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Received: 13 October 2016 Accepted: 19 March 2017 DOI: 10.1111/jen.12403
ORIGINAL CONTRIBUTION
Statistical indicators for insects caught in the development trap R. P. Blackshaw1
| P. Esbjerg2
1 Blackshaw Research and Consultancy, Chudleigh, Devon, UK
Abstract
2
Department of Plant and Environmental Sciences, Copenhagen University, Frederiksberg C, Denmark
The effects of climate change on insect phenologies are of current interest, but little
Correspondence Rod P. Blackshaw, Blackshaw Research and Consultancy, New Pound Parade, Chudleigh, Devon, UK. Email:
[email protected]
merical simulation modelling to show that increased mortality from a partial second
attention has been given to the potential driver for population decline of increased mortality arising from the failure to reach a viable overwintering stage. We use nugeneration results in the weakening of density dependence, whereas increasing mortality within the first generation does not. These general results are then compared with annual trap count data for the moth Agrotis segetum (Denis and Schiffermüller) in Denmark, a species which is in decline there because a partial second generation fails to survive the winter. Results from the moth data are consistent with those from the simulations, and we conclude that the development trap phenomenon can be detected by the application of simple statistical tests to time-series data. KEYWORDS
Agrotis segetum, climate change, density dependence, lost generation hypothesis, modelling, time-series data
1 | INTRODUCTION
whereby ectotherms can be driven into population decline as the climate changes, despite a shortening life cycle.
Phenological responses of insects to climate change have been
This is a phenomenon that may afford an additional explanation
the focus of many studies (O’Connor, Selig, Pinsky, & Altermatt,
for some observed population declines, and so there is a question of
2012). Typically, these have investigated changes in emergence date
whether such effects can be detected at the species level using exist-
(Altermatt, 2010a, 2012; Karlsson, 2014; O’Neill et al., 2012; Roy
ing time-series data. In this article, we take a simple population model
& Sparks, 2000; Westgarth-Smith, Roy, Scholz, Tucker, & Sumpter,
for a univariate insect, modify it to incorporate increased mortality
2012), synchronization with resources (Altermatt, 2010b; Forrest &
within or between the generations and use numerical simulations to
Thompson, 2011; Hegland, Nielsen, Lazaro, Bjerkness, & Totland, 2009;
investigate whether such mortality effects show systematic patterns
Van Asch & Visser, 2007; Visser & Holleman, 2001) and geographic
that are detectable using simple statistical analyses. These results are
range (Asher, Fox, & Warren, 2011; Menendez et al., 2007; Williams &
then compared with data for a moth species, Agrotis segetum (Denis
Liebhold, 2002).
and Schiffermüller), which is in decline as a result of a development
Some authors have assumed that warming, at least in temperate
trap (Esbjerg & Sigsgaard, 2014).
regions, will enhance population growth, especially if an additional
Agrotis segetum, commonly known as the turnip moth, is a pest
generation is added (Juszczak, Kuchar, lesny, & Olejnik, 2013; Kiritani,
species with a wide distribution in north-west Europe. Historically
2013; O’Connor et al., 2012). However, in some circumstances, ac-
it was thought of as a problem arising from a single generation (e.g.
celerated development may result in population decline. An import-
see Jones & Jones, 1974) but is increasingly seen to have a second
ant aspect is whether an overwintering stage can be reached before
generation flying in late summer which has been attributed to an ear-
conditions deteriorate (Altermatt, 2010a). This idea was recently for-
lier emergence date and a shortened generation interval (Esbjerg &
malized as the “lost generation hypothesis” leading to the concept of
Sigsgaard, 2014). The soil-dwelling larvae show an increasing capacity
a development trap (Van Dyck, Bonte, Puls, Gothard, & Maes, 2015)
to cope with adverse conditions as they develop through instars but,
272 | wileyonlinelibrary.com/journal/jen © 2017 Blackwell Verlag GmbH
J Appl Entomol. 2018;142:272–276.
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in Denmark at least, need to reach the sixth instar if they are to survive winter conditions (Esbjerg & Sigsgaard, 2014).
simple univariate insect model, and then show that analyses of changes in moth count levels over time conform to expected outcomes from the numerical simulation modelling. We conclude that there are simple
Mean count
In this study, we demonstrate that the population dynamics of the moth have a density-dependent component justifying the use of the
statistical indicators that can be used to identify species that may be subject to the development trap effect.
2 | MATERIALS AND METHODS
Sampling year
2.1 | Simulating the timing of mortality We take a density-dependent model developed to describe annual
F I G U R E 1 Long-term trends in annual sex pheromone trap catches of Agrotis segetum in Denmark [Colour figure can be viewed at wileyonlinelibrary.com]
changes in populations of the univoltine Tipula paludosa Meig (Blackshaw & Petrovskii, 2007). The generic form of this model is as follows: ) ( Nt ΔNt + 1 = α − β log log Nt
(1)
and in its stochastic form: ( ΔNt = Nt
[ α+r
10
Nt
)
]−β
−1
(2)
In this model, α is the regression intercept and functions as a population-limiting factor. In other words, the higher the value of α, the more extreme the environmental conditions are and the greater will be within-generation mortality. β is the regression slope representing the intensity of the density-dependent feedback, is the long-term mean population and r is a random variable drawn from a uniform distribution. As this model describes the density-dependent annual fluctuations in numbers of a univoltine species, it can simulate what happens when additional mortality is introduced either within the generation (year) by altering the value of α to represent mortality from differently limited environments or by applying an additional mortality factor after Nt+1 has been calculated to represent mortality arising from a partial second generation. The T. paludosa model presented by Blackshaw and Petrovskii (2007) had empirical values of −0.822 for β, −0.0252 for α and r ranging between −22.2% and +22.2%. We used these values in numerical simulation models except where indicated below. Three sets of numerical simulations were run: (i) varying α over 5 levels from 0 to −2 with an average population () of
F I G U R E 2 Outcomes from numerical simulations that varied α over five levels from 0 to −2 in Equation 2 to represent increased within-generation mortality. The data show the mean slopes and R2 values (±SE) from regressions of ΔNt on Nt
0.5 × 106 ha−1, (ii) varying mean population level with = 0.25, 0.5
Ten replicate simulations were run for each of these consisting of
and 1 × 106 ha−1, applying a partial second-generation mortality factor
1,000 time steps so that each simulation resulted in 1,000 values of
of 0%–90% by reducing the calculated population at Nt+1 prior to calculating the population at Nt+2, (iii) application of a maximum value for
Nt and 999 of ΔNt. Regression of ΔNt on Nt was performed and plots
made of the relationship between mean slope and mean R2 values
r of ±22.5, 45 or 90% with = 0.5 × 106 ha−1, applying the partial
against either the values for α (set 1) or percentage entering a second
second-generation mortality factor of 0%–90%.
generation (sets 2 and 3).
The intention behind this choice of models was to determine whether there were detectable systematic outcomes resulting from varying within-generation mortality, the proportion of a population
2.2 | Agrotis segetum dynamics
entering a non-viable second-generation stage and changing environ-
A full description of the A. segetum regional sampling programme is given
mental variability.
elsewhere (Esbjerg & Sigsgaard, 2014). To summarize: sex pheromone
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1
1 0.8
.5
0.6
Slope
0.4
Slope
0.2
0
0
–0.5
–0.2 –0.4
–1
–0.6 –0.8
.4
–1
R2
.3
.4
.2 .1
R2
.3
0
.2 .1 0
0
10 20 30 40 50 60 70 80 90 Percentage entering a second generaon
F I G U R E 3 Outcomes from numerical simulations varying the long- term mean population level () in Equation 2. The data show the mean slopes and R2 values from regressions of ΔNt on Nt with a partial second-generation mortality factor by having different proportions of the population entering a partial second generation. The three lines are = 0.25 × 106 (dot), 0.5 × 106 (dash) and 1 × 106 (solid) ha−1 [Colour figure can be viewed at wileyonlinelibrary.com]
traps were operated at sites in Denmark each summer yielding a total number of captured adult males in the first generation. The trapping
0
10
20
30
40
50
60
70
80
Percentage entering a second generation
90
F I G U R E 4 Outcomes from numerical simulations varying the stochastic element (r) in Equation 2. The data show the mean slopes and R2 values from regressions of ΔNt on Nt with additional mortality arising from different proportions of the population entering a partial second generation. The three lines are rmax = 22.5% (dot), 45% (dash) and 90% (solid) the next (ΔNt in Equation 2). The subsequent data were then tested for significance using log-log linear regression (Blackshaw & Petrovskii, 2007) to test whether density dependence is evident for A. segetum. This exercise was undertaken separately for the two time periods 1981–1991 and 1997–2009 and the combined data.
3 | RESULTS There were no significant effects of varying α in simulations on ei-
ther the slope or R2 value of the relationship between ΔNt and Nt
data we use in this study spanned two periods: 1981–1991 and 1997–
(Figure 2). Both the slope and R2 values changed with the percentage
2009. Sites differed between these two periods with seven sampled in
entering a partial second generation, but this was not dependent on
the earlier study compared with 20 from 1997 onwards. Not all sites
either the value of (Figure 3) or r (Figure 4).
were sampled each year. Mean annual counts showed a decline over time as well as a reduction in amplitude (Figure 1). The analytical method used for T. paludosa (Blackshaw & Petrovskii, 2007) was applied to the A. segetum sex pheromone trap counts. Data
The regressions of log(per capita increase + 1) against log(relative abundance) for all A. segetum data and the two time series are shown in Figure 5. The relationship was weaker for the 1997–2009 data than for 1981–1991 period.
points were included if they satisfied the condition of being able to calculate a population change from 1 year to the next. For each sampling site within the two time periods 1981–1991 and 1997–2009
4 | DISCUSSION
meeting this condition, the mean of the site time series was calculated. This provided the value for in Equation 2. A per capita increase
In addition to the long-term decline in numbers shown in Figure 1,
was then calculated from the difference in trap counts from 1 year to
we have demonstrated that there is density-dependent feedback
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Our numerical simulations show that systematic changes in the relationship between ΔNt and Nt are consistent with mortality arising from a partial second generation that does not survive the winter (Figures 3 and 4). Both the slope of the regression and its strength decline as the proportion entering the second generation increases. This effect is not observed when additional mortality is applied only within the first generation (Figure 2). The data for A. segetum follow a similar pattern with a decline in mean annual population size (Figure 1) and a weakening of the regression slope and its statistical significance (Figure 5). These observations are consistent with the hypothesis that the decline in observed numbers of this pest arises from increasing numbers entering a second (lethal) generation. Agrotis segetum has declined in importance as a pest as the surveys were started in 1981 to the point at which Danish farmers hardly anticipate problems (Esbjerg & Sigsgaard, 2014). There may come a point when sufficient change in the phenology has occurred to allow a second generation to reach the sixth instar and so survive the winter, becoming a serious pest once more. Interestingly, there is a suggestion from the simulation modelling that the density-dependent feedback could switch from negative to positive at percentages >80% entering the second generation, and so there may be the potential for sporadic outbreaks in advance of wider pest resurgence. The ability to reach a secure developmental stage for successful overwintering has only recently been recognized as a potential driver in the decline of some species. The bigger question is whether these findings have relevance to the reported declines of other Lepidoptera (e.g. Fox, 2013) and insects more generally. Where long time-series data sets exist for other species in decline, the approach we have developed here could be applied to seek evidence for systematic changes in the relationship between ΔNt and Nt. We suggest that reduction in the strength and significance of this regression over time is indicative of increased overwintering mortality. It is not, however, conclusive by itself and needs to be interpreted through understanding the biology and ecology of the species. Nevertheless, it is a tool that can help better focus research to aid both F I G U R E 5 Plots of log(per capita increase + 1) against log(relative abundance) providing evidence of density-dependent feedback and conformity to the general model: (a) all data, (b) 1981 to 1991 and (c) 1997 to 2009
conservation and pest management.
AU T HO R CO NT R I B U T I O N PE collected the data. RPB analysed the data and undertook the simulation modelling. Both authors contributed to writing the paper.
operating on A. segetum population dynamics (Figure 5) in a similar way to that shown for T. paludosa (Blackshaw & Petrovskii, 2007), legitimizing our modelling approach. The average strength of the density-dependent feedback for A. segetum is less than that previously reported for T. paludosa, regression slopes of −0.495 (Figure 5a) and −0.822 (Blackshaw & Petrovskii, 2007), respectively. The strength of the feedback relationship declined from the earlier trapping period (Figure 5b) to the later one (Figure 5c). The question that we ask in this study is whether this provides evidence of changes in the relationship that can be linked to the decline in numbers evident from Figure 1.
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How to cite this article: Blackshaw RP, Esbjerg P. Statistical indicators for insects caught in the development trap. J Appl Entomol. 2018;142:272–276. https://doi.org/10.1111/ jen.12403
