Individual-based modelling of moth dispersal to improve biosecurity incursion response

Authors

  • Sylvain Guichard,

    Corresponding author
    1. Scion, PB 3020 Rotorua, New Zealand
    2. CSIRO Ecosystem Sciences and CRC National Plant Biosecurity, GPO Box 1700, Canberra, ACT, Australia
      Correspondence author. E-mail: Sylvain.Guichard@hotmail.com
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    • Present address: CIRAD, UPR AGIRs, F-34398 Montpellier, France.

  • Darren J. Kriticos,

    1. CSIRO Ecosystem Sciences and CRC National Plant Biosecurity, GPO Box 1700, Canberra, ACT, Australia
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  • Agathe Leriche,

    1. CSIRO Ecosystem Sciences and CRC National Plant Biosecurity, GPO Box 1700, Canberra, ACT, Australia
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    • Present address: IMEP, CNRS, UMR 6116, University of Aix Marseille 3, F-13545 Aix en Provence, France.

  • John M. Kean,

    1. AgResearch, Private Bag 4749, Christchurch, New Zealand
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  • Susan P. Worner

    1. Bio-Protection Research Centre, Lincoln University, New Zealand
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Correspondence author. E-mail: Sylvain.Guichard@hotmail.com

Summary

1. Some biosecurity systems aimed at reducing the impacts of invasive alien species that employ sentinel trapping systems to detect the presence of unwanted organisms. Once detected, the next challenge is to locate the source population of the invasive species. Tools that can direct search efforts towards the most likely sources of a trapped invasive alien species can improve the chance of rapidly delimiting and eradicating the local population and may help to identify the original introduction pathway. Ground-based detection and delimitation surveys can be very expensive, and methods to focus search efforts to those areas most likely to contain the target organisms can make these efforts more effective and efficient.

2. An individual-based semi-mechanistic model was developed to simulate the spatio-temporal dispersal patterns of an invasive moth. The model combines appetitive and pheromone anemotaxis behaviours in response to wind, temperature and pheromone conditions. The model was trained using data from a series of mark–release–recapture experiments on painted apple moth Teia anartoides.

3. The model was used to create hindcast simulations by reversing the time course of environmental conditions. The ability of the model to encompass the release location was evaluated using individual trap locations as starting points for the hindcast simulations.

4. The hindcast modelling generated a pattern of moth flights that successfully encompassed the origin from 86% of trap locations, representing 95% of the 1464 recaptures observed in the mark–release–recapture experiments.

5. Comparing the guided search area defined using the hindcast model with the area of a simple point-diffusion search strategy revealed an optimized search strategy that combined searching a circle of 1 km radius around the trap followed by the area indicated by hindcast model predictions.

6.Synthesis and applications. Incorporating this novel moth dispersal model into biosecurity sentinel systems will allow incursion managers to direct search effort for the proximal source of the incursion towards those areas most likely to contain a local infestation. Such targeted effort should reduce the costs and time taken to detect the proximal source of an incursion.

Introduction

Management policies need to be supported by effective biosecurity systems to manage the increasing risk of biological invasions under globalization and climate change (Perrings et al. 2005; Lodge et al. 2006; Hulme et al. 2008). An important characteristic of an effective biosecurity system is the ability to detect and respond rapidly and effectively to an incursion when prevention fails, as this enhances the likelihood of eradication success (Myers et al. 2000; Byers et al. 2002). Modelling can help to optimize the balance between surveillance and eradication in a biosecurity strategy (Bogich, Liebhold & Shea 2008). We suggest that modelling can also improve incursion response capacity by optimizing surveys to determine the geographic source of the founder population of an incursion: increasing the likelihood of detecting the proximal source of the incursion and reducing the time and costs of the survey.

One way to detect some types of insect incursions is the use of sentinel traps baited with an odour attractant. This practice is used for targeted biosecurity threats such as gypsy moth Lymantria dispar (L.) (Maynard, Hamilton & Grimshaw 2004; Acosta & White, 2011) and fruit flies (Maynard, Hamilton & Grimshaw 2004; Suckling et al. 2008). Surveillance programmes typically deploy traps around perceived high-risk sites such as airports, seaports and shipping container transitional facilities and may cover hundreds of square kilometres (Bulman 2008; Wylie, Griffiths & King 2008). Depending on the lag time between incursion of founder propagules and detection, insects caught in these sentinel traps could be used to retrospectively inform biosecurity managers about the likely location of the local founder population. If the proximal source of an incursion can be identified, then the pathway of introduction can be investigated and perhaps attenuated, reducing the risk of future introductions. Knowledge of the spatial and temporal origin of an incursion can also guide efforts to delimit the extent of the incursion and model its subsequent spread.

Spatially explicit statistical methods such as geostatistics are appropriate for modelling insect dispersal patterns (Liebhold, Rossi & Kemp 1993), but are limited in highly variable environments and inappropriate in the biosecurity context when an incursion may be detected initially in a single trap only. We suggest, in this study, an original approach that can enable more rapid and efficient detection of founder populations; we developed a semi-mechanistic, individual-based dispersal model to simulate the dispersal paths of individual adult moths in relation to dynamic wind fields, air temperatures and time of day. This model can be run in a forward (forecast) or backward (hindcast) mode. In the forecast mode, the model simulates the paths by which a moth disperses from a point such as a pupation site or an intentional mark–recapture–release point. When run in hindcast mode, it simulates the paths by which a moth could have arrived at a sentinel trap. The model was based on insect flight behaviour, parameterized from published mark–release–recapture studies and subsequently validated and applied in hindcast mode. It was trained on a subset of mark–release–recapture data from Suckling et al. (2005) and validated on the remainder of the data. Although the mark–release–recapture experiment was undertaken with painted apple moth Teia anartoides (Walker) in New Zealand, characteristics of moth biology were taken from the European gypsy moth L. dispar (Linnaeus), another Lymantriid species that shares common traits, especially partially diurnal male flight and flightless females (Reineke & Zebitz 1998), and for which there is sufficient detailed knowledge of its flight behaviour.

The benefits of the model run in the hindcast mode were also evaluated as an operational biosecurity tool for the best delimitation strategy and potential to reduce the costs of surveillance.

Materials and methods

Modelling Approach

The model described in this study is a semi-mechanistic, individual-based model (IBM), written as a series of modules in the Python object–oriented programming language. The IBM approach introduces stochasticity in the model as each insect responds slightly differently to environmental conditions and behavioural rules. The semi-mechanistic nature of the model supports hindcasting by applying the same behaviour rules but reversing the flight direction, the wind direction and the chronology. The object-oriented language optimizes the algorithm by invoking the same modules in both forecast and hindcast modes.

The model was used in forecast mode to track an insect from a release location to a pheromone trap. It was used in hindcast mode to model the potential paths by which an insect could have dispersed to a pheromone trap. To distinguish between biological observations and the simulation modelling, we use the term ‘agent’ to describe an individual simulated flying moth.

Forecast Modelling

A male insect seeking a mate potentially flies some distance before encountering a pheromone plume. The appetitive behaviour (Elkinton & Cardé 1983) during this initial flying period may be random (Yamanaka, Tatsuki & Shimada 2003) or a net downwind flight pattern (Reynolds et al. 2007; Guichard et al. 2010a). Following this initial behaviour, moths typically start orienting their flight direction depending on the concentration of pheromones or other chemical elicitors encountered, which is termed ‘anemotaxis’. In this study, we used the collective appetitive behaviour inferred by Guichard et al. (2010a) on the same insect species and the same data set. In forecast mode, appetitive behaviour was simulated as passive downwind displacement at the current wind speed, with no response to pheromones. This assumption was based on the observation that recapture patterns between different replicates seemed to extend further downwind when the wind speed was greater (Guichard et al. 2010a). The downwind direction of the agent deviated for the whole downwind course by a randomly selected angle within a uniform distribution of a defined range (Table 1), referred to as the ‘downwind deviation range’. The sign of the deviation angle was also selected randomly. This modelling process was designed to account for insect downwind headings as well as the averaging of wind direction over the scale of 10 min.

Table 1.   List of parameters fitted by the genetic algorithm with their respective range and the value for the best fitted set of parameter. Ranges in which the genetic algorithm was allowed to select values were defined ad hoc
ParametersRange in the genetic algorithmBest fitted value
  1. *The anemotaxis timer is defined as the proportion of the population that exit the anemotaxis mode during 1 day; a value of 2 should be interpreted as the whole population that exits the anemotaxis mode in half a day.

Downwind deviation range (°)25, 4538
Downwind timer (probability per time step)0·0014, 0·00350·0026
Anemotaxis frequency of direction reversal (reversal by time step)1/10, 11/6
Minimum temperature (°C)8·0, 12·08·2
Maximum wind speed (m s−1)6·0, 10·07·2
Anemotaxis timer (day−1)*0·1, 2·01·0
Trap range (m)2·5, 5·04·4

The function used to shift between the appetitive and anemotaxic phases depends on whether the model is deployed in forecast or hindcast mode (Fig. 1). In forecast mode, all agents disperse downwind after they commence flying, with a constant probability of shifting to the anemotaxic phase at each time step, the ‘downwind timer’ in Table 1. Thresholds for insect flight were also defined for the minimum temperature and the maximum wind speed. The flight was stopped if the temperature was below the flight temperature threshold or if the wind speed exceeded the wind speed threshold. We assumed a flight period between 10·00 and 15·00 h daily, based on the main flight period of painted apple moth (Suckling et al. 2005).

Figure 1.

 Schematic diagram showing the succession of processes in hindcast and forecast modes. Forecast mode is the parameter fitting step: the insects start the simulation from the release location ‘R’; they fly downwind (a) until the downwind timer stops their flight; they start the anemotaxis behaviour, i.e. mainly crosswind (b) and mainly upwind (c), respectively outside (b) and inside of the pheromone plume (c, grey area); the simulation stops when they are caught in a trap ‘T’ (d) or when the anemotaxic flying time elapses (e, anemotaxis timer). Hindcast mode is the biosecurity application after the detection of an insect in a sentinel trap: insects start the simulation from the trap location ‘T’, they fly using the reverse of the anemotaxis flight (f), until the anemotaxis timer stops their flight; they subsequently start the reverse of the downwind flight (g) until the time for downwind flight elapses and the simulation stops (h, downwind timer); the probable origin of the caught insect is identified within the convex hull around all terminal locations (h).

When an insect in an appropriate physiological state (anemotaxic phase) detects the presence of its pheromone, it attempts to track the plume upwind to the source. This pheromone anemotaxis behaviour was originally studied by Kennedy & Marsh (1974) and has been subsequently described for a wide range of species (reviewed by Cardé & Willis 2008). Pheromone anemotaxis can be summarized as a series of upwind and sideways displacements elicited by the detection of a pheromone plume, interspersed with sideways casting behaviour during those periods when a pheromone has not been encountered for some time. Anemotaxis behaviour has been well documented at a fine scale (centimetres) but less so at a scale of metres. Here, we applied the behavioural rules quantified by David, Kennedy & Ludlow (1983) and Guichard et al. (2010b) for insect flight orientation and speed and extrapolated this behaviour up to a scale of two metres granularity for use in a broader setting (Fig. 2).

Figure 2.

 Behaviour rules applied for insects flying in the anemotaxis mode. Probability density functions of insect flying direction as a function of a flight inside (grey bars) or outside (white bars) of the pheromone plume (David, Kennedy & Ludlow 1983) and speed of the insect (black line) associated with its flying direction (Guichard et al. 2010b).

We used the anemotaxis rules (Fig. 2) based on the frequency distribution of flight direction by David, Kennedy & Ludlow (1983) for the deviation to the wind in the range 0–180° and associated ground speed derived by Guichard et al. (2010b) in the range 0–135°. To be consistent with the agent movement in the range 0–135°, ground speed was linearly extrapolated to 2·3 m s−1 for deviations between 135 and 180° from the wind. The time step for flight was set to 1·5 s to reproduce track segments at least 2 m long as defined in the study by David, Kennedy & Ludlow (1983) and Guichard et al. (2010b). Insect anemotaxis is a combination of mainly upwind behaviour when insects are inside a pheromone plume, and mainly crosswind behaviours when they are outside of a pheromone plume (David, Kennedy & Ludlow 1983). In the model, at each time step, the agent selects a flight direction randomly from one of these two frequency distributions depending on the pheromone concentration and the probability of detecting the pheromone. These rules (Fig. 2) defined the movement of the agent in the range 0–180° to the wind, and by reflection in the range 180–360°; we defined an additional probability of shifting from one side of the wind to the other, allowing the agent to reverse direction (Table 1).

Inside a pheromone plume, the insect experiences an environment composed of a complex fine-scale structure of successions of pheromone filaments separated by gaps of clean air (reviewed by Riffell, Abrell & Hildebrand 2008). To apply the model at the appropriate scale of several square kilometres, however, it was necessary to simplify the pheromone plume response by considering only its mean concentration. A pheromone detection function was used to switch the agent between inside and outside of plume behaviours. This was derived from observations of wing fanning behaviour (Hagaman & Cardé 1984) where the percentage of wing fanning was interpreted as the probability of the agent detecting the pheromone (see Appendix S1 in Supporting Information).

In forecast mode, agent flight was terminated by either mortality or trapping (Fig. 1). Total mortality represents all processes (such as predation and exhaustion) determining the difference between the number of insects released and the number recaptured. In the model, mortality was defined by the proportion of the population that died during 1 day and was applied on randomly selected agents by the reduction in the population every 10 min. Mortality affected essentially agents in anemotaxis phase: we called this function the ‘anemotaxis timer’. The agent was assumed to be captured in a trap if it flew within a defined distance to a trap. The temperature and wind speed thresholds, ‘anemotaxis timer’ and trap range parameters (Table 1) were all fitted during the model training.

Hindcast Modelling

In hindcast mode, agents were flown in reverse by reversing the chronology and wind directions. The appetitive and anemotaxic phases were also reversed, so that agents commenced in the anemotaxic phase. The ‘anemotaxis timer’ was used to identify when each agent should exit the anemotaxic phase and enter the appetitive phase, flying upwind until stopped by the ‘downwind timer’ (Fig. 1). Similarly, during the anemotaxic phase, agents respond to the concentration of the pheromone but in the reverse direction, and the trap capture routine is not applied.

The main difference between forecast and hindcast models is an overestimation of anemotaxic phase in the hindcast model, as it did not include trapping as a means of terminating anemotaxy. As the objective of the hindcast modelling was to encompass the origin, we judged this simplification appropriate.

Release–Recapture Data Set

The model was developed and tested using data from an incursion response for T. anartoides in Auckland, New Zealand (Suckling et al. 2005). Data from sixteen release–recapture events were used, from February and March 2003, the months in which the highest recapture rates were observed (Table 2). The 400-km2 study area was separated into three zones depending on the release location and associated recaptures: Hobsonville 36°47′35″S 174º39′12″E, Ranui 36°51′59″S 174°35′52″E and Waikumete Cemetery 36°54′04″S 174°38′42″E (Fig. 3). Within these regions, respectively, 116, 621 and 762 georeferenced virgin female-baited traps were deployed. Meteorological data were processed using CALMET and CALPUFF air quality modelling systems to generate spatio-temporal gridded estimates of wind and pheromone (see Appendix S2 in Supporting Information).

Table 2.   Number of male Teia anartoides moths released and recaptured at the different locations and release dates considered in the present study
Release dateLocation
HobsonvilleWaikumete CemeteryRanui
ReleaseRecaptureReleaseRecaptureReleaseRecapture
  1. The data set used to train the model is indicated by bold font and validation data set by normal font.

19 February 20034136343432
28 February 20031128103143632433039
6 March 200381481795131892175
13 March 200314443412921011440111
21 March 2003119125112959103613
28 March 200386619850154
Figure 3.

 Situation map of the three different zones (Hobsonville, Ranui and Waikumete Cemetery, respectively, from North to South) of the mark–release–recapture experiment (adapted from Suckling et al. 2005) highlighting the baited traps where recaptures were observed.

Parameter Fitting

A genetic algorithm was used to explore the ranges of the different parameters and was used to fit the parameters on four replicates (bold entries in Table 2, 659 recaptures). Only four replicates were used for parameter fitting because of the large computation time required. The Ranui zone was selected for validation, and the remaining eight replicates from Hobsonville and Waikumete Cemetery zones were also included in the validation data set (plain font entries in Table 2, 805 recaptures). Genetic algorithms are optimization methods inspired by genetic processes of evolutionary biology (inheritance, mutation, selection and crossover) where candidate solutions, called ‘genomes’, are grouped into a ‘population’ evolving according to the principle of survival of the fittest (Beasley, Bull & Martin 1993).

Genetic algorithms utilize a ‘population’ of vectors, each containing values for each of the parameters to be fitted. Each of the vectors was initialized with values that were randomly assigned to each parameter from within the ranges given in Table 1. The ‘fitness’ of each vector was determined by comparing the model projections with observations from the mark–release–recapture experiments where the model used the same meteorological conditions and the same initial number of agents as the field experiments (Table 2). The fitness score was used to rank the vectors, and the best vectors were hybridized and used in the next iteration of the algorithm. By repeating this procedure many times, it is possible to select sets of parameter values that produce models of maximum fitness (in this study defined as the level of model agreement with the field data).

The distance-weighted sum of squared differences on paired results (DSSDP) was used to fit the parameters. The DSSDP is a novel fitness function that performed better than the sum of squared differences and Cohen’s kappa for the adjustment of the model parameters in our genetic algorithm (see Appendix S3 in Supporting Information; Guichard et al. 2009).

Model Validation

With the best fitted set of parameters, hindcast simulations were run not only on the training data set (bold entries in Table 2) but also on all other scenarios (plain font entries in Table 2). Each recapture location from mark–release–recapture observations became a release location in hindcast simulations, and the release locations from mark–release–recapture experiment became the model target locations. For each recapture location, we tested whether the target location was included within the convex hull enclosing the cloud of agent locations at the end of the hindcast simulation for 1000 simulated insects.

Model performance was defined for each release–recapture experiment as the proportion of hindcast simulations that included the target location inside the convex hull. This was tested under two scenarios: first by considering only the spatial extent of the trap captures (naïve) and secondly by including consideration of the abundance of trap captures (abundance informed). For the naïve analysis, we identified the proportion of convex hulls that encompassed the origin and calculated the accuracy estimate. This frequency has a maximum of 1 if all hindcast simulations from different trap locations encompassed the origin. In the abundance informed analysis (precision estimate), the number of convex hulls included in the proportion that encompassed the origin was weighted by the trap recapture abundance for the scenario. The abundance informed analysis provides a correction for the fact that in an incursion setting, the hindcast simulation is likely to only have a single trap for initializing the simulations and that the spatial distribution of this trap in relation to the source site is likely to be described by the patterns of recaptures observed in the mark–release–recapture experiments. We would generally expect a better fit from the abundance informed assessment than the naïve assessment.

The hindcast model was designed to target the origin of a trap catch in a biosecurity context. To quantify the benefit of using the model, we compared the minimum survey areas indicated by the hindcast model and the use of a simple point-diffusion searching strategy. For the latter, this was simply the area of a circle with radius equal to the distance between the trap location and the origin location (Fig. 4). The minimum survey area indicated by the hindcast model was defined by the minimum area needed to encompass the origin when we decreased the number of agent locations included in the construction of the convex hull, from a convex hull with all the 1000 simulated agents to a smaller convex hull centred to the highest density of agent locations (Fig. 4). From a convex hull with an initial cloud of agent locations, the subset of agent locations with the highest aggregation was obtained by sequentially removing, dot by dot, the agent location furthest from the centre of mass of the cloud of agent locations (see Appendix S4 in Supporting Information).

Figure 4.

 Hindcast simulations, based on a release from the Cemetery Waikumete location (black square) on the 28 February 2003, from two different trap locations: (a) the trap (grey square) is located 632 m away from the release location and (b) the trap (grey square) is located 5892 m away from the release location (note the differences in scale between graphs a and b). Representation of the convex hull (thin line) for all the 1000 simulated agents (open circles) at the end of the simulation. Minimum survey areas to detect the origin with hindcast model (thick line) and simple point-diffusion (dashed circle).

Results

The goodness-of-fit for the best fitted parameter set for the training data set in forecast mode is summarized in Table 3. These were not the best fitting parameters in each of the four scenarios individually, but gave the best fit across the training data sets and performed well for three of four scenarios (Table 3).

Table 3.   Average estimates of the goodness-of-fit for the training data set (four replicates) simulated in forecast mode
Scenario
estimate
HobsonvilleWaikumete Cemetery
28 February28 February6 March13 March
  1. *Numbers in parenthesis are the values from mark–release–recapture experiment.

  2. DSSDP, distance-weighted sum of square differences on paired results (see Appendix S3 in Supporting Information; Guichard et al. 2009). The sum of squared difference is calculated on recaptures normalized by the number of released Teia anartoides in so that scenarios are comparable.

DSSDP [−∞, 100]−167636560
Total number of recapture192 (103)*233 (324)*97 (131)*159 (101)*
Number of trap with recapture24 (15)*57 (28)*38 (26)*41 (22)*
Shared extent area (%)39%57%70%61%
Kappa [0, 1]0·280·350·470·45
Sum of square difference [0, +∞]0·001750·010940·000580·00268

The best parameter set was used in hindcast mode from each of the traps where at least one recapture was observed using the meteorological conditions for the release day. Figure 4 illustrates the location of the 1000 agents for each of two traps at the end of the hindcast simulation and the minimum survey area. Searching the convex hull from the highest to lowest density of agent activity for all the 1000 agents would have successfully detected the release location of the mark–release–recapture experiment once the defined ‘minimum survey area’ is reached.

To estimate the performance of the hindcast model, the accuracy and the sensitivity estimates (naive and abundance informed analyses) were calculated on the 265 traps in which recaptures were observed and the 1464 insect recaptures on the whole data set, respectively. Overall, the release location was encompassed by the convex hulls for hindcast simulation for 86% of the trap locations, which represents 95% of all recaptures (Table 4). The same analyses were undertaken after splitting the data set by release time, distance and release locations that were considered important explanatory variables. When the data set was split by release time or by release locations, the accuracy and the precision were similar within the different subsets and the Pearson’s chi-square test was not significant (Table 4). However, when the data set was split by distance classes, performance was significantly different over the classes with respect to precision, but not accuracy: the failure of the model to encompass the source location was more accentuated for traps located further from release location in which only a few insects were recaptured (Table 4, Fig. 5).

Table 4.   Performance of hindcast modelling segregated by either the release time, trap distance, release location or over the whole data set. For each trap location, accuracy represented the correct hindcast model prediction of the origin in relation to the number of traps. For each recapture, precision represented the correct hindcast model prediction of the origin in relation to the number of recaptures
Data setAccuracy (total number of traps)Chi-square test on accuracyPrecision (total number of recaptures)Chi-square test on precision
  1. The Pearson’s chi-square test was conducted on the raw distributions of hindcast prediction and total number of trap or recaptures.

Release
19 February
88% (16)χ2 = 1·25
d.f. = 5
= 0·939
98% (95)χ2 = 1·13
d.f. = 5
= 0·951
Release
28 February
93% (59)99% (466)
Release
6 March
88% (67)98% (387)
Release
13 March
89% (61)91% (246)
Release
21 March
79% (34)93% (97)
Release
28 March
64% (28) 90% (173) 
Distance
(0–500 m)
99% (78)χ2 = 8·59
d.f. = 4
= 0·072
99% (1061)χ2 = 9·83
d.f. = 4
= 0·044
Distance
(500 m–1 km)
97% (62)95% (188)
Distance
(1–2 km)
85% (68)91% (126)
Distance
(2–4 km)
66% (47)71% (63)
Distance
(4–10 km)
10% (10) 10% (10) 
Hobsonville91% (53)χ2 = 0·16
d.f. = 2
= 0·921
98% (325)χ2 = 0·21
d.f. = 2
= 0·901
Cemetery Waikumete83% (120)94% (801)
Ranui87% (92)96% (338)
All data86% (265)95% (1464)
Figure 5.

 Location of the trap from which the hindcast model failed to encompass the release location into the convex hull with the maximum size. Black stars, black squares and black dots represent failures to detect the release points for Hobsonville, Ranui and Waikumete cemetery release locations, respectively. Open dots represent the trap from which the hindcast model successfully detects the release location. A combination of two symbols shows locations where the detection of the release location occurred for some weeks but not others.

The minimum area required to successfully identify the release location with our hindcast model was compared with the minimum area of the simple point-diffusion search strategy. The simple point-diffusion strategy is generally employed in current biosecurity operations to identify the source populations and to subsequently delimit the population. Differences between approaches are presented in Fig. 6. The differences in the area searched using the two approaches are similar for traps located close to the release location but increasingly favour the use of our model for traps located further from the release location. The search area using a point-diffusion strategy is smaller in 100 of 137 cases for distance between release and recapture locations below 1 km (110 of 227 cases for the whole data set, Fig. 6). This result indicates that critical distance between trap and release location, at which a point-diffusion searching strategy becomes less efficient than using the hindcast model, is around 1 km (Fig. 6). Given that it cannot be known until afterwards how far from the source location a moth is trapped, these results suggest that an optimum search strategy for detecting a moth in a surveillance trap is to search the nearest 1 km first, then, if nothing is found, to search beyond 1 km according to where the model suggests is the greatest probability of origin.

Figure 6.

 Difference in the minimum area with potential to detect the origin between the hindcast model (open circles) and a point-diffusion search strategy (black squares). Insert is focused on the comparison for situations where trap and origin were close.

Discussion

The parameterization of the model using mark–release–recapture data has resulted in a powerful model. In accordance with Guichard et al. (2009), we found that the DSSDP handled well the right-skewed distribution of the frequency of trap recaptures with respect to the distance to the release location (Fig. S3 in Supporting Information), as well as the inherent stochasticity in the real and simulated processes of insect dispersal and recapture.

We found that the trap range parameter (Table 1) and the variations in initial population and total number of recaptures between different scenarios (Table 2) greatly influenced the DSSDP scores (Table 3), explaining both why the fitness function performed well on one scenario only and why we found that the trap range parameter has a great influence between scenarios. However, variation in the trap range both between traps and over different days is not surprising, as the trap range is dependent on surface roughness and also on meteorological conditions such as the wind strength and its variability (Britter & Hanna 2003).

The hindcast model generally performed well but shows its limitations when modelling the origin from traps located further away from the release location. However, if the observed density of recaptures from the mark–release–recapture experiment reflects the probability of detecting an incursion in a sentinel trap, then in a biosecurity context, we have to concentrate search effort and resources on the most highly probable areas identified by the hindcast model. So, while the model has limitations, we recommend its use for improving the detection of proximal source populations. Indeed, the comparison between a point-diffusion searching strategy and the use of our model clearly indicates an advantage for targeting the source location using our modelling approach. However, for distances within 1 km of the trap location, even if our model can predict a search area in which the release location was located, a point-diffusion search was often more efficient. The best searching strategy would be a combination of a point-diffusion search up to a radius of 1 km and then the use of our model to direct the search pattern (Fig. 7). Applying our model in hindcast mode can improve the search for the source population. Once the source has been identified, our model could be used in forecast mode to delimit the area occupied by the invading organism and within which to concentrate eradication measures (Fig. 7). Before applying our model in this manner however, the parameters would need to be re-fitted using a slightly modified goodness-of-fit function that increased the sensitivity of the projections at the expense of model specificity. The rationale for this is that when delimiting the area occupied by an invasive organism during an incursion, the costs of underestimating the area occupied and perhaps missing some individuals may be far greater than overestimating it and searching an area that does not contain the target organism. Some aspects of operational searching have not been included in the two searching strategies, such as the presence of water bodies or any other landscape features that constitute unsuitable habitat. We recommend that the search area identified by the model be intersected with land-use layers and geographic barriers to dispersal to restrict the search area to suitable habitat.

Figure 7.

 Sequence of the use of hindcast and forecast modelling in different biosecurity applications. (a) After the detection of an incursion in a sentinel trap (inline image), a delimitation survey concentrates first inside of a 1-km circle (dotted line) and extends to survey areas of increasing size predicted by the hindcast model (dashed line). (b) Delimitation survey (thin line) stops when the perceived source (inline image) is found (e.g. the presence of old egg mass and damages). Detection of a secondary population (inline image) (e.g. fresh egg mass and adults) can also occur during this survey. c) Survey area (thin line) predicted by the forecast model from the identified source (inline image) and subsequent detection of other secondary populations (inline image) originating from the same source.

As far as we know, our model is the first biosecurity tool based on insect behaviour designed to improve delimitation surveys. Developed on painted apple moth, it provides the framework for application to other insect species. However, further research is required to (i) investigate the transferability of the parameters to other case study species, (ii) assess the sensitivity of the simulation results to the frequency with which meteorological data are collected and (iii) assess the sensitivity of simulation results to the density of meteorological stations in relation to landscape roughness characteristics. This knowledge can guide the development of a meteorological and simulation-based surveillance system with improved precision and response capability.

To support a timely biosecurity response, it is critical that the wind field data are processed into gridded form in near real-time. This modelling step is time-consuming, and to have it calculated automatically would cost little to maintain once processes of automatic capture and cleaning of field meteorological data are established. If appropriate precalculated meteorological data sets are available, then simulations could be commenced as soon as an incursion detection is reported.

The sensitivity of our model parameters to the specific organism needs to be tested through multiple case studies. Priority should be given to those species (i) that are thought to pose the greatest threat, (ii) for which attractants are available, (iii) for which early detection would be beneficial and (iv) that have been or can be readily researched. Thought should be given to applying effort across broad taxonomic groups. In our particular application, the pheromone anemotaxis behaviour for T. anartoides was based on detailed observations of the closely related gypsy moth. Further investigation into anemotaxis in other moth species would be beneficial for testing this assumption and quantifying the degree of commonality between species. If commonality is found between species, then the use of a representative parameter set would greatly facilitate the use of our mechanistic model for other target moths.

Although our IBM is complex in comparison with the diffusion approach, it is based on simple ecological processes and successfully links observed recapture patterns with insect behaviour. It has the advantage of providing a semi-mechanistic insect response to its environment, and as such provides a framework that is easily reversed to identify the potential origin of a target insect. At first glance, some other approaches, such as diffusion with wind drift, may appear significantly simpler to implement, but in practice, these too would require spatio-temporal estimation of wind strength and direction. A possible advantage of our semi-mechanistic approach is that it may be more accurate than simpler approaches across a wider range of environmental conditions. For example, diffusion approaches are likely to overestimate downwind dispersal and underestimate upwind dispersal in low winds. Clearly, a useful next step will be to compare the performance of our IBM approach with others such as wind-directed diffusion.

Finally, it is likely that the full potential of insect tracing models such as ours will only be realized with the use of automated traps that enable precise time-stamping of captures, such as those currently being developed for fruit fly monitoring (Jiang et al. 2008). This would allow the hindcast simulations to be more precisely synchronized with the environmental data sets, thereby initiating the models at the correct time and place.

Acknowledgements

We would like to thank B. Murphy and the anonymous reviewers for helpful comments on the paper. This work was funded by New Zealand’s Foundation for Research, Science & Technology through contract C02X0501, the Better Border Biosecurity (B3) programme (http://www.b3nz.org).

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