Toward a General Model of Rangeland Grasshopper
(Orthoptera: Acrididae) Phenology in the
Steppe Region of Montana
WILLIAM P. KEMP1 AND BRIAN DENNIS2
KEY WORDS
Insecta, integrated pest management, insect development, phenology
(Orthoptera: Acrididae) development has important implications for
integrated pest management efforts in much of the
western United States and Canada. Recent work
has suggested that the general progression of assessment and, if necessary, control activities should
follow and be linked to the occurrence patterns of
the various phenological stages of rangeland grasshoppers. For example, Onsager (1987a) suggested
that assessment of rangeland grasshopper communities (a collection of co-occurring populations
of individual species) should be conducted at "peak
third instar" to determine whether or not a problem exists and to allow for mobilization of resources
for control activities, if warranted. The term "peak
third instar" refers to the point in time when the
proportion of grasshoppers in that development
stage reaches a maximum (Dennis & Kemp 1988).
Other important development "signposts" (peak
fourth and fifth instars, 75% adult) of rangeland
grasshoppers have been identified as appropriate
times for applying different biological and chemical controls (Onsager 1987a,b). However, in general, there has been very little research on rangeland grasshopper phenology that would allow
rangeland pest managers to use the management
guidelines described by Onsager (1987a,b).
RANGELAND GRASSHOPPER
1
USDA-Agricultural Research Service, Rangeland Insect Laboratory, Bozeman, Mont. 59717-0366.
2
College of Forestry, Wildlife, and Range Sciences, University
of Idaho, Moscow, Idaho 83843.
Readers interested in obtaining a collection of programs for
parameter estimation and statistical inferences are invited to send
a PC-formatted 5VS, 1.2 MB disk to W.P.K.
One serious problem facing rangeland pest managers is the fact that grasshoppers comprise a complex of nearly 200 species in the western United
States and Canada. It is common to find anywhere
from 30 to 40 species of grasshoppers on a 10-ha
site over the course of the year (Onsager 1987b).
Furthermore, the rangeland grasshopper community at a site is influenced by plant community
characteristics (e.g., Kemp et al. 1990a,b). The
rangeland resource manager is therefore faced with
a complex of species that vary in space and time,
unlike many other pest management situations with
only one or a few clearly defined pest species. Fortunately, only «15 rangeland grasshopper species
are responsible for most forage losses and, frequently, 3-5 species comprise between 75 and 95%
of the overall local community abundance (Onsager 1987b), especially during outbreak years.
In spite of the obvious economic importance of
rangeland grasshoppers and the importance of phenology to pest management, surprisingly little work
has been conducted on quantifying phenological
patterns. Newton et al. (1954) described the general
patterns of hatching, adult presence, and oviposition for 46 rangeland grasshopper species at an
unspecified number of sites in Montana and Wyoming over a 2-yr period. Other studies have reported on general trends for hatching or phenological points similar to the work of Newton et al.
(1954) (Shotwell 1941, Hewitt 1979). However, none
of these studies provides information on rangeland
grasshopper developmental signposts for communities that can be used in a pest management context.
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Environ. Entomol. 20(6): 1504-1515 (1991)
ABSTRACT A 4-yr study was conducted to examine the phenology of rangeland grasshoppers at 12 sites throughout Montana. A six-species complex of common and economically
important rangeland grasshoppers was selected to facilitate comparisons between sites in this
environmentally heterogeneous state. Results showed that a published phenology model
(developed by Dennis, B., W. P. Kemp & R. C. Beckwith. 1986. A stochastic model of insect
phenology: estimation and testing Environ. Entomol. 15: 540-546, and Dennis, B. & W. P.
Kemp. 1988. Further statistical inference methods for a stochastic model of insect phenology.
Environ. Entomol. 17: 887-893) provided good estimates of "general" grasshopper phenology
for each site and year. Comparisons of developmental "signposts" (75% first instar, peak
second to fifth instars, and 75% adults) for grasshoppers between sites and years indicated
that they can be used by resource managers for estimating when development stages of
rangeland grasshoppers are likely to occur. The developmental signposts were separated, on
average, by 8-12 d. Implications of these results for rangeland insect pest management are
discussed.
December 1991
1505
KEMP & DENNIS: MODEL OF RANGELAND GRASSHOPPER PHENOLOGY
Materials and Methods
Sentinel Sites. In 1986, 10 sentinel sites were
established throughout Montana for the purpose of
monitoring yearly phenology of rangeland grasshoppers. The number of sentinel sites was expanded to 12 in 1987 and thereafter remained constant
through 1989 (Fig. 1). Sites were located over a
range of long-term plant phenological zones (see
Kemp 1987, 365, fig. 24.6) in an attempt to include
the range of climatic conditions characteristic of
sites within either the Agropyron spicatum or the
Bouteloua gracilis provinces of the steppe region
of Montana (Daubenmire 1978). All but one of the
sites were located within 3.20 km of a National
Oceanic and Atmospheric Administration (NOAA)
weather station. On-site temperatures were recorded at the Three Forks site because there was
no nearby NOAA station. Four of the sentinel sites
(Broadus, Jordan, Great Falls, and Glasgow) were
moved locally before sampling in 1987 to ensure
HAURE 1
-STA
C~^
/i
I JORDAN
' i——
MILES
cirv
C.
roRxt j ^ ,
I BILlINCSt-.
•LODCE7
UY L
° *
'—
BROOD
100 ka
Fig. 1. Sentinel sites used for collection of rangeland
grasshopper phenology data 1986-1989, Montana.
long-term access (<2 km away on similar vegetation).
Weather permitting, weekly sweep net samples
(each sweep consisting of an area of 180° through
the vegetation [Evans et al. 1983, Evans 1988]) were
collected each year at all sites during the interval
between mid-April and October. The number of
net sweeps at a site in 1986-1987 was variable,
although a minimum of 100 grasshoppers were
collected at each sample date during the nymphal
period. This was standardized to 100 sweeps in
1988-1989. Grasshoppers collected via sweep net
were placed in plastic bags, put on ice, and taken
to the laboratory for identification to species and
determination of development stages.
As described previously, we expected the species
composition of grasshopper communities to differ
with site and to some extent with year (Kemp et
al. 1990a,b). Therefore, we selected six major species for comparisons among sites. The six species
chosen were Ageneotettix deorum (Scudder), Amphitornus coloradus (Thomas), Aulocara elliotti
(Thomas), M. infantilis Scudder, M. packardii
Scudder, and M. sanguinipes (F.) and were the
same species that were used in previous studies
(Kemp & Onsager 1986, Kemp 1987). Because of
extremely low densities at Chester (1986-1988),
Red Lodge (1986-1988), Wyola (1986-1988), and
Jordan (1988) during this study, phenology data
from these sites could not be used in analyses.
Modeling Phenology. The methods described
by Dennis et al. (1986) and Dennis & Kemp (1988)
were used to describe the phenology of the sixspecies community complex of rangeland
grasshoppers. Data from 1986-1988 were used in
analyses and data from 1989 were used for model
evaluation. The reader should refer to Dennis et
al. (1986) and Dennis & Kemp (1988) for complete
details of the technical aspects of model development; however, we briefly summarize below the
methods and steps followed.
At each site, a series of samples of size nu n2,
. . . , nq was collected from the grasshopper community at times tu t2, . . . , tq. If there are r development stages (in grasshoppers, first to fifth instars
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Most of the work on phenology prediction for
rangeland grasshoppers has been conducted in
Canada. Mukerji & Randell (1975) developed an
embryonic development model for Melanoplus
sanguinipes (F.) eggs in the fall, and Randell &
Mukerji (1974) reported on a springtime hatching
model for the same species, which was driven by
air temperatures. Also, Gage et al. (1976) developed a predictive model for the seasonal occurrence of a group of three grasshoppers, two of
which (Camnula pellucida (Scudder) and M. bivittatus (Say)) are more commonly associated with
crops in Montana.
Kemp & Onsager (1986) reanalyzed data collected by Hewitt (1979) and compared the phenological patterns of six individual rangeland grasshopper species. The data were collected during
1975-1976 at Roundup, Mont. The analyses showed
that in spite of significant differences in phenology
parameter estimates (for methods, see Dennis et al.
1986, Dennis & Kemp 1988) among the individual
species, sufficient similarities existed so that it was
reasonable to treat these species as a group in terms
of phenology for pest management purposes (Kemp
1987). As noted by Onsager (1987a,b), rangeland
grasshopper pest management activities, at present,
do not generally distinguish among individual species. Rather, management activities (assessment and
control) are generally directed toward the heterogeneous mix of springtime-emerging grasshopper
species.
Based on the results of previous investigations
(Kemp & Onsager 1986, Kemp 1987), we established a study to investigate the statewide variation
of rangeland grasshopper communities in Montana. The major goal of this research was to provide
rangeland resource managers with a straightforward method for estimating the timing of assessment and control activities for grasshopper populations in Montana.
1506
ENVIRONMENTAL ENTOMOLOGY
{1 -I- exp[-(a, {1 + exp[-(a, - 0 / W ] }
_
- {1 + exp[-(a,_, t)/Vvt]}-1,
i = 2, . . . , r - 1;
1 - {1 + exp[-(a r _, t)/Vvt}}-\
i = r.
(1)
This expression arises from assuming that an insect's underlying continuous development level,
denoted by X(t), has a logistic probability distribution with mean t and variance (=ir2uf/3) proportional to t. Then Pr[Y(t) < i] = Pr[Y(t) < a(] is
the cumulative distribution function of a logistic
distribution:
0, i = 0 (a0 = -oo);
{1 + exp[-(a, t)/Vvt]}-\
Pr[Y(t) < t] =
i = 1, .. ., r - 1;
l,i
= r(aT=
+oo).
(2)
The proportion
as Pr[Y(t) < i]
a,, i = 1, . . . , r
t at which half
p,(t) is obtained from equation 2
- Pr[Y(t) < i - 1]. The quantity
— 1 can be interpreted as the time
of the community is in stage i or
b e l o w : Pr[Y(at)
< i] = P r [ Y ( a , ) > i ] = Vz (fig. 1 o f
Dennis & Kemp 1988). The quantity v is a measure
of the variability of development rates among insects in the community. In applications, t is usually
measured in degree-days.
If there are r development stages, then the model
has r unknown parameters. The unknown parameters can be written as a column vector, 6:
6 = [a,, a2, . . . , ar_,, v]'.
Also, the proportions pt(t) defined in equation 1
can be written as p,(t; 6) to emphasize their dependence on 0.
These parameters can be estimated from data
using the maximum likelihood (ML) method. Nonlinear regression packages can be used to perform
the ML calculations as explained by Dennis et al.
(1986) and Dennis & Kemp (1988).
Model Evaluation. The complexity of a data set
is reflected by the number of parameters required
to describe its structure (Bishop et al. 1975). Any
model that describes the structure of the data with
fewer parameters than the number of cells (x,/s) is
unsaturated. The saturated model, because it describes the data set structure completely with one
parameter per cell, is used for comparison with
other models containing fewer parameters. In our
case, we were interested in describing a grasshopper phenology data set with the fewest parameters
necessary.
With a data set that spans three years (19861988) and nine sites (12 original sites minus Chester
1986-1988, Jordan 1988, Red Lodge 1986-1988,
and Wyola 1986-1988) (Fig. 1), parameters could
be estimated according to several alternative hypotheses. First, data could be pooled over sites (nine)
and years (three or two in the case of Jordan), and
a single set of six parameters (d,, . . . d5) v) could
describe the general development trends. Alternatively, either a set of six parameters could be
estimated for each of 3 yr over all sites for a total
of 18 parameters (3 yr x 6 parameters each year),
or a set of six parameters could be estimated for
each of nine sites over all years for a total of 54
parameters (9 sites x 6 parameters for each site).
If it were necessary to keep sites and years separate,
a total of 156 parameters would be needed. Thus,
the complexity of the data will determine which
alternative model we select.
In this study, we used the Akaike Information
Criterion (AIC) (Sakamoto et al. 1986) to compare
alternative models. We refer the reader to Sakamoto et al. (1986) for a detailed description of the
AIC. In summary, however, the AIC has advantages over simply using the log likelihood (Dennis
et al. 1986, Dennis & Kemp 1988) because the log
likelihood is a biased estimator of the mean expected log likelihood. The somewhat awkward term
"mean expected log likelihood" refers to the fact
that the quantity results from taking the expected
value of the log likelihood twice: first, with respect
to the underlying "true" model, and second, with
respect to the underlying "true" distribution of the
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and adult; r = 6), then the jth sample would consist
of the counts xlf, x2j,. . . , xrl, where xit is the number
of sampled insects in development stage i at time
tj and where ns = 2,x,7. In this case, t{ is measured
in degree-days (DD) computed in °F (above a
threshold of 17.8°C) with a starting date of 1 January (Allen 1976). Because year-round weather recording at the Three Forks site was not established
until 1989, the starting Julian dates (JD) for temperature collections were 59, 64, and 57 for 19861988, respectively. Given that degree-days do not
generally begin to accumulate until after JD 90 at
the Three Forks site, we were confident that the
later starting dates for this site did not influence
our results.
The counts x1/; x2j, . . . , xrj can be described as
having a multinomial distribution conditional on
the sample size ny. The underlying proportion of
the community in each development stage would
be expected to change with time as the individual
population members develop.
Let Y(f) be the stage of a randomly sampled
member of the community at time t; possible values for Y(t) are [1, 2,. . . , r\ The phenology model
of Dennis et al. (1986) assumes that an insect's
development is really a continuous stochastic process consisting of accumulated small development
increments. However, Y(t) is the fundamental observed random variable because a sampled insect
is recorded as having reached a discrete development stage. We define p,(t) = iMY(f) = *] a s t n e
proportion of the population in development stage
i at time t, i — 1, . . . , r.
The model of Dennis et al. (1986) takes the proportion p,(t) to be
Vol. 20, no. 6
December 1991
KEMP & DENNIS: MODEL OF RANGELAND GRASSHOPPER PHENOLOGY
1507
35
PARAHETER MODEL
28
(18 PARAMETER MODEL (YEARS)
21
o.o
51 PARAHETER MODEL (SITES)
150
225
300
525
450
375
O
Fig. 2. Six phenological "signposts" for rangeland
grasshoppers in Montana, as estimated by the DennisKemp model (Dennis et al. 1986, Dennis & Kemp 1988).
ML estimate of 0. The mean expected log likelihood
is a measure of the goodness of fit of a model; the
larger the mean expected log likelihood, the better
the fit of the model (Sakamoto et al. 1986), that is,
the closer the hypothesized model is to the underlying "true" model. Sakamoto et al. (1986) show
that the maximum log likelihood tends to overestimate the mean expected log likelihood, particularly when models have unnecessarily large numbers of free parameters. The AIC is computed as
156 PARAMETER NODEL
(SITES AND YEARS)
SATURATED MODEL
(2661 PARAMETERS)
log (Parameters)
Fig. 3. Akaike Information Criterion (AIC) values
computed for various parameterization options for the
Dennis-Kemp model (Dennis et al. 1986, Dennis & Kemp
1988) for a rangeland grasshopper data set consisting of
nine sites and 3 yr (except Jordan, which had only 2 yr
AIC = — 2(maximum log likelihood of the model) of data), Montana.
+ 2(number of free parameters),
and is an unbiased estimate of (minus two times)
the mean expected log likelihood. Because the
model -that minimizes the AIC is considered to be
the most appropriate, it is clear that the " +
2(number of free parameters)" term is a penalty
for overparameterization. The AIC has many useful applications in comparing models within the
entomological literature outside of the specific purposes of this study.
Table 1. Percentage of rangeland grasshopper populations comprising six selected species, nine locations and
three years, Montana"
j Population in six species^
1986 1987 1988
Glasgow
Havre
Miles City
Jordan
Fort Benton
Broadus
Billings
Great Falls
Three Forks
91
55
88
72
95
93
79
89
96
77
57
76
86
83
87
82
69
95
85
74
84
c
86
91
84
57
96
X
SD
84.3cd
62.0d
82.6cd
79.0cd
88.0c
90.3c
82.7cd
71.7cd
95.3c
7.0
10.4
6.1
9.8
6.2
3.1
2.5
16.2
0.6
Like letters indicate no significant difference (df = 17, a — 0.05;
ANOVA, Tukey's studentized range test [SAS Institute 1988]).
0
Data from Kemp et al. (1992).
b
Six selected species used by Kemp & Onsager (1986): Ageneotettix deorum (Scudder), Amphitornus coloradus (Thomas),
Aulocara elliotti (Thomas), Melanoplus infantilis Scudder, M.
packardii Scudder, M. sanguinipes (F.).
c
Densities too low to make accurate estimates.
Comparisons Between Sites. Once parameters
for a community at a given site and year were
estimated, two additional estimates for the DennisKemp model were computed (Dennis & Kemp
1988). First, the peak time of p,{t) and the associated confidence interval was computed for each
of the second to fifth instars for each site and year
(Fig. 2) (see equations 16-22 of Dennis & Kemp
1988). Second, the estimated time and confidence
interval for T was computed for 75% first instar
and 75% adult (see below). All estimates were produced in terms of degree-days as well as Julian
date for site-to-site comparisons.
Estimating the Time at Which 100 £% of the
Population is in Stage i or Less. This section describes statistical methods for estimating the time
at which 100 •£% of the population is in stage i or
less, where 0 < £ < 1. For instance, the time at
which 75% of the population is adult (i.e., 25% is
fifth instar or less) is one of the "signposts*' used in
this paper, along with the time at which 75% is
first irtstar. The remaining signposts used are peak
second to fifth instars; statistical methods for peak
instars have been described elsewhere (Dennis &
Kemp 1988).
The probability that an insect is in stage i or less
is given by equation 2 under the model of Dennis
et al. (1986). As a function of t, the quantity Pr[Y(t)
< i] is a declining sigmoid curve (e.g., stage 1, Fig.
2). We obtain the value of t at which this curve
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Degree Days
Vol. 20, no. 6
ENVIRONMENTAL ENTOMOLOGY
1508
1.0
0.8
0.6
0.4
0.0
0
100 200 300 400 500
100 200 300 400 500
100 200 300 400 500
I.U
D
c 0.8
o
._
+->
i
0.6
o
Q.
/ \
0.4
/
O
Q_
/
0.2
/
\
\
\
0.2
/
* \
0.0
0
100 200 300 400 500
Degree Days
0.0
100 200 300 400 500
0
100 200 300 400 500
Fig. 4. Comparison of raw data (plotted points) and model results (solid line) for the proportion of the grasshopper
community in each developmental state as a function of accumulated degree-days, Havre, Montana, 1986 (log
likelihood = -52.63). (A) First instar. (B) Second instar. (C) Third instar. (D) Fourth instar. (E) Fifth instar. (F)
Adult.
attains the value £ as follows. Let T be the time
(i.e., value of t) at which Pr[Y(t) < i] = £ for some
given stage i. Thus T and £ are related by
+ exp
This expression can be solved for T:
evaluated at a and v. The approximate variance
of f, and a 100(1 — a)% confidence interval for T,
can be derived with the 5 method (see Dennis &
Kemp 1988 for a discussion of the 8 method). The
8 method requires the following derivatives of T
with respect to a, and v.
8a,
= 1,
8T
2
VI where p = log[£/(l — £)]. Let j8 be a column vector
of these derivatives,
0 = [Sr/Sa,
v\4a, + v\ log
(3)
The resulting expression (equation 3) defines r as
a function of £ (selected by the investigator) and
two model parameters, a, and v.
Once ML estimates, a, and v, have been obtained,
the ML estimate of T, denoted f, is just equation 3
8T/8V]',
and let S be the 2 x 2 large-sample variancecovariance matrix for the ML estimates a, and v.
The 8 method is essentially a theorem from mathematical statistics stating that the large-sample distribution of T is normal with a mean of T and a
variance of jS'SjS. The variance can be estimated
by picking S out of the estimated variance-co-
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0.2
December 1991
KEMP
&
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
150
200
250
300
250
300
0.0
100
150
200
250
300
150
200
250
300
1.0
D
0.8
— 0.6
O
Q. 0.4
O
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
Q_ 0.2
o.oU.
>\>tttHt^L
100 150 200 250 300 0.0
100
Julian Date
0.0
150
200
250
300
100
Fig. 5. Comparison of raw data (plotted points) and model results (solid line) for the proportion of the grasshopper
community in each developmental state as a function of Julian date, Havre, Montana, 1986 (log likelihood =
-52.63). (A) First instar. (B) Second instar. (C) Third instar. (D) Fourth instar. (E) Fifth instar. (F) Adult.
variance matrix obtained from fitting the model to means among sites, there was considerable overlap
data (see Dennis & Kemp 1988) and by substituting (Table 1). Based on these results, it appeared reaa, and v in fi. Then
sonable to use the six-species complex for further
comparisons of phenology among communities
from the nine sites.
Model Comparisons. The AIC was used to deis an approximate 100(1 — a)% confidence interval
for T. Here za/2 is the 100[l — (a/2)]th percentile of termine the number of parameters necessary to
describe the data for nine sites over 3 yr (Fig. 3).
the standard normal distribution.
Standard ANOVA and regression methods were Results showed that the most appropriate way to
used to compare species percentages among grass- describe the data was with the Dennis et al. (1986)
hopper communities and the timing of rangeland model fit to data from each site each year because
grasshopper phenological signposts (estimated from this method had the lowest AIC (Fig. 3). For comthe model). Where appropriate, multiple compar- parison, the AIC was computed for the saturated
isons were made with Tukey's studentized range model (the "saturated model" estimates r parameters, that is, r stage proportions, for every sample,
test (SAS Institute 1988).
subject to the constraint that the parameters add
to 1) with 2,664 parameters. Fig. 3 shows that there
Results and Discussion
is little improvement in the AIC with the addition
Communities. The six selected species consti- of >10 times as many parameters when compared
tuted >50% of the communities at the nine sites with the sites and years model. Therefore, the modduring 1986-1988 (Table 1). The proportion of the el that describes the data with 156 parameters (i.e.,
communities made up of the six species at Three the Dennis et al. (1986) model fit to data sets from
Forks was consistently high. Although there were individual sites and years) was the most appropriate
significant differences among the 3-yr proportion for our purposes. Fig. 4-7 show the range of log
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1.0
0.0U100
1509
DENNIS: MODEL OF RANGELAND GRASSHOPPER PHENOLOGY
1510
Vol. 20, no. 6
ENVIRONMENTAL ENTOMOLOGY
1.0
1.0
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
*
0.0
100 200 300 400 500
0
0.0
0
1.0
0
. t, .», , < .—rt-
0.0
100 200 300 400 500
0
100 200 300 400 500
100 200 300 400 500
0
100 200 300 400 500
1.0
100 200 300 400 500 0.0
Degree Days
0
Fig. 6. Comparison of raw data (plotted points) and model results (solid line) for the proportion of the grasshopper
community in each developmental state as a function of accumulated degree-days, Three Forks, Montana, 1987
(log likelihood = -497.94). (A) First instar. (B) Second instar. (C) Third instar. (D) Fourth instar. (E) Fifth instar.
(F) Adult.
likelihoods encountered and provide a contrast between results expressed in Julian date and degreedays.
Although describing the data by parameterizing
the Dennis et al. (1986) model for each year and
site is appropriate (Table 2), this poses problems
for the pest manager. It suggests that every site
and year is different, even when trying to estimate
phenology for the six-species complex. Although
this is true to some degree, we examined the results
further to consider the variation in estimates of
specific developmental signposts that are important
to resource managers involved in grasshopper pest
management.
Population Signposts. Julian date and degreeday estimates for the six rangeland grasshopper
signposts at each of the sentinel sites are contained
in Table 3. For each signpost, comparisons of Julian
date means among the sites showed there were no
significant differences. Further, although significant differences were found among sites for the
mean number of degree-days across sites for sign-
posts peak third instar through 75% adult, there
was considerable overlap and no clear patterns
emerged. In all cases where there were significant
differences in degree-days, it was the result of contrasts between Three Forks and Jordan or Broadus.
Overall, the average occurrence dates (nonleap
year) for the six phenological signposts are JD 138
(May 18) for 75% first instar, JD 146 (May 26) for
peak second instar, JD 158 (June 7) for peak third
instar, JD 167 (June 16) for peak fourth instar, JD
177 (June 26) for peak fifth instar, and JD 188 (July
7) for 75% adult (Table 3).
With the same data used to construct Table 3,
we computed the Julian date and degree-day differences between each of the major grasshopper
development signposts (Table 4). In all cases, sites
were not significant (Table 4). This suggests that
once hatching occurs, there is a fairly orderly progression in the phenological sequence for the sixspecies complex over the period of study. The mean
Julian date and degree-days separating developmental signposts are similar to those used by On-
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1.0
December 1991
150
200
250
&
1511
DENNIS: M O D E L O F R A N G E L A N D GRASSHOPPER PHENOLOGY
300
100
150
200
250
300
100
150
200
250
300
0.0
100 150 200 250 300 0.0
. .. ~ .
100 150 200 250 300
100 150 200 250 300
Julian Date
Fig. 7. Comparison of raw data (plotted points) and model results (solid line) for the proportion of the grasshopper
community in each developmental state as a function of Julian date, Three Forks, Montana, 1987 (log likelihood
= -497.94). (A) First instar. (B) Second instar. (C) Third instar. (D) Fourth instar. (E) Fifth instar. (F) Adult.
sager (1983) in simulation studies of rangeland
grasshopper growth, survival, and forage consumption.
Grasshopper populations drastically declined
throughout Montana between 1988 and 1989.
Therefore, we were able to compare only the general results collected from 1986 to 1988 with data
from three sites collected during 1989 (Table 5).
The term "observed," in this case, refers to the
estimate for this stage computed by fitting the Dennis et al. (1986) model to 1989 data, then calculating the signpost estimates (Dennis & Kemp 1988
and as above).
Given the "observed" date of peak second instar,
the average differences between signposts (Table
4) were then used to "forecast" occurrence dates
of the peak third instar through 75% adult signposts
in 1989 (Table 5, forecasted Julian date). We had
hoped to start with the observed date of 75% first
instar at each of the three sites as a given and then
use the average differences between signposts found
in Table 4 for forecasting. However, low densities
and poor weather conditions (that prevent sam-
pling) prevented us from obtaining precise observed estimates of the timing of 75% first instar
during 1989 (estimates had very large confidence
intervals). Therefore, forecasts (Table 5) were initiated with the observed dates for peak second instar at each of the three sites. Comparisons between
observed and forecasted signposts shown in Table
5 suggest that the average Julian date differences
between the phenological signposts for the 26 siteyears reported in Table 4 have value in forecasting
the phenological progression of populations over a
wide range of conditions in Montana. However,
this result must be tempered by the understanding
that the use of Table 4 depends on a reasonable
knowledge of the timing of peak second instar and,
ultimately, of hatching.
Further work will be required before we are
able to estimate the differences among sites in
grasshopper hatching dates in an environmentally
heterogeneous state like Montana (Hewitt 1979).
However, Kemp et al. (1992) found that the beginbloom phenophase of purple common lilac, Syringa vulgaris (L.) (a commonly grown ornamental
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100
KEMP
1512
Vol. 20, no. 6
ENVIRONMENTAL ENTOMOLOGY
Table 2. Parameter estimates and asymptotic standard errors ( ) for nine sites during 1986-1988 in Montana for
a model (Dennis et al. 1986) describing a six-species population complex of rangeland grasshopper phenology0
Site
Glasgow
<*3
o4
188.260
(3.485)
249.366
(4.794)
267.839
(7.452)
265.072
(4.058)
316.813
(4.457)
364.896
(6.498)
372.493
(3.917)
395.998
(5.138)
488.741
(7.646)
7.451
(0.405)
3.535
(0.306)
4.694
(0.449)
51.278
(4.898)
95.712
(2.832)
71.138
(2.859)
146.707
(3.091)
176.433
(3.908)
123.654
(4.755)
161.178
(7.782)
138.876
(2.644)
129.873
(2.724)
203.346
(6.001)
200.381
(3.542)
231.597
(3.789)
255.151
(5.633)
270.098
(3.403)
323.193
(4.190)
314.051
(4.779)
325.370
(3.967)
448.043
(6.176)
1.715
(0.256)
4.359
(0.320)
3.095
(0.230)
69.793
(4.745)
107.939
(4.714)
124.577
(3.453)
154.760
(3.825)
196.425
(3.660)
218.864
(4.467)
290.312
(5.701)
275.745
(5.618)
400.393
(5.289)
372.614
(5.252)
5.570
(0.416)
5.771
(0.493)
1988
13.666
(7.197)
67.972
(7.560)
241.412
(14.355)
357.321
(10.565)
500.989
(12.010)
9.069
(1.196)
1986
143.102
(5.199)
158.269
(4.100)
207.028
(5.155)
242.051
(3.323)
304.504
(5.790)
318.701
(3.323)
397.850
(4.254)
398.571
(3.896)
521.794
(3.707)
512.547
(5.499)
4.799
(0.310)
5.722
(0.336)
139.843
(3.148)
175.744
(2.039)
62.858
(1.749)
196.310
(2.342)
208.703
(2.329)
122.546
(2.791)
264.308
(2.407)
268.045
(2.631)
212.462
(3.184)
344.171
(2.577)
332.567
(2.854)
297.464
(4.323)
434.007
(2.830)
418.284
(3.762)
431.538
(5.457)
4.272
(0.189)
3.027
(0.171)
5.238
(0.307)
157.184
(2.205)
150.015
(1.977)
94.702
(2.197)
211.294
(2.636)
223.315
(2.661)
150.150
(2.813)
271.708
(3.715)
305.336
(3.635)
229.577
(3.539)
356.782
(4.702)
336.837
(3.696)
348.428
(4.245)
474.503
(3.779)
427.881
(4.720)
521.072
(7.458)
4.856
(0.257)
6.543
(0.374)
7.834
(0.439)
1986
94.197
(2.816)
127.214
(3.811)
233.954
(8.756)
301.769
(6.472)
390.719
(3.859)
3.780
(0.325)
1987
137.081
(1.846)
57.957
(2.814)
169.015
(1.437)
112.905
(3.305)
209.679
(1.673)
196.915
(3.960)
260.499
(2.766)
283.165
(4.456)
353.234
(3.866)
408.574
(6.319)
1.654
(0.118)
6.884
(0.469)
126.817
(2.552)
164.162
(6.467)
56.892
(5.354)
167.605
(2.175)
231.130
(4.497)
112.451
(4.097)
221.926
(1.894)
305.619
(3.421)
176.534
(3.755)
272.984
(2.558)
370.631
(3.609)
262.853
(5.518)
333.563
(2.486)
428.101
(4.298)
372.283
(7.117)
2.202
(0.134)
4.834
(0.367)
6.504
(0.596)
91.606
(1.215)
92.040
(0.954)
97.670
(0.902)
121.316
(1.107)
111.868
(0.868)
151.460
(1.001)
169.940
(1.268)
145.184
(0.896)
189.215
(1.141)
220.141
(1.463)
195.567
(1.477)
255.945
(1.564)
297.670
(1.745)
258.721
(1.893)
354.496
(2.714)
3.540
(0.117)
3.215
(0.111)
2.069
(0.083)
Year
a\
1986
102.527
(2.771)
125.625
(3.992)
65.718
(3.792)
1987
1988
Havre
1986
1987
Miles City
1986
1987
Jordan
1987
Fort Benton
1986
1987
1988
Broadus
1986
1987
1988
Billings
1988
Great Falls
1986
1987
1988
Three Forks
1986
1987
1988
Estimates are in degree-days starting 1 January, 17.8°C base (Allen 1976).
shrub), preceded the estimated hatch (date of 75%
first instar) of this six-species complex of grasshoppers by «10 d (24 site-years). Therefore, it seems
that the use of a plant phenological indicator like
the begin-bloom phenophase of purple common
lilac is appropriate for estimating an initial reference date for this six-species complex of rangeland
grasshoppers. Given an estimated hatch date, resource managers can then use differences between
the phenological signposts (Table 4) to forecast the
occurrence of the remaining signposts in a given
year. Because the timing of the begin-bloom phase
of purple common lilac is a good indicator of accumulated heat (if not water-stressed [Caprio et al.
1970]) and was significantly related to hatch (y =
30.36 + 0.84x, where y = JD 75% first instar [spring
hatch] and x = JD of the begin-bloom phase of
purple common lilac; F = 0.0001, r2 = 0.51), it is
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1988
V
December 1991
Table 3. Mean estimated developmental signposts (average of n years) for irangeland grasshoppers in Montana (1986-1988) in Julian and degree-days
Hatch
(75% 1st instar)
Site
JD
n
Glasgow
3
(9.5)
3
136
Miles City
1
125
(-)
Jordan
2
141
(8.6)
(13.4)
Fort Benton
3
137
(12.2)
Broad us
3
138
Billings
3
137
(12.5)
(9.9)
Great Falls
3
146
(10.6)
Three Forks
3
139
(11.1)
No
24
138
(9.8)
76.7
(28.0)
58.3
(17.0)
84.0
3
148
3
144
3
133
2
152
(8.5)
(13.2)
(2.8)
3
148
(10.1)
3
145
3
143
(10.8)
(8.5)
3
157
(10.4)
3
143
(10.8)
No
No
88.4
(34.0)
(SD)
(4.6)
(-)
123.0
(8.5)
104.3
(53.8)
106.0
(32.5)
79.3
(41.1)
95.0
(50.2)
77.3
(4.9)
26
JD
146
(10.3)
DD
JD
(SD)
117.7
(29.0)
104.3
(8.1)
82.3
(47.6)
182.0
(17.0)
146.3
(53.0)
157.7
(37.8)
112.0
(36.8)
138.3
(57.3)
108.0
(12.3)
No
125.5
(42.2)
158
(3.2)
161
(6.4)
148
(5.0)
165
(2.1)
157
(8.6)
159
(8.3)
156
(6.8)
166
(7.6)
151
(14.3)
No
158
(8.5)
DD
Peak
5th instar
JD
Yes
189.1
(42.2)
165
(4.2)
170
(4.7)
161
(5.3)
172
(4.2)
166
(7.5)
166
(7.5)
165
(8.1)
177
(6.5)
162
(6.1)
No
167
(7.0)
75% adult
JD
(SD)
(SD)
186.0
(24.6)
174.0
(7.9)
159.0
(20.0)
262.0
(17.0)
207.3
(40.4)
224.7
(39.2)
170.3
(21.1)
197.7
(62.7)
145.0
(21.7)
DD
269.7
(46.7)
243.7
(26.3)
255.7
(28.9)
349.5
(4.9)
282
(28.6)
301.3
(18.7)
243.3
(17.9)
264.7
(62.1)
192.7
(26.5)
Yes
263.7
(47.9)
175
(3.8)
179
(3.8)
171
(5.0)
183
(2.1)
178
(5.5)
175
(6.0)
173
(7.4)
187
(9.5)
171
(5.6)
No
177
(7.1)
DD
(SD)
361.7
(55.5)
319.3
(54.5)
358.7
(53.3)
451.5
(3.5)
371.3
(13.0)
403.7
(26.1)
328.3
(20.3)
335.0
(51.3)
260.7
(39.8)
Yes
350.7
(59.6)
187
(9.5)
189
(4.5)
182
(6.1)
199
(4.2)
189
(10.5)
187
(8.2)
182
(8.4)
201
(8.5)
182
(7.4)
No
188
(9.3)
n
<V
i—i
472.7
(61.8)
400.7
(81.5)
488.0
(81.2)
578.0
(2.8)
476.7
(15.4)
538.7
(53.5)
429.0
(45.3)
425.3
(58.1)
338.0
(47.0)
Yes
456.3
(81.6)
U
M
z
5*
O
o
M
r
•iSO
z
o
rM
z
O
50
o>•/
"-B
""O
M
SO
X
M
I—'
03
Downloaded from https://academic.oup.com/ee/article/20/6/1504/2394163 by guest on 07 February 2022
Significant differences among
sites (a = 0.05)
All sites/years
71
DD
Peak
4th instar
IIS:
Havre
JD
DD
(SD)
137
Peak
3rd instar
Peak
2nd instar
1514
Vol. 2 0 , no. 6
ENVIRONMENTAL ENTOMOLOGY
Table 4. Differences between predicted occurrence dates for populations of rangeland grasshoppers in Montana,
1986-1988
Sites
Interval
75% 1st instar-peak 2nd instar
Peak 2nd instar-peak 3rd instar
Peak 3rd instar-peak 4th instar
Peak 4th instar-peak 5th instar
Peak 5th instar-75% adults
n
Julian date
(SD)
24
26
26
26
26
8.5 (4.9)
12.1 (5.9)
9.2 (3.9)
9.7 (1.8)
11.9(3.4)
Degree-days
(SD)
42.5
63.5
74.6
87.1
105.5
(10.6)
(19.3)
(24.5)
(23.9)
(28.5)
Values are not significantly different (df = 8, a = 0.05; ANOVA [SAS Institute 1988]).
Table 5. Comparison of "observed" 1989 versus fore
casted occurrence dates for major phenological events of
a six-species complex of grasshoppers at three sites in
Montana
Stage
Observed
Julian date
for site/year
Peak 2nd instar
Peak 3rd instar
Peak 4th instar
Peak 5th instar
75% adult
Fort Benton"
159
174
185
194
205
Peak 2nd instar
Peak 3rd instar
Peat 4th instar
Peak 5th instar
75% adult
Havre
162
170
181
188
202
Peak 2nd instar
Peak 3rd instar
Peak 4th instar
Peak 5th instar
75% adult
Three Forks
155
173
183
188
197
Forecasted
Julian date
from general
differences
—
171
180
190
202
6
—
174
183
193
205
per phenological signposts provided reasonable
forecasts of grasshopper development. These re
sults, combined with a separate but related study
linking spring hatch with the begin-bloom phenophase of purple common lilac, provide a reason
able general model of rangeland grasshopper phe
nology in Montana.
Implications for Pest Management. Until this
study was conducted, there was little specific in
formation on the phenological progression of grass
hoppers that could be used in a pest management
context (Shotwell 1941; Newton et al. 1954; Hewitt
1979, 1980). T h e results of our study can be used
by resource managers as they attempt to imple
ment the recommendations of Onsager (1986,
1987a,b) for the timing of rangeland grasshopper
assessment and control activities.
Predicting the phenological progression of spe
cies assemblages will continue to challenge both
researchers and land managers interested in pest
management. At present, however, predicting the
phenological progression of the six-species complex
appears reasonable in view of the variation found
(Tables 3 and 4) and the occurrence patterns of
these species at each site throughout the study (Ta
ble 1). Depending on their location, resource man
agers may find that local conditions more closely
resemble the observed differences between sign
posts at an individual site (Table 3) rather than the
overall mean differences shown in Table 4. Future
work with environmental covariates (Kemp et al.
1990a,b) may offer a way of improving forecast
accuracy and, at the same time, help us understand
this extremely complex grassland-herbivore sys
tem. Furthermore, the establishment of the U S D A A F H I S - P P Q sentinel site system (for grasshop
pers) is a very important first step in understanding
the large-scale variability that must be addressed
if future rangeland pest management programs are
to be successful.
c
0
b
c
Six species, 85% of population.
Six species, 77% of population.
Six species, 98% of population.
—
167
176
186
198
Acknowledgment
We thank J. S. Berry, J. Holmes, K. Curtiss, T. Engle,
D. Gillis, and V. Hagestad for technical assistance. The
reviews and comments of earlier drafts of this manuscript
by J. Lockwood, J. S. Berry, and P. Evenson are sincerely
appreciated. Thanks also go to S. Osborne for manuscript
preparation. The sentinel site system in Montana is a
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reasonable to consider the use of this indicator
(Kemp et al. 1992) pending the development of
more sophisticated models for the prediction of
springtime hatch of rangeland grasshoppers. T h e
use of a plant that is a good indicator of accu
mulated heat to initiate grasshopper forecasts has
merit in that year-to-year differences in accumu
lated heat before hatch will result in the earlier or
later occurrence of the plant phenological stage.
By observing lilac plants, land managers can de
termine whether conditions of a given year vary
substantially from individual site means for hatch
ing or for hatching in general (Table 3) and make
appropriate adjustments in forecasting the occur
rence of the remaining signposts.
In summary, the AIC showed that the Dennis et
al. (1986) model provided good estimates of rangeland grasshopper phenology on an individual siteyear basis, based on accumulated heat. Further,
average Julian date differences between grasshop-
December 1991
KEMP & DENNIS: M O D E L O F RANGELAND GRASSHOPPER PHENOLOGY
cooperative program between USDA-ARS and USDAAPHIS-PPQ. This work was supported in part by a co
operative agreement with the Grasshopper IPM Dem
onstration Program, USDA-APHIS-PPQ, Boise, Idaho.
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1515