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Sector sampling is a new and simple approach to sampling objects or borders. This approach would be especially useful for sampling objects in small discrete areas or “polygons” with lots of internal or external edge, but it may be extended to sampling any object regardless of polygon size. Sector plots are wedge-shaped with a fixed sector angle. The probability of object selection is constant and equal to the sector angle in degrees divided by 360°. A unique property of sector sampling is that the point from which the angle originates may be located subjectively when the sector direction is at random. Another advantage over traditional sampling (such as fixed or variable area plots) is that there is no edge effect; that is, there is no altering of selection probabilities of objects close to polygon boundaries. Various approaches are described for deriving polygon means and totals with their associated variances. We review the genesis of sector sampling and develop two new components: sub-sampling using fixed area plots and line sampling using the sector arcs as transects. Sector sampling may be extended to measuring a variety of objects such as trees, shrubs, plants, birds, animal trails and polygon borders.

Sector sampling [

Sector sampling is a new sampling technique in the forest and ecological literature and consequently there is little practical experience and few articles published. There have previously been papers in other disciplines using an angular section of a circle or ellipse such as: sampling the number of myelin or nerve fibers in the traverse sections on nerve fiber bundles [

Initial sector sampling applications in forestry have included:

sampling young trees growing in and around groups of older leave trees, or “variable retention” [

estimating tree size in narrow, sinuous riparian strips [

sampling trees and small scattered woodlots outside the main forest [

The purpose of this paper is to review general sector sampling properties and current applications in the forest literature and to discuss and suggest additional potential ecological uses. Sector sampling may help extend sampling of some novel conditions with considerable edge that are not particularly well sampled using traditional approaches such as points or quadrats [

Schematic representation of sector sampling (Adapted from [

For an arc passing through an object, a random direction angle,

If fixed or variable area plots are established around an object and straddle a polygon or sample area boundary then the object selection probability is altered [

The probability of object selection under sector sampling

If actual sector area is known, then per unit area values can be calculated directly. For instance basal area (BA) may be calculated for each sector by summing each tree BA and dividing that total by the sector area to give basal area per unit area. In this case, the appropriate estimate is a ratio-of-means (ROM) estimator for means and variances (BA/area): larger sectors account for larger areas and are weighted more [

ROM formulae may be used when direction angles are established randomly (“random angle” method). It appears to be generally more efficient, however, to base sector direction angle on “random points” achieved by establishing sector direction through points randomly located in the polygon. This ensures that objects in larger parts of the polygon get sampled in proportion to area; the data are already “weighted” correctly so that SRS formulae for means and variances may be used rather than ROM formulae [

A systematic sample of sectors reduces the variability between sectors by averaging out the area differences (

A 10% systematic sample of objects in a polygon using four orthogonal 9° sectors. Objects (trees) shown as black dots. Based on [

The sector area increases proportionally with distance from the pivot-point, with a consequent increase in the number of objects to be counted. To reduce field work the sector can be divided into two or more sectors along the central axis and one selected at random. The trees would then need to be weighted appropriately (e.g., weight is 2 if sector is bisected into two). If a smaller subsample needs to be made then a systematic selection of an annulus bounded by the sector plot edges may be made at fixed or random points along the sector central axis. The probability of object selection is then equal to [α/360° ° (length of the partial annulus along sector central ray)/(sub-sample interval)].

A sector plot sub-sampling system comprising small fixed area plots established along the central ray may also be used (see

where EF

The probability of object selection is more complex at both extremities of the central ray; for a plot centered at the pivot-point the selection probability is bounded at

Sub-sampling sectors using fixed area plots.

Sampling down objects using sector plots: a systemic location of two partial-arcs with a random start is shown; α is the internal sector angle.

The presence of down trees or horizontal linear objects such as dead woody debris may be sampled using sector plots. Traditionally, linear transects have been used [

Number of down or linear objects per hectare equation 2

where

It is also possible to use sector sample transects to help estimate the total length of game trails, roads, hedgerows, streams or other linear features, see [

Horizontal object or feature length in meters per hectare equation 3

This same general approach may be extended to down woody debris volume by calculating the cross sectional area of debris crossing the partial-arc and “spreading-out” along the partial sector length, s, to get the average “depth” of wood along s. This number can then be multiplied by 360°/

In several parts of the world, for instance, in some forested areas of Tasmania [

The procedure was a two-stage one. In the first stage smaller sub-sample areas were delineated that tessellated the area. Here, areas from one up to two hectares were marked using roads and permanent features in the clearcut and unharvested control. This is shown fully for the clearcut, 10% and 20% group retention areas and partially for the 30% retention area (

Five sub-sample areas were selected at random in the clearcut and control areas and full sector plots with a 36° internal angle located at plot center using a random direction angle and sectors extending to the sub-sample boundary (

In the harvested, 10%, 20% and 30% variable retention experiment treatments the aggregated retention patches and surrounding harvested areas were demarcated using roads or other permanent survey features and three patches chosen randomly in each treatment. In the approximate center of each selected patch per treatment four orthogonal systematic sectors, each 9° and summing to 36° (a 10% sample), were established with a random orientation and extended to the sub-sample boundary.

The objective was to monitor the development of the retained, regenerating and planted trees in N, S, E and W directions. In the clearcut and unharvested control area this azimuthal hypothesis was not tested so the four sectors were collapsed into one. The plots are easy to install in the field: simply establish the central axis using GPS, laser or by lining up stations and use radial or distances offsets to locate sector sides. We have found that using a 10% sample (36°) is a useful operational starting point though more work could be done to develop the most efficient sector angle for a given set of conditions.

There are numerous other sampling applications that might be envisaged—as an example: the inventory of fauna and flora in small areas, copses or hedgerows. The sector plot could be positioned in the center of a clearcut or field and used to randomly sample forest edges or boundaries for windthrow or hedges for nesting birds. In the ocean, corals may be readily sampled, as would small areas around moored boats. Birds or other animals could be counted using a fixed angle gauge with random orientation along linear strips or on lake surfaces. Distance along the sector might also be used to examine environmental gradients. Items on the ground such as nests or animal tracks and trails could also be measured. For fast moving objects crossing the sector plots photographs or videos might be taken and enumerated at a later date. Another variant is to use sector sampling to sub-sample point distance samples [

Schematic example of sector plot layout in an aggregated retention forested setting experimental area. The control area is unharvested, the clearcut area is harvested and the 10%, 20% and 30% groups have small groups of trees (approx. 0.3 ha in size) surrounded by harvested areas. “10% Groups” refers to 10% of the treatment area covered in retained groups,

Sector plots were originally designed to sample objects in small polygons with extensive edges. There is no edge overlap bias as there is in fixed or variable plots that select objects which straddle a polygon boundary. Corona

Sector plots may be conveniently sub-sampled by splitting longitudinally in a successive fashion along a central axis and/or latitudinally into annuli. Small fixed area plots may be more easily set up in the field; for instance in sub-sampling dense brush or regeneration, but edge effect biases require correction.

Down woody debris or other linear features may conveniently be sampled using the partial-arcs of sector plots. In this situation the advantage of subjective plot location is of significant practical convenience for plot establishment such as in a high windthrow area with many down trees to count and measure. If a part of the object designated as defining the object to be “in” the polygon is within the sector there is no edge effect problem for the number of objects; that might be the midpoint, or the largest end of the object, for instance.

Sector sampling is a new sampling technique so that few applications have been made or documented, yet many applications can be envisaged. Potential new applications might include sampling boundaries such as hedgerows for bird nests or species composition or counts of objects at forest edges such as windthrow trees. Small islands of vegetation or grouped structures such as ponds, swamps, rocky outcrops, lakes, sea corals, shell fish beds or ocean vents could also be effectively enumerated.

Sector plots are a new sampling methodology particularly suited to sampling objects in small areas and/or situations with lots of edge. The advantages are that the plot center can be located subjectively and there are no edge effects biasing object selection near the boundaries of sampling units. If large numbers of objects are being sampled then the sector plots may be readily sub-sampled. Statistics are also easy to calculate. Plot establishment is simple and straightforward. The plot centre can be established to avoid inconvenient locations and to improve visibility and monumentation. In addition, count items at ground level such as leaves, branches, fungal mycelia or rabbit burrows may also be easily enumerated. Sector sampling may have a place in monitoring and experimental verification of new and novel and complex habitats especially those with excessive edges.

The authors declare no conflict of interest.