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Aspen and their hybrids have demonstrated high biomass productivity and can produce abundant regeneration in the form of root suckers. This makes aspen particularly intriguing for bio-energy production, because replanting costs can be avoided and additional biomass can be obtained by thinning the regenerating stands. Mechanical strip thinning (removal of stems in parallel strips) has been proposed as a fast and efficient method for capturing biomass that would otherwise be lost to mortality in such stands. However, determining the appropriate width for the residual rows is challenging, due to the difficulty of conducting inventories with traditional sampling tools and the variability in gap sizes between root suckers in the residual rows. In this study, we describe the development and testing of a simple inventory tool that may be used to conduct either fixed-area or variable-radius sampling in these stands. Also described is the development and testing of an equation that uses such inventory data along with Poisson distribution theory to predict the size of the largest gap between root suckers within residual rows, which in turn can be used to inform strip thinning operations. Based on the promising results of our limited tests, we encourage further evaluation of these methods with regeneration from planted and natural aspen stands, as well as other root suckering species.

Aspen and their hybrids have proven capable of producing more than 10 Mg ha^{-1} yr^{-1} of dry biomass in short-rotation (8 to 10 year) plantations in the United States (^{-1} after one growing season (

Strip thinning (defined for the purposes of this study as the mechanical removal of aspen regeneration in parallel strips between which rows of residual stems are retained) has been proposed as a method for capturing biomass that would otherwise be lost to mortality (

An equation which relates the maximum gap size within the residual row to the width of the row is therefore desirable. Such an equation should logically derive from stand density, as this is the inverse of stem spacing. However, the rapid growth and high density of these stands (

In this technical report, we describe the development and testing of: (1) a simple inventory tool for conducting inventory measurements in dense stands of aspen root suckers; and (2) an equation to facilitate strip thinning of such stands by relating the size of the largest gap within a residual row to the width of the row, based on root sucker density (as determined by inventory) and Poisson distribution theory. Together, these methods provide a framework to inventory and strip thin dense young stands of root suckers, which we expect to be useful for sustainably managing regeneration of aspen as well as other root suckering species.

The inventory tool developed in this study was composed of relatively inexpensive and readily-available materials; the basic design is shown in

To use the inventory tool, the rod should be oriented vertically while the tip is placed at the sample point. To maintain the sample point during measurements (as well as for future measurements), a flag or PVC pipe may be placed in the soil; in the case of a pipe, the interior diameter should be just large enough for the tip of the tool to fit inside, and its height should be short enough that it does not interfere with the measuring tape. The nylon measuring tape (which due to its flexibility is easily moved between stems) can then be used to identify tally trees based on either fixed-area or variable-radius methods. With fixed-area sampling, trees are tallied if they lie within a prescribed radius of the sample point. Stand density (stems per unit area) for each sample point is then calculated by dividing the number of tally trees by the plot area. At our site, a fixed-area plot size of 1.7 × 10^{-5} ha (≈ 23 cm radius) was used to ensure the number of tally trees per sample point (3 to 4 on average - Ruigu & Hall, unpublished data) was both manageable and approximately on par with that typical of variable-radius sampling (

With variable-radius sampling, tally trees are selected based on the ratio of their distance from the sample point to their stem diameter. In mature stands, this method is widely employed using an angle gauge or prism that has an implicit distance:diameter ratio associated with its basal area factor (BAF). The stand density represented by each tally tree can then be estimated as the BAF divided by the basal area of the tally tree, and produces similar estimates of stocking in considerably less time than fixed-area sampling (^{2} ha^{-1}), 3:1 (BAF = 2.78 m^{2} ha^{-1}), and 2:1 (BAF = 6.22 m^{2} ha^{-1}), and found that the 3:1 ratio resulted in a similar number of tally trees per sample point as the aforementioned fixed-area sampling.

The inventory tool was tested at a site near Ames, IA (USA), that contained hybrid aspen regeneration which sprouted following the harvest of a mature plantation in March of 2008. The original plantation consisted of a staggered-row design (

Two main assumptions were made in developing the strip thinning equation. First, it was assumed that the spatial distribution of aspen root suckers can reasonably be described as random. Second, it was assumed that the width of the residual row of root suckers would be small relative to the length of the row. Under these two assumptions, the distances between root suckers in the residual row are analogous to the distances between randomly distributed points on a line, which can be described by Poisson probabilities. Specifically, Poisson probabilities describe the distribution of random events in linear time or space based on the following equation (

where _{x}(

Based on Hida’s third theorem (

where _{max} is the expected size of the largest observed gap, and

To apply this equation for root suckers in the residual row, the following definitions and relationships are needed:

^{-2}; calculated by dividing stems ha^{-1} by 10 000 m^{2} ha^{-1});

^{-1} of row length);

Thus, according to Poisson theory, the expected size of the largest observed gap may be estimated by re-arranging

It is instructive to consider here several points about this equation and its relationships. First, according to the equation above, the size of the largest observed gap in the row increases as the length of the row increases. While this may seem counter-intuitive, it is in fact logical if one recalls that the equation is derived from probabilities. Considering the entire population of gaps as a Poisson distribution curve, and the observed gaps in any given row as being a sample of this population, then it becomes clear that the probability of observing the largest gaps in the population (_{max} to be estimated for multiple, equally long rows using a single calculation). Otherwise, measurements of the physical distance between the first and last stem in each row would be required along with separate calculations of _{max} for each of these distances, which would be particularly impractical as the length and/or number of rows becomes very large. In addition, if the user considers the growing space at the ends of the rows to be of similar interest and importance as that between stems, then including these gaps in the calculations is a logical step. Third, it should also be noted that the effect of the row width dimension on the distances between stems in the row will be negligible for small row widths, but will become more pronounced for larger row widths. In such cases, the planar distance between stems may be more informative than the linear distance along the row, and can be estimated using the simple geometric relationship described by the Pythagorean theorem for right triangles: ^{2} + ^{2} = ^{2}, where _{max} in the dimension of _{max}. For simplicity and brevity, however, we will consider only linear _{max} for the remainder of this paper.

To test

Based on our 27 sample points, stand density of the 1-year-old root suckers was estimated to be 185 000 stems ha^{-1} using fixed-area sampling (^{-1} using variable-radius sampling (^{2} ha^{-1}). While the estimated stand density was higher for variable-radius sampling than for fixed-area sampling, the 95% confidence intervals for the two methods showed considerable overlap (fixed-area = 140 000 to 230 000 stems ha^{-1}; variable-radius = 118 000 to 296 000 stems ha^{-1}). The reduced precision (^{2} ha^{-1} produced a similar estimate of total stand density with a smaller confidence interval (likely related to the greater number of tally trees), whereas a BAF of 6.22 m^{2} ha^{-1} produced a considerably lower estimate of total stand density and larger confidence interval (likely related to the smaller number of tally trees). The under-estimation of stand density appeared to be linked to a failure to detect small stems, as the BAF of 6.22 m^{2} ha^{-1} estimated about half as many stems in the smallest dhh class (5mm) compared to the other two BAFs.

It should be noted that some of the variability in estimated stand density in the present study may be partially attributable to the relatively large genetic diversity represented at the site. The original plantation contained 32 different genotypes of hybrid aspen planted in a randomized design (

The test for conformity to the Poisson distribution showed that the distribution of the 2-year-old root suckers did not differ significantly from Poisson (p = 0.28, deviance = 53.28, df = 48), although a minor clumping effect (overdispersion) was indicated by the deviance:df ratio being >1. The stand densities were found to be significantly different (p = 0.02) between rows, with the east row having significantly higher mean density (9.1 stems m^{-2}) than the west row (6.8 stems m^{-2}). For the simulations based on randomly dropping sprouts from the rows, linear regression showed a strong relationship (^{2} = 0.87) between actual maximum gap sizes and those predicted by

Our results suggest that the Poisson distribution can be reasonably applied to the spatial distribution of aspen root suckers.

It should be noted that we did not include stump sprouts in our inventory measurements because our strip thinnings were centered over the stump rows which precluded them from contributing to the residual rows in terms of stem density or gap sizes, and also because the stump sprouts were not considered a viable long-term source of regeneration due to the disease/breakage issues previously described. However, if their inclusion in the inventory is desired (as may be the case with natural aspen stands where stump rows do not exist), it should be noted that the non-random (

Finally, it should also be noted that the spatial distribution of root suckers may not always be random or remain that way over time; thus, the importance of testing for conformity to the Poisson distribution prior to applying the strip thinning equation (and adjusting its use as needed) cannot be overstated. For example, root suckers arising from very poorly stocked stands may exhibit significant clumping effects, in which case ^{-1} of row length).

The results of our limited tests of the inventory tool and strip thinning equation indicate that they are both potentially useful for managing dense young stands of aspen regeneration. Specifically, the inventory tool can be used to estimate stand density by either fixed-area or variable-radius sampling methods, and the strip thinning equation can be used to relate the size of the largest gap within the row to the width of the row at a given stand density (as determined by inventory) and row length (as dictated by study scale). However, our tests involved a relatively narrow range of conditions, and so we invite and encourage additional testing of these inventory and strip thinning methods with a wider variety of stand densities, ages, sites, and root suckering species.

The authors would like to thank the US Forest Service Northern Research Station Institute for Applied Ecosystem Studies, Iowa State University College of Agriculture and Life Sciences (CALS), and the CALS Agriculture Systems Initiative for their support in this project. They would also like to thank Phil Dixon, Ron Zalesny Jr., and Steve Jungst for their review and helpful comments on earlier drafts of the paper.

Stand of 1-year-old hybrid aspen regeneration near Ames, IA (USA) in early spring of 2009. Root sucker density is approximately 200 000 stems ha^{-1}, with individual stems measuring up to 3 m tall and up to 3 cm diameter at harvestable height (dhh; measured 10 cm aboveground).

Schematic of a simple inventory tool that can be used for either fixed-area or variable-radius sampling in densely regenerating stands of aspen root suckers. Photo inset (upper right) shows the tool as used in the field.

View looking down the west row of the strip thinning field test near Ames, IA (USA), during the summer of 2010. Stump sprouts and root suckers were cleared from the left and right sides, leaving the residual row of 2-year-old root suckers (0.3 m wide by 50 m long) shown in the center.

Actual _{max}, m), based on simulations in which sprouts were randomly dropped from 2 rows with 3 simulations for each row, for a total of 6 simulations. Dashed line represents a perfect 1:1 relationship.

Example of diagram for estimating the mean size of the largest gap in the rows (_{max}, m) associated with different row widths (^{-2} (dotted lines).

Comparison of mean stand density estimates (stems ha^{-1}) obtained from variable-radius methods, using three different basal area factors (BAFs - m^{2} ha^{-1}) resulting in different numbers of tally trees (n). Stand density estimates are shown by diameter class, totals across all diameter classes, and 95% confidence intervals (CI) for totals. Diameter classes listed are the midpoints of intervals of 5 mm (

BAF(m^{2} ha^{-1}) |
n(trees) | Mean Stand Density (10^{4} stems ha^{-1}) by diameter class |
|||||
---|---|---|---|---|---|---|---|

5mm | 10mm | 15mm | ≥20mm | Total | 95% CI | ||

1.56 | 165 | 12.9 | 4.6 | 1.3 | 0.5 | 19.3 | 13.4 - 25.2 |

2.78 | 93 | 13.7 | 5.2 | 1.4 | 0.4 | 20.7 | 11.8 - 29.6 |

6.22 | 38 | 6.8 | 5.0 | 2.0 | 0.3 | 14.1 | 5.7 - 22.6 |