Solving the pitfalls of pitfall trapping: a twocircle method for density

Methods in Ecology and Evolution 2013, 4, 865–871
doi: 10.1111/2041-210X.12083
Solving the pitfalls of pitfall trapping: a two-circle method
for density estimation of ground-dwelling arthropods
Zi-Hua Zhao1†, Pei-Jian Shi1†, Cang Hui2, Fang Ouyang1, Feng Ge1* and Bai-Lian Li3
1
State Key Laboratory of Integrated Management of Pest Insects and Rodents, Institute of Zoology, Chinese Academy of
Sciences, Beijing 100101, China; 2Centre for Invasion Biology, Department of Botany and Zoology, Stellenbosch University,
Matieland 7602, South Africa; and 3Ecological Complexity and Modeling Laboratory, Department of Botany and Plant
Sciences, University of California, Riverside, CA 92521-0124, USA
Summary
1. Pitfall traps are widely used for investigating ground-dwelling arthropods, but have been heavily criticized
due to their species-, habitat- and attractant-specific trapping radius which produces unreliable estimation of species diversity and density.
2. We developed a two-circle method (TCM) for simultaneously estimating densities of ground-dwelling arthropods and the effective trapping radius. Multiple pairs of traps are located different distances apart, and the intersection of trapping areas can be calculated using the inverse trigonometric function. The density and effective
trapping radius can be estimated from a nonlinear regression of the change in the total number of individuals
caught with the distance between the paired pitfall traps.
3. We compared the performance of TCM with the estimator based on the nested-cross array (NCA) for arranging pitfall traps, by comparing predicted densities from these two methods with the real density obtained from
the suction sampling method (SSM).
4. Simulations with known arthropod densities and effective trapping radius suggested that TCM produced
accurate density estimation, while NCA significantly underestimated the known density. Pitfall trapping of
ground-dwelling arthropods on two habitats (crop field and desert steppe) confirmed this conclusion when comparing estimation from TCM and NCA with densities obtained from the SSM.
5. TCM is a promising technique for the density estimation of ground-dwelling arthropods, especially for traps
with liquid attractant and areas with relatively homogenous habitat and away from habitat edges.
Key-words: nested-cross array, pitfall traps, suction sampling method, trapping radius, two-circle
method
Introduction
Ground-dwelling arthropods are highly diverse and abundant in crop fields and semi-natural habitats across the
world (Finke & Snyder 2010; Chaplin-Kramer et al. 2011;
Tscharntke et al. 2012) and have important functions in
agroecosystems such as controlling pests and maintaining
food chain robustness (Landis, Wratten & Gurr 2000;
Tscharntke et al. 2005; Holland, Birkett & Southway
2009). Pitfall traps have been the standard and most frequently used approach for surveying ground-dwelling
arthropods because they are easy to handle and can collect
high numbers of individuals and species efficiently (Perner
& Schueler 2004; Schmidt et al. 2005; Shrestha & Parajulee
2010). However, trapping efficiency is often sensitive to the
population density of a species, its locomotion and olfaction, and the habitat specificity (Perner & Schueler 2004;
Niemel€a & Kotze 2009; Schirmel et al. 2010). Arthropod
*Correspondence author. E-mail: gef@ioz.ac.cn
†These two authors contributed equally to this work.
species also respond differently to the choice of liquid
attractant and detergent, and the arrangement of traps
(Schmidt et al. 2006; Niemel€
a & Kotze 2009). Due to these
complications, density estimation and community assemblage structures portrayed from pitfall trapping are often
biased (Mommertz et al. 1996; Melis et al. 2010; Hummel
et al. 2012).
A standard sampling design of pitfall trapping is needed to
resolve the above drawbacks and allow comparisons of results
from the literature across scales and localities (Holland &
Smith 1999; Holland, Birkett & Southway 2009). Although
some methods are available for estimating real population densities of ground-dwelling arthropods using additional removal
and suction sampling, or soil extraction techniques (Mommertz et al. 1996), they are expensive and difficult to handle,
defying the exact nature of pitfall trapping. To this end, specific
experiment designs with posterior mathematical analyses have
also been proposed to capture the real population density, and
yet they often require the knowledge of many parameters of
locomotion and complicated deduction (Hui, McGeoch &
Warren 2006; Hui, Boonzaaier & Boyero 2012; Petrovskii
© 2013 The Authors. Methods in Ecology and Evolution © 2013 British Ecological Society
866 Z.-H. Zhao et al.
et al. 2012). Recently, Perner & Schueler (2004) proposed a
method of nested-cross array for arranging pitfalls which can
estimate the population density of ground-dwelling arthropods
with a single hyperbolic function. Although this method has
been widely discussed in theoretical literature (Wolkovich,
Bolger & Holway 2009; Wolkovich 2010; Zurell et al. 2010;
Lange, Gossner & Weisser 2011), it has hardly been used in
field experiments because this method requires neutral preservative in pitfall traps (Perner & Schueler 2004). In addition,
how this method performs when using liquid attractant is still
largely unknown.
To solve these pitfalls of pitfall trapping (i.e., density estimation relies on a known effective trapping radius, whilst the
trapping radius is often unknown due to its sensitivity to species’ behaviour, mobility and olfactory threshold, as well as
the attractant and habitat specificity), we here have developed
a new practical sampling design for estimating densities of
ground-dwelling arthropods by allocating pairs of traps with
different distances apart. This method can simultaneously
predict population density and effective trapping radius as
outputs, contrasting conventional methods that require the
effective trapping radius to estimate densities, bypassing these
drawbacks of pitfall trapping. We first conducted a theoretical simulation with known densities and effective trapping
radius to evaluate the accuracy and sensitivity of these two
methods. We then compared the performance of our methods and the nested-cross array with the real population densities obtained from the suction sampling method in two
habitats (crop field and desert steppe). We conclude by discussing the restrictions of these methods and recommending
our sampling design and subsequent data analysis approach
(a)
as a reliable method for the density estimation of grounddwelling arthropods.
Materials and methods
TWO-CIRCLE METHOD
This method requires the design of multiple pairs of traps with different
distances between the pairs (Fig. 1a). The effective trapping area of a
pair can be estimated as the joint area using the inverse trigonometric
function (Fig. 1c,d). Specifically, let h be an inverse cosine function
defined as h = arccos(d/2r), where d is the distance between the centres
of the paired traps and r is the effective trapping radius for the focal
species. Let A1 (=pr2) be the trapping area of a single trap; let O be
the overlapping areaqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
of two paired traps (Fig. 1c):
O ¼ 2r2 arccosðd=2rÞ d r2 ðd=2Þ2 if d ≤ 2r; O = 0 if d > 2r. The
effective trapping area of the paired traps (A2) can be estimated as
A2 = 2A1-O (Fig. 1d). The number of individuals caught in the paired
traps will be N = A2D, where D is the population density; that is,
8
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
d
<
2
2
2 d 2 D
2pr
2r
arccos
þ
d
r
2r
2
N¼
:
if d [ 2r:
2pr2 D
if d 2r;
As both D and r are unknown, we need multiple paired traps with different distances apart to estimate these two variables.
Evidently, this two-circle method presumes that the trapping area of
a trap is round (assumption of isotropy) and the density at different
trapping areas is constant (assumption of homogeneity). In addition,
the effective trapping radius (r) of a specific liquid attractant is also
assumed to be a constant parameter for a given ground-dwelling
arthropod species (assumption of no within-species variation). The estimate of D is clearly not sensitive to the biological characteristics of the
(b)
1·5 m
2·0 m
2·5 m
15 m
15 m
(c)
(d)
Pitfall trap
r
θ
A1
O
A1
d
Fig. 1. An illustration of the spatial arrangement of pitfall traps for the two-circle method (a) and the nested-cross array (b). (c) Two traps d distance
apart and their effective trapping radius (r). (d) Two traps, with each having an effective trapping area of A1 and an overlapped trapping area of O.
© 2013 The Authors. Methods in Ecology and Evolution © 2013 British Ecological Society, Methods in Ecology and Evolution, 4, 865–871
A two-circle method for density estimation
species (e.g. body size, mobility and olfactory sensitivity). In our following experiment, paired traps were set 15, 20 and 25 m apart (we also
included a single trap, i.e. d = 0), and observations of N and d were
then used to estimate D and r using a nonlinear fitting method (nls function in R 2.15.1; R Development Core Team 2012).
EVALUATION
We compare the performance of our method with Perner & Schueler’s
(2004) nested-cross array for density estimation. This method arranges
pitfall traps in a cross-shape with distances between adjacent traps
increasing when further away from the origin of the cross. Let yd be the
mean number of individuals caught in the four traps that are of d distance away from the centre, and Perner & Schueler (2004) suggested a
hyperbolic relationship, yd = ad/(b+d), where a and b are regression
coefficients, from which they derived the effective trapping radius
(r = b) and the density estimation (D = a/(2pb2)). We set the distances
between the traps on the two arms to the origin as 05, 15, 35, 65,
105, 155, 215, 285, 365 and 455 m, respectively, with a total of 41
traps needed for each nested-cross array (Fig. 1b).
To assess effectiveness and sensitivity of the two-circle method and
the nested-cross array, we first developed a simulation with known densities and effective trapping radius. The calculation of D and r, as well
as the simulation, was conducted using R 2.15.1 (R Development Core
Team 2012; see Appendix S1 and S2 for R codes), with four sets of
known D and r and 200 runs of the simulation for each set of D and r.
For empirical evaluation in the field, we conducted a field experiment
in 2012, surveying the population densities of carabid beetles, phytophagous insects and spiders on two different habitat types: corn field in
Shandong, Eastern China (Fig. S1a), and desert steppe in the Inner
Mongolia Autonomous Region, Northwest China (Fig. S1b); see
details in Appendix S3 online Supporting Information. Grounddwelling arthropods were collected using pitfall traps (transparent
plastic cups) with 9 cm in diameter, 11 cm deep and filled with 60 ml
of 3333% (vol/vol) ethylene glycol with 3% detergent (Sasakawa 2007;
Aristophanous 2010; Braun et al. 2012). For each habitat type, six 1-ha
sites (100 m 9 100 m experimental site) were selected, three for testing
the two-circle method and the other three for nested-cross array, with
pitfalls arranged according to Fig. 1(a,b). We here chose three dominant arthropod species in each habitat (desert steppe: Blaps femoralis
Fischer-Waldheim (Coleoptera: Tenebrionoidea), Anacolica mucronata
Reitter (Coleoptera: Tenebrionoidea) and Argiope bruennichi (Scopoli)
(Araneae: Araneidae); corn field: Chlaenius bioculatus Motschulsky
(Coleoptera: Carabidae), Teleogryllus mitratus (Burmeisteir) (Orthoptera: Gryllidae) and Pardosa astrigena L. Koch (Araneae: Lycosidae))
to calculate population density and effective trapping radium of traps.
Real population densities of ground-dwelling arthropods were estimated by the suction sampling method (Elliott et al. 2006; Brook et al.
2008). Each experimental site was divided into seven equal size subsamples. Using a 1 m2 circular toothed sampling metal frame, we collected
a single 15 cm deep sample for each subsample. The metal frame was
placed at a random position in each subsample, toothed side down and
inserted into the soil to block adult ground-dwelling arthropods from
escaping. The area within the frame was sampled using a D-vac fitted
with a ventilated 60 cm long cylindrical metal extension. After suction
sampling within the frame for approximately 30 min, the interior of the
frame was searched for adult ground-dwelling arthropods (carabid beetles, phytophagous arthropods and spiders). Hand searching was continued within the frame for 10 min, with plants, the soil surface and
underneath loose soil thoroughly inspected for ground-dwelling arthropods, which were then collected in a hand-held container. All ground-
867
dwelling arthropods were stored in glass bottles filled with 90% ethyl
alcohol for preservation and identification. We calculated the percentage accuracy PA = 100%9(Dpred – Dobs)/Dobs for evaluating the performance of the two trapping methods (i.e. the two-circle method and
the nested-cross array).
Results
The simulation confirmed that the two-circle method could
produce reliable density estimation of ground-dwelling
(a)
(b)
Fig. 2. Simulations using the nested-cross array and two-circle
method. (a) Relationship between the mean sampled individuals caught
and the distance from the origin of the nested-cross array. (b) Relationship between the number of individuals caught in paired pitfalls and
the distance apart between the paired pitfalls of the two-circle method.
Solid curves are the best fit according to each model; dashed lines in (a)
indicate both function parameters a/2 and b. Data are from the simulation with a known density (D = 15 individuals per m2; Appendix S1)
© 2013 The Authors. Methods in Ecology and Evolution © 2013 British Ecological Society, Methods in Ecology and Evolution, 4, 865–871
868 Z.-H. Zhao et al.
Table 1. Simulation results (means standard errors) with known densities (D) and effective trapping radius (r), estimated by the two-circle method
(TCM) and the nested-cross array (NCA) (see Appendix S1 & S2 for details).
TCM
Known
D
D
D
D
=
=
=
=
1, r
1, r
2, r
2, r
NCA
D
=
=
=
=
15
25
15
25
095
100
204
211
r
004
005
006
007
154
249
148
242
003
007
002
005
R2
D
074
082
074
091
053
037
109
072
R2
r
003
002
005
002
153
310
150
316
004
008
003
006
072
088
081
091
chi was merely 19 % of the real density in fields. This is alarming especially as the data from the nested-cross array fit well to
the single hyperbolic function as proposed by Perner & Schueler’s (2004) (Table 2).
arthropods. Although the relationship between mean individuals caught by the nested-cross array and the distance to the centre fitted the single hyperbolic function (Fig. 2a), the density
was underestimated by about half (Table 1). In contrast, the
inverse trigonometric function of the two-circle method fitted
well with the relationship between total individuals caught by a
pair of traps and their distance apart (Fig. 2b) and produced
accurate estimation of population density and effective
trapping radius (Table 1).
From the field experiment, we collected 1646 individuals in
corn fields and 2114 individuals in desert steppe for the six
dominant arthropod species. The effective trapping radius of
pitfall traps estimated from the two-circle method varied from
118 to 161 m (Table 2; Fig. 3). The estimations of population
density are not significantly different from the real densities
estimated from the suction sampling method, ranging from
111 (C. bioculatus) to 169 (T. mitratus) individuals per m2
(Table 2, Fig. 3). Although the population densities of some
species were slightly underestimated by the two-circle method
(B. femoralis and T. mitratus), the accuracy was still high, with
the absolute values of PA < 5% (Table 2). The population
densities of the other four species were determined accurately
by the two-circle method.
The population densities estimated from the nested-cross
array were significantly lower than the real densities from the
suction sampling method, with the estimation ranging from
merely 003 (A. bruennichi) to 046 (C. bioculatus) individuals
per m2 (Table 2). The accuracy of the nested-cross array was
extremely low; for instance, the density estimate of A. bruenni-
Discussion
The two-circle method can accurately estimate the population
density of ground-dwelling arthropods in different habitats.
Population densities of some ground-dwelling arthropods were
slightly lower than the real population densities in the field, yet
the difference is not significant. The population density of
ground-dwelling arthropods in literature ranges from 006 to
22 individuals per m2 (Thomas, Parkinson & Marshall 1998;
Elliott et al. 2006), suggesting that the real population densities
in our experiment are relatively low. However, the population
densities of these dominant species were consistent with the
observations of Clark, Luna & Youngman (1995), Clark et al.
(2006) and Elliott et al. (2006). Specifically, Clark, Luna &
Youngman (1995) reported that the population density of Anisodaclus sanctaecrucis was 174–240 individuals per m2 when
using the removal sampling method, and the density of dominant species (Scarites quadriceps) in no-till cropping system
was 136 044 individuals per m2 (Clark et al. 2006). Garcıa,
Griffiths & Thomas (2000) had also found that the mean population density of Nebria brevicollis was approximately 09 individuals per m2. However, all these results were calculated
through mark–recapture, removal sampling data, traps on
grids or trapping webs in combination with distance measure
Table 2. Estimates (Dpred) of population density (means standard errors) for ground-dwelling arthropods in desert steppe and corn field, based on
the two-circle method (TCM) and nested-cross array (NCA, together with the two parameters a and b), as well as the real density (Dreal) estimated
from the suction sampling method (SSM).
TCM
NCA
SSM
Species
Dpred
r
R2
a
b
Dpred
R2
Dreal
Desert steppe
Anacolica mucronata
Blaps femoralis
Argiope bruennichi
128 029
146 029
157 041
158 021
142 016
119 017
081
086
062
446 011
661 016
635 037
242 031
170 035
551 137
012 003
037 017
003 002
070
059
052
123 012
151 012
156 013
Corn field
Chlaenius bioculatus
Teleogryllus mitratus
Pardosa astrigena
111 028
169 027
144 028
128 019
162 015
134 015
073
089
084
937 016
870 026
719 023
181 021
326 047
345 052
046 011
013 004
010 003
077
069
067
112 009
171 019
142 013
© 2013 The Authors. Methods in Ecology and Evolution © 2013 British Ecological Society, Methods in Ecology and Evolution, 4, 865–871
A two-circle method for density estimation
(a)
(b)
(c)
(d)
(e)
(f)
869
Fig. 3. Relationship of the number of individuals caught in paired traps and the distance apart from the two-circle method for six arthropod species
in different habitats. Desert steppe: (a) Anacolica mucronata, (b) Blaps femoralis, (c) Argiope bruennichi; Corn fields: (d) Chlaenius bioculatus, (e)
Teleogryllus mitratus, (f) Pardosa astrigena.
© 2013 The Authors. Methods in Ecology and Evolution © 2013 British Ecological Society, Methods in Ecology and Evolution, 4, 865–871
870 Z.-H. Zhao et al.
analysis (Thomas, Parkinson & Marshall 1998; Perner &
Schueler 2004). Therefore, we consider that the real density
estimation from the suction sampling method is reliable, and
the two-circle method is consequently an efficient sampling
approach to be recommended.
Perner & Schueler (2004) reported that their method might
underestimate the population density of ground-dwelling
arthropods. Although we have slightly changed the nestedcross array (specifically, the increasing distance of traps from
the centre was 05 m, and we used liquid attractant instead of
neutral preservative), the data captured fit the proposed single
hyperbolic function. However, the nested-cross array and its
estimation method obviously underestimated the real population densities of ground-dwelling arthropods. We suspect the
formulae derived by Perner & Schueler (2004) could be problematic, and a thorough correction is needed for the nestedcross array to be used in real field experiments. Other factors
such as the requirement of using a neutral preservative instead
of a liquid attractant could have also affected the performance
and accuracy of the nested-cross array (Perner & Schueler
2004).
The pitfall trapping method has been heavily criticized as
different species respond to the traps and the liquid attractant
differently, making the reliable estimation of community
assemblage structures nearly impossible (Clark, Luna &
Youngman 1995; Schirmel et al. 2010). Methods that are capable of handling this species sensitivity are often time- and
labour-consuming (e.g. the mark–recapture technique; Clark,
Luna & Youngman 1995; Mommertz et al. 1996; Tufto et al.
2012), and they could be unfeasible for small species that cannot be labelled or unpractical for species with flexible skin (e.g.
spiders). To this end, many prefer to use only water or detergent for trapping. The two-circle method can simultaneously
estimate the real population density of ground-dwelling
arthropods and the effective trapping radius for a specific
liquid attractant. In so doing, the estimation of population
density becomes independent from the effective trapping
radius, and thus makes the two-circle trapping method a
strong and reliable candidate of sampling design for studying
community assemblage structures.
In our experiment, paired traps set at four different distances apart (0, 15, 2, and 25 m) were used to conduct the
field experiment and simulation. The population density of
ground-dwelling arthropods was accurately estimated by the
two-circle method. However, the design of distance between
traps should be adjusted depending on specific species. Using
more paired traps could further improve the accuracy and
reliability of density estimation. When using the coefficient
of variation (CV) to quantify the level of population aggregation (Hui, Veldtman & McGeoch 2010), species with
highly aggregated distribution demands more replications of
paired traps per distance apart to ensure accurate estimation.
In practice, to ensure the goodness-of-fit for observations
versus predictions (R2) is > 094, we need five replications of
paired traps per distance apart if CV = 10%, 15 replications if CV = 20% and 30 replications if CV = 30% (see
Appendix S4).
As we only tested the two-circle method for dominant
species, tests for rare species are still needed in further
research. We have noticed that the density estimation
appeared to be more accurate in corn fields than in desert
steppe, potentially because corn fields are more homogenous
than desert steppe. How habitat heterogeneity and disturbance affect the accuracy of estimation warrants further
investigation (Cole et al. 2010; Gillingham et al. 2012).
Taken together, by solving both population density and
effective trapping radius simultaneously, the two-circle
method resolves the drawbacks of pitfall trapping that often
estimate population density based on unknown or biased
trapping radius due to its species, habitat and attractant
specificity. Consequently, it also avoids estimating the effective trapping radius as an intermediate step which often suffers from the gradient effect where the likelihood of trapping
an individual declines with its distance from the pitfall trap.
Our results thus suggest that the two-circle method has great
potential for accurate and efficient monitoring of grounddwelling arthropods in agricultural and natural areas.
Acknowledgements
We are grateful to Robert Freckleton, Samantha Ponton and two anonymous
reviewers for insightful comments, to Yucheng Comprehensive Experimental Station, Chinese Academy of Sciences, for allowing us to use their corn fields for
arthropod collections. This project is supported by the State Key Program of
National Natural Science of China (No. 31030012), the National Key Technology R & D Program (2012BAD19B05) and University of California Agricultural
Experiment Station. CH is supported by the Incentive Research Programme of
the National Research Foundation.
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Received 28 February 2013; accepted 10 June 2013
Handling Editor: Robert Freckleton
Supporting Information
Additional Supporting Information may be found in the online version
of this article.
Appendix S1. R scripts of three functions (‘tc.simulations’, ‘tcm’ and
‘tc.points’) for the two-circle method and its simulation tests.
Appendix S2. R scripts of the function (‘nca’) for testing the nestedcross array proposed by Perner & Schueler (2004).
Appendix S3. Descriptions of study sites.
Appendix S4. Comparisons of estimated densities with known values
under different coefficients of variation.
© 2013 The Authors. Methods in Ecology and Evolution © 2013 British Ecological Society, Methods in Ecology and Evolution, 4, 865–871