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The authors recognize Forest Protection Limited as a commercial funding source and the employer of R. Drew Carleton as well as providing in-kind contributions to this research program. This does not alter the authors' adherence to all PLOS ONE policies on sharing data and materials.

Conceived and designed the experiments: RDC SBH. Performed the experiments: RDC. Analyzed the data: RDC SBH. Contributed reagents/materials/analysis tools: RDC SBH PJS. Wrote the paper: RDC SBH PJS. Project coordinator: PJS. Protocol approval: PJS.

Estimation of pest density is a basic requirement for integrated pest management in agriculture and forestry, and efficiency in density estimation is a common goal. Sequential sampling techniques promise efficient sampling, but their application can involve cumbersome mathematics and/or intensive warm-up sampling when pests have complex within- or between-site distributions. We provide tools for assessing the efficiency of sequential sampling and of alternative, simpler sampling plans, using computer simulation with “pre-sampling” data. We illustrate our approach using data for balsam gall midge (

Insects and other pests are responsible for enormous financial and production losses in agriculture and forestry. However, pest control can be expensive and often engenders concern over environmental impacts. A central goal of modern integrated pest management is to deploy pest-control interventions as efficiently as possible, in order to reduce crop damage at minimum cost and with minimum collateral damage to the environment.

Perhaps the most basic requirement for any pest management program is the availability of a sampling method for assessing the level of infestation (either estimating mean pest density, or judging whether density exceeds a threshold beyond which intervention is deemed necessary). For simplicity, in this paper, we use vocabulary associated with insect pests, although our discussion is equally applicable to other types of pest. Estimating insect densities in the field is far from a simple task, and it involves decisions about when to sample during host or insect phenology (e.g.,

One important technique for efficient estimation is sequential sampling, which is widely applied in agriculture and forestry

The key to a sequential sampling scheme (whether designed for estimating density or evaluating density against a threshold) is a “stopping rule” that formalizes the decision to continue or stop sampling after each new sample is taken. For estimating density, the stopping rule takes the form “stop sampling if a confidence interval around the estimate is narrower than X”. For decisions about density thresholds, the stopping rule takes a slightly more complex form: “stop sampling if the cumulative insect count for _{1}(n)_{2}(n)_{1}(n)_{2}(n)_{1}_{2}

Specification of these stopping rules depends on the ability to fit insect densities to known distributions with well-estimated parameters ^{2}

Single-parameterization methods offer practical assessment tools that demand only moderate mathematical ability of practitioners in the field. Unfortunately, though, the assumption that a single parameterization can be applied to every population of a given insect is frequently violated. Instead, it is common for not just mean density but also the form of an insect's density distribution to shift in space (e.g., ^{2}_{0}_{0}

The high efficiency promised by sequential sampling may not always be realized. Parameterization may fail outright (for instance, if distributional parameters vary even within sites), within-site spatial autocorrelation may make even local parameterization misleading

In this paper, we develop new tools for assessing the feasibility of sequential sampling for a particular pest system, and furthermore, for assessing the performance of alternative sampling strategies for insect pests. Use of these tools will allow the deployment of sequential sampling when it can deliver savings in overall sampling effort, while recognizing cases where alternatives outperform sequential sampling: for instance, when adequate estimates of mean density can be made with sample sizes too small for good estimates of nuisance parameters like

We illustrate our approach with data for the balsam gall midge,

In eastern Canada, the sale of Christmas tree and wreath products from

At low densities,

For several reasons,

We surveyed

We began data analyses by assessing the fit of our

We then asked how well we could estimate

We tested for spatial autocorrelation in infestation rates within each site using function ‘mantel.rtest’ of R package ‘ade4’. We visualized spatial pattern via semivariograms using function ‘variog’ of package ‘geoR’ in R. All of our R scripts are provided (

The distributional complexity revealed by the foregoing analyses motivated us to explore alternative approaches to estimating

Our random sampling procedure drew trees with replacement from the larger data set for each site (

Ordered sampling by collection number included trees in the same order as they were encountered in our original field sampling. In each case, this meant a back-and-forth raster starting at one corner of the stand, sampling along an edge, moving 10 m deeper into the stand and returning parallel to the edge, and so on until the entire stand had been sampled (

Ordered sampling by belt transect included trees as encountered along a series of parallel belt transects through the stand (

For each simulated sampling approach, we added trees one at a time to the sample (

Our seven sampled Christmas tree farms experienced

Site | N | Mean gall count | Estimated |
?^{2} |
df | Mean % galling | Precision of estimate | Estimated |
?^{2} |
df | ||

A | 100 | 38.2 | 0.511 | 152 | 54 | ^{−10} |
3.80 | ±23% | 0.763 | 15.9 | 14 | 0.32 |

B | 200 | 43.0 | 0.888 | 197 | 84 | ^{−10} |
4.95 | ±12% | 1.46 | 22.6 | 18 | 0.21 |

C | 200 | 77.6 | 1.07 | 270 | 115 | ^{−13} |
7.02 | ±13% | 1.44 | 44.2 | 26 | |

D | 200 | 54.2 | 0.773 | 241 | 97 | ^{−13} |
4.53 | ±15% | 1.15 | 33.8 | 19 | |

E | 200 | 11.0 | 0.595 | 85.9 | 39 | ^{−5} |
1.04 | ±17% | 1.37 | 7.35 | 6 | 0.29 |

F | 100 | 11.8 | 0.686 | 63.9 | 32 | ^{−4} |
1.12 | ±22% | 2.72 | 4.55 | 4 | 0.34 |

G | 200 | 17.4 | 0.510 | 142 | 50 | ^{−9} |
1.80 | ±19% | 0.73 | 16.2 | 12 | 0.18 |

Both raw gall counts and percentages of galled needles showed highly right-skewed distributions, and neither could be credibly fit to normal distributions (results not shown). Attempts to fit raw gall counts to a negative binomial distribution also failed (

Site B is typical of sites with acceptable fits, whereas Site C is the worst-fitting site. Fits for all seven sites appear in

Estimates of the negative binomial clumping parameter,

Horizontal line indicates the true value of

We detected significant within-site spatial autocorrelation at four of our seven sites (

Site | Mantel correlation | |

A | ||

B | 0.0389 | 0.071 |

C | 0.00280 | 0.45 |

D | 0.0135 | 0.31 |

E | ||

F | ||

G |

Random sampling produced, as expected, infestation estimates that approached the true mean with increasing

Dashed lines show two representative randomizations; 95% of the 10,000 randomizations lie between the solid lines. Confidence envelopes still have finite width at

Expected errors in infestation estimates for random sampling decrease rapidly with ^{th} percentile for random sampling and very often below the average for random sampling. Transect sampling performed even better (^{th} percentile for random sampling and was below the average for random sampling more often than above, even for small

Our sampling data indicate that both within- and between-site distributions of

Our

Fortunately, our simulations showed that simpler approaches to sampling provide adequate density estimates for

We can offer a very simple recommendation for Christmas tree farmers in Atlantic Canada.

There is an enormous amount of literature on the design of sampling strategies for the estimation of population densities in nature. Its existence is good evidence that sampling well is difficult - and being confident that you are sampling well is no less so. Although more accurate estimates usually come from larger sample sizes and more sophisticated sampling, this rule is not inescapable. As a result, tools that allow practitioners to increase efficiency and to assess sampling strategies in advance of large-scale field work will always be valuable.

Our work with

Of course, the specific sampling scheme we recommend for

Pre-sampling and simulation methods offer the chance to compare and optimize potential sampling strategies before they are brought to real-world applications. Our method is not the first of this type. For example, geostatistical analyses have been used to identify optimum sample sizes for pheromone trap monitoring

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We thank Chris Bringloe, Bill Coleman, Gerry Redmond, Don Scott, and Gordon Young for permission to sample their Christmas tree farms, and Blake Edwards and Katie Burgess for field assistance. We also thank Chris Dickie at Infor New Brunswick and Eldon Eveleigh at Natural Resources Canada, Canadian Forest Service for logistical and organizational support. Jeff Fidgen, Quentin Geissmann, Rob Johns, Dan Quiring, and two anonymous reviewers made valuable comments on the manuscript.