Ecological Modelling 254 (2013) 54–70
Contents lists available at SciVerse ScienceDirect
Ecological Modelling
journal homepage: www.elsevier.com/locate/ecolmodel
A mechanistic model for a tritrophic interaction involving soybean aphid, its host
plants, and multiple natural enemies
Christine A. Bahlai a,∗ , Ross M. Weiss b , Rebecca H. Hallett a
a
b
School of Environmental Sciences, University of Guelph, Guelph, ON, Canada N1G 2W1
Agriculture and Agri-Food Canada, Saskatoon Research Centre, 107 Science Place, Saskatoon, SK, Canada S7N 0X2
a r t i c l e
i n f o
Article history:
Received 17 September 2012
Received in revised form 7 January 2013
Accepted 11 January 2013
Keywords:
Aphis glycines
Aphelinus certus
Coccinella septempunctata
Harmonia axyridis
Orius insidiosus
DYMEX
Deterministic model
a b s t r a c t
Soybean aphid (Aphis glycines) is a severe pest of soybean in North America with a diverse natural enemy
guild. A large body of literature exists examining aspects of the biology and ecology of this species, but
these studies have not been synthesized in a quantitative context, limiting the understanding of the
relative importance of environmental and ecological factors in the population dynamics of this species.
Existing models for population dynamics of A. glycines are geographically restricted, and do not incorporate host plant phenology or natural enemy impact on aphid population dynamics and phenology. In this
paper, a mechanistic tritrophic population and phenology model is developed for this species, incorporating environmental cues, host plant cues and natural enemy dynamics. Individual natural enemy species
differ with respect to prey consumption rates and foraging behaviours and may occur at different times in
the lifecycle of a prey species in response to environmental cues, densities, or the availability of alternate
prey. Additionally, the natural enemy complex of A. glycines differs in composition and abundance in
different parts of the aphids range. Because of these factors, we developed a strategy to quantify impact
of the natural enemy guild that would facilitate the incorporation of natural enemy complexes occurring
at multiple locations. In order to standardize the impact of natural enemy guilds on prey species, we
used the Natural Enemy Unit (NEU), where NEU is defined as the number of individuals of a predatory
species that can kill 100 individual prey in 24 h. After calibration of the NEU calculation to incorporate a
type III functional response to prevent natural enemies from driving aphid populations to local extinction, the model performed very well in predicting the dynamics between populations of natural enemies
and A. glycines when compared to field observations. Simulations suggest that natural enemy abundance
impacts A. glycines abundance more strongly than environmental conditions, but host plant phenology
also dramatically influences dynamics of this species.
© 2013 Elsevier B.V. All rights reserved.
1. Introduction
Soybean aphid (Aphis glycines Matsumura) is a severe pest
of soybean in North America (Ragsdale et al., 2004). A. glycines
undergoes a complicated lifecycle: it is both heteroecious, utilizing buckthorn and soybean as hosts, and holocyclic, producing
viviparous morphs (i.e. female aphids that produce asexually, and
give birth to live young) through the spring and summer and a
single mating generation in fall. Soybean aphid is a well-studied
organism: numerous individual studies and several major reviews
have been published on its biology and ecology (Ragsdale et al.,
2004, 2011; Tilmon et al., 2011; Wu et al., 2004), but the literature lacks empirical integration. Population dynamics of A. glycines
∗ Corresponding author. Present address: Department of Entomology, Michigan
State University, Center for Integrated Plant Systems Laboratory, Room 204, 578
Wilson Road, East Lansing, MI 48824, USA. Tel.: +1 517 432 5282.
E-mail address: [email protected] (C.A. Bahlai).
0304-3800/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.ecolmodel.2013.01.014
have been modelled previously (Onstad et al., 2005) however that
model was empirically derived, did not account for natural enemy
populations, and did not incorporate environmental nor phenological cues from host plants. As Onstad et al. (2005) cautioned, the
applicability of their model was limited to A. glycines occurring in
fields in southern Illinois, and only in late July through August. Thus,
development of a model for the population ecology and phenology of A. glycines, which predicts the dynamics and life history of
this organism over its entire lifecycle and which can be generalized
to multiple geographic areas, is warranted. A mechanistic model
for A. glycines would allow the integration of existing literature to
develop insights into the biology of this species in North America.
Models describing the phenology and population ecology of
aphids must incorporate biotic and abiotic factors in order to
develop realistic predictions. Morph determination and fecundity
of aphids are dependent on density, photoperiod, temperature and
host plant cues, and all of these factors may interact with each
other to moderate their relative influence (De Barro, 1992). Natural enemy populations are important regulators of (and responders
C.A. Bahlai et al. / Ecological Modelling 254 (2013) 54–70
Lady beetles
‘coccinellid’
Predatory bug
‘orius’
Parasic wasp
‘wasp’
Natural
Enemy Unit
Soybean aphid
density
Soybean aphid
‘aphid’
Crop
‘soybean’
Fig. 1. Schematic of biotic model components. The model consists of five lifecycle
submodels ‘soybean,’ ‘aphid,’ ‘coccinellid,’ ‘orius,’ and ‘wasp’ interacting with each
other through external calculations of soybean aphid density measures and the
natural enemy unit, as well as with environmental conditions.
to) aphid density, but the strength of density dependence in aphid
population dynamics and morph production is, in general, poorly
understood (Newman et al., 2003).
Since its introduction to North America in 2000, a diverse natural
enemy guild including both predators and parasitoids has adopted
A. glycines as prey (Bahlai and Sears, 2009; Costamagna et al., 2008;
Desneux et al., 2006; Fox et al., 2004, 2005; Frewin et al., 2010;
Gardiner and Landis, 2007; Kaiser et al., 2007; Mignault et al., 2006;
Nielsen and Hajek, 2005; Rutledge et al., 2004). The species composition of the natural enemy guild varies among locations, but in the
eastern portion of the North American range of A. glycines, several
coccinellids (Coccinella septempunctata L. and Harmonia axyridis
Pallas), the predatory bug Orius insidiosus (Say), and the parasitic
wasp Aphelinus certus Yasnosh, are consistently observed in field
surveys when A. glycines is present (Bahlai et al., 2010; Hallett et al.,
unpublished data).
Natural enemies are important regulators of the population
growth of pest species, and a high diversity of natural enemies
typically enhances biological control. When a natural enemy guild
consists of multiple predator and parasitoid species, an increased
proportion of prey insects is typically consumed in comparison
with systems where a single natural enemy species is present
(Aquilino et al., 2005). Straub and Snyder (2008) found that diversity in natural enemy communities enhanced aphid suppression in
two cropping systems; they attributed this enhancement to interspecific differences in foraging patterns allowing prey resources to
be partitioned more effectively within the trophic level. Additionally, they found that as predator diversity decreased, individuals of
a given predatory species often allocate less time to foraging.
When natural enemy communities are diverse, however, it can
be difficult to empirically determine the net impact of the guild
on the prey species. Individual natural enemy species differ with
Soybean
seed
Soybean
vegetave
Ve
respect to prey consumption rates and foraging behaviours (Frewin
et al., 2010; Xue et al., 2009). Predatory species may occur at different times in the lifecycle of a prey species because of differential
responses to environmental cues, prey density, or the availability
of alternate prey items (Yoo and O’Neil, 2009). In order to standardize the impact of natural enemy guilds on prey species, the Natural
Enemy Unit (NEU) concept was developed (Bahlai et al., 2010). One
NEU is defined as the number of individuals of a predatory species
that can kill 100 individual prey in 24 h, assuming an excess of prey,
and this measure was originally used to quantify the net impact of
a pesticide application on resident biocontrol services (Bahlai et al.,
2010).
DYMEXTM 3.0 (Hearne Scientific Software Ltd., South Yarra,
Australia) is a mechanistic, lifecycle-based population modelling
software package. Mechanistic population models constructed in
DYMEX have been developed for a variety of applications, such as
to model the adult emergence events of a crucifer pest (Hallett et al.,
2009), the dynamics between a pathogen and its host crop (White
et al., 2004), insect–pathogen–crop dynamics under climate change
conditions (Griffiths et al., 2010), and to examine the effect of environmental conditions on the feeding efficiency and potential for
non-target effects of an introduced herbivorous biocontrol insect
(Kriticos et al., 2009).
This paper describes a tritrophic model for A. glycines, soybean,
and three natural enemy taxa. Mortality of A. glycines due to predation by natural enemies is modelled using the NEU, which facilitates
the inclusion of additional natural enemy species in future iterations of the model. This model is used to forecast dynamics of these
species under varied environmental and agronomic conditions.
2. Model structure
The model uses a one-day time step in computing all parameters, and requires user input of meteorological data and latitude.
The model consists of five interacting species lifecycle sub-models,
with inputs from external modules calculating environmental
parameters, NEUs and density dependent factors (such as fecundity
and consumption rates of natural enemies) (Fig. 1). The lifecycle
sub-models include ‘aphid,’ ‘coccinellid,’ ‘orius,’ and ‘wasp’ and
‘soybean.’ Schematics of lifecycle sub-models specifying all life
stages for soybean, the natural enemies, and aphids are given
in Figs. 2–4 respectively. The ‘soybean’ model was configured to
be highly customizable because of wide variation in phenology
between varieties and maturity groups of soybean, but the default
parameterization used in the model is representative of the average
phenology of varieties typically grown in Ontario (Cara McCreary,
personal communication). The natural enemy guild was divided
into three groupings to represent the dominant members of this
group. The ‘coccinellid’ model is based on the thermal responses of
C. septempunctata, because the environmental control of the phenology of this species is well-documented in the literature (Banks,
1956; Obrycki and Tauber, 1981; Phoofolo et al., 1995), though
some aspects of H. axyridis phenology are incorporated. The ‘orius’
model is based on the biology of the predatory bug O. insidiosus.
The ‘wasp’ model is based on the parasitic wasp A. certus. These
four species dominate the natural enemy guild in the eastern North
American range of A. glycines (Hallett et al., unpublished data), but
Soybean
reproducve
R1
55
Soybean
mature
Soybean pod
R6
R7
Fig. 2. Schematic of ‘soybean’ submodel. Stages vulnerable to feeding by soybean aphid are shaded. Labels below life stages correspond to soybean developmental stages as
described by Pedersen (2009).
56
C.A. Bahlai et al. / Ecological Modelling 254 (2013) 54–70
cohort. If the stage the cohort of organisms transfers to is another
immature stage, they begin to accrue age until the next development threshold is reached, but if the cohort transfers into the adult
form, though physiological and chronological age are still accrued,
the primary function of the model is to calculate factors affecting
progeny production rate for individuals in this cohort. At each time
step, the cohort is subjected to various mortality factors, and in the
aphid submodel, the environmental conditions experienced by the
immature forms govern which adult morph an immature aphid will
transition into (Fig. 4).
Coccinellid submodel
Coccinellid
egg
Coccinellid
larva
Coccinellid
pupa
Coccinellid
adult
Wasp submodel
Wasp egg
Wasp
mummy
Wasp adult
2.1. Model specification
Orius submodel
Orius egg
Orius
nymph
Orius adult
Fig. 3. Schematic of natural enemy submodels. Predatory life stages (shaded) were
used in the computation of Natural Enemy Units (NEUs) acting on aphid populations.
Because adult parasitic wasps are rarely observed in the field, wasp mummies were
used in the computation of observable NEUs, which were used to validate the model
with field data.
the model can be altered to incorporate additional natural enemy
species occurring throughout the range of A. glycines.
In general, at each time step, each cohort of organisms is subjected to the accruement of chronological and physiological age.
The accruement of chronological age is constant with each time
step, physiological age is environmentally dependent and, in this
model, takes the form of degree day accumulations (i.e. amount
of time above a given temperature threshold, multiplied by the
amount by which the threshold is exceeded). When a group of
immature organisms accrues enough age, that is, reaches a development threshold, the model initiates a stage transition for this
Parameterization of the lifecycle submodels is given in
Tables 1–5, and a description of the computation of all model
inputs is given below. Model computations are described in the
equations below; in these equations, y represents the response variable (proportion of organisms responding, number of organisms
in the population, rate of accruement of physiological age, etc.)
and x an independent environmental variable (temperature, population density, etc.). Each lifecycle submodel consisted of the life
stages of a given organism, with life stage specific parameters governing mortality, development and either stage transfers (i.e. egg
to larva and larva to pupa) or fecundity and progeny production
rate (i.e. adult to egg or nymph). Unless otherwise noted, lifecycle
submodels incorporated cohort-based stage transfers based on a
step function (Tables 1–5), i.e.
y=
0,
x < Th
SH,
x ≥ Th
(1)
where SH is the step height and Th is the threshold. Stage transfers
used a step height of 0.75 (i.e. once a condition is met, 75% of the
population will transfer to the next life stage at each time step; if
Summer host (soybean)
Environmental
condioning
Nymphs
Apterae condioned to
produce sexuals
Apterae
Alates
Gynoparae
winged forms
Alates
Apterae
Nymphs
Spring eggs
Diapause
eggs
Oviparae
Overwintering host (buckthorn)
Fig. 4. Schematic of ‘aphid’ submodel. For clarity, aphid life stages are always referred to followed by the host on which they originated (in brackets). Note that ‘environmental
conditioning’ is a dummy life stage because the number of paths a lifecycle can take when leaving a given life stage is limited to two by software. Life stages vulnerable to
predation are shaded.
C.A. Bahlai et al. / Ecological Modelling 254 (2013) 54–70
57
Table 1
Description of functions governing developmental processes in ‘soybean’ submodel. All processes are continuous (i.e. applied to the relevant life stage at each time step),
unless noted as an establishment process. Establishment processes were applied to a given cohort once, upon entry into the relevant life stage. See Fig. 2 for a schematic of
the soybean lifecycle.
Process
Life stage
Function useda
Driving variable
Parametersa
Notes
Development
Seed, vegetative,
reproductive, pod
LAT
Daily cycle
T0 = 10 ◦ C, m = 1
A 10 ◦ C development threshold was used
for all soybean life stages
Stage transfer
Seed to vegetative
Step
Chronological age
Th = 10 days, SH = 0.75
Reproductive to pod
Pod to maturity
Vegetative to reproductive
Step
Step
Step
Chronological age
Chronological age
Physiological age
Th = 43, SH = 0.75
Th = 18, SH = 0.75
Th = 587 DD, SH = 0.75
Threshold based on average time from
planting to emergence for cultivars used in
southwestern Ontario
As above
As above
Soybean flowering is both photoperiod and
temperature dependent, but because
photoperiodic response varies so greatly
between cultivars, a threshold of 587 DD,
based on the average degree day
requirements for several cultivars (Kumar
et al., 2008), was used to initialize model
a
LAT = linear-above-threshold, Eq. (4) in text; T0 = lower threshold; m = slope. For step functions, SH = step height; Th = threshold.
the condition continues to be satisfied at the next time step, 75% of
the remaining population will make the stage transfer, and so on):
1
X(t + 1) = X(t)
4
(2)
where X(t) is the population in a given stage at time t. This approach
introduces some variation in response of simulated populations to
environmental conditions, i.e. not all individuals in a cohort will
transfer on the same day. Daily progeny production for all insects in
reproductive life stages was also modelled using a step function (Eq.
(1)), with the threshold occurring at the physiological or chronological age at which oviposition is first observed, and a step height
equal to the maximum number of progeny which can be produced
in one day (Tables 2–5). Unless the literature indicated otherwise,
a development threshold of 10 ◦ C was used for all organisms to
accrue physiological age. A sex ratio of 1:1 was assumed for all natural enemy species for reproductive purposes (Tables 2–4), and in
the aphid model, it was assumed that populations of apterae conditioned to produce sexual morphs produced males and gynoparae
at a 1:1 rate (Table 5).
Several mathematical functions were used to describe various
aspects of organismal biology. These will be described in general
below, and constants used in the model are specified in the lifecycle
parameterization tables (Tables 1–5). A linear function,
y = mx + b
(3)
where m is the slope and b is the intercept were used to incorporate
functions or values computed elsewhere in the model (i.e. mortality
due to predation of a specific life stage, which is density dependent
and thus cannot be computed for a cohort of organisms within a
computation of their own density and is thus computed separately
in the NEU module).
A linear-above-threshold function (LAT),
y=
0,
x ≤ T0
m(x − T0 )
x > T0
(4)
where T0 is the lower threshold was used to model biological
parameters occurring above a threshold such as heat stress and
temperature-dependent development.
A linear-below-threshold function (LBT),
y=
m(x − T1 )
x < T1
0,
x ≤ T1
(5)
where T1 is the upper threshold was used to model aspects of biology occurring below a threshold, such as cold stress.
A linear-between-threshold function (LBtwT),
y=
⎧
0,
⎪
⎨
⎪
⎩
x ≤ T0
m(x − T0 )
T0 < x < T1
m(T1 − T0 )
x ≥ T1
(6)
was used to model ecological parameters affected by inputs
between two thresholds, such as density dependence in progeny
production.
For situations requiring the combination of parameters (i.e. multiple sources of mortality or multiple factors affecting progeny
production) acting simultaneously, one of the two combination
rules were applied. A product combination rule
y = y1 × y2 × · · · × yn
(7)
was used to combine factors 1, 2, . . ., n in all cases, except for mortality (e.g. multiplying a maximum daily progeny production rate
by a function describing the effect of an environmental condition
on progeny production). A compliment product rule
y = 1 − (1 − y1 ) × (1 − y2 ) × · · · × (1 − yn )
(8)
where yn is the mortality due to factor n was used to combine
mortality factors 1, 2, . . ., n, as survivorship (not mortality) is the relevant measure when combining individual mortality factors within
the DYMEXTM framework, because it is assumed that each subsequent mortality condition acts on the survivors of the previous
condition (Maywald et al., 2007).
Environmental parameters were computed based on user-input
meteorological and location data. A ‘Daylength’ module computed
the daily photoperiod based on latitude and day of year, and a
separate module computed scotoperiod (=24 h − photoperiod). A
‘Circadian’ module was used to compute the daily temperature
cycle (daily cycle) using daily maximum and minimum values and a
composite sine + exponential daily temperature module, was computed in 24 hourly increments. Average daily temperature (average
temperature) was computed from the numerical average of the daily
maximum and minimum temperatures. Seven day running mean
daily temperature, seven day running mean minimum temperature,
and seven day running mean maximum temperature were computed
for each time step using the numerical mean of the value for mean,
minimum and maximum temperature, respectively, for the current
and six previous time steps.
In order to incorporate density-dependent factors and relevant density outputs that could be related to field conditions into
the model, a number of computations had to be performed outside the individual lifecycle sub-models. For each time step, these
58
C.A. Bahlai et al. / Ecological Modelling 254 (2013) 54–70
Table 2
Description of functions governing developmental processes in ‘coccinellid’ submodel. All processes are continuous (i.e. applied to the relevant life stage at each time step),
unless noted as an establishment process. Establishment processes were applied to a given cohort once, upon entry into the relevant life stage. See Fig. 3 for a schematic of
the coccinellid lifecycle.
Process
Life stage
Function useda
Driving variable
Parametersa
Notes
Development
Egg
LAT
Daily cycle
T0 = 6.8 ◦ C, m = 1
Larva
LAT
Daily cycle
T0 = 12.6 ◦ C, m = 1
Pupa
LAT
Daily cycle
T0 = 12.1 ◦ C, m = 1
Development threshold for C. septempunctata
eggs (Obrycki and Tauber, 1981)
Average development threshold for four larval
instars of C. septempunctata (Obrycki and
Tauber, 1981)
Development threshold for C. septempunctata
pupae (Obrycki and Tauber, 1981)
Egg to larva
Step
Physiological age
Th = 50.4 DD, SH = 0.75
Larva to pupa
Step
Physiological age
Th = 104.9 DD, SH = 0.75
Pupa to adult
Step
Physiological age
Th = 50.7 DD, SH = 0.75
Egg, larva, pupa
LBT
7 day running mean
minimum temperature
T1 = 4 ◦ C, m = −0.111
Adult
LBT
7 day running mean
minimum temperature
T1 = 4 ◦ C, m = −0.0204
Egg
Constant
–
0.214
Larva, pupa
Step
Chronological age
Th = 2 days, SH = 0.03
Stage transfer
Cold stress
mortality
Random mortality
Degree day requirements for egg hatch of C.
septempunctata (Obrycki and Tauber, 1981).
Total degree day requirements all four larval
instars of C. septempunctata (Obrycki and
Tauber, 1981).
Degree day requirements for pupal eclosion of
C. septempunctata (Obrycki and Tauber, 1981).
Coccinellids overwinter as adults, so assume
temperatures under 4 ◦ C are sub optimal for
immature stages, and that complete mortality
occurs at −5 ◦ C.
Assume that though conditions under 4 ◦ C are
sub optimal, adults will have greater tolerance
for cold conditions than larvae, and that
complete mortality does not occur until adults
are exposed to −40 ◦ C
Eggs have high rates of sibling cannibalism and
a portion of each brood are unfertilized and do
not develop. C. eptempunctata had an egg
mortality rate of 21.4% (Banks, 1956)
Up to 6% mortality was observed for
coccinellid larvae and pupae over 48 hours in
the field (Schellhorn and Andow, 1999)
Assume 1% random mortality per day for adults
Adult
Step
Chronological age
Th = 1 days, SH = 0.01
Mortality due to
soybean
senescence
Egg
Linear
Proportion mature
soybean
m = 1, b = 0
As soybean senesces, eggs will fall off with
leaves and fewer oviposition sites will be
available
Fecundity
Adult
Constant
–
32
Total fecundity for C. septempunctata was up to
65 eggs per female (Banks, 1956). Assume a 1:1
sex ratio
Progeny
production
Adult
Step
Chronological age
Th = 7.4 days, SH = 9
Adult
LBtwT
Vulnerable aphids per
soybean plant
T0 = 0, T1 = 50, m = 0.02
Adult
Step
Th = 0.5, SH = 1
Adult
LBtwT
Proportion vulnerable
soybean
Daily cycle
H. axyridis had a pre-oviposition interval of
7.4 days and laid, on average, 18 eggs per day
(Lanzoni et al., 2004). Assume 1:1 sex ratio
Assume coccinellids will not lay eggs in the
absence of food, and assume progeny
production rate is proportional to number of
vulnerable aphids present in ecosystem, with
maximum progeny production rate reached at
50 aphids per soybean plant
Assume vulnerable soybean plants are needed
to provide oviposition sites for coccinellids
Threshold for ovarian development in adult C.
septempunctata is 13.3 ◦ C, with an optimum
reached at approximately 30 ◦ C (Phoofolo et al.,
1995). Assume progeny production is linearly
proportional to ovarian development rate
T0 = 13.3, T1 = 30,
m = 0.05999
a
LAT = linear-above-threshold, Eq. (4) in text; T0 = lower threshold; m = slope. LBT = linear-below-threshold, Eq. (5) in text; T1 = upper threshold; m = slope. LBtwT = linearbetween-thresholds, Eq. (6) in text; T0 = lower threshold; T1 = upper threshold; m = slope. For step functions, SH = step height; Th = threshold; for general step functions,
SHo = step height before; SH1 = step height after; Th = threshold.
computations were performed prior to calculations within the lifecycle sub-models, thus it is relevant to note that outputs associated
with these calculations are based on the populations occurring on
the day before the time step being reported. For the first calculation, all of these functions are set to their default value of 0, and
after one iteration, they are updated to include relevant outputs
from the lifecycle sub-models. The total vulnerable aphids, that is,
the number of non-alate aphids occurring on both buckthorn and
soybean that are vulnerable to predation, was defined as the sum
of all nymphs, apterae and oviparae occurring on buckthorn, and
nymphs, apterae and apterae conditioned to produce sexuals occurring on soybean. Alates and gynoparae were excluded from this
calculation because it was assumed that these morphs were less
vulnerable to predation, due to their increased mobility, and eggs
were excluded because many causes of egg mortality are not well
understood. Total vulnerable aphids on soybean were defined as the
sum of all nymphs, apterae and apterae conditioned to produce sexuals occurring on soybean. Total soybean was defined as the total
number of soybean plants in all life stages, while total vulnerable
soybean was defined as the total number of plants in vulnerable
C.A. Bahlai et al. / Ecological Modelling 254 (2013) 54–70
59
Table 3
Description of functions governing developmental processes in ‘wasp’ submodel. All processes are continuous (i.e. applied to the relevant life stage at each time step), unless
noted as an establishment process. Establishment processes were applied to a given cohort once, upon entry into the relevant life stage. See Fig. 3 for a schematic of the wasp
lifecycle.
Process
Life stage
Function useda
Driving variable
Parametersa
Notes
Development
Egg
LAT
Daily cycle
T0 = 9.1, m = 1
Mummy
LAT
Daily cycle
T0 = 11.6 ◦ C, m = 1
Thermal threshold for egg development of
A. certus is 9.1 ◦ C (Frewin et al., 2010)
Thermal threshold for A. certus mummy
development is 11.6 ◦ C (Frewin et al., 2010)
Egg to mummy
Step
Physiological age
Th = 96 DD, SH = 0.75
Mummy to adult
Step
Physiological age
Th = 90 DD, SH = 0.75
Cold stress mortality
Egg, mummy
LBT
7 day running mean
minimum temperature
T1 = 10 ◦ C, m = −0.1
It is unknown how A. certus overwinters, so
for this model, it is assumed the
overwintering form is the adult and cold
stress only affects immature forms. The
development rate of A. certus immature
drops considerably below 10 ◦ C, and
presumably cannot survive at
temperatures below 0 ◦ C (A. Frewin,
personal communication)
Heat stress mortality
Egg, mummy, adult
LAT
7 day running mean
maximum temperature
T0 = 32 ◦ C, m = 0.056
In laboratory colonies, all life stages of A.
certus do poorly at temperatures above
32 ◦ C (A. Frewin, personal communication).
We assume 100% mortality at 50 ◦ C
Random mortality
(establishment process)
Egg
Direct
Wasp egg establishment
mortality
–
Mummy
Constant
–
0.12
Computed using Eqs. (4)–(13) in text.
Constrains survivorship of wasp eggs so
that new eggs will not survive, if more
than 90% of the vulnerable aphid
population is parasitized
Approx. 12% of mummies never produced
adult A. certus wasps (Frewin et al., 2010)
Old age mortality
Adult
General step
Chronological age
SHo = 0.01, SH1 = 0.90,
Th = 10 days
Adult A. certus live 10–14 days (A. Frewin,
personal communication). Assume random
mortality of 1% per day until a wasp is
10 days old, then 90% mortality per day
thereafter
Fecundity
Adult
Constant
–
100
Determined empirically in calibration
process. The upper ceiling on total
fecundity of A. certus is unknown (A.
Frewin, personal communication)
Progeny production
Adult
Step
Chronological age
Th = 1 days, SH = 10
Adult
LBtwT
Vulnerable aphids per
soybean plant
T0 = 0, T1 = 50, m = 0.02
Adult
LBtwT
Daily cycle
T0 = 15, T1 = 30,
m = 0.067
Functional response experiments for A.
certus were initiated 24 h (1 days) after
eclosion, and females produced, on
average, 20 eggs per day (Frewin et al.,
2010). Assuming a 1:1 sex ratio, 10 eggs
per adult can be produced daily.
Wasps cannot lay eggs in the absence of
food; assume progeny production rate is
proportional to number of vulnerable
aphids present in ecosystem, with
maximum progeny production rate
reached at 500 aphids per soybean plant
A. certus oviposition tends to occur
between 15 and 30 ◦ C and is temperature
dependent (A. Frewin, personal
communication)
Stage transfer
Degree day accumulation required for
mummy formation in A. certus is 96 DD
(Frewin et al., 2010)
Degree day accumulation required for
adult eclosion from mummy in A. certus is
90 DD (Frewin et al., 2010)
a
LAT = linear-above-threshold, Eq. (4) in text; T0 = lower threshold; m = slope. LBT = linear-below-threshold, Eq. (5) in text; T1 = upper threshold; m = slope. LBtwT = linearbetween-thresholds, Eq. (6) in text; T0 = lower threshold; T1 = upper threshold; m = slope. For step functions, SH = step height; Th = threshold; for general step functions,
SHo = step height before; SH1 = step height after; Th = threshold.
life stages (i.e. vegetative, reproductive, and pod stages). Proportion mature soybean was defined as the number of mature soybean
plants divided by total soybean; proportion vulnerable soybean was
defined as total vulnerable soybean divided by total soybean. Vulnerable aphids per soybean plant were computed by dividing total
vulnerable aphids on soybean by total soybean. For the purposes
of model calibration and validation, an additional variable four
day running mean aphids per soybean plant was also generated to
minimize the effect of short-term population fluctuations predicted
by the model.
The natural enemy unit (NEU) is defined as:
NEU =
N
i=1
ni Vi
(9)
60
C.A. Bahlai et al. / Ecological Modelling 254 (2013) 54–70
Table 4
Description of functions governing developmental processes in ‘orius’ submodel. All processes are continuous (i.e. applied to the relevant life stage at each time step), unless
noted as an establishment process. Establishment processes were applied to a given cohort once, upon entry into the relevant life stage. See Fig. 3 for a schematic of the orius
lifecycle.
Process
Life stage
Function useda
Driving variable
Parametersa
Notes
Development
Egg
LAT
Daily cycle
T0 = 10.2, m = 1
Nymph
LAT
Daily cycle
T0 = 13.7 ◦ C, m = 1
Development threshold computed using data
presented in Isenhour and Yeargan (1981)
Development threshold computed using data
presented in Isenhour and Yeargan (1981)
Egg to nymph
Step
Physiological age
Th = 73 DD, SH = 0.75
Nymph to adult
Step
Physiological age
Th = 145 DD, SH = 0.75
Cold stress mortality
Egg, nymph
LBT
7 day running mean
minimum temperature
T1 = 10 ◦ C, m = −0.1
O. insidiosus overwinters as an adult so it is
assumed immature forms will be affected by
cold stress. McCaffrey and Horsburgh (1986)
present a lower estimate of developmental
threshold for O. insidiosus, so it is assumed cold
stress accumulates below this temperature
and, as in the wasp model, complete mortality
occurs at 0 ◦ C
Heat stress mortality
Egg, nymph, adult
LAT
7 day running mean
maximum temperature
T0 = 32 ◦ C, m = 0.056
Though no records exist of O. insidiosus
suffering from heat stress in temperate
climates, several studies examine O. insidiosus
biology at constant temperatures and do not
report data from temperatures above 32 ◦ C
(Isenhour and Yeargan, 1981; McCaffrey and
Horsburgh, 1986). thus assumed that O.
insidiosus begins to suffer from heat stress at
32 ◦ C and complete mortality occurs at 50 ◦ C,
as in the wasp submodel
Random mortality
(establishment process)
Nymph
Constant
–
0.03
Approximately 3% of immature O. insidiosus do
not reach adulthood due to random mortality
(Kiman and Yeargan, 1985)
Old age mortality
Adult
General step
Chronological age
SHo = 0.03, SH1 = 0.95,
Th = 40 days
Female O. insidiosus lived up to 40 days (Kiman
and Yeargan, 1985). Assume 3% random
mortality before and 95% mortality after 40th
day of life
Fecundity
Adult
Constant
–
50
A maximum of 100 eggs were laid per female
when fed an optimal diet (Kiman and Yeargan,
1985). Assume 1:1 sex ratio, resulting in a net
fecundity of 50 eggs per adult
Progeny production
Adult
Step
Chronological age
Th = 1 days, SH = 1
Adult
LBtwT
Vulnerable aphids per
soybean plant
T0 = 0, T1 = 1, m = 1
Adult
LBtwT
Daily cycle
T0 = 15, T1 = 30,
m = 0.067
Adult
General step
Scotoperiod
SHo = 1, SH1 = 0,
Th = 10.05 h
Approximately two eggs per day were
produced per female (Kiman and Yeargan,
1985), so a net of one egg per day can be
produced by each adult
Assume Orius will not lay eggs in the absence
of food, but because of lower fecundity rate
compared to coccinellids and wasps,
maximum progeny production rate is reached
at 1 aphid per soybean plant
As in the wasp model, assume progeny
production by Orius is thermally dependent
between 15 and 30 ◦ C
Adult female O. insidious collected in the
Guelph area had entered reproductive
diapause after Aug 15 (Schmidt et al., 1995),
corresponding to a scotoperiod of 10.05 h
Stage transfer
Degree day requirements computed using data
presented in Isenhour and Yeargan (1981)
Degree day requirements computed using data
presented in Isenhour and Yeargan (1981)
a
LAT = linear-above-threshold, Eq. (4) in text; T0 = lower threshold; m = slope. LBT = linear-below-threshold, Eq. (5) in text; T1 = upper threshold; m = slope. LBtwT = linearbetween-thresholds, Eq. (6) in text; T0 = lower threshold; T1 = upper threshold; m = slope. For step functions, SH = step height; Th = threshold; for general step functions,
SHo = step height before; SH1 = step height after; Th = threshold.
where N is the total number of natural enemy species, ni is the total
number of individuals of natural enemy species i observed on 10
plants, and Vi is the average voracity of natural enemy species i, that
is, the number of pest insects it can kill in 24 h divided by 100 (Bahlai
et al., 2010). Voracities given in Bahlai et al. (2010) were used to
weight the individual species in the model NEU computation:
NEU = 1 × (ncoccinellid adults + ncoccinellid larvae ) + 0.08(norius adults
+ norius nymphs + nwasp mummies OR adults )
(10)
NEUs were computed in two ways: total NEUs and observable NEUs,
because although parasitic wasp adults are the stage which attacks
and kills aphids, mummies (i.e. dead aphids in which larval parasitic wasps develop) are the stage most frequently observed in field
surveys. Total NEU was calculated using the number of wasp adults,
and observable NEU was calculated using the number of mummies.
NEU per plant, a variable directly comparable to field survey data,
was computed by dividing observable NEU by total soybean. As with
vulnerable aphids per plant, an additional variable four day running
mean NEU per soybean plant was also generated using observable
C.A. Bahlai et al. / Ecological Modelling 254 (2013) 54–70
61
Table 5
Description of functions governing developmental processes in ‘aphid’ submodel. All processes are continuous (i.e. applied to the relevant life stage at each time step), unless
noted as an establishment process. Establishment processes were applied to a given cohort once, upon entry into the relevant life stage. See Fig. 3 for a schematic of the
aphid lifecycle. For each life stage, host plant where the aphid originated is given in brackets. Note that because DymexTM limits the number of stage transfer possibilities for
a given life stage to two, ‘nymph: environmental conditioning (soybean)’ is a dummy life stage to allow nymphs (soybean) to become apterae (soybean), alates (soybean) or
apterae conditioned to produce sexuals (soybean).
Process
Life stage (host)
Function useda
Driving variable
Parametersa
Notes
Development
Spring egg (buckthorn)
LAT
Daily cycle
T0 = 10 ◦ C, m = 1
Nymph (buckthorn),
nymph (soybean), apterae
conditioned to produce
sexuals (soybean),
gynoparae (soybean),
oviparae (buckthorn)
LAT
Daily cycle
T0 = 9.5 ◦ C, m = 1
Development threshold for A. glycines
eggs (Bahlai et al., 2007)
Development threshold for A. glycines
nymphs (Hirano et al., 1996)
Diapause egg (buckthorn)
to spring egg (buckthorn)
Step
Chronological age
Th = 120 days, SH = 0.75
Spring egg (buckthorn) to
nymph (buckthorn)
Step
Physiological age
Th = 54 DD, SH = 0.75
Nymph (buckthorn) to
apterae (buckthorn)
Step
Physiological age
Th = 57.1 DD, SH = 0.75
Nymph (buckthorn) to
alate (buckthorn)
Step
Physiological age and
vegetative soybean:
total number
Th = 57 DD, SH = 0.75
and Th = 1, SH = 0.95
Nymph (soybean) to
nymph: environmental
conditioning (soybean)
Step
Physiological age
Th = 57.1, SH = 0.75
Nymph (soybean) to alate
(soybean)
Step and general
step
Physiological age and
vulnerable aphids
per soybean plant
Th = 57, SH = 0.75 and
SHo = 0.05, SH1 = 0.99,
Th = 4000
Nymph: environmental
conditioning (soybean) to
apterae (soybean)
Nymph: environmental
conditioning (soybean) to
apterae conditioned to
produce sexuals
Step
Chronological age
Th = 1 days, SH = 0.95
Step
Scotoperiod
Th = 10.7 h, SH = 0.25
Stage transfer
Stage transfer
Eggs of A. glycines which were laid
before early November did not hatch
when exposed to warm conditions
until late February of the following
year, suggesting an obligate chilling
period of approx. 120 days (Bahlai
et al., 2007)
A degree day accumulation of 54 DD
was required for egg hatch of A.
glycines (Bahlai et al., 2007)
A degree day accumulation of 57.1 DD
was required for nymphs A. glycines to
mature (Hirano et al., 1996)
As above, but DD requirements
rounded down to allow this condition
to be met prior to the condition
governing transition to apterae
(buckthorn). Second condition allows
alates to be produced only after
soybean has begun to emerge from
ground
A degree day accumulation of 57.1 DD
was required for nymphs A. glycines to
mature (Hirano et al., 1996)
As above, but DD requirements
rounded down to allow this condition
to be met prior to the condition
governing transition to nymph:
environmental conditioning (soybean).
Second condition makes formation of
alates density-dependent. When aphid
density is less than 4000 aphids per
plant, <5% of nymphs become alates
(Donaldson et al., 2007)
Dummy stage to allow conditions for
apterae conditioned to produce sexuals
production to be met
Sexual morphs are likely triggered at a
photoperiod of 13.3 h and decreasing
(=scotoperiod of 10.7 h and increasing)
(Section 3)
Cold stress mortality
Nymph (buckthorn),
apterae (buckthorn), alate
(buckthorn), nymphs
(soybean), alate (soybean),
apterae (soybean), apterae
conditioned to produce
sexuals (soybean),
gynoparae (soybean),
oviparae (buckthorn)
LBT
7 day running mean
minimum
temperature
T1 = 10 ◦ C, m = −0.1
Assume that aphids are tolerant to
brief periods of freezing temperatures
but begin to do poorly when minimum
temperatures are below 10 ◦ C and
complete mortality occurs when
minimum daily temperatures do not
exceed 0 ◦ C, on average, for 7 days
Heat stress mortality
Nymph (buckthorn),
apterae (buckthorn), alate
(buckthorn), oviparae
(buckthorn)
LAT
7 day running mean
maximum
temperature
T0 = 27 ◦ C, m = 0.043
Nymph (soybean), alate
(soybean), apterae
(soybean), apterae
conditioned to produce
sexuals (soybean)
gynoparae (soybean)
LAT
7 day running mean
maximum
temperature
T0 = 32 ◦ C, m = 0.056
Buckthorn-dwelling morphs of A.
glycines began to die when exposed to
27 ◦ C constant temperatures (CB,
personal observation). We
assumed100% mortality occurs at 50 ◦ C
Assume soybean-dwelling morphs
have greater heat tolerance than
buckthorn-dwelling morphs and that
they begin to accumulate heat stress
above 32 ◦ C. We assumed100%
mortality occurs at 50 ◦ C
62
C.A. Bahlai et al. / Ecological Modelling 254 (2013) 54–70
Table 5 (Continued)
Process
Life stage (host)
Function useda
Driving variable
Parametersa
Notes
Density dependent
mortality
Nymph (soybean), apterae
(soybean)
LAT
Vulnerable aphids
per soybean plant
T0 = 1000,
m = 0.0000345
Typical plant capacity is around 20,000
to 30,000 aphids per soybean plant (C.
DiFonzo, personal communication).
Assume aphids begin to be affected by
crowding at 1000 aphids per plant, and
100% mortality is reached at 30,000
aphids per plant
Mortality due to
soybean phenology
Nymphs (soybean), alate
(soybean), apterae
(soybean), apterae
conditioned to produce
sexuals (soybean)
Step
Mature soybean:
total number
Th = 1, SH = 0.25
As soybean begins to reach maturity,
assume resident aphids will be
negatively affected
Mortality due to
soybean senescence
Nymphs (soybean), alate
(soybean), apterae
(soybean), apterae
conditioned to produce
sexuals (soybean)
Step
Proportion mature
soybean
Th = 0.95, SH = 1
When soybean reaches full maturity,
all resident aphids will die
Random mortality
(establishment
process)
Diapause egg (buckthorn)
Constant
–
0.70
Approx. 70% mortality is observed in
overwintering eggs (Welsman et al.,
2007)
Other mortality
factors
Apterae (buckthorn)
Step
Vegetative soybean:
total number
Th = 1, SH = 0.75
Apterae (buckthorn)
Step
Day of year
Th = 166, SH = 1
Gynoparae (soybean)
Step
Day of year
Th = 300, SH = 1
Oviparae (buckthorn)
Step
Day of year
Th = 310, SH = 1
Assume once soybean begins reach
reproductive stage, buckthorn is a
sub-optimal host and apterae
(buckthorn) begin to die out
By June 15 (=166 Julian day), no A.
glycines were observed on buckthorn
(Welsman et al., 2007)
Gynoparae are not permitted to
survive the winter, even if cold
conditions never occur
Oviparae are not permitted to survive
the winter, even if cold conditions
never occur
Predation mortality
Nymph (buckthorn),
apterae (buckthorn),
nymph (soybean), apterae
(soybean), apterae
conditioned to produce
sexuals (soybean), oviparae
(buckthorn)
Linear
Proportional
predation mortalityi
m = 0.75, b = 0
Computed using Eqs. (4)–(12). This
function accounts for predation
mortality risk at each life stage i, and
must be multiplied by the total
number of individuals occurring in life
stage i. A linear function, rather than a
direct function, was used in order to
allow user customization of the degree
of impact a natural enemy guild has on
aphid populations. A slope of 0.75 was
empirically determined suggesting
that mortality due to predation is
slightly less than predicted
Old age mortality
Apterae (buckthorn),
apterae (soybean), apterae
conditioned to produce
sexuals (soybean), oviparae
(buckthorn)
Step
Chronological age
Th = 15 days, SH = 0.75
Adult aphids that have not flown live
approx. 15 days (Zhang et al., 2009)
Old age mortality
Alate (buckthorn), alate
(soybean), gynoparae
(soybean)
Step
Chronological age
Th = 10 days, SH = 0.75
Adult aphids that have engaged in
flight live approx. 10 days (Zhang et al.,
2009)
Fecundity
Apterae (buckthorn)
apterae (soybean)
Constant
–
61
Alate (buckthorn), alate
(soybean), gynoparae
(soybean)
Alate (buckthorn), alate
(soybean), gynoparae
(soybean)
Constant
–
15
Constant
–
0.001
Apterae conditioned to
produce sexuals (soybean)
Constant
–
30
Mean fecundity of female A. glycines at
25 ◦ C was 61 progeny (McCornack
et al., 2004)
A. glycines that had flown had a
reduced total fecundity of 15 progeny
per female (Zhang et al., 2009)
Taylor (1974) suggested that only one
in one thousand alate aphids found a
suitable host for larviposition after
leaving their native host patch
Mean fecundity of female A. glycines at
25 ◦ C was 61 progeny (McCornack
et al., 2004). Assuming apterae
conditioned to produce sexuals
produce gynoparae and males at 1:1
ratio, approx. 30 gynparae are
produced by each aptera on average
C.A. Bahlai et al. / Ecological Modelling 254 (2013) 54–70
63
Table 5 (Continued)
Process
Progeny production
Progeny production
Life stage (host)
Function useda
Driving variable
Parametersa
Notes
Oviparae (buckthorn)
Constant
–
5
A. glycines produces 4–5 eggs per
ovipara when occurring on common
buckthorn, R. cathartica (Yoo et al.,
2005)
Apterae (buckthorn), alate
(buckthorn), alate
(soybean), apterae
(soybean), apterae
conditioned to produce
sexuals (soybean)
Apterae conditioned to
produce sexuals (soybean),
gynparae (soybean)
Step
Chronological age
Th = 1 days, SH = 7
McCornack et al. (2004) found a
reproductive period of 9 days, and a
total fecundity of 61 for A. glycines,
suggesting that aphids can produce
approx 7 progeny per day
Step
Physiological age
Th = 57 DD, SH = 7
Oviparae (buckthorn)
Step
Physiological age
Th = 57 DD, SH = 0.5
As above, but including physiological
time to develop from nymphs (Hirano
et al., 1996), as nymphal stages of these
two morphs are not explicitly
considered in the model
Estimate progeny production rate as
one every two days per ovipara.
Function includes physiological time to
develop from nymphs (Hirano et al.,
1996), as nymphal stages of oviparae
are not explicitly considered in the
model
Apterae (soybean)
LBT
Vulnerable aphids
per soybean plant
T1 = 20,000,
m = −0.00005
Apterae (buckthorn), alate
(buckthorn), alate
(soybean), apterae
(soybean), apterae
conditioned to produce
sexuals (soybean),
gynoparae (soybean),
oviparae (buckthorn)
LBtwT
Daily cycle
T0 = 10, T1 = 26,
m = 0.0625
Oviparae (buckthorn)
Step
Day of year
Th = 274, SH = 1
Assume fecundity is density
dependent, and that typical plant
capacity is around 20,000 aphids per
soybean plant (C. DiFonzo, personal
communication). Assume full nymph
production at 0 aphids per plant, and
practically none at 20,000
Progeny production is temperature
dependent for all reproductive life
stages. Assume the lower threshold for
progeny production is 10 ◦ C, the lower
development threshold, and peaks at
26 ◦ C, the optimum temperature for
development amongst summer
morphs (Bahlai et al., 2007; McCornack
et al., 2004)
In surveys, eggs of A. glycines have
never been observed before October 1
(=274 day of year) (CB, personal
observation)
a
LAT = linear-above-threshold, Eq. (4) in text;T0 = lower threshold; m = slope. LBT = linear-below-threshold, Eq. (5) in text; T1 = upper threshold; m = slope. LBtwT = linearbetween-thresholds, Eq. (6) in text; T0 = lower threshold; T1 = upper threshold; m = slope. For step functions, SH = step height; Th = threshold; for general step functions,
SHo = step height before; SH1 = step height after, Th = threshold.
NEU to minimize the effect of short-term population fluctuations
on model calibration. All subsequent calculations involving the NEU
refer to total NEU, because this is the relevant measure for mortality and density-dependent calculations. Vulnerable aphids per
NEU were computed by dividing total vulnerable aphids by total
NEU. Absolute mortality due to predation, that is, the total number
of aphids consumed by the natural enemy guild in a given time step,
was calculated under the assumption that the voracity of a natural
enemy is a function of the total available prey in the ecosystem,
and details of this computation are provided below. The maximum
possible predation by the natural enemy guild is 100 aphids per
NEU, or 100 × total NEU, but when there are few prey per NEU or
prey and NEU are both low, the mortality due to predation will
be lower than the theoretical maximum. This equation is based on
relevant functional response studies (Xue et al., 2009; Frewin et al.,
2010; Hallett et. al., unpublished data), in which individual natural
enemy species all exhibited type II functional responses. The type II
functional response is usually modelled using a rectangular hyperbola function, however, this function was found to perform poorly
at very low prey densities. Instead a type III functional response,
which can be approximated using a sigmoid function, was used. A
type III functional response behaves very much like a type II functional response at higher prey densities but allows for decreased
foraging efficiency at lower prey densities. Thus, a sigmoid function
was used to describe estimated mortality due to predation:
estimated mortality due to predation = 100 ×
total NEUs
1 + e(−0.2(total vulnerable aphids−100))
(11)
but this expression was found to have poor performance at low values of vulnerable aphids to NEU or vulnerable aphids per soybean
plant, so this expression was nested into an absolute mortality due to
predation expression designed to constrain mortality under these
conditions. This expression was in the form of several nested ifthen-else statements which can be expressed as:
IF total NEUs ≤ 0, mortality due to predation is zero, else:
IF vulnerable aphids per soybean plant >25
THEN if the maximum possible predation 100 × total NEU < 90% total
vulnerable aphids,
THEN absolute mortality due to predation is 100 × total NEUs,
ELSE absolute mortality due to predation is limited to 90% of the total
vulnerable aphids
ELSE if estimated mortality due to predation < total vulnerable
aphids × vulnerable aphids per soybean plant ÷ 100
THEN absolute mortality due to predation is equal to estimated
mortality due to predation
ELSE absolute mortality due to predation is limited to total vulnerable
aphids × vulnerable aphids per soybean plant ÷ 100
64
C.A. Bahlai et al. / Ecological Modelling 254 (2013) 54–70
Proportional predation mortality risk, that is, the risk of mortality
due to predation to a given life stage i, was computed as follows:
proportional predation mortality riski = Ni ×
absolute mortality due to predation
2
(total vulnerable aphids)
(12)
where Ni is the total number of aphids in vulnerable life stage i
during that time step. This calculation assumes no preference for a
given morph or life stage by natural enemies, and was computed for
total vulnerable aphids (nymphs, apterae and oviparae) on buckthorn, and total vulnerable aphids (nymphs, apterae and apterae
conditioned to produce sexuals) on soybean.
Because parasitic wasps are directly dependent on vulnerable
aphids for oviposition sites, wasp egg survivorship had to be constrained by the availability of unparasitized aphids. Thus, a wasp
egg establishment mortality function was created (Table 3):
wasp egg establishment mortality =
0,
Four day running means of aphids and NEU per soybean plant
from the model output were compared to scouting data using both
ordinary least square and weighted least square regression. In the
weighted regression, data points were weighted by the inverse of
the standard deviation in observed values, to account for variability in the observed data. Model parameterization was adjusted, as
appropriate, to improve model fit of field data. Four day running
means were used to minimize the effect of fluctuations in predicted
values on model calibration. Parameters adjusted in the calibration
process are noted in the model specification tables.
2.3. Model validation
Aphid and natural enemy scouting data from an observation soybean field near Arva, ON (43.1◦ N, 81.3◦ W), in 2009 were
nwasp egg + nwasp mummy < 0.9 × total vulnerable aphids
1, nwasp egg + nwasp mummy ≥ 0.9 × total vulnerable aphids
2.2. Model calibration
Because population data for A. glycines and its natural enemy
complex are largely confined to the soybean growing season, with
only relative measures of population density and phenology occurring through much of the aphid’s lifecycle, quantitative calibration
of this model is restricted to that time period. Challenges in validation are common for process-based simulation models such as
these because of a lack of quantitative, whole-season scouting data
(Kriticos et al., 2003), and thus it must be cautioned that interpretation of the results of this model outside the soybean growing season
should be limited to qualitative assertions.
In order to establish parameter values used in the model, we
used field scouting data for aphids and their natural enemies
obtained in 2007 from fields near Alvinston (42.8◦ N, 81.9◦ W) and
Shetland, ON (42.7◦ N, 82.0◦ W) (Hallett et al., unpublished data), and
weather data (maximum and minimum daily temperature and total
precipitation) obtained from the Environment Canada National Climate Archive (http://www.climate.weatheroffice.gc.ca/). Scouting
data consisted of whole-plant counts of aphids and natural enemies, performed weekly on plants from these two observation
fields. The model was initialized using 500 soybean plants, planted
20 May, and soybean phenology was iteratively adjusted to match
observed phenology in the field at each site. Aphid and natural
enemy observation data were scaled to aphids or natural enemies
per 500 soybean plants to match the scale of the model. Aphid
and natural enemy lifecycle sub-models were initialized based on
the first observation of a given taxon in the field, but it was also
assumed that all taxa had some low level of activity beneath the
limits of detection by scouting. One coccinellid adult, two wasp
adults, and one orius adult were programmed to arrive at the 500
soybean patch every day for the duration of the simulation; this will
henceforth be referred to as ‘background NEUs’; 15 aphid nymphs
(soybean) were deposited in the system each day as well to account
for nymphs being produced by alates moving in from other locales.
Because evacuated mummies of A. certus often remain on a plant
after adult eclosion (A. Frewin, personal communication) and are
often counted in surveys, and given the weekly sampling resolution of the input data, the initialization stage of the wasp module
was partitioned between adult wasp and mummies at an empirically derived, site-specific proportion totalling to the number of
mummies recorded on the date they were first observed in the field.
Proportions were determined by simulation and chosen by which
best approximated the population growth of wasps observed in the
subsequent sampling week in field data.
(13)
obtained from the Ontario Ministry of Agriculture, Food and Rural
Affairs (C. McCreary, personal communication). These data, collected by a different research group using a similar sampling
procedure as for calibration sites, were used to validate the calibrated model to examine its performance at a different site in a
different growing season. Appropriate weather data were obtained
from Environment Canada, as in the calibration experiments. O.
insidiosus individuals were never observed at this site and so they
were excluded from the ‘background NEUs’ initialization.
2.4. Sensitivity analysis
After validation, the model was initialized for full-season runs
starting on May 1 with 1000 spring eggs on buckthorn, a 500soybean initialization for the habitat patch, and background NEUs
as described in the model calibration section. Soybean lifecycle
parameters were set to their defaults to represent average soybean
phenology, and May 20 was used as a default planting date. Key
model parameters, specifically, step height associated with stage
transfers for host plants, aphids and natural enemies, and fecundity of aphids and natural enemies, were then systematically varied
to determine the impact each of these parameters have on model
performance.
2.5. Simulations
The model was initiated using conditions described in Section
2.4. A series of simulations were then performed to determine the
effect of growing season (using 2007 and 2009 weather data), natural enemy density (using background NEUs and 10 × background
NEUs) and planting date (using soybean planting dates of May 6,
May 20, and June 4) on predicted populations of aphids on soybean over the growing season and diapause aphid eggs occurring
in winter.
3. Results
3.1. Model calibration and validation
Performance of the model at the Alvinston and Shetland sites
after calibration is given in Figs. 5 and 6, and performance of the
model at the validation site, Arva is presented in Fig. 7. In general,
natural enemy populations were better explained by the model
than aphid populations, however, field observations of both natural enemies and aphids were variable, limiting the precision with
C.A. Bahlai et al. / Ecological Modelling 254 (2013) 54–70
Alvinston
Aphids
500
400
300
200
100
0
C
3
2.5
2
1.5
1
0.5
0
195
205
215
225
Julian day
235
245
255
B
400
= 0.9816
x R2=0.754
OLS ySlop
e=0.98,
R² = 0.5464
WLS Slope=0.87,
300
R2=0.554
200
100
0
50
0
100
215
225
235
245
255
Julian day
600
500
205
195
Observed NEUs/ plant (mean ± SE)
Observed aphids/ plant (mean ± SE)
NEU
3.5
A
NEUs/ plant (mean ± SE)
Aphids/ plant (mean ± SE)
600
65
150
200
250
Predicted aphids/ plant
300
3.5
D
3
2.5
OLS ySlop
e=1.30,
= 1.3051
x R2=0.983
R² = 0.9722
2
WLS Slope=0.92, R2=0.699
1.5
1
0.5
0
350
0.5
0
1
Predicted NEUs /plant
1.5
2
Fig. 5. Model performance at Alvinston calibration site in 2007. (A) Predicted () and observed () aphid populations by Julian day; (B) predicted vs. observed aphid-perplant populations, (C) predicted () and observed () NEUs by Julian day; and (D) predicted vs. observed NEU-per-plant populations. Regression lines in (B) and (D) were
constrained to have a zero intercept. Solid line represents ordinary least square regressions; slopes and R2 values for both ordinary least square (OLS) and weighted least
square (WLS) regressions are given, where regression parameters were weighted by the variability in the observed data. Dashed line represents 1:1 predicted to observed
ratio. All regressions were significant at ˛ = 0.05.
Shetland
Aphids
A
NEU s/ plant (mean ± SE)
Aphids / plant (mean ± SE)
2500
NEU
2000
1500
1000
500
0
2500
205
215
225
Julian day
235
245
255
B
2000
y = 1.0559
OLS Slop
e=1.06,x R2=0.841
1500
R² = 0.7008
WLS Slope=1.07, R2=0.594
1000
500
0
0
200
400
600
800
Predicted aphids/plant
1000
1200
C
195
Observed NEUs/ plant (mean ± SE)
Observed aphids/plant (mean ± SE)
195
16
14
12
10
8
6
4
2
0
16
205
215
225
Julian day
235
245
255
D
14
12
10
y =e=1.89,
1.8982xR2=0.985
OLS Slop
8
WLS Slope=1.13, R2=0.629
R² = 0.9792
6
4
2
0
0
1
2
3
Predicted NEUs /plant
4
5
Fig. 6. Model performance at Shetland calibration site in 2007. (A) Predicted () and observed () aphid populations by Julian day; (B) predicted vs. observed aphid-perplant populations, (C) predicted () and observed () NEUs by Julian day; and (D) predicted vs. observed NEU-per-plant populations. Regression lines in (B) and (D) were
constrained to have a zero intercept. Solid line represents ordinary least square regressions; slopes and R2 values for both ordinary least square (OLS) and weighted least
square (WLS) regressions are given, where regression parameters were weighted by the variability in the observed data. Dashed line represents 1:1 predicted to observed
ratio. All regressions were significant at ˛ = 0.05.
66
C.A. Bahlai et al. / Ecological Modelling 254 (2013) 54–70
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
NEUs/plant (mean ± SE)
3.5
NEU
C
3
2.5
2
1.5
1
0.5
0
205
195
Observed aphids/plant (mean ± SE)
Aphids
A
1600
215
225
Julian day
235
245
1400
OLS Slope=0.142, R2=0.960
y = 0.1424x
1000
205
215
225
235
245
255
Julian day
B
1200
195
255
Observed NEUs/plant (mean ± SE)
Aphids/ plant (mean ± SE)
Arva
R23
=0.936
WLS Slope=0.141,
R² = 0.937
800
600
400
200
0
3.5
D
3
2.5
= 0.6953
x
OLSySlop
e=0.6956,
R2=0.711
R² = 0.5847
2
WLS Slope=0.558, R2=0.629
1.5
1
0.5
0
0
2000
4000
6000
Predicted aphids/plant
8000
10000
0
0.5
1
Predicted NEUs/plant
1.5
2
Fig. 7. Model performance at Arva site in 2009, used for model validation. (A) Predicted () and observed () aphid populations by Julian day; (B) predicted vs. observed
aphid-per-plant populations, (C) predicted () and observed () NEUs by Julian day; and (D) predicted vs. observed NEU-per-plant populations. Regression lines in (B)
and (D) were constrained to have a zero intercept. Solid line represents ordinary least square regressions; slopes and R2 values for both ordinary least square (OLS) and
weighted least square (WLS) regressions are given, where regression parameters were weighted by the variability in the observed data. Dashed line represents 1:1 predicted
to observed ratio. All regressions were significant at ˛ = 0.05.
which the model could be calibrated. Ordinary and weighted least
square regression gave similar results when used to evaluate performance of the model (Figs. 5–7).
3.2. Sensitivity analysis
Model outputs were affected by changing key parameters. Fig. 8
shows how the number of aphids and NEU per plant are affected
by changing the variability of stage transfers, i.e. changing the step
height (Eq. (1)) from 0.75 to 1 for soybean, aphid and NEU submodels, and by halving the net fecundity of reproductive stages
for aphid and NEU submodels. Predicted aphid and natural enemy
populations were most dramatically impacted by decreasing variability for aphid stage transfers: populations of both aphids and
natural enemies grew more quickly than in the base model. Aphid
populations appeared to be more vulnerable to environmental variability when the model did not include variability in response to
environmental conditions: at about day 260 of the simulation, a
period of time unfavourable for aphids occurred. Despite starting
this period with a greater population density than in the baseline
simulation, the model where aphid stage transfers had no variability (i.e. step height of 1) predicted that aphid populations would
rapidly drop below the population density predicted by the base
model.
The model parameterized to decrease the net fecundity of aphid
reproductive morphs only slowed the early season population
growth of the aphids: after about day 235 of the simulation, the
model with decreased aphid fecundity did not predict aphid numbers that deviated appreciably from the baseline model. However,
a season-long depression in the numbers of natural enemies was
observed in output.
Natural enemy numbers were increased in the simulation
parameterized to decrease the variability of stage transfers in
natural enemy populations, and both aphid and natural enemy
populations were predicted to be negatively affected, but only late
in the growing season, by decreasing the variability in host plant
stage transfers.
3.3. Simulations
The abundance of aphid morphs as predicted by model simulation for the 2007 growing season is presented in Fig. 9. Density of
A. glycines over the growing season and overwintering egg populations of A. glycines, as predicted by the model for both growing
seasons and as a function of planting date and natural enemy abundance are illustrated in Figs. 10 and 11, respectively. In both the
2007 and 2009 growing season simulations, for both natural enemy
levels (Fig. 10), the aphid populations increased the fastest in the
simulation with the moderate planting date, and declined most
quickly at the end of the season in the simulation with the earliest planting date. The aphid population time series predicted by the
simulations were very similar for all planting dates within a natural
enemy treatment in 2009, but predicted aphid populations varied
by soybean planting date in the very early and very late portions of
the growing season in 2007. The high level of natural enemies (one
order of magnitude higher) suppressed peak aphid populations by
almost two orders of magnitude in simulations based on weather
data from both years. Aphid egg populations (Fig. 11) increased
with later planting dates in 2007, but were relatively uniform
across planting dates in 2009. Higher natural enemy populations
suppressed aphid egg populations in both years, regardless of planting date.
C.A. Bahlai et al. / Ecological Modelling 254 (2013) 54–70
14000
A
Base model
12000
Predicted aphids/plant
67
50% fecundity (aphids)
50% fecundity (natural enemies)
10000
no variability in stage transfers (aphids)
no variability in stage transfers (natural enemies)
no variability in stage transfers (host plants)
8000
6000
4000
2000
0
150
25
170
190
210
230
250
270
290
230
250
270
290
B
Predicted NEUs/plant
Base model
50% fecundity (aphids)
20
50% fecundity (natural enemies)
no variability in stage transfers (aphids)
no variability in stage transfers (natural enemies)
15
no variability in stage transfers (host plants)
10
5
0
150
170
190
210
Julian day
Fig. 8. Model outputs for aphid and NEU density when selected parameters are varied. (A) Predicted aphids per plant and (B) predicted NEU per plant. The ‘base’ model refers
to the model initiated under the conditions described in the text in Section 2.4. The ‘50% fecundity’ simulations consisted of the base model with fecundity parameters being
cut to half their literature values, within the aphid and natural enemy submodels. The ‘no variability in stage transfers’ simulations consisted of the baseline model with the
step height (Eq. (1)) changed from 0.75 to 1 within a given submodel.
4. Discussion
18
diapause eggs
16
spring eggs
apterae (buckthorn)
14
alate (buckthorn)
Log aphid populaon
apterae (soybean)
12
10
alates (soybean)
apterae condioned to produce
sexuals (soybean)
gynoparae
oviparae
8
6
4
2
0
01-May 26-May 20-Jun
15-Jul
09-Aug 03-Sep
28-Sep
23-Oct
17-Nov 12-Dec
Date
Fig. 9. Abundance of soybean aphid morphs by date as predicted by the model.
The model was initiated on 5 January, using 2007 weather data from an Environment Canada weather station near London, ON, with 1000 ‘spring eggs’, 500 soybean
plants planted on 20 May, and ‘background’ natural enemies (as described in text).
All aphid life stages are given on this figure except for nymphs occurring on buckthorn and soybean. Arrow indicates location of possible second peak of gynoparae
activity.
Interfacing the impact of natural enemies through the NEU
calculation proved to be a straightforward way of predicting the
impact of the guild on prey population density. The calibration
process resulted in a model that performed very well in predicting aphid and NEU population growth at both sites (Figs. 5 and 6).
The model slightly under-predicted NEU density observed at the
end of the growing season, which could be explained by two factors. Firstly, it is possible field surveys overestimate the density of
parasitic wasps late in the growing season. The aphid mummy may
remain on the plant for some time after emergence of the adult
wasp, which means scouting data later in the growing season may
represent partially cumulative counts of parasitized aphids, rather
than a time step cohort. Secondly, as aphid density increases, it is
probable that natural enemies occurring in adjacent habitats will
move into soybean fields to feed, so the natural enemy complex at
the end of the growing season likely represents both resident and
immigrant populations of these taxa.
The ability of the model to predict both aphid and natural
enemy populations would be enhanced by allowing individuals
of all taxa to migrate in and out of a habitat patch in response to
appropriate conditions. Currently, the model does not specifically
account for immigration of aphids, nor their natural enemies,
and yet, these events are likely both common and influential on
200
180
160
140
120
100
80
60
40
20
0
2007
A
06-May
20-May
04-Jun
200
180
160
140
120
100
80
60
40
20
0
B
06-May
20-May
04-Jun
12000
10000
8000
8000
6000
6000
4000
4000
2000
2000
0
0
145
152
159
166
173
180
187
194
201
208
215
222
229
236
243
250
257
264
271
278
285
10000
D
145
152
159
166
173
180
187
194
201
208
215
222
229
236
243
250
257
264
271
278
285
Low NEUs
vulnerable aphids per plant
12000
2009
C
145
152
159
166
173
180
187
194
201
208
215
222
229
236
243
250
257
264
271
278
285
145
152
159
166
173
180
187
194
201
208
215
222
229
236
243
250
257
264
271
278
285
High NEUs
C.A. Bahlai et al. / Ecological Modelling 254 (2013) 54–70
vulnerable aphids per plant
68
Julian day
Julian day
Fig. 10. Aphid density (in vulnerable aphids per plant) over the growing season for three soybean planting dates, two natural enemy treatments, and weather data from two
different growing seasons, as predicted by the model. The model was initiated on 5 January of each simulation year, and weather data was obtained from an Environment
Canada weather station near London, ON, with 1000 ‘spring eggs’, and 500 soybean plants Each panel consists of predicted aphid population densities for the planting dates
6 May, 20 May and 4 June, for (A) 2007 weather and high NEUs (background NEUs, as described in the text, increased by an order of magnitude); (B) 2007 weather and low
NEUs (background NEUs only); (C) 2009 weather and high NEUs; and (D) 2009 weather and low NEUs. Weather data for 2007 and 2009 were obtained from an Environment
Canada weather station near London, ON.
population dynamics of these species (Bahlai, 2012; Costamagna
et al., 2012). Future versions of DYMEXTM software will allow spatially explicit dispersal patterns to be incorporated into the model
(Parry et al., 2011). This development will enhance model applicability in highly dispersive species like A. glycines by incorporating
spatial dynamics of the species.
The model was well correlated with the population growth
of natural enemies at the validation site, however, it predicted
that populations of A. glycines would reach much higher numbers than observed (Figs. 5–7). The poor performance of the aphid
model is likely due, in part, to field-specific differences in natural enemy abundances, observer effects leading to systematic
under-estimation of natural enemy abundance at this site, and/or
mis-estimation of aphid density. No O. insidiosus individuals were
recorded at the validation site over the growing season, yet at
sites monitored by our group in the vicinity that year, O. insidiosus
was abundant (Bahlai et al., 2010; Hallett et al., unpublished data).
Also, in these data, as aphid numbers exceeded 250/plant, aphid
densities were estimated rather than counted, leading to greater
potential for observer bias. Another factor which may have affected
model performance at this site is the likely presence of additional
natural enemy species not included in the present model. In concurrent research trials in the vicinity, we observed several additional
natural enemy species including predatory fly larvae (e.g. syrphids
and Aphidoletes midges) and lacewing nymphs feeding on A. glycines
(Bahlai et al., 2010; Hallett et al., unpublished data). Future versions
of this model should include these taxa to increase precision.
At our calibration sites, it was determined that proportional
predation mortality likely over-estimated the impact of the natural enemy community on population growth of A. glycines. Thus,
an empirically determined correction factor of 0.75 was applied
when proportional predation mortality was incorporated into the
aphid submodel. This correction factor may reflect the degree of
search effort employed in our surveys; considerable effort was
made in our field surveys (Hallett et al., unpublished data) to
characterize the natural enemy community of A. glycines, which
may not reflect survey data that is collected under less controlled
scouting conditions. Thus the correction factor may not need be
needed under all circumstances: for instance, at the validation
site, where we suspect natural enemy counts were systematically
under-estimated compared to our surveys for the reasons described
above.
Deterministic population models such as this one typically
have poorer performance at low population numbers because they
ignore demographic stochasticity (Hardman, 1976). In general,
stochastic population models are better at predicting population
fluctuations in tritrophic systems than are deterministic population models (Ives and Jansen, 1998). Soybean aphids often
have patchy distributions in fields (Huang et al., 1992; Su et al.,
1996) and natural enemies may follow similar patterns (Wang
et al., 1991), though random distribution is usually observed
when aphid populations reach high densities (Shusen et al.,
1994). The large standard deviation in average aphid and natural enemy populations at our calibration and validation sites
suggest that patchy distributions within soybean fields occur
through much of the growing season. This lack of uniform distribution complicates model calibration but may be resolved by
increased sampling. Similarly, model calibration could be improved
by increased temporal resolution in sampling: the model predicts fluctuations in both aphids and NEU occurring at periods
shorter than one week, and thus the model was calibrated
using a four-day running mean of predicted values compared
to field conditions to minimize the effect of these fluctuations.
C.A. Bahlai et al. / Ecological Modelling 254 (2013) 54–70
log diapause eggs
14
A
2007
12
10
High NEUs
8
Low NEUs
6
4
2
0
4-Jun
log diapause eggs
14
B
20-May
Planting date
6-May
2009
12
10
High NEUs
8
Low NEUs
6
4
2
0
4-Jun
20-May
Planting date
6-May
Fig. 11. Abundance of diapause eggs of soybean aphid on December 27 (end of simulation) as a function of planting date, natural enemy abundance and growing season,
as predicted by model. The model was initiated on 5 January of each simulation year,
and weather data was obtained from an Environment Canada weather station near
London, ON, with 1000 ‘spring eggs’, and 500 soybean plants. Each panel consists of
predicted aphid diapause egg abundances for the planting dates 6 May, 20 May and
4 June at low NEUs (i.e. background NEUs, as described in the text) and high NEUs
(i.e. background NEUs increased by an order of magnitude) after a given growing
season. (A) 2007 and (B) 2009. Weather data for 2007 and 2009 were obtained from
an Environment Canada weather station near London, ON.
The model was used to examine abundance of aphid morphs
over the course of the growing season which suggested a possible
secondary peak of gynoparae occurring later in the fall (Fig. 9). A
secondary peak of gynoparae flight activity was observed under
field conditions (Bahlai, 2012) and it was suggested that each
peak corresponded to a different environmental cue, with the
early-fall peak most closely linked with degree day accumulation,
and the second more closely linked with photoperiod. This differential response to cues by gynoparae was not built into the
model, and apterae conditioned to produce sexuals, the morphs
that produce gynoparae, follow a similar bimodal activity distribution earlier in the season, suggesting that conditions leading to
the bimodal activity distribution of gynoparae occur at least one
generation before gynoparae are produced. It is possible that a single unfavourable weather event led to a brief period of suppressed
activity for all morphs of A. glycines, and this effect could be passed
on to subsequent generations. A similar pattern was observed for
oviparae, which may support this hypothesis. To test this, simulations should be performed to generate data that can be used to
compare gynoparae production over several growing seasons to
data from the North American aphid suction trap network (Schmidt
et al., 2012).
The model predicts natural enemies have a very important role
in overall aphid suppression, but the effect of plant phenology on
aphid phenology seems to be variable, depending on the growing
season (Fig. 10). An interesting effect was observed in the fullgrowing season simulations (Fig. 10). In these simulations, despite
being planted earlier, aphid populations built more slowly in the
simulations where soybean was planted early than on those planted
69
on the more moderate planting date. This is a result of populations
of natural enemies being able to establish and reproduce earlier in
these simulations: by the time the growing season reached temperatures optimal for aphid development, reproduction of natural
enemies had already been triggered within the model, slowing the
initial phases of rapid population growth beyond that which was
observed in the simulations with the moderate soybean planting
date. The impact of plant phenology on aphid dynamics behaved
more predictably late in the growing season: aphid populations
decreased earlier in simulations where host plants reached senescence earlier, however, the magnitude of difference between plant
phenology simulations varied by simulation year.
In 2007, late growing season population dynamics of A. glycines
were dramatically affected by planting date, but in 2009, very little variation was predicted to occur in late-season soybeans. Fewer
eggs are produced in all simulations with higher levels of natural
enemy suppression (Fig. 11). Planting date of soybean had a dramatic impact on the predicted number of aphid eggs produced at
the end of the season in simulations using 2007 weather data, with
fewer eggs produced in simulations using earlier planting dates
(Fig. 11A), but this effect was not observed with 2009 weather data
(Fig. 11B). This result suggests that relative influence of plant phenology on the phenology and population ecology of A. glycines is
highly interactive with environmental conditions. These responses
are difficult to observe in purely empirical research, because it is
impossible to de-couple the effects of environment and host plant
phenology in the field.
5. Conclusions
The model described in this paper represents an integration
of the available literature on A. glycines and its dominant natural enemy taxa in eastern North America. Future iterations of this
model should include additional natural enemy taxa to increase
generalizability, and should incorporate factors accounting for the
movement of all species into and out of a given habitat patch.
Acknowledgements
The authors would like to thank two anonymous reviewers, whose comments greatly improved the logical flow of this
work, Darren Kriticos (CSIRO Australia) and Jonathan Newman
(University of Guelph) for advice and comments offered during
development of this model, Cara McCreary (University of Guelph
Soybean Breeding Program and Ontario Ministry of Agriculture,
Food and Rural Affairs) and Tracey Baute (Ontario Ministry of
Agriculture, Food and Rural Affairs) for information on soybean
phenology and scouting data, and Andrew Frewin (University of
Guelph) for extensive conversation about the biology of A. certus. CB
was funded by a Natural Sciences and Engineering Research Council
of Canada PGS-D3 fellowship.
References
Aquilino, K.M., Cardinale, B.J., Ives, A.R., 2005. Reciprocal effects of host plant and
natural enemy diversity on herbivore suppression: an empirical study of a model
tritrophic system. Oikos 108, 275–282.
Bahlai, C.A., 2012. Abiotic and Biotic Factors Affecting the Distribution and Abundance of Soybean Aphid in Central North America. Doctoral dissertation. School
of Environmental Sciences, University of Guelph, Guelph.
Bahlai, C.A., Sears, M.K., 2009. Population dynamics of Harmonia axyridis and Aphis
glycines in Niagara Peninsula soybean fields and vineyards. Journal of the Entomological Society of Ontario 140, 27–39.
Bahlai, C.A., Welsman, J.A., Schaafsma, A.W., Sears, M.K., 2007. Development of soybean aphid (Homoptera: Aphididae) on its primary overwintering host, Rhamnus
cathartica. Environmental Entomology 36, 998–1006.
Bahlai, C.A., Xue, Y., McCreary, C.M., Schaafsma, A.W., Hallett, R.H., 2010. Choosing organic pesticides over synthetic pesticides may not effectively mitigate
environmental risk in soybeans. PLoS One 5, e11250.
70
C.A. Bahlai et al. / Ecological Modelling 254 (2013) 54–70
Banks, C.J., 1956. Observations on the behaviour and mortality in Coccinellidae
before dispersal from the egg shells. Proceedings of the Royal Entomological
Society of London. Series A, General Entomology 31, 56–60.
Costamagna, A.C., Landis, D.A., Brewer, M.J., 2008. The role of natural enemy guilds
in Aphis glycines suppression. Biological Control 45, 368–379.
Costamagna, A.C., McCornack, B.P., Ragsdale, D.W., 2012. Alate immigration disrupts soybean aphid suppression by predators. Journal of Applied Entomology,
http://dx.doi.org/10.1111/j.1439-0418.2012.01730.x, Online first preprint.
De Barro, P., 1992. The role of temperature, photoperiod, crowding and plant
quality on the production of alate viviparous females of the bird cherryoat aphid, Rhopalosiphum padi. Entomologia Experimentalis et Applicata 65,
205–214.
Desneux, N., O’Neil, R.J., Yoo, H.J.S., 2006. Suppression of population growth of the
soybean aphid, Aphis glycines Matsumura, by predators: the identification of
a key predator and the effects of prey dispersion, predator abundance, and
temperature. Environmental Entomology 35, 1342–1349.
Donaldson, J.R., Myers, S.W., Gratton, C., 2007. Density-dependent responses of soybean aphid (Aphis glycines Matsumura) populations to generalist predators in
mid to late season soybean fields. Biological Control 43, 111–118.
Fox, T.B., Landis, D.A., Cardoso, F.F., Difonzo, C.D., 2004. Predators suppress Aphis
glycines Matsumura population growth in soybean. Environmental Entomology
33, 608–618.
Fox, T.B., Landis, D.A., Cardoso, F.F., Difonzo, C.D., 2005. Impact of predation on establishment of the soybean aphid, Aphis glycines in soybean, Glycine max. Biocontrol
50, 545–563.
Frewin, A.J., Xue, Y., Welsman, J.A., Broadbent, B.A., Schaafsma, A.W., Hallett, R.H.,
2010. Development and parasitism by Aphelinus certus (Hymenoptera: Aphelinidae), a parasitoid of Aphis glycines (Hemiptera: Aphididae). Environmental
Entomology 39, 1570–1578.
Gardiner, M.M., Landis, D.A., 2007. Impact of intraguild predation by adult Harmonia axyridis (Coleoptera: Coccinellidae) on Aphis glycines (Hemiptera:
Aphididae) biological control in cage studies. Biological Control 40,
386–395.
Griffiths, W., Aurambout, J.-P., Parry, H., Trebicki, P., Kriticos, D., O’Leary, G., Finlay, K.,
Barro, P.D., Luck, J., 2010. Insect–pathogen–crop dynamics and their importance
to plant biosecurity under future climates: barley yellow dwarf virus and wheat
– a case study. In: Proceedings of 15th Agronomy Conference 2010, Lincoln, New
Zealand.
Hallett, R.H., Goodfellow, S.A., Weiss, R.M., Olfert, O., 2009. MidgEmerge, a new
predictive tool, indicates the presence of multiple emergence phenotypes of
the overwintered generation of swede midge. Entomologia Experimentalis et
Applicata 130, 81–97.
Hardman, J.M., 1976. Deterministic and stochastic models simulating the growth of
insect populations over a range of temperatures under Malthusian conditions.
The Canadian Entomologist 108, 907–924.
Hirano, K., Honda, K., Miyai, S., 1996. Effects of temperature on development,
longevity and reproduction of the soybean aphid, Aphis glycines (Homoptera:
Aphididae). Applied Entomology and Zoology 31, 178–180.
Huang, F., Ding, X., Wang, X., Huang, Z., 1992. Studies on the spatial distribution pattern of soybean aphid and sampling techniques. Journal of Shenyang Agricultural
University 23, 81–87.
Isenhour, D.J., Yeargan, K.V., 1981. Effect of temperature on the development of Orius
insidiosus, with notes on laboratory rearing. Annals of the Entomological Society
of America 74, 114–116.
Ives, A.R., Jansen, V.A.A., 1998. Complex dynamics in stochastic tritrophic models.
Ecology 79, 1039–1052.
Kaiser, M.E., Noma, T., Brewer, M.J., Pike, K.S., Vockeroth, J.R., Gaimari, S.D., 2007.
Hymenopteran parasitoids and dipteran predators found using soybean aphid
after its midwestern United States invasion. Annals of the Entomological Society
of America 100, 196–205.
Kiman, Z.B., Yeargan, K.V., 1985. Development and reproduction of the predator
Orius insidiosus (Hemiptera: Anthocoridae) reared on diets of selected plant
material and arthropod prey. Annals of the Entomological Society of America
78, 464–467.
Kriticos, D.J., Brown, J.R., Maywald, G.F., Radford, I.D., Mike Nicholas, D.,
Sutherst, R.W., Adkins, S.W., 2003. SPAnDX: a process-based population
dynamics model to explore management and climate change impacts
on an invasive alien plant, Acacia nilotica. Ecological Modelling 163,
187–208.
Kriticos, D.J., Watt, M.S., Withers, T.M., Leriche, A., Watson, M.C., 2009. A
process-based population dynamics model to explore target and nontarget impacts of a biological control agent. Ecological Modelling 220,
2035–2050.
Kumar, A., Pandey, V., Shekh, A.M., Kumar, M., 2008. Growth and yield response of
soybean (Glycine max L.) in relation to temperature, photoperiod and sunshine
duration at Anand, Gujarat, India. American-Eurasian Journal of Agronomy 1,
45–50.
Lanzoni, A., Accinelli, G., Bazzocchi, G.G., Burgio, G., 2004. Biological traits and life
table of the exotic Harmonia axyridis compared with Hippodamia variegata,
and Adalia bipunctata (Col., Coccinellidae). Journal of Applied Entomology 128,
298–306.
Maywald, G.F., Kriticos, D.J., Sutherst, R.W., Bottomley, W., 2007. Dymex Model
Builder v.3 User Guide. Hearn Scientific Software, Melbourne.
McCaffrey, J.P., Horsburgh, R.L., 1986. Biology of Orius insidiosus (Heteroptera:
Anthocoridae): a predator in Virginia apple orchards. Environmental Entomology 15, 984–988.
McCornack, B.P., Ragsdale, D.W., Venette, R.C., 2004. Demography of soybean aphid
(Homoptera: Aphididae) at summer temperatures. Journal of Economic Entomology 97, 854–861.
Mignault, M.-P., Roy, M., Brodeur, J., 2006. Soybean aphid predators in Québec and
the suitability of Aphis glycines as prey for three Coccinellidae. Biocontrol 51,
89–106.
Newman, J.A., Gibson, D.J., Parsons, A.J., Thornley, J.H.M., 2003. How predictable
are aphid population responses to elevated CO2 ? Journal of Animal Ecology 72,
556–566.
Nielsen, C., Hajek, A.E., 2005. Control of invasive soybean aphid, Aphis glycines
(Hemiptera: Aphididae), populations by existing natural enemies in New York
State, with emphasis on entomopathogenic fungi. Environmental Entomology
34, 1036–1047.
Obrycki, J.J., Tauber, M.J., 1981. Phenology of three coccinellid species: thermal
requirements for development. Annals of the Entomological Society of America
74, 31–36.
Onstad, D.W., Fang, S., Voegtlin, D.J., 2005. Forecasting seasonal population growth of
Aphis glycines (Hemiptera: Aphididae) in soybean in Illinois. Journal of Economic
Entomology 98, 1157–1162.
Parry, H.R., Aurambout, J.-P., Kriticos, D.J., 2011. Having your cake and eating it: a
modelling framework to combine process-based population dynamics and dispersal simulation. In: 19th International Congress on Modelling and Simulation,
Perth, Australia, pp. 2535–2541.
Pedersen, P., 2009. Soybean Growth and Development. PM 1945. Iowa State University Extension, Ames.
Phoofolo, M.W., Obrycki, J.J., Krafsur, E.S., 1995. Temperature-dependent ovarian
development in Coccinella septempunctata (Coleoptera: Coccinellidae). Annals
of the Entomological Society of America 88, 72–79.
Ragsdale, D.W., Landis, D.A., Brodeur, J., Heimpel, G.E., Desneux, N., 2011. Ecology
and management of the soybean aphid in North America. Annual Review of
Entomology 56, 375–399.
Ragsdale, D.W., Voegtlin, D.J., O’Neil, R.J., 2004. Soybean aphid biology in North
America. Annals of the Entomological Society of America 97, 204–208.
Rutledge, C.E., Neil, R.J., Fox, T.B., Landis, D.A., 2004. Soybean aphid predators and
their use in integrated pest management. Annals of the Entomological Society
of America 97, 240–248.
Schellhorn, N.A., Andow, D.A., 1999. Mortality of Coccinellid (Coleoptera: Coccinellidae) larvae and pupae when prey become scarce. Environmental Entomology
28, 1092–1100.
Schmidt, J.M., Richards, P.C., Nadel, H., Ferguson, G., 1995. A rearing method for the
production of large numbers of the insidious flower bug, Orius insidiosus (Say)
(Hemiptera: Anthocoridae). The Canadian Entomologist 127, 445–447.
Schmidt, N.P., O’Neal, M.E., Anderson, P.F., Lagos, D., Voegtlin, D., Bailey, W., Caragea,
P., Cullen, E., DiFonzo, C., Elliott, K., Gratton, C., Johnson, D., Krupke, C.H., McCornack, B., O’Neil, R., Ragsdale, D.W., Tilmon, K.J., Whitworth, J., 2012. Spatial
distribution of Aphis glycines (Hemiptera: Aphididae): a summary of the suction
trap network. Journal of Economic Entomology 105, 259–271.
Shusen, S., Boren, Y., Dianshen, L., Yanjie, Y., 1994. Study on space dynamics of a natural population of Aphis glycines Matsumura. Journal of Jilin Agriculture University
16, 75–79 (Translation).
Straub, C.S., Snyder, W.E., 2008. Increasing enemy biodiversity strengthens herbivore suppression on two plant species. Ecology 89, 1605–1615.
Su, J., Hao, K., Shi, X., 1996. Spatial distrubution and sampling technique of Aphis
glycines Matsumura. Journal of Nanjing Agricultural University 13, 55–58 (Translation).
Taylor, L.R., 1974. Insect migration, flight periodicity and the boundary layer. Journal
of Animal Ecology 43, 225–238.
Tilmon, K.J., Hodgson, E.W., O’Neal, M.E., Ragsdale, D.W., 2011. Biology of the soybean
aphid, Aphis glycines (Hemiptera: Aphididae) in the United States. Journal of
Integrated Pest Management 2, A1–A7.
Wang, X., Ding, X., Huang, F., 1991. Studies on the spatial distribution of aphideating ladybirds in soybean fields. Journal of Shenyang Agricultural University
22, 13–16 (Translation).
Welsman, J.A., Bahlai, C.A., Sears, M.K., Schaafsma, A.W., 2007. Decline of soybean aphid (Homoptera: Aphididae) egg populations from autumn to spring
on the primary host, Rhamnus cathartica. Environmental Entomology 36,
541–548.
White, N.A., Chakraborty, S., Murray, G., 2004. A linked process-based model to study
the interaction between Puccinia striiformis and wheat. In: 4th International Crop
Science Congress, Brisbane, Australia.
Wu, Z., Schenk-Hamlin, D., Zhan, W., Ragsdale, D.W., Heimpel, G.E., 2004. The soybean aphid in China: a historical review. Annals of the Entomological Society of
America 97, 209–218.
Xue, Y., Bahlai, C.A., Frewin, A., Sears, M.K., Schaafsma, A.W., Hallett, R.H., 2009.
Predation by Coccinella septempunctata and Harmonia axyridis (Coleoptera:
Coccinellidae) on Aphis glycines (Homoptera: Aphididae). Environmental Entomology 38, 708–714.
Yoo, H.J.S., O’Neil, R.J., 2009. Temporal relationships between the generalist predator, Orius insidiosus, and its two major prey in soybean. Biological Control 48,
168–180.
Yoo, H.J.S., O’Neil, R.J., Voegtlin, D.J., Graves, W.R., 2005. Host plant suitability of
Rhamnaceae for soybean aphid (Homoptera: Aphididae). Annals of the Entomological Society of America 98, 926–930.
Zhang, Y., Kongming, W.U., Wyckhuys, K.A.G., Heimpel, G.E., 2009. Trade-offs
between flight and fecundity in the soybean aphid (Hemiptera: Aphididae).
Journal of Economic Entomology 102, 133–138.