)
p=vector of parameters: a=attack rate, b/a=handling time, m=interference
constant (=c in BD and CM models)
y=state variable (initial prey density)
v=initial prey density of experimental treatment
N=prey densities at time t
np=number of predators; set to np=1 if there is a single predator
T=total number of hours of functional response experiment
n=number of observations
lss=FALSE is sums of squares, and lss=TRUE is the log sums of squares
fr=functional response type: "LV"=Lotka-Volterra,"HO"=Holling Type II,
"HV=Hassell-Varley","AA"=Arditi-Akcakaya,"BD"=Beddington-DeAngelis",
"CM"=Crowley-Martin
# the two functions sum.sq and fun.resp require bblme and deSolve packages
library(bbmle)
library(deSolve)
sum.sq<-function(p,v,e,np) {
a<-p[1]
if (a<0) return(NA)
fun.resp<-function(y,t,p) {
with(as.list(p), {
y<-v
N<-y
if (fr=="LV") {
dN<- -a*N*np
}
if (fr=="HO") {
dN<- -a*N/(1+b*N)*np
b<-p[2]
}
if (fr=="HV") {
dN<- -a*N/(np^m)*np
m<-p[2]
}
if (fr=="AA") {
dN<- -a*N/(b*N+np^m)*np
b<-p[2]
m<-p[3]
}
if (fr=="BD") {
dN<- -a*N/(1+b*N+m*(np-1))*np
b<-p[2]
m<-p[3]
}
if (fr=="CM") {
dN<- -a*N/((1+b*N)*(1+m*(np-1)))*np
b<-p[2]
m<-p[3]
}
return(list(dN))
})
}
# Lotka-Volterra
# Holling
# Hassell-Varley
# Arditi-Akcakaya
# Beddington-DeAngelis
# Crowley-Martin
Electronic Supplementary Material (ESM): Online Resource 2
Online Resource 2. Description of R code programming used to estimate functional response
parameters.
y0<-c(N=v)
T<-24
t<-0:T
out<-ode(y=y0,times=t,func=fun.resp,parms=p)
pred<-(out[1,2:(length(v)+1)]-out[(T+1),2:(length(v)+1)])/np
obs<-e/np
if (obs<=0 || pred<=0) return(NA)
if (lss)
ss<- sum((log(obs)-log(pred))^2)
else
ss<- sum((obs-pred)^2)
return(ss)
}
# Set options for analysis - Example using Arditi and Akcakaya
fr<-"AA"
lss<-FALSE
# Define parameters (a) for all models; (a,b) for HO, AA, BD, and CM;
# (a,m)for HV; and (a,b,m) for AA, BD, and CM
parnames(sum.sq)=c("a","b","m")
# Maximum likelihood estimation
mod1<-mle2(sum.sq,start=c(a=0.1,b=0.01,m=0.01),data=list(v=v,e=e,np=np))
print(fr)
summary(mod1)
AIC(logLik(mod1))
# Profile likelihoods
pr1<-profile(mod1)
plot(pr1)
# Example using Holling Type II
fr<-"HO"
parnames(sum.sq)=c("a","b")
mod2<-mle2(sum.sq,start=c(a=0.1,b=0.01),data=list(v=v,e=e,np=np))
print(fr)
summary(mod2)
AIC(logLik(mod2))
Electronic Supplementary Material (ESM): Online Resource 2
Online Resource 2. Description of R code programming used to estimate functional response
parameters.
References
Beddington JR (1975) Mutual interference between parasites or predators and its effect on
searching efficiency. Journal of Animal Ecology 45: 331–340.
Bolker B, R Development Core Team (2011) bbmle: Tools for General Maximum Likelihood
Estimation. R package version 1.0.0. http://CRAN.R-project.org/package=bbmle.
Crowley PH, Martin EK (1989) Functional responses and interference within and between year
classes of a dragonfly population. Journal of the North American Benthological Society 8:
211–221.
DeAngelis DL, Goldstein RA, O’Neill RV (1975) A model for trophic interaction. Ecology 56:
881–892.
Skalski GT, Gilliam JF (2001) Functional responses with predator interference: viable
alternatives to the Holling Type II model. Ecology 82: 3083–3092.
Soetaert K, Petzoldt T, Woodrow S (2010) Solving Differential Equations in R: Package
deSolve. Journal of Statistical Software 33: 1–25. http://www.jstatsoft.org/v33/i09/
Electronic Supplementary Material (ESM): Online Resource 3
Online Resource 3. Statistical results and additional data from analysis of field mesocosm study.
Predator interference alters foraging behavior of a generalist predatory arthropod
List of Authors. –
Jason M. Schmidt1, *, Thomas O. Crist1, Kerri Wrinn1 and Ann L. Rypstra2
1
Department of Zoology, Miami University, Oxford, OH, 45056, USA
2
Department of Zoology, Miami University, Hamilton, OH, 45011, USA
*Corresponding author present address and contact information:
Jason M Schmidt PhD
Assistant Professor | Biocontrol lab
UGA Entomology | Coastal Plain Experimental Station
2360 Rainwater Rd, Tifton, GA 31793
Ph: (229) 386-7251 |Email: jschmid2@uga.edu
http://www.ent.uga.edu/personnel/Schmidt/index.html
Electronic Supplementary Material (ESM): Online Resource 3
Online Resource 3. Statistical results and additional data from analysis of field mesocosm study.
Description of procedure.
Body condition measurements for wolf spiders in the field experiment. Body condition was
measured from seven wolf spiders, Pardosa milvina, from each treatment. Prey treatments
indicate whether prey were removed or added prior to introduction of the spider abundance
treatments. Spider abundance represent low = 7 spiders or high = 28 spiders. Spiders from the
high-density treatment were randomly selected from the 28 spiders initially entered into the
enclosures.
Prey treatment
Predator
abundance
treatment
Number of
spiders measured
Carapace width
mean (±1std) mm
Abdomen width
mean (±1std)
mm
Removed
Low
56
2.13 (0.22)
2.10 (0.39)
Removed
High
56
2.14 (0.17)
2.07 (0.41)
Added
Low
56
2.09 (0.23)
1.97 (0.38)
Added
High
56
2.11 (0.19)
2.03 (0.46)
Results from fitting a generalized linear model to the binomial response variable, proportion of
Pardosa milvina leaving field based enclosures. Coefficients represent the intercept and predictor
variables in the model. The prey availability treatments were either prey removed or added and
predator abundance treatments were low and high abundance (7 and 28 spiders respectively).
Coefficients
Estimate
Intercept
Prey availability
Predator abundance
Interaction
-0.99
0.90
-0.93
1.02
Std. Error
t value
0.16
0.21
0.43
0.55
-6.34
4.15
-2.15
1.88
P
<0.0001 ***
<0.0001 ***
0.031 *
0.061
Analysis of fixed effects from a linear mixed model analysis of consumption of prey, change in
abdomen width (mm), by Pardosa milvina in response to prey availability and predator
abundance treatments in field enclosures (n = 8 per treatment combination).
df
Intercept
Prey treatment
Predator abundance
Interaction
1, 149
1, 23
1, 23
1, 23
F-value
9.51
13.22
0.01
1.45
P
0.002
0.001
0.926
0.241
Electronic Supplementary Material (ESM): Online Resource 3
Online Resource 3. Statistical results and additional data from analysis of field mesocosm study.
0.4
Mean proportion ±1SE of spiders, Pardosa milvina, cannibalized (e.g. ratio of the number
missing to recovered from within the enclosures or attached cups) at the end of the 24-hr
experimental period as an estimate of the frequency of cannibalism. Enclosures were the
experimental unit where both prey and spiders were introduced that contained holes drilled to
allow for spiders to exit into attached pitfall cups to measure emigration.
0.3
0.2
0.1
0.0
Proportion cannibalism
High
Low
Added
Removed
Prey treatment