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A Likelihood-Based Biostatistical Model for Analyzing Consumer Movement in Simultaneous Choice Experiments Author(s)


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Consumer feeding preference among resource choices has critical implications for basic ecological and evolutionary processes, and can be highly relevant to applied problems such as ecological risk assessment and invasion biology. Within consumer choice experiments, also known as feeding preference or cafeteria experiments, measures of relative consumption and measures of consumer movement can provide distinct and complementary insights into the strength, causes, and consequences of preference. Despite the distinct value of inferring preference from measures of consumer movement, rigorous and biologically relevant analytical methods are lacking. We describe a simple, likelihood-based, biostatistical model for analyzing the transient dynamics of consumer movement in a paired-choice experiment. With experimental data consisting of repeated discrete measures of consumer location, the model can be used to estimate constant consumer attraction and leaving rates for two food choices, and differences in choice-specific attraction and leaving rates can be tested using model selection. The model enables calculation of transient and equilibrial probabilities of consumer-resource association, which could be incorporated into larger scale movement models. We explore the effect of experimental design on parameter estimation through stochastic simulation and describe methods to check that data meet model assumptions. Using a dataset of modest sample size, we illustrate the use of the model to draw inferences on consumer preference as well as underlying behavioral mechanisms. Finally, we include a user's guide and computer code scripts in R to facilitate use of the model by other researchers.
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A Likelihood-Based Biostatistical Model for Analyzing Consumer
Movement in Simultaneous Choice Experiments
Author(s): Adam R. Zeilinger, Dawn M. Olson and David A. Andow
Source: Environmental Entomology, 43(4):977-988. 2014.
Published By: Entomological Society of America
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A Likelihood-Based Biostatistical Model for Analyzing Consumer
Movement in Simultaneous Choice Experiments
Environ. Entomol. 43(4): 977Ð988 (2014); DOI:
ABSTRACT Consumer feeding preference among resource choices has critical implications for basic
ecological and evolutionary processes, and can be highly relevant to applied problems such as
ecological risk assessment and invasion biology. Within consumer choice experiments, also known as
feeding preference or cafeteria experiments, measures of relative consumption and measures of
consumer movement can provide distinct and complementary insights into the strength, causes, and
consequences of preference. Despite the distinct value of inferring preference from measures of
consumer movement, rigorous and biologically relevant analytical methods are lacking. We describe
a simple, likelihood-based, biostatistical model for analyzing the transient dynamics of consumer
movement in a paired-choice experiment. With experimental data consisting of repeated discrete
measures of consumer location, the model can be used to estimate constant consumer attraction and
leaving rates for two food choices, and differences in choice-speciÞc attraction and leaving rates can
be tested using model selection. The model enables calculation of transient and equilibrial proba-
bilities of consumer-resource association, which could be incorporated into larger scale movement
models. We explore the effect of experimental design on parameter estimation through stochastic
simulation and describe methods to check that data meet model assumptions. Using a dataset of modest
sample size, we illustrate the use of the model to draw inferences on consumer preference as well as
underlying behavioral mechanisms. Finally, we include a userÕs guide and computer code scripts in
R to facilitate use of the model by other researchers.
KEY WORDS attraction rate, host selection, leaving rate, movement ecology, transient dynamics
Consumer feeding preference among resources has
critical implications for larger ecological and evolu-
tionary patterns and processes. Feeding preference
can be a signiÞcant driver of ecological specialization,
assortative mating, and thus speciation (Linn et al.
2003). Feeding preference of a disease vector for dif-
ferent hosts of a pathogen has important and complex
implications for infectious disease spread in both
plant and animal host populations (Kingsolver 1987,
Zeilinger and Daugherty 2014). In invasion biology,
feeding preference has been used to support the biotic
resistance hypothesis (Morrison and Hay 2011). In
ecological risk assessment, feeding preference is often
used to help assess potential nontarget effects of in-
troduced biological control agents (Babendreier et al.
2005) and genetically engineered organisms (Prager
et al. 2014).
Consumer preference is also an important process
in optimal foraging theory. In optimal patch foraging
models, Þtness is a function of residence time of the
consumer within a patch (Stephens and Krebs 1986).
Patch residence time should be a function of both
attractiveness and consumption rate of the resource;
both of which are fundamental components of feeding
preference (Nicotri 1980, Schoonhoven et al. 2005).
Optimal patch foraging models are essentially models
of consumer movement (Nathan et al. 2008). Describ-
ing and understanding the movement of consumers
among multiple resourcesÑin other words, relating
preference to movementÑcould help inform optimal
patch foraging models.
Within consumer choice experiments or assaysÑ
where two or more choices are provided simultane-
ously to a consumerÑfeeding preference is inferred
from either measures of relative consumption among
resource choices (Larrinaga 2010, Morrison and Hay
2011), or measures of initial consumer movement or
consumer location (Nicotri 1980, Rovenska´et al. 2005,
Bakonyi et al. 2006, Zirbes et al. 2011). Measures of
consumption and measures of movement provide dis-
tinct and complementary information about feeding
preference. Measures of consumption may be more
relevant for investigating the potential for a consumer to
suppress a resource, such as in a test of a potential bio-
Conservation Biology Program, Department of Entomology, Uni-
versity of Minnesota, 1980 Folwell Ave., St. Paul, MN 55108.
Present Address: Adam Zeilinger, Berkeley Initiative for Global
Change Biology, University of California Berkeley, 3101 Valley Life
Sciences Bldg., Berkeley, CA 94720.
Corresponding author, e-mail:
Crop Protection and Research Management Unit, USDAÐARS,
2747 Davis Rd., Tifton, GA 31793.
Department of Entomology and Center for Community Genetics,
University of Minnesota, 1980 Folwell Ave., St. Paul, MN 55108.
logical control agent (Babendreier et al. 2005). Move-
ment-based measures of feeding preference, however,
may incorporate elements of habitat preference (Un-
derwood et al. 2004). As a result, compared with mea-
sures of consumption, measures of movement may be
more relevant for investigating questions relating to the
degree of association of a consumer with different re-
sources, such as in optimal patch foraging models and in
investigations into the evolutionary and ecological re-
sponses of consumers to novel resources (Linn et al.
2003). Movement can be quantiÞed for any mobile con-
sumer, whereas consumption can be difÞcult to measure
for consumers with haustellate or sucking mouthparts.
Moreover, the transient dynamics and equilibria associ-
ated with consumer movement behavior can, in some
cases, be more revealing about consumer preference
than consumption experiments, especially for mobile
species. For example, leaving rates are probably related
to assessment, handling, and consumption times, and
provide a broader perspective than consumption exper-
iments by themselves.
For at least four decades, biologists have debated
and reÞned the design and analysis of consumer
choice experiments based on measures of relative con-
sumption, resulting in a rigorous set of methodologies
(Manly 1974, 1993; Roa 1992; Horton 1995; Lockwood
III 1998; Prince et al. 2004; Underwood et al. 2004;
Taplin 2007; Larrinaga 2010). However, design and
analysis of choice experiments based on measures of
movement have lagged behind. At the same time,
recent analyses of organismal movement have made
signiÞcant advances using stateÐspace models, which
link probabilistic statistical models of observations of
organismal location to biologically relevant stochastic
models of movement (Jonsen et al. 2003, Patterson et
al. 2008).
Rigorous analysis of repeated measures of move-
ment within consumer choice experiments have been
lacking because frequentist goodness-of-Þt tests for
repeated-measures multinomial data do not exist.
While measures of movement have been used exten-
sively in choice experiments, preference is often in-
ferred from a single movement event, such as a con-
sumerÕs Þrst choice or location at the end of a trial
(Nicotri 1980, Bakonyi et al. 2006, Zirbes et al. 2011).
In such cases, the transient behavior of the consumer
is ignored, the parameters estimated often have little
biological relevance, and the results are difÞcult to
relate in a quantitative manner to larger scale models
of movement (e.g., Nathan et al. 2008).
In the present article, we develop a simple, likeli-
hood-based, biostatistical model to analyze repeated
measures of consumer location between paired re-
source choices. The model incorporates all available
information on consumer location to and from choices
during the trial, but does not require constant obser-
vation. Estimated choice-speciÞc attraction and leav-
ing rates are then used to make inferences on prefer-
ence: higher attraction rates, lower leaving rates, or
both, associated with one food choice indicate a
greater preference. The model also allows for calcu-
lation of transient and equilibrial probabilities of as-
sociation between consumer and resource choices.
Using stochastic simulation, we explore elements of
the model relevant to experimental design. Finally,
using an empirical dataset on herbivorous stink bug
preference, we illustrate that the model can be used
to draw inferences on consumer preference.
Materials and Methods
Theory and Model Development. In general, move-
ment among potential resource choices is a stochastic
process comprising probabilities of movement to (at-
traction) and from (leaving) a resource item or patch.
Following the work of Haccou and Meelis (1992) on
statistical analysis of continuous and discrete obser-
vations of animal behavior, we modeled the move-
ment of a consumer between two choices as a con-
tinuous time, stochastic Markov chain model. In
contrast to Haccou and Meelis (1992), we focus only
on movements relevant to food choice with the goal
of estimating attraction and leaving rates for each
choice in a paired-choice experiment. Let P
probability that a consumer is feeding on or associated
with state jat observation time t
,where j1,2,...,
nfor an experiment with n1 food choices and i
1,2,... , mfor mtotal number of discrete-time ob-
servations of consumer location per trial. The proba-
bility that a consumer is in the neutral space, i.e., not
at a food choice, deÞned as P
), at time t
Pjti. [1]
The probability that the consumer is associated with
choice j, where jn, P
), is a function of the
probability that the consumer is feeding on food
choice jat time t
t, deÞned as P
t), and the
probability that the consumer is in the neutral space
at time t
t, deÞned as P
t). We assume that
consumers leave food choice jat a choice-speciÞc
constant leaving probability
tand move toward
food choice jat a choice-speciÞc attraction probability
t. We further assume that consumers can only
move to a food choice from the neutral space; in other
words, a switching event from one choice to the other
can be decomposed into two independent eventsÑ
leaving the Þrst choice and subsequent attraction to-
ward the second choice (Fig. 1). Note that the model
assumes that some amount of physical distance exists
between choices that could reasonably considered
neutral space; the boundary between neutral space
and a choice can at times be vague and researchers
should consider this in their experimental design.
The probability that the consumer is at food choice
where o(t) are higher order terms of t. As tgoes
to zero, equation 2 becomes
jPjpjPn. [3]
Combining equations 1 and 3 and considering the
special case of an experiment with only two choices,
j1, 2, the system can be modeled as
where the parameters p
are Þtted
constants (Fig. 1), and P
is a special case of equation
1 for a system with only two choices. We substituted
the equation for P
into the differential equations to
produce the following two-equation model of linear,
nonhomogeneous differential equations:
dt 
dt 
2p2P2p2P1p2. [5]
We solved system (5) analytically with respect to t
using KolmogoroffÕs forward differential equations
method (Tijms 2003) to produce a set of three dy-
namic probability functions P
), P
), and P
where c
and c
are arbitrary constants and
are eigenvalues of the system (Supp Material 1 [online
The system of equation 6 describes the probability
that the consumer is associated with choice 1 or choice
2 at time tprojected from time 0. In an experi-
mental context, a researcher will often want to mea-
sure the location of each consumer multiple times over
the course of the trials. Given mtotal observations at
times t
where i1,2,....,m, then the conditional
probabilities of consumer association, P
,can be cal-
culated for the interval
where c
and c
are determined by the observed dis-
tribution of consumers at time t
. The system (7)
describe the conditional probabilities of Þnding con-
sumers in states 1, 2, and 3, given that an observed
number of them were found in each state at the be-
ginning of the time interval.
Given Ntotal consumers and that their distribution
at time t
is (n
), n
), n
)), then c
can be found by solving the initial value problem,
where P
)/N, P
)/N, and
. [8]
Once system (8) is solved for c
and c
and the solu-
tions are substituted into equation 7, the conditional
probability for any time interval and any initial ob-
servation can be calculated in terms of the parameters
of interest. For the initial conditions of the experiment
(i.e., all consumers start in the neutral state), c
and c
have been calculated explicitly in the appendix. Be-
cause of the Markov properties of the model, these
sequential conditional probabilities are independent
(Tijms 2003).
To derive a likelihood function, let n
), n
), and
) be the observed number of consumers at each
location at observation time t
. Then P
), P
), and
) can be modeled as the parameters of a multi-
nomial distribution, so (n
), n
), n
)) Multi-
nom(N, [P
), P
), P
)]), for Nsample size and
i1 ... mnumber of observation times per trial.
Accordingly, the log-likelihood function at each time
point, (
), is the log of the probability mass func-
tion for the multinomial distribution (Boos and Ste-
fanski 2013). Summing over all observations produces
the following likelihood function:
Fig. 1. Conceptual diagram of host plant choice and
movement between three locations within a paired-choice
experimental arena. The three circles represent the three
possible states or locations: the two food choices (choices 1
and 2) and the neutral space between the choices. The
arrows represent possible movements between the three
locations. P
and P
probability that consumers are on
choices 1 and 2, respectively; P
probability that consumers
are in neutral space; p
and p
attraction rates to choices
1 and 2, respectively;
leaving rates from choices
1 and 2, respectively.
is a vector of model parameters p
, and
. Note that, whereas p
tin equation 2
were deÞned as attraction and leaving probabilities for
choice j, respectively, here in system (7) and likeli-
hood function (9), p
are deÞned as attraction
and leaving rates, respectively.
Statistical Inference. From this model, consumer
feeding preference can be inferred from differences
between the choice-speciÞc attraction and leaving
rates. To test for differences in preference between
choices, we compared four variants of the likelihood
function (9). First, we set both the attraction rates and
the leaving rates equal to each other, which we call the
Fixed model (p
). In the Fixed model,
the optimization algorithm is forced to Þt one attrac-
tion rate and one leaving rate for the data from both
choices; the Fixed model represents a null model of no
preference. Second, in the Free Leaving model, we set
attraction rates, p
and p
,equal to each other but
allowed the leaving rates to vary (p
Third, in the Free Attraction model, we allowed the
attraction rates to vary but set the leaving rates,
, and
, equal to each other (p
). Finally, in
the Free model, we allowed all four parameters to be
Þt independently (p
). Differences
among the maximum likelihood estimates (MLEs) of
these four model variants can be tested with AkaikeÕs
information criterion (AIC). Models do not need to be
nested for AIC (Bolker 2008, Burnham et al. 2011), so
all variants can be tested together. Inference can be
made either based on the best modelÑthe one with
the lowest AIC valueÑor through model averaging
(Burnham and Anderson 2002).
Variances for parameter estimates can be estimated
using either the proÞle method or the normal approx-
imation method, if the MLE is at or near the global
minimum (Bolker 2008, Millar 2011). In the normal
approximation method, variances are extracted from a
varianceÐcovariance matrix that is calculated by in-
verting the Hessian matrix of the MLE (Bolker 2008),
which is often an output of derivative-based MLE
algorithms. However, if a parameter estimate is on the
boundary of the inequality constraint, then the MLE
is unlikely to be at the global minimum and the proÞle
and normal approximation methods for estimating
variance are no longer valid. In this case, variances and
SEs can be estimated using jackknife methods. Im-
portantly, CIs should not be calculated from jackknife
estimates of SE because, in general, their probability
distributions are unknown (Efron and Tibshirani
Finally, parameter estimates can be used to calcu-
late the probabilities, at equilibrium, that a consumer
will be associated with the two choices using equations
(A12) in Supp Material 1 (online only).
Testing Model Assumptions. The present model as-
sumes that attraction and leaving rates are constant for
the duration of the trials, although it is possible to
develop more general models with time-varying pa-
rameters. The assumption of time-constancy can be
interrogated using graphical inspection of ln(t
) ver-
sus ln{ln[S(t
)]}from KaplanÐMeier survival func-
tions of the attraction rates and leaving rates, where t
is the time of an attraction or leaving event, and S(t
is the proportion of individuals remaining at time t
the data follow the line of best Þt, then the attraction
or leaving rates are constant (Machin et al. 2006). Also,
Machin et al. (2006) note that the y-intercept of the
line of best Þt provides an estimate of the natural log
of the constant hazard rate, ln(
). This estimate of the
hazard rate,
, can be used as an initial parameter value
in the MLE algorithm.
The model also assumes that consecutive consumer
choices are independent from previous choices. This
assumption can be interrogated with contingency ta-
ble analyses in which consecutive choices are the
factors: Þrst choice versus second choice, second
choice versus third choice, etc. (Andow and Kiritani
1984). Note that such an analysis requires following
individuals through time. Alternatively, indepen-
dence between choices can be assessed by examining
correlations between model parameter estimates at
the MLE. As described in the Statistical Inference
section, the varianceÐcovariance matrix can be cal-
culated from the Hessian matrix. When the varianceÐ
covariance matrix is scaled to the variances, then the
off-diagonal elements of the matrix provide correla-
tions between parameter estimates (Bolker 2008).
Contingency table analysis will be invalid when move-
ment event frequencies are too small; namely, when
one or more table cells are 0. Estimating correlations
between parameter estimates will be invalid when
parameter estimates are on a constraint boundary.
Stochastic Simulation. To explore the behavior of
the model and maximum likelihood estimation of pa-
rameters, we used stochastic simulation to investigate
how various dimensions of consumer choice experi-
mental design inßuence parameter estimation. We
simulated consumer location data, n
), n
), using a Markov stochastic process (Pielou 1969)
of model (7). The simulated data were used with the
likelihood function (8) to estimate the parameters
using the Free model variant.
First, we explored how sample size inßuences pa-
rameter estimation by simulating data at low, medium,
and very large sample sizes: N10, 20, and 1,000,
respectively. We also explored how the rate of move-
ment by experimental consumers may inßuence pa-
rameter estimation. SpeciÞcally, we hypothesized
that, for accurate parameter estimation, the distribu-
tion of observation times should match the rate of
movement by consumers such that both the transient
dynamics and equilibrium are observed. In the slow
consumer scenario, we simulated data using each com-
bination of low and high parameter values in which
the observation times covered only the transient dy-
namics; the low and high values were 0.02 and 0.1,
respectively (Table 1). This generated 16 different
combinations of true parameter values. In the fast
consumer scenario, we repeated this process with low
and high parameter values that allowed for observa-
tion of both transient dynamics and the equilibrium. In
this case, the low and high parameter values were 0.2
and 0.6.
Second, we explored how the number of and inter-
vals between per trial observations inßuenced param-
eter estimation. We simulated data at low, medium,
and high numbers of per trial observation times: m
10, 20, and 40, respectively. For each level of m, we
compared two different interval schemes: when those
observations were evenly spaced at a constant interval
of 1 time step and when the observations were
weighted toward the beginning of the experiment
(i.e., front-loaded observations).
To assess the performance of the MLE process, we
calculated expected proportional bias as E((d
where d
ˆis the maximum likelihood parameter esti-
mate and dis the true parameter value, from 4,000
simulation runs for each true parameter combination
(PC). The MLE converged in 100% of the simulations.
Consumer Choice Experiment. To illustrate the
practical use of the model, we used data from an
experiment conducted to test for feeding preference
of nymphs of the herbivorous stink bug species Eu-
schistus servus Say and Nezara viridula L. (Heterop-
tera: Pentatomidae) between a cotton plant (Gos-
sypium hirsutum L.) that had been damaged by a larval
Helicoverpa zea (Boddie) (Lepidoptera: Noctuidae)
and an undamaged cotton plant. The study was de-
signed to test the hypothesis that induced plant re-
sponses to H. zea herbivory inßuenced stink bug feed-
ing preference (Zeilinger et al. 2011). Brießy, three
possible locations of the stink bug were recorded in
each trial: on the undamaged plant, on the damaged
plant, or in neutral space between plants. We moni-
tored the location of the stink bug at 10, 30 min, 1, 12,
18, 24, and 36 h from the start of the experiment. We
focused our observations in the beginning of the ex-
periment, i.e., front-loaded observations because stink
bug movement was most likely to occur during this
period (A.R.Z, unpublished data). We obtained sam-
ple sizes of 15 and 19 for trials with E. servus and N.
viridula, respectively. For model selection, we used
AIC corrected for small sample size (AIC
). Variances
and 95% CIs were calculated using the normal approx-
imation method (Bolker 2008, Millar 2011). Parameter
estimates and variances were averaged for all models
with AIC
7 following Burnham et al. (2011). For
more detail on the experimental design see Zeilinger
Table 1. True parameter values (p
, and
) for fast consumers (0.2 and 0.6) and slow consumers (0.02 and 0.1), equilibrium
values (P
*, and P
*), and the time to equilibrium of the model for each PC
PC p
*Time to
Fast consumer true parameter values
1 0.2 0.2 0.2 0.2 0.33 0.33 0.33 18
2 0.6 0.2 0.2 0.2 0.60 0.20 0.20 12
3 0.2 0.6 0.2 0.2 0.20 0.60 0.20 12
4 0.6 0.6 0.2 0.2 0.43 0.43 0.14 8
5 0.2 0.2 0.6 0.2 0.14 0.43 0.43 35
6 0.6 0.2 0.6 0.2 0.33 0.33 0.33 43
7 0.2 0.6 0.6 0.2 0.08 0.69 0.23 26
8 0.6 0.6 0.6 0.2 0.20 0.60 0.20 30
9 0.2 0.2 0.2 0.6 0.43 0.14 0.43 35
10 0.6 0.2 0.2 0.6 0.69 0.08 0.23 26
11 0.2 0.6 0.2 0.6 0.33 0.33 0.33 43
12 0.6 0.6 0.2 0.6 0.60 0.20 0.20 30
13 0.2 0.2 0.6 0.6 0.20 0.20 0.60 11
14 0.6 0.2 0.6 0.6 0.43 0.14 0.43 8
15 0.2 0.6 0.6 0.6 0.14 0.43 0.43 8
16 0.6 0.6 0.6 0.6 0.33 0.33 0.33 6
Slow consumer true parameter values
1 0.02 0.02 0.02 0.02 0.33 0.33 0.33 177
2 0.1 0.02 0.02 0.02 0.71 0.14 0.14 99
3 0.02 0.1 0.02 0.02 0.14 0.71 0.14 99
4 0.1 0.1 0.02 0.02 0.45 0.45 0.09 63
5 0.02 0.02 0.1 0.02 0.09 0.45 0.45 389
6 0.1 0.02 0.1 0.02 0.33 0.33 0.33 405
7 0.02 0.1 0.1 0.02 0.03 0.81 0.16 146
8 0.1 0.1 0.1 0.02 0.14 0.71 0.14 255
9 0.02 0.02 0.02 0.1 0.45 0.09 0.45 389
10 0.1 0.02 0.02 0.1 0.81 0.03 0.16 146
11 0.02 0.1 0.02 0.1 0.33 0.33 0.33 405
12 0.1 0.1 0.02 0.1 0.71 0.14 0.14 255
13 0.02 0.02 0.1 0.1 0.14 0.14 0.71 80
14 0.1 0.02 0.1 0.1 0.45 0.09 0.45 63
15 0.02 0.1 0.1 0.1 0.09 0.45 0.45 63
16 0.1 0.1 0.1 0.1 0.33 0.33 0.33 36
Time to equilibrium indicates the min. time step where P
(t) P
*to a precision of 5 decimal places.
All programming was done in R 3.1.0 (R Core Team
2014, Vienna, Austria). To maximize the negative log-
likelihood function, we used the optimx function
(Nash and Varadhan 2011) with the BarzilaiÐBorwein
spectral projected gradient (spg) optimization al-
gorithm (Varadhan and Gilbert 2009). The spg
method was used because preliminary simulations
showed that other constrained optimization algo-
rithms, namely L-BFGS-B, did not consistently con-
verge on an MLE (results not shown). For MLE of
simulated and empirical data, convergence tolerance
was set at 10
and the number of maximum itera-
tions was set at 10,000. To improve MLE convergence,
we used inequality constraints of 10
0.0001 and
supplied exact gradient functions. Gradient functions
were derived in Mathematica 9 (Wolfram Research,
Inc. 2012, Champaign, IL) and veriÞed by calculat-
ing numerical derivatives with the grad function in
R (Gilbert 2012). To facilitate the future use of the
model, we have developed a userÕs guide (Supp
Material 2 [online only]) and supplied R script for
maximum likelihood estimation with the four model
variants, model selection, variance estimation using
the normal approximation method, and jackknife
method, and testing assumptions (Supp Material 3
[online only]). Current R scripts and future revi-
sions and extensions to the model will also be avail-
able at:
Stochastic Simulation of Sample Size. Some of the
16 PCs were reciprocals, in which the true parameter
values were switched between the two choices, and in
these cases, bias estimates were switched and equiv-
alent (Supp Fig. 1 [online only]). For example, PC 6
0.6, p
0.02) is reciprocal
to PC 11 (p
0.2, p
likewise, p
was overestimated in PC 6, whereas p
overestimated in PC 11 (Supp Fig. 1 [online only]).
That estimated bias was equivalent between recipro-
cal PCs indicates that accuracy in parameter estimates
between choice 1 and choice 2 were equivalent. Fol-
lowing this, we show only results from the 10 unique
PCs (Figs. 2 and 3).
Estimated proportional bias was generally greatest
at low sample size (N10), decreased at intermediate
sample size (N20), and was negligible at very large
sample size (N1,000; Fig. 2). These results suggest
that bias was a sampling problem, and not intrinsic to
the model and estimation method. Bias estimates were
generally positive, indicating that the parameter esti-
mates were greater than the true values (Fig. 2).
Estimated proportional bias also depended on the
overall movement rates (Fig. 2). The patterns of bias
indicate that low accuracy (high bias) may be because
of poor estimation of either the transient dynamics
(when the model moves quickly to equilibrium) or
equilibrium values (when the model moves slowly to
Fig. 2. Sample Size Simulation. Expected proportional bias estimates, E((d
ˆd)/d) for rate parameters over a range
of sample sizes, N10, 20, and 1,000, for 10 unique PCs from 4,000 simulation runs. Left-side panels (Fast movement)
represent combinations of greater true parameter values: 0.2 and 0.6 for high and low values, respectively (see Table 1).
Right-side panels (Slow movement) represent combinations of smaller true parameter values: 0.02 and 0.1. Number of
observation times m40 for each simulation and spaced at 1 time step. These values were within the range of initial parameter
estimates from empirical data from trials with herbivorous stink bugs on cotton plants (Zeilinger et al. in review).
equilibrium). The model requires four degrees of free-
dom (dfs) to estimate the four parameter values. The
equilibria of the three state variables provide two dfs,
so the remaining information is in the transient dy-
namics of the system. We evaluated the time to equi-
librium for each PC using equations (A12). Consistent
with our hypothesis, the greatest bias estimates oc-
curred with PCs that caused the system to move to
equilibrium quicklyÑPCs 2 and 16Ñand PCs that
caused the system to move to equilibrium slowlyÑ
PCs 1, 5, and 6 (Fig. 2; Table 1) relative to the time
step and duration of observations. SpeciÞcally, all
instances of high bias are associated with PCs in
which there are insufÞcient observations of both the
transient period and the equilibrium. For instance,
under the slow consumer scenario, PCs 1, 2, 5, and
6 take 99 time steps to reach equilibrium (Table 1)
while observations were made up to 40 time steps,
excluding any observations of the equilibria. How-
ever, when rates of movement were increasedÑ
under the fast consumer scenarioÑthe time to equi-
librium approached 40 and bias estimates were
greatly reduced (Fig. 2; Table 1).
Stochastic Simulation of Per Trial Observation
Times. Using the fast consumer scenario, we explored
the effects of varying the per trial observation timesÑ
both total number and intervals between observa-
tionsÑon parameter estimation. As with the sample
size simulation, estimated proportional bias was great-
est at a low number of observation times (m10) and
decreased substantially at intermediate and large
numbers of observation times (m20 and m40,
respectively; Fig. 3).
We also found that the interval schemeÑconstant
intervals of 1 time step or front-loaded observationsÑ
affected bias estimates (Fig. 3). Bias estimates tended
to be greater when observations were evenly spaced;
front-loading observations resulted in consistently
small bias estimates (proportional bias 1) across PCs,
particularly for m20.
Consumer Choice Experiment. For the assumption
of independent consecutive choices, we tested for
independence between Þrst and second choices for N.
viridula using contingency table analysis; the frequen-
cies of E. servus movement were too small for such
analysis (Table 2). Consecutive choices made by N.
viridula nymphs were independent (odds ratio 0.06;
95% CI [0.0007, 1.34]; P0.07). Independence is
also supported by correlations between parameter es-
timates, calculated from the Hessian matrix of the Free
Choice model; correlation between
and p
was 0.09 and correlation between
and p
was 0.14. For E. servus, parameter correlations sug-
gested that choices were independent as well; r
0.009 and r
0.039. For the assumption of con-
stant attraction and leaving rates, the data available
followed the line of best Þt, indicating that the attrac-
tion and leaving rates were constant during the ex-
periment (Fig. 4).
Fig. 3. Number of Per trial Observation Times Simulation. Expected proportional bias estimates, E((d
ˆd)/d), for rate
parameters over a range of number of per trial observations and intervals between observation times for 10 unique PCs from 4,000
simulation runs. Range of number of per trial observations included m10, 20, and 40. Left-side panels (Constant intervals)
represent simulations with constant intervals between observations, with an observation every 1 time step. Right-side panels
(Front-loaded observations) represent simulations with a greater concentration of observations, with shorter intervals, at the
beginning of trials. PC numbers correspond to those in Table 1. Sample size, N, for each simulation 20.
For E. servus trials, the Free Attraction model Þt the
data best, but all models were good with AIC
(Table 3). Averaged parameter estimates and CIs from
these models showed that E. servus was signiÞcantly
more attracted to undamaged plants than to H. zea-
damaged plants. Differences in attraction rates had a
strong effect in determining preference, whereas leav-
ing rates between choices were indistinguishable (Fig.
5). Based on the model-averaged parameter estimates
(Fig. 5), the probability that E. servus is associated
with undamaged plants is predicted to be much
greater than the probability of association with H.
zea-damaged plants (Fig. 6).
For N. viridula, the best model was the Fixed model
but once again all four model variants were good with
7 (Table 3). Using all four models to estimate
model-averaged parameter values, we found that N.
viridula attraction rates and leaving rates were equiv-
alent between undamaged and damaged plants (Fig.
5). At equilibrium, we predict that N. viridula will be
Table 2. Contingency tables of the outcomes of consecutive
choices made by stink bugs between H. zea-damaged and undam-
aged cotton plants
Species First choice Second choice
Damaged Undamaged
E. servus Damaged 2
Undamaged 1 1
N. viridula Damaged 1 4
Undamaged 6 1
Second choice
Third choice
Damaged Undamaged
E. servus Damaged 0 1
Undamaged 0 0
N. viridula Damaged 0 3
Undamaged 2 0
Number of stink bug nymphs on the damaged plant for their Þrst
choice and damaged plant for their second choice, meaning that the
stink bug was observed to have left the damaged plant and to have
returned to the damaged plant. Only the Þrst contingency table,
between Þrst and second choices, was analyzed.
Fig. 4. Graphical inspection of model assumptions: con-
stant attraction rates (AÐD) and leaving rates (EÐH) for each
stink bug species, E. servus (A, C, E, and G) and N. viridula (B,
D, F, and H), on undamaged cotton plants (A, B, E, and F) and
H. zea-damaged plants (C, D, G, and H). The variable timeon
the x-axis indicates the time (in hours) when an attraction or
leaving event occurred (i.e., when one or more stink bugs
moved to a plant or left a plant). The variable S(t)on the y-axis
indicates the proportion of individuals remaining, i.e., surviv-
ing,in neutral space or remaining on the plant after the event
at time t. Each datum represents the proportion of stink bugs
that moved from a choice jat observation time t
out of the total
number of stink bugs at location jat observation time t
that each panel is used to assess one rate parameter; thus each
must be assessed using different plots. If the data points
follow the line of best Þt, then the rate is constant.
Table 3. Degrees of freedom, information criterion corrected
for small sample size (AIC
) values, and change in AIC
) for
each model variant in the stink bug choice experiment
Stink bug
species Model variant df
E. servus Free attraction model 3 56.66 0
Free leaving model 3 60.19 3.53
Free model 4 60.46 3.80
Fixed model 2 62.50 5.84
N. viridula Fixed model 2 50.40 0
Free attraction model 3 52.65 2.25
Free leaving model 3 53.02 2.62
Free model 4 55.50 5.10
Degrees of freedom associated with the model variant.
indicates the change in AIC
relative to the minimum AIC
value among model variants. Model variants are ordered according to
Models with AIC
7 were considered good models and se-
lected for averaging following Burnham et al (2011).
Fig. 5. Model-averaged parameter estimates 95% CIs for
attraction rates (A) and leaving rates (B) for E. servus EsÕ,
closed circles) and N. viridula NvÕ, open circles) trials for
undamaged and H. zea-damaged cotton plants. Parameter esti-
mates are averaged from good models identiÞed in Table 3.
equally distributed between undamaged and H. zea-
damaged plants (Fig. 6).
Methods for the design and analysis of consumer
choice assays using measures of consumption have
been debated and reÞned for at least four decades
(Manly 1974, 1993; Roa 1992; Horton 1995; Prince et
al. 2004; Underwood et al. 2004; Taplin 2007; Larrinaga
2010). In contrast, similar attention has been lacking
for choice assays using measures of movement. Mea-
sures of movement provide distinct and complimen-
tary insight into feeding preference compared with
measures of consumption; movement-based infer-
ences on preference may be more directly related
than measures of consumption to optimal patch for-
aging models and other classes of movement models
(Stephens and Krebs 1986, Patterson et al. 2008). Sim-
ilar to some state-space models described by (Patter-
son et al. 2008), we modeled the probability of a
mobile consumer being associated with two resource
choices as a function of choice-speciÞc attraction and
leaving rates. Using repeated measures of consumer
location with choice trials, attraction and leaving rates
were estimated using maximum likelihood estimation
and inferences on the differences of these rates de-
termined by model selection methods. Finally, tran-
sient and equilibrial probabilities of association be-
tween the consumer and the resource choices can be
calculated from the model.
We simulated data to explore the effects on param-
eter estimation from variation in movement rates, sam-
ple size, the number of per trial observation times, and
the intervals between observation times. Increasing
sample size and increasing the number of observations
generally improved the accuracy of parameter esti-
mates. Greater sample sizes should enhance valleys
and ridgesin the likelihood surface, making it easier
to Þnd the MLE (Bolker 2008). Increasing the number
of observation times and changing the spacing of ob-
servations improve the accuracy of parameter estima-
tion because they allow information to be gathered on
both transient dynamics and the equilibrium. Ac-
curate parameter estimation depends on multiple
observations covering both transient and equilibrial
periods of consumer movement. Overall, bias esti-
mates tended to be positive, indicating that param-
eter estimates tended to be greater than the true
values. Importantly, parameter bias was symmetri-
cal between choices, indicating that difference be-
tween the choices in parameter estimates relate to
real differences in consumer choice rather than
artifacts from the model or the MLE procedure.
Our simulations suggest that capturing both tran-
sient dynamics and the equilibrium of consumer lo-
cation are important. We were able to improve accu-
racy by increasing sample size, increasing the per trial
number of observation times, or changing the spacing
of observations to better estimate transients and equi-
libria. From an experimental perspective, increasing
the number of observation times and changing their
temporal spacing would be more efÞcient than in-
creasing sample size. In practice, the number of per
trial observations and their spacing must be deter-
mined by the movement behavior of the consumer(s)
under study.
In the analysis of stink bug feeding preference data,
we found greater attraction rates toward undamaged
plants for E. servus relative to H. zea-damaged plants
and equivalent movement rates between choices for
N. viridula. The E. servus results correspond to PC 2 in
the stochastic simulation (Table 1). The simulation
results predict that such a PC at a modest sample size,
modest number of observation times, and front-loaded
observations should result in moderate overestimation
of the leaving rate of the less-preferred choice (Figs.
2 and 3). While the leaving rate from the H. zea-
damaged plant may be overestimated, the implications
from the estimated parameters were not affected. In-
deed, if it is overestimated, the true effect is even
greater than the estimated effect. We expect little bias
in the parameter estimates for N. viridula and all es-
timates to be biased equally. In both cases, the pre-
dicted biases in the parameter estimates do not alter
the interpretation of the results.
Data on the feeding preference of stink bug nymphs
between H. zea-damaged and undamaged cotton
plants largely conformed to the assumptions of the
model; stink bug attraction and leaving rates were
constant over the duration of the trials and consecu-
tive choices were independent. The number of data
points produced from KaplanÐMeier survival analysis
will depend on the number of observations and the
intervals between observations in relation to mobility
of the consumer. In our data on E. servus, the number
of observations was too few to rigorously test the
assumption of constant movement rates. Again, the
Fig. 6. Predicted dynamics of E. servus (A) and N.
viridula (B) selecting H. zea-damaged cotton plants (solid
line) and undamaged plants (dashed line), calculated using
model-averaged parameter estimates shown in Fig. 5.
number of per trial observations and their spacing
should be determined by the behavior of the con-
sumer under study.
The model also assumes that movement choices are
sequentially independent, violation of which will not
necessarily invalidate parameter estimates and model
selection. Rather, positive correlation between con-
secutive choices may inßate attraction rates. For
highly mobile consumers, it may be difÞcult to observe
the consumer in neutral space, possibly resulting in
more switching events being recorded than leaving-
and-returning events and a violation of the indepen-
dent choice assumption. This could be resolved by
increasing the frequency of per trial observations.
Alternatively, consider a scenario of extreme choice
dependence, where no observations are made of the
consumer in neutral space and each attraction rate is
exactly equal to the leaving rate from the opposite
choice. In this case, P
0 and
If parameter
is the rate of switching from choice 1
to choice 2 and
is the rate of switching from choice
2 to choice 1, then system (4) reduces to
and the assumption of independent choice is relaxed.
However, using model (10) does not allow one to
distinguish between preferences through greater at-
traction versus lower leaving rates.
The present model deÞnes preference as the bal-
ance between choice-speciÞc attraction and leaving
rates. A difference in attraction rates between choices
indicates that feeding preference is likely inßuenced
by consumer selection behavior (Vinson 1976, Ber-
nays and Chapman 1994, Schoonhoven et al. 2005) and
that cues detected from a distance may be important
determinants of preference. However, a difference in
leaving rates indicates that preference is likely inßu-
enced by consumer acceptance behavior and patch
giving up times. A wide variety of cues are known to
affect acceptance behavior, including visual cues, ol-
factory cues in the hostÐfood headspace, or surface or
internal chemistry (Vinson 1976, Bernays and Chap-
man 1994). Information on whether preference is de-
termined by attraction rates or leaving rates would
facilitate developing hypotheses on the particular
mechanisms underlying preference for testing in fur-
ther research.
The distinction between preference owing to at-
traction rates and leaving rates can be ecologically
valuable. The feeding preference of vectors of plant
and animal pathogens can greatly inßuence pathogen
spread (Kingsolver 1987). Theory predicts that the
epidemiological importance of preference will de-
pend on disease prevalence but only when preference
is determined when selecting a host, i.e., by attraction
rates (Sisterson 2008). Preference determined after
vector feedingÑrelating to differences in leaving
ratesÑwill have a relatively minor inßuence on dis-
ease spread. Further, the host manipulation hypoth-
esis predicts that spread of nonpersistent vector-borne
pathogens (pathogens that do not enter the circula-
tory system of the vector) will be greatest if vectors are
preferentially attracted to infected hosts but also leave
them quickly (Mescher 2012). Thus, our model pro-
vides an efÞcient way to estimate the inßuence of
vector feeding preference on disease spread and test
the host manipulation hypothesis using simple feeding
preference experiments.
Leaving rates are used widely in optimal patch for-
aging models, but the assumed processes underlying
patch leaving in optimal foraging models differ from
those assumed in our model. Here, we assume that
leavingÐinducing cues are constant over the duration
of the experiment. If, however, leaving rates are de-
termined by resource depletionÑwhich is central to
optimal patch foraging models (Stephens and Krebs
1986)Ñthen leaving rates will not be constant, but will
increase over time, and this will be apparent from tests
of model assumptions (e.g., Fig. 4). Indeed, tests of
timeÐconstancy in parameters could potentially de-
tect any changes in the resource choices during the
experiment that are relevant to preference, including
autogenic changes (Manly 1993).
From estimated attraction and leaving rates, the
model can be used to calculate transient and equilib-
rial probabilities that the consumer will be associated
with the resource choices tested. Such probabilities
could be incorporated into movement and foraging
models, or to test the inßuence of preference in as-
sociations of consumer and resource. For example, do
innate preferences for different resources or the rel-
ative abundance of those resources explain consumerÐ
resource associations in the environment (Spotswood
et al. 2013)?
Our consumer movement model described here
could also be used to analyze data from repeated
measures of consumer colonization of habitat patches.
In particular, the method would be well suited for
markÐreleaseÐrecapture data, where individuals are
followed to habitat patches (Kuussaari et al. 1996).
The model described here provides all of the advan-
tages of state-space models recently developed for
movement ecology data: it enables the estimation of
states (probabilities of location), biologically mean-
ingful model parameters (attraction and leaving
rates), observation error (variance of parameter esti-
mates), and enables statistical inferences from model
selection among biologically relevant models (Patter-
son et al. 2008). The technique can be used for paired-
choice experiments of any duration, with any number
of repeated observations of consumer location, and
any interval scheme between observation times as
long as observation times are allocated in both the
transient and equilibrium periods. Possible future ex-
tensions of the model include time-varying parame-
ters and adaptations to experiments using more than
two simultaneous choices or more than one consumer
per arena.
This study was partially supported by a grant from the
National Research Initiative of the U.S. Department of Ag-
riculture, National Institute of Food and Agriculture (grant
2008-02409) to D.A.A. and D.M.O., an IGERT grant from U.S.
National Science Foundation to the University of Minnesota,
and a Thesis Research Grant, Doctoral Dissertation Fellow-
ship, and grants from the DaytonÐWilkie Fund from the
Graduate School and Bell Museum of Natural History, Uni-
versity of Minnesota, to A.R.Z. We thank the R Help online
community for assistance with R programming, and M. Ga-
nesh and R. Almeida for access to the Lawrence Berkeley
LaboratoryÕs Computation Genomics Research Laboratory
computing cluster to run the stochastic simulation. We also
thank C. Neuhauser, M. Daugherty, K. Anderson, H. Regan,
J. Sarhad, A. Fahimipour, S. Hayes, H. Hulton, P. Rueda-
Cedil, and R. Swab for helpful comments on earlier drafts.
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Received 11 October 2013; accepted 9 June 2014.
... While video recordings can facilitate collection of more observation time points, studies employing videos sometimes condense these data to the percent time spent associated with each choice (Thoen et al. 2016). Few studies report on the transitory movements between positions, which can reveal important aspects about the process of choice (Zeilinger et al. 2014). Herbivores may be attracted to a preferred resource, ignoring resources of poorer quality with an efficient searching behavior. ...
... We first utilized log-linear models to determine whether differential attraction and/or leaving rates existed between plants with different nitrogen content. Next, we used a likelihood-based biostatistical model, described by Zeilinger et al. (2014) to quantify differences in attraction and leaving rates in trials where differences were identified. From these estimated rates, we then calculated average tenure time on preferred and dispreferred plant resources. ...
... Next, to quantify any differences in attraction (ρ) and leaving (μ) rates, we extended a biostatistical maximum-likelihood estimator model developed for individuals to an arbitrary number of individuals (Zeilinger et al. 2014). This model consists of four model-variants: the Fixed Model, which assumes no preference (ρ 1 = ρ 2, μ 1 = μ 2 ), the Free Attraction Model, which assumes that preference is based solely on preferential attraction (ρ 1 ≠ ρ 2, μ 1 = μ 2 ), the Free leaving Model, which assumes that preference is based solely on differential leaving rates (ρ 1 = ρ 2, μ 1 ≠ μ 2 ), and the Free Model, which allows both preferential attraction and differential leaving (ρ 1 ≠ ρ 2, μ 1 ≠ μ 2 ). ...
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Effective insect management strategies require a firm understanding of the factors determining host preference, particularly in highly mobile insect herbivores. Host preference studies commonly employ average or first position as a proxy for preference. Yet few studies have explored host preference in relation to transitory attraction and leaving rates, yet these are both components of host plant selection. We investigated the transitory dynamics of preference by the green rice leafhopper, Nephotettix cincticeps (Uhler) (Hemiptera: Cicadellidae) by conducting experiments on groups of females, males, or mixed-sex leafhoppers, and recording their position over time between low-N and normal-N rice plants. Utilizing a log-linear model and variants of a biostatistical model we used these positional data to extract attraction, leaving and tenure rates to better understand the process of host-plant selection. We found a general preference for normal-N over low-N plants at equilibrium. However, between sexes there was variation in the relative significance of attraction or leaving rates on that preference. Female leafhoppers were more attracted to host plants with higher nitrogen content. Male leafhoppers were less discriminate in their initial attraction to hosts but left low-N hosts at a faster rate. Whereas estimated tenure times on both normal- and low-N plants exceeded transmission times for the leafhopper-transmitted rice dwarf virus, longer tenure on normal-N plants likely increases the likelihood of virus acquisition from these plants. Our findings support previous recommendations that growers can mitigate the risks of leafhopper damage and pathogen transmission by optimizing their application of nitrogenous fertilizers.
... For the paired choice experiment, preference was inferred from attraction (p s and p m ) and leaving (m s and m m ) rates of juveniles for seagrass and macroalgae, respectively. The rates were estimated using a continuous-time, likelihoodbased model developed by Zeilinger et al. (2014) and differences between these rates were tested using model selection. Four models of likelihood were compared: a Fixed model representing a null model of no preference where both the attraction rates and the leaving rates were equal to each other (p s ¼ p m , m s ¼ m m ), a Free Leaving model where attraction rates were equal but leaving rates were allowed to vary (p s ¼ p m , m s = m m ), a Free Attraction model where attraction rates were allowed to vary and leaving rates were equal (p s = p m , m s ¼ m m ), and a Free model where all four parameters were allowed to fit independently (p s = p m , m s = m m ). ...
... In the actual experiment, both wild and cultured juveniles were distributed nearly equally between seagrass and macroalgae by 06:15 h. Due to the nature of the paired choice data, the assumptions of the preference model on independent consecutive choices and constant attraction and leaving rates set by Zeilinger et al. (2014) were violated, hence parameter estimates may be biased. However, because the Fixed Model was clearly the best model, and parameter estimates suggested little difference between choices, such bias is unlikely to affect interpretation of the results. ...
... horrens in shallow waters probably avoid light for the same reason. Stichopodid sea cucumbers have body walls composed mainly of type 1 collagen (Cui et al., 2007;Abedin et al., 2013;Zhong et al., 2015), that has been shown to undergo extensive damage under UV light (Miles et al., 2000;Jariashvili et al., 2012). Negative phototaxis and pigmentation patterns in brittlestars are also thought to facilitate defensive shelter seeking and confer camouflage against predatory fish in varying light conditions (Hendler, 1984). ...
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Animals develop behavioural strategies throughout life to improve their survival in nature. Juvenile activity and behaviour of the commercial tropical sea cucumber Stichopus cf. horrens were examined considering factors that may influence survival at this critical developmental stage. Wild juveniles were observed in situ to describe diel activity and movement. Wild and hatchery-reared juveniles were observed in the laboratory to evaluate the influence of different light-dark cycles and microhabitats on feeding and sheltering behaviour. All juveniles (4–54 g) displayed a distinct nocturnal activity pattern both in the field and laboratory. Nocturnal activity was strongly associated with feeding and locomotion. Wild and hatchery-reared juveniles were most active at night, displayed intermediate activity during twilight, and minimal to no activity during daytime. Movement rates of wild juveniles in situ were significantly influenced by time and size to a lesser extent. Under constant light and constant dark for 48 h, juvenile feeding rhythm was endogenously controlled and strongly entrained to natural light-dark cycles. Sheltering was directly affected by light and linked to strong phototactic and thigmotactic reflexes. Juveniles preferred vegetation as shelter compared to coral, sand or open space, and showed equal preference for seagrass and macroalgae. Deviations in behaviour of hatchery-reared juveniles under laboratory conditions indicate some degree of acclimation to an artificial environment with minimal threats and a decreased sensitivity to light. The implications of nocturnal feeding, light-induced sheltering, shelter preferences and acclimation to artificial conditions are discussed in relation to juvenile survival in nature and potential restocking of the species.
... The primary exception is aphids, where measures of location are used (Gianoli, 2000;Messina et al., 2002;Zytynska & Preziosi, 2013). Measures of consumption relate directly to resource quality but provide little information about the attractiveness of the choices (Nicotri, 1980;Schoonhoven et al., 2005;Zeilinger et al., 2014). In contrast, measures of location or movement can provide insight into both resource quality and attractiveness (Zeilinger et al., 2014). ...
... Measures of consumption relate directly to resource quality but provide little information about the attractiveness of the choices (Nicotri, 1980;Schoonhoven et al., 2005;Zeilinger et al., 2014). In contrast, measures of location or movement can provide insight into both resource quality and attractiveness (Zeilinger et al., 2014). Taken together, measures of consumption and movement may provide complementary insights into the nature of consumer choice. ...
... The probability that a herbivore is associated with a given host choice is the balance of the herbivore's attraction rate to and leaving rate from that choice (Zeilinger et al., 2014). Whether the preference is determined by attraction or by leaving may provide clues to the most relevant causes. ...
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1. Herbivory often induces systemic plant responses that affect the host choice of subsequent herbivores, either deterring or attracting them, with implications for the performance of both herbivore and host plant. Combining measures of herbivore movement and consumption can efficiently provide insights into the induced plant responses that are most important for determining choice behaviour. 2. The preferences of two frugivorous stink bug species, Nezara viridula and Euschistus servus between cotton plants left undamaged or damaged by Helicoverpa zea and Heliothis virescens larvae were investigated. A novel consumer movement model was used to investigate if attraction rates or leaving rates determined preferences. Stink bug consumption rates were measured using salivary sheath flanges. Finally, the systemic induction of selected phenolic-based and terpenoid secondary metabolites were measured from heliothine herbivory on developing cotton bolls, to investigate if they explained stink bug feeding responses. 3. Heliothine herbivory did not affect the N. viridula feeding preference. However, we found opposing effects of H. zea and H. virescens herbivory on the behaviour of E. servus. Avoidance of H. zea-damaged plants is not obviously related to phenolic or terpenoid induction in cotton bolls; whereas a preference for H. virescens-damaged plants may be related to reductions in chlorogenic acid in boll carpel walls. 4. The present results highlight the inferential power of measuring both consumer movement and consumption in preference experiments and combining behavioural responses with phytochemical responses. Furthermore, while plant-mediated interactions among herbivorous insects are well studied, interactions among frugivorous species specifically have been poorly documented.
... Br. tournefortii life stages were replicated as follows: 23 at the rosette stage, 30 that were bolting, and 13 senescent. Because it was not feasible to confidently assay Ba. hilaris oviposition given the size of the cages and amount of plant biomass, we instead tracked insect position within cages over time as a proxy for some combination of orientation and feeding preference (Sisterson 2008, Zeilinger et al. 2014. A single un-mated adult, Ba. hilaris, was introduced into the experimental arena within two d of eclosion. ...
... However, preference was driven primarily by bolting Br. tournefortii and largely disappeared with senescent Br. tournefortii. The design of our trials was comparable to other studies that use the specific location of herbivores over time or their leaving rates from a given plant as an indication of relative preference (Zeilinger et al. 2014). Although egg laying was not quantified in these preference bioassays, it is worth noting that the large differences in the number of Ba. hilaris nymphs in the field experiment may be consistent with a higher oviposition preference for Br. ...
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Indirect interactions among native and invasive species are notoriously difficult to predict. Here, we apply theory from trait‐mediated indirect effects and plant–insect interactions to explain the outcomes of multiple invader interactions. The present study investigates the roles of herbivore preference and plant ontogeny in mediating associational effects among a southern California native shrub, Atriplex canescens, an invasive annual forb, Brassica tournefortii, and an invasive stink bug, Bagrada hilaris. Ba. hilaris have been observed to form dense aggregations on A. canescens in late spring following senescence of Br. tournefortii, with subsequent increased mortality of A. canescens. A manipulative experiment found Ba. hilaris recruited to A. canescens in approximately 70 times greater numbers when neighbored by Br. tournefortii than when alone. Ba. hilaris nymph production, while minimized experimentally, occurred only on Br. tournefortii, suggesting A. canescens is not of sufficient quality for Ba. hilaris reproduction. In greenhouse preference trials, Ba. hilaris exhibited an overall preference for Br. tournefortii over A. canescens; however, the magnitude of preference depended on ontogenetic stage of Br. tournefortii. Overall, our results suggest significant potential for associational susceptibility mediated by a combination of Ba. hilaris preference for reproductive Br. tournefortii, substantial aggregation of Ba. hilaris onto Br. tournefortii, and a marked decline in Ba. hilaris preference for Br. tournefortii with advancing ontogeny—triggering spillover onto neighboring plants. Our results demonstrate an important role for multiple invaders and phenologically driven trait changes in mediating associational susceptibility.
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Host defense against vector‐borne plant pathogens is a critical component of integrated disease management. However, theory predicts that traits that confer tolerance or partial resistance can, under certain ecological conditions, enhance the spread of pathogens and spillover to more susceptible populations or cultivars. A key component driving such epidemic risk appears to be variation in host‐selection behavior of vectors based on infection status of the host. While recent theory has further emphasized the importance of infection‐induced host‐selection behavior by insect vectors for plant disease epidemiology, experimental tests on the relationship between vector host‐selection preference and transmission are lacking. We test how host plant defense—conferred by the PdR1 gene complex—mediates vector host‐selection preference and transmission of the pathogenic bacterium Xylella fastidiosa among grapevine cultivars. We confirmed that PdR1 confers resistance against X. fastidiosa by reducing both pathogen population size and disease severity. We found that vector transmission rates to new hosts exhibited unimodal dynamics over the course of infection when both susceptible and resistant were infected and acted as sources of the pathogen. Transmission from susceptible plants initially increased and then declined as insect vectors avoided severely diseased plants. While transmission from PdR1‐resistant plants also initially increased and then declined as well, this was not due to avoidance by vectors, although the exact mechanism remains unclear. We show that (1) vector preference changes over the course of disease progression, (2) vector preference is clearly important but a poor predictor of transmission, and (3) the post‐latent incubation period—in which plant hosts are infectious but asymptomatic—is likely a key period for vector transmission of X. fastidiosa. Our results suggest that, consistent with theory, defensive traits lengthen the duration of the incubation period, increasing X. fastidiosa transmission. However, defensive traits may over the long‐term ultimately reduce spread possibly through induced resistance. Vector host‐selection preference, host resistance, and transmission are clearly dynamic, changing over the course of disease progression. Understanding these dynamics is critical for broader insights into the epidemiology of vector‐borne plant pathogens, theory development, and deploying disease‐resistant cultivars in an effective and sustainable manner.
One of the fundamental challenges of pre-release studies in classical biological weed control is to assess and predict the likelihood and consequences of non-target effects. Unless a candidate biological control agent is proven to be monophagous through conventional starvation and host-specificity tests in quarantine, open-field host range studies can be important in predicting the likelihood of non-target effects since they reveal the host selection of herbivores displaying the whole array of pre- and post-alightment behaviours. Over the course of its 53-year history, the purpose and the design of open-field host range studies have changed considerably, with more recent studies clarifying or refining specific questions related to one or a few test plant species and using a set design. We discuss the opportunities and challenges of this approach and suggest that future open-field host range studies should be more hypothesis-driven and apply different experimental designs that facilitate the interpretation of the results.
Vector preference based on host infection status has long been recognized for its importance in disease dynamics. Prior theoretical work has assumed that all hosts are uniformly susceptible to the pathogen. Here we investigated disease dynamics when this assumption is relaxed using a series of vector–host epidemiological compartment models with variable levels of host resistance or tolerance to infection – collectively termed defense. In our models, vectors cannot acquire the infection from resistant hosts but can acquire from tolerant hosts. Specifically, we investigated the interacting effects of vector preference and host defense in a series of single- and two-patch models. Results indicate that resistant host types generally reduce disease prevalence and pathogen spillover, independent of vector preference. The epidemiological consequences of host tolerance, however, depended on vector preference. When vectors preferred diseased hosts, tolerance reduced incidence compared to susceptible hosts; when vectors avoided diseased hosts, tolerance enhanced disease prevalence. Finally, a variation of the model that included preference-based vector patch leaving rates suggests that both resistance and tolerance can promote pathogen spillover if vectors prefer diseased hosts, because of increased vector dispersal into susceptible patches. Collectively, we found complex, context-dependent effects of vector preference and host defense on disease dynamics. In the context of management programs for vector-borne diseases, managers should consider both the precise form of host defense present in a population, breed, or cultivar, as well as vector feeding behavior.
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Individual movement of 29 Nephotettix cincticeps was observed to determine the fine structure of N. cincticeps movement in homogeneous environments. Movement was considered to be a series of place to place transitions, and each transition was composed of a tenure time followed by movement to a new position. Tenure time and movement distance were independent. Tenure times were independent of each other, followed a Poisson process, and their frequency distributions were identical. However, they apparently decreased with adult age. Movement distances were identically distributed, but not independent. Some individuals tended to move farther than others. From these results, it was concluded that the simple random walk and the simple diffusion model are good first approximations of N. cincticeps movement. © 1984, JAPANESE SOCIETY OF APPLIED ENTOMOLOGY AND ZOOLOGY. All rights reserved.
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The adoption of transgenic Bt cotton has, in some cases, led to environmental and economic benefits through reduced insecticide use. However, the distribution of these benefits and associated risks among cotton growers and cotton-growing regions has been uneven due in part to outbreaks of non-target or secondary pests, thereby requiring the continued use of synthetic insecticides. In the southeastern USA, Bt cotton adoption has resulted in increased abundance of and damage from stink bug pests, Euschistus servus and Nezara viridula (Heteroptera: Pentatomidae). While the impact of increased stink bug abundance has been well-documented, the causes have remained unclear. We hypothesize that release from competition with Bt-susceptible target pests may drive stink bug outbreaks in Bt cotton. We first examined the evidence for competitive release of stink bugs through meta-analysis of previous studies. We then experimentally tested if herbivory by Bt-susceptible Helicoverpa zea increases stink bug leaving rates and deters oviposition on non-Bt cotton. Consistent with previous studies, we found differences in leaving rates only for E. servus, but we found that both species strongly avoided ovipositing on H. zea-damaged plants. Considering all available evidence, competitive release of stink bug populations in Bt cotton likely contributes to outbreaks, though the relative importance of competitive release remains an open question. Ecological risk assessments of Bt crops and other transgenic insecticidal crops would benefit from greater understanding of the ecological mechanisms underlying non-target pest outbreaks and greater attention to indirect ecological effects more broadly.
We briefly outline the information-theoretic (I-T) approaches to valid inference including a review of some simple methods for making formal inference from all the hypotheses in the model set (multimodel inference). The I-T approaches can replace the usual t tests and ANOVA tables that are so inferentially limited, but still commonly used. The I-T methods are easy to compute and understand and provide formal measures of the strength of evidence for both the null and alternative hypotheses, given the data. We give an example to highlight the importance of deriving alternative hypotheses and representing these as probability models. Fifteen technical issues are addressed to clarify various points that have appeared incorrectly in the recent literature. We offer several remarks regarding the future of empirical science and data analysis under an I-T framework.