- Email: [email protected]
Accuracy in population estimation: A methodological consideration
Ecological Complexity 7 (2010) 208–211
Contents lists available at ScienceDirect
Ecological Complexity journal homepage: www.elsevier.com/locate/ecocom
Accuracy in population estimation: A methodological consideration C. Li a,*, H.J. Barclay b, H. Hans a, J. Liu c, R. Klos c, G. Carlson c a
Canadian Wood Fibre Centre, Canadian Forest Service, Natural Resources Canada, 5320 – 122 Street, Edmonton, Alberta, Canada T6H3S5 Pacific Forestry Centre, Canadian Forest Service, 506 Burnside Road, Victoria, British Columbia, Canada c Forestry Branch, Manitoba Conservation, Box 70, 200 Saulteaux Cres., Winnipeg, Manitoba, Canada b
A R T I C L E I N F O
A B S T R A C T
Article history: Received 9 January 2009 Received in revised form 18 January 2010 Accepted 4 February 2010 Available online 25 February 2010
Accuracy in population estimation from individual measurement has been traditionally a research focus in both theoretical and applied ecology. In forest sciences, estimation of productivity and value recovery of forest products is essential for decision-making to achieve the goal of sustainable forest management. In this paper, we review the basic structure of data in forest sciences, describe commonly used statistical procedures in obtaining population estimates, and examine the accuracy associated with the forest products value estimation using forest inventory data of Manitoba, Canada. Our results suggested that simplified statistical procedures could bring about a wide range of bias in estimating lumber value recovery at the stand level, and improved understanding of stand structure and its reconstruction through computer simulation could be essential in reducing the bias involved in the estimation. Crown Copyright ß 2010 Published by Elsevier B.V. All rights reserved.
Keywords: Population estimation Accuracy Value recovery Modeling Manitoba
1. Introduction Population measurement or estimation has been traditionally one of the central topics in ecological research (Holt, 1987). The accuracy of the estimation is essential in the expression of population measurement. Its importance is primarily from a practitioner’s perspective such as understanding the dynamics of ecosystems and making appropriate decisions on resource management. In forest research, a population can be defined as a collection of individual trees in a forest stand, and the variables associated with this population are the estimates such as wood volume that will determine the quantity of potential forest products. With the increasing challenges facing the forest sector, the valuation of forest product options becomes an important issue in determining optimal wood utilization strategies for the purpose of enhancing market competitiveness and maintaining sustainable resources (Sekot, 2007; Guthrie and Kumareswaran, 2009; Li, 2009). Considerable statistical analysis is involved in this valuation. Owing to the fast development in information technology in recent decades, many complicated statistical methods and procedures can be implemented easily given changing computing speed and availability of software packages. Consequently, practitioners can employ a variety of methods and procedures for population estimation with an improved accuracy.
* Corresponding author. Tel.: +1 780 435 7240; fax: +1 780 435 7359. E-mail address: [email protected] (C. Li).
In this paper, we review the basic structure of data in forest research, describe commonly used statistical procedures for obtaining population estimates, and test a hypothesis that there is no significant difference between the estimated values of lumber recovery from different statistical procedures. We show that the hypothesis did not hold in our case study using forest inventory plot data from the boreal shield of central-east Manitoba, Canada. As a result, the statistical procedure chosen could influence the accuracy of value estimation of forest products. Our results suggested that simplified statistical procedures might not always provide confident answers, and the reconstruction of stand structure from the inventory plot data is probably needed to obtain much reliable value estimation, and this can be realized through computer simulations. 2. Materials and methods 2.1. Basic data structure in forest research Data in forest research can be categorized into groups of spatial and non-spatial data. The spatial data are usually referred to as spatial forest inventory at regional to national scales. The regional forest inventory is polygon-based and often used in the strategic (up to 200 years), tactical (20 years), and operational (ranging from 1 to 5 years) forest management (harvest) planning performed at the levels of the provinces and Forest Management Licenses (FMLs) (Li et al., 2010). Each polygon has its unique ID associated with its geographical locations, landform strata, and administrative structure expressed as region, district, management unit, etc.
1476-945X/$ – see front matter . Crown Copyright ß 2010 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.ecocom.2010.02.002
C. Li et al. / Ecological Complexity 7 (2010) 208–211
Other variables in each polygon include land cover, tree species composition, stand origin, density expressed as crown closure or density classes, site condition, disturbance history, etc. Most current forest inventories are generated from the interpretation of aerial-photos and validated through ground truthing with plot sampling data. The non-spatial data are usually obtained from field measurements. Inventory sampling plots are a kind of temporary sample plot (TSP) designed for the development of operational forest inventory and they are chosen in either a systematic or a stratified sampling manner. They are one kind of non-spatial sampling plot data in forest research. Timber cruise data also belong to TSP and they are the randomly selected sites under investigation. The other kind of non-spatial sampling plot data is from the measurement of permanent sample plots (PSP). The main difference between PSP and TSP data is the repeated measurement in PSP but not in TSP. In British Columbia, Canada, PSP are established in natural stands for high quality and long-term local data on growth of the existing forest for a variety of species, sites, and stand conditions. They are a major part of forest growth and yield program, and provide information on rates of growth, mortality, and changes in stand structure. They are measured repeatedly at a certain intervals, such as 5 or 10 years. The data structures of PSP and TSP are the same or very similar. In each plot, only those trees with a diameter at breast height (DBH) larger than a certain standard are measured, as is often the case, i.e., not all the trees in the plot are measured. For all the measured trees, species, age, DBH, and height (H) are recorded. Other variables may also be recorded such as site condition, disturbance, etc. This data structure can provide within plot species composition, distributions of diameter and height, relationship between height and diameter, tree density or stocking, age, total volume and merchantable volume per unit area. They are the essential information for modeling tree-based growth, describing stand structure, and calibrating and validating growth and yield models that are unit area-based for inventory projection. 2.2. Case study area and forest inventory The Forest Management License (FML) #1 of Manitoba, Canada, located in central-eastern Manitoba has been chosen as our study area (see http://www.gov.mb.ca/conservation/forestry/forestpractices/companies/fml1.html). The total size of this FML is 889,471 ha, and about two-thirds of it is considered to be productive and potentially productive forest land, under the management of the Pine Falls Operations, Tembec Industries Inc. Fig. 1 shows the location of our study area. The operational forest inventory was generated based on the 1997 aerial-photos, and took 5 years to complete (Manitoba Conservation, 2006). The sizes of the polygons can be from less
209
than 1 ha to as large as 390 ha for forested lands. There are 163,699 polygons with a size larger than 1 ha, and the mean size of the polygons is about 6.9 ha. During the 5 years more than 700 polygons were selected for field plot sampling and they contain three 100 m2 plots per polygon. In each plot all the trees with a DBH larger than 7.1 cm were measured and that resulted in about 26,000 trees in total for developing this forest inventory. DBH and H are among the measured variables. Other variables were also recorded in the field sampling such as site conditions, understory vegetation, and disturbance type and history, etc. Through enormous investment of time and work, this forest inventory provides the best information on forest conditions to support the provincial forest management agency and forest industry to make sound strategic and operational management planning for the region. Since April 2009, the Nopiming Provincial Park has been excluded from this FML for harvest thus the total size of the FML is reduced. A test plot (located at easting 750,156 and northing 5,646,985 of the UTM Zone 14) dataset was used in this study first for a detailed examination of whether the standard procedure of estimating stand volume can be directly used in the value recovery estimate at the stand level. The plot is within an almost pure black spruce (Picea mariana (Mill.) B.S.P.) stand with an age of 68 years. The plot data were collected on April 16, 2002, and contained the measurements of 116 individual black spruce trees. Tree taper was calculated from the diameter inside the bark (DIB) between 15 cm above ground and the tree height at 5 cm DIB from the top based on the method of Klos et al. (2007). The same analytical procedure was applied to all the polygon plots in the study area with a black spruce component of at least 10% (499 plots in total) to investigate the potential influence of the standard procedure on the accuracy of lumber value recovery estimates. 2.3. Methods of valuation of lumber recovery A general approach of estimating stand level forest wood volume from measurements of individual trees is to develop individual tree-based volume equations first and estimate stand level volume according to the stand structure through using these volume equations. However, it is usually simplified in operation to a simple procedure as (1) obtain the mean values of measured DBH and H of all sampled trees for a given tree species under investigation, and (2) use these mean values as representative of all trees in the stand and multiplied by the total number of trees of the stand to calculate the mean wood volume per unit area using the volume equations. This procedure has become more or less standard in the forest inventory construction and is used in many forest growth and yield modeling practices. With the shift of forest management paradigm from being volume-based to value-based, an assumption that value creation potential is proportional to wood volume may have been used in
Fig. 1. Study area location indicated by the grey coloured area (data as March 2009).
C. Li et al. / Ecological Complexity 7 (2010) 208–211
210
Table 1 Lumber value recovery estimates from the test plot dataset. Items
Value recovery ($)
VReal VMean VMean VReal B (%)
669.88 484.74 185.14 27.6
Table 2 The relative contribution to the biased lumber value recovery from DBH, H, and T. Items
Actual value ($)
Sensitivity (10% increase) value ($)
B (%)
Relative contribution (%)
DBH H T
669.88 669.88 669.88
617.01 515.34 501.72
71.4 16.5 9.2
73.5 17.0 9.4
estimating value recovery of wood volume without detailed examination using empirical observations. In this study, we use a plot dataset from our study area to test a hypothesis that there is no significant difference between the estimated values of lumber recovery from different statistical procedures. This hypothesis test is aimed at determining whether the standard procedure in volume recovery estimates can be directly used in value recovery estimation without experiencing significant bias. If this hypothesis is true, the lumber value recovery calculated from this standard method should be equal or very similar to the true value, which is the sum of lumber value recovery from all individual trees. The tree level lumber value recovery, VLumber, can be calculated as a function of DBH and H (Zhang et al., 2006), in which the Optitek software1 was used to maximize the lumber recovery of a black spruce. V Lumber ¼ 0:002 H0:6423 DBH2:5315 T 0:3612
(1) Fig. 2. Biased lumber value estimates of all the inventory plots with a black spruce component in the study area (499 plots in total).
where T is tree taper calculated as: T¼
DBHStum p15 DBHTo p10 HTo p10 0:15
(2)
where HTo p10 is the top height at the DIB of 10 cm, and the DBHStum p15 and DBHTo p10 are the DBH at the stump height of 15 cm and top height at the DIB of 10 cm, respectively. 2.4. Data analysis Eq. (1) was used to calculate the real value recovery for each individually measured tree, and the summation of all the value recoveries was used as the real value for the plot’s value creation potential, VReal. The statistical procedure of volume recovery estimate was applied to the plot data by obtaining the mean values of DBH, H, and T, and then Eq. (1) was used to calculate mean value recovery of all the individual trees in the plot, and the plot’s value creation potential, VMean, is obtained by multiplying by the number of trees. The estimate of the percentage of biased value recovery from the true value recovery, B, by using the mean values of DBH, H, and T was calculated as: V Mean V Real B¼ 100% V Real
(3)
A sensitivity analysis was also carried out by individually varying the mean values of measured variables by 10% increments, and then calculating the relative contributions of the variables to the bias estimation. 3. Results Table 1 shows the true lumber value recovery of the trees in the test plot dataset and the one estimated using the simplified statistical procedure. The value from the simplified procedure 1 The Optitek software package was developed by the Forintek Division of the FPInnovations, Canada for sawmills to optimize log cutting pattern for maximizing the percentage of lumber volume recovery.
underestimated the true value by 27.6%. Therefore, the hypothesis that there is no significant difference between the estimated lumber value recovery from the simplified statistical procedure and the true value did not hold in this case. Table 2 shows the relative contribution to the biased lumber value recovery from DBH, H, and T. Our sensitivity analysis results in Table 2 suggests that among these three variables DBH contributed the most (74%), and followed by H (17%), and T (9%). Therefore, more attention should be paid to DBH and its distribution within a stand. Fig. 2 is the results of applying the test procedure to all the inventory plots that contain a black spruce component (499 plots in total). The distribution of the biased estimates was very scattered along the stand age, with 17.8% underestimate the true value in average. The range of the bias was from a 73.5% underestimate to a 3.5% overestimate. 4. Discussion 4.1. Forest valuation—forest product options Forest valuation provides useful information for forest manager’s decision-making on whether a harvest operation should be performed and what to do with it when trees are harvested. From the forest economics perspective, the harvest operation should probably be performed only when that operation could result in a certain level of benefits, which is determined by the net or marginal value (based on either current or future value) of the forest, i.e., the difference between forest value and the costs associated with the product production. Our discussion is focused on forest valuation (or the value creation potential of the forest) with fixed costs for simplification. A number of product options could be available for each of the forests from a forest manager’s perspective, and the determination of an optimal wood utilization from the forest is perhaps the best way to maximize the value creation potential. Consequently, the information required for this
C. Li et al. / Ecological Complexity 7 (2010) 208–211
determination will be the value creation potential estimates for various product options. We focused on the lumber product option in this study because of its likely higher expectation in economic return from harvested trees than that of other forest product options. It is also because they are relatively straightforward to account for because they are priced goods and services from the forests. However, our results suggested that the valuation of this product option could still be complicated by different statistical procedures. Nevertheless, this complication could be resolved through application of correct statistical procedure, i.e., to calculate lumber value recovery for each individual tree first, and then sum them up to obtain plot level lumber value recovery. In other words, one needs to reconstruct the stand structure before estimating lumber value recovery of the stand. Forest valuation can be complicated by other factors, such as changes in industry structure, mill infrastructure, forest policy, and fluctuations in market conditions. It can also be complicated by the complex, hierarchical, and adaptive dynamics of forest ecosystems (Costanza and Jørgensen, 2002), coupled with human systems (Liu et al., 2007). Human behaviour as another important aspect in decision-making has also gained increasing attention in bioeconomics research (Clark, 2007; Breda et al., 2008; Brede and Boschetti, 2009). However, they are beyond the scope of this paper and will be discussed elsewhere. 4.2. Information flow across scales Information flow across scales has been one of the central concerns in ecology in the past couple of decades (Makarieva et al., 2004). It concerns whether the research results or observations made at a lower level of hierarchical structure can be appropriately used in the next higher level of ecosystem structures. For instance, can observations made at the individual tree level be appropriately used in the presentations of stand level research results? With this information scaling-up process, detailed presentation of variables measured at the individual tree level could be lost. However, this information is represented in frequency distributions of the variables and species composition within the stand. Whether this loss of detailed information is acceptable for the purpose of information presentation and whether the detailed information can be reconstructed from the aggregated presentation of information are probably the most important issues facing forest managers. Considering that it is not feasible or desirable to measure every individual tree and/or stand, certain kinds of approximation must be made and this is perhaps one of the main focuses in the study of information flow across scales. Our case study is aimed at addressing a practical question of whether the simplified statistical procedure in volume estimation can be directly used for the estimation of lumber value recovery. Our results from a single plot dataset suggest that about a 27% bias in underestimating black spruce lumber value recovery could occur when the simplified procedure is used. A wider range of biases were found when the same statistical procedure applied to all the plot data in the study area with a black spruce component. Though the results are a surprise, it is still understandable from a sampling theory perspective since the bias was probably caused by the nonlinear nature of the lumber value recovery function (Eq. (1)), together with the fact that the sampled distributions of
211
DBH and H do not follow the normal probability distribution. The overall results suggest that the simplified statistical procedure should be avoided. Computer simulations based on the reconstruction of stand structure could provide a solution to reduce the possible population level estimates, which will be discussed in a separate article. 4.3. Management application Our recommendations from the results of this study include: (1) due to the loss of detailed information in aggregated presentation, simplifications in analytical procedures should be avoided whenever it is possible to ensure the accuracy in estimation; (2) forest managers and researchers can take advantage of fast developing information technology and increasing computing power, to test simplifications and assumptions carefully before applying them widely; and (3) reconstruction of stand structure through computer simulations could improve the accuracy of population estimates, and achieve the goal of information flow across multiple scales without losing accuracy significantly. 5. Conclusions Simplified statistical procedures could bring about a wide range of biases in population estimation, specifically in lumber value recovery estimates from the forest inventory plot data of Manitoba, Canada. Improved understanding of stand structure and its reconstruction could be essential in reducing the bias. References Brede, M., Boschetti, F., 2009. Commons and anticommons in a simple renewable resource harvest model. Ecological Complexity 6, 56–63. Breda, M., Boschetti, F., McDonald, D., 2008. Strategies for resource exploitation. Ecological Complexity 5, 22–29. Clark, C.W., 2007. The Worldwide Crisis in Fisheries: Economic Models and Human Behavior. Cambridge University Press. Costanza, R., Jørgensen, S.E. (Eds.), 2002. Understanding and Solving Environmental Problems in the 21st Century: Toward a New, Integrated Hard Problem Science. Elsevier. Guthrie, G., Kumareswaran, D., 2009. Carbon subsidies, taxes and optimal forest management. Environmental and Resource Economics 43, 257–293. Holt, R.D., 1987. Population dynamics and evolutionary processes: the manifold roles of habitat selection. Evolutionary Ecology 1, 331–347. Klos, R.J., Wang, G., Dang, Q.L., East, E.W., 2007. Taper equations for five major commercial tree species in Manitoba, Canada. Western Journal of Applied Forestry 22, 163–170. Li, C., 2009. Toward full, multiple, and optimal wood fibre utilization: a modeling perspective. Forestry Chronicle 85, 377–381. Li, C., Liu, J., Lafortezza, R., Chen, J., 2010. Managing forest landscapes under changing global scenarios. In: Li, C., Lafortezza, R., Chen, J. (Eds.), Landscape Ecology and Forest Management: Challenges and Solutions in a Changing Globe. HEP-Springer, in press. Liu, J., Dietz, T., Carpenter, S.R., Alberti, M., Folke, C., Moran, E., Pell, A.N., Deadman, P., Kratz, T., Lubchenco, J., Ostrom, E., Ouyang, Z., Provencher, W., Redman, C.L., Schneider, S.H., Taylor, W.W., 2007. Complexity of coupled human and natural systems. Science 317, 1513–1516. Makarieva, A.M., Gorshkov, V.G., Li, B.L., 2004. Body size, energy consumption and allometric scaling: a new dimension in the diversity–stability debate. Ecological Complexity 1, 139–175. Manitoba Conservation, 2006. Wood supply report for forest management licence area #1. Accessed January 4, 2010. Sekot, W., 2007. European forest accounting: general concepts and Austrian experiences. European Journal of Forest Research 126, 481–494. Zhang, S.Y., Lei, Y.C., Jiang, Z.H., 2006. Modelling the relationship of tree-level product value with tree characteristics in black spruce. Forestry Chronicle 82, 690–699.
Contents lists available at ScienceDirect
Ecological Complexity journal homepage: www.elsevier.com/locate/ecocom
Accuracy in population estimation: A methodological consideration C. Li a,*, H.J. Barclay b, H. Hans a, J. Liu c, R. Klos c, G. Carlson c a
Canadian Wood Fibre Centre, Canadian Forest Service, Natural Resources Canada, 5320 – 122 Street, Edmonton, Alberta, Canada T6H3S5 Pacific Forestry Centre, Canadian Forest Service, 506 Burnside Road, Victoria, British Columbia, Canada c Forestry Branch, Manitoba Conservation, Box 70, 200 Saulteaux Cres., Winnipeg, Manitoba, Canada b
A R T I C L E I N F O
A B S T R A C T
Article history: Received 9 January 2009 Received in revised form 18 January 2010 Accepted 4 February 2010 Available online 25 February 2010
Accuracy in population estimation from individual measurement has been traditionally a research focus in both theoretical and applied ecology. In forest sciences, estimation of productivity and value recovery of forest products is essential for decision-making to achieve the goal of sustainable forest management. In this paper, we review the basic structure of data in forest sciences, describe commonly used statistical procedures in obtaining population estimates, and examine the accuracy associated with the forest products value estimation using forest inventory data of Manitoba, Canada. Our results suggested that simplified statistical procedures could bring about a wide range of bias in estimating lumber value recovery at the stand level, and improved understanding of stand structure and its reconstruction through computer simulation could be essential in reducing the bias involved in the estimation. Crown Copyright ß 2010 Published by Elsevier B.V. All rights reserved.
Keywords: Population estimation Accuracy Value recovery Modeling Manitoba
1. Introduction Population measurement or estimation has been traditionally one of the central topics in ecological research (Holt, 1987). The accuracy of the estimation is essential in the expression of population measurement. Its importance is primarily from a practitioner’s perspective such as understanding the dynamics of ecosystems and making appropriate decisions on resource management. In forest research, a population can be defined as a collection of individual trees in a forest stand, and the variables associated with this population are the estimates such as wood volume that will determine the quantity of potential forest products. With the increasing challenges facing the forest sector, the valuation of forest product options becomes an important issue in determining optimal wood utilization strategies for the purpose of enhancing market competitiveness and maintaining sustainable resources (Sekot, 2007; Guthrie and Kumareswaran, 2009; Li, 2009). Considerable statistical analysis is involved in this valuation. Owing to the fast development in information technology in recent decades, many complicated statistical methods and procedures can be implemented easily given changing computing speed and availability of software packages. Consequently, practitioners can employ a variety of methods and procedures for population estimation with an improved accuracy.
* Corresponding author. Tel.: +1 780 435 7240; fax: +1 780 435 7359. E-mail address: [email protected] (C. Li).
In this paper, we review the basic structure of data in forest research, describe commonly used statistical procedures for obtaining population estimates, and test a hypothesis that there is no significant difference between the estimated values of lumber recovery from different statistical procedures. We show that the hypothesis did not hold in our case study using forest inventory plot data from the boreal shield of central-east Manitoba, Canada. As a result, the statistical procedure chosen could influence the accuracy of value estimation of forest products. Our results suggested that simplified statistical procedures might not always provide confident answers, and the reconstruction of stand structure from the inventory plot data is probably needed to obtain much reliable value estimation, and this can be realized through computer simulations. 2. Materials and methods 2.1. Basic data structure in forest research Data in forest research can be categorized into groups of spatial and non-spatial data. The spatial data are usually referred to as spatial forest inventory at regional to national scales. The regional forest inventory is polygon-based and often used in the strategic (up to 200 years), tactical (20 years), and operational (ranging from 1 to 5 years) forest management (harvest) planning performed at the levels of the provinces and Forest Management Licenses (FMLs) (Li et al., 2010). Each polygon has its unique ID associated with its geographical locations, landform strata, and administrative structure expressed as region, district, management unit, etc.
1476-945X/$ – see front matter . Crown Copyright ß 2010 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.ecocom.2010.02.002
C. Li et al. / Ecological Complexity 7 (2010) 208–211
Other variables in each polygon include land cover, tree species composition, stand origin, density expressed as crown closure or density classes, site condition, disturbance history, etc. Most current forest inventories are generated from the interpretation of aerial-photos and validated through ground truthing with plot sampling data. The non-spatial data are usually obtained from field measurements. Inventory sampling plots are a kind of temporary sample plot (TSP) designed for the development of operational forest inventory and they are chosen in either a systematic or a stratified sampling manner. They are one kind of non-spatial sampling plot data in forest research. Timber cruise data also belong to TSP and they are the randomly selected sites under investigation. The other kind of non-spatial sampling plot data is from the measurement of permanent sample plots (PSP). The main difference between PSP and TSP data is the repeated measurement in PSP but not in TSP. In British Columbia, Canada, PSP are established in natural stands for high quality and long-term local data on growth of the existing forest for a variety of species, sites, and stand conditions. They are a major part of forest growth and yield program, and provide information on rates of growth, mortality, and changes in stand structure. They are measured repeatedly at a certain intervals, such as 5 or 10 years. The data structures of PSP and TSP are the same or very similar. In each plot, only those trees with a diameter at breast height (DBH) larger than a certain standard are measured, as is often the case, i.e., not all the trees in the plot are measured. For all the measured trees, species, age, DBH, and height (H) are recorded. Other variables may also be recorded such as site condition, disturbance, etc. This data structure can provide within plot species composition, distributions of diameter and height, relationship between height and diameter, tree density or stocking, age, total volume and merchantable volume per unit area. They are the essential information for modeling tree-based growth, describing stand structure, and calibrating and validating growth and yield models that are unit area-based for inventory projection. 2.2. Case study area and forest inventory The Forest Management License (FML) #1 of Manitoba, Canada, located in central-eastern Manitoba has been chosen as our study area (see http://www.gov.mb.ca/conservation/forestry/forestpractices/companies/fml1.html). The total size of this FML is 889,471 ha, and about two-thirds of it is considered to be productive and potentially productive forest land, under the management of the Pine Falls Operations, Tembec Industries Inc. Fig. 1 shows the location of our study area. The operational forest inventory was generated based on the 1997 aerial-photos, and took 5 years to complete (Manitoba Conservation, 2006). The sizes of the polygons can be from less
209
than 1 ha to as large as 390 ha for forested lands. There are 163,699 polygons with a size larger than 1 ha, and the mean size of the polygons is about 6.9 ha. During the 5 years more than 700 polygons were selected for field plot sampling and they contain three 100 m2 plots per polygon. In each plot all the trees with a DBH larger than 7.1 cm were measured and that resulted in about 26,000 trees in total for developing this forest inventory. DBH and H are among the measured variables. Other variables were also recorded in the field sampling such as site conditions, understory vegetation, and disturbance type and history, etc. Through enormous investment of time and work, this forest inventory provides the best information on forest conditions to support the provincial forest management agency and forest industry to make sound strategic and operational management planning for the region. Since April 2009, the Nopiming Provincial Park has been excluded from this FML for harvest thus the total size of the FML is reduced. A test plot (located at easting 750,156 and northing 5,646,985 of the UTM Zone 14) dataset was used in this study first for a detailed examination of whether the standard procedure of estimating stand volume can be directly used in the value recovery estimate at the stand level. The plot is within an almost pure black spruce (Picea mariana (Mill.) B.S.P.) stand with an age of 68 years. The plot data were collected on April 16, 2002, and contained the measurements of 116 individual black spruce trees. Tree taper was calculated from the diameter inside the bark (DIB) between 15 cm above ground and the tree height at 5 cm DIB from the top based on the method of Klos et al. (2007). The same analytical procedure was applied to all the polygon plots in the study area with a black spruce component of at least 10% (499 plots in total) to investigate the potential influence of the standard procedure on the accuracy of lumber value recovery estimates. 2.3. Methods of valuation of lumber recovery A general approach of estimating stand level forest wood volume from measurements of individual trees is to develop individual tree-based volume equations first and estimate stand level volume according to the stand structure through using these volume equations. However, it is usually simplified in operation to a simple procedure as (1) obtain the mean values of measured DBH and H of all sampled trees for a given tree species under investigation, and (2) use these mean values as representative of all trees in the stand and multiplied by the total number of trees of the stand to calculate the mean wood volume per unit area using the volume equations. This procedure has become more or less standard in the forest inventory construction and is used in many forest growth and yield modeling practices. With the shift of forest management paradigm from being volume-based to value-based, an assumption that value creation potential is proportional to wood volume may have been used in
Fig. 1. Study area location indicated by the grey coloured area (data as March 2009).
C. Li et al. / Ecological Complexity 7 (2010) 208–211
210
Table 1 Lumber value recovery estimates from the test plot dataset. Items
Value recovery ($)
VReal VMean VMean VReal B (%)
669.88 484.74 185.14 27.6
Table 2 The relative contribution to the biased lumber value recovery from DBH, H, and T. Items
Actual value ($)
Sensitivity (10% increase) value ($)
B (%)
Relative contribution (%)
DBH H T
669.88 669.88 669.88
617.01 515.34 501.72
71.4 16.5 9.2
73.5 17.0 9.4
estimating value recovery of wood volume without detailed examination using empirical observations. In this study, we use a plot dataset from our study area to test a hypothesis that there is no significant difference between the estimated values of lumber recovery from different statistical procedures. This hypothesis test is aimed at determining whether the standard procedure in volume recovery estimates can be directly used in value recovery estimation without experiencing significant bias. If this hypothesis is true, the lumber value recovery calculated from this standard method should be equal or very similar to the true value, which is the sum of lumber value recovery from all individual trees. The tree level lumber value recovery, VLumber, can be calculated as a function of DBH and H (Zhang et al., 2006), in which the Optitek software1 was used to maximize the lumber recovery of a black spruce. V Lumber ¼ 0:002 H0:6423 DBH2:5315 T 0:3612
(1) Fig. 2. Biased lumber value estimates of all the inventory plots with a black spruce component in the study area (499 plots in total).
where T is tree taper calculated as: T¼
DBHStum p15 DBHTo p10 HTo p10 0:15
(2)
where HTo p10 is the top height at the DIB of 10 cm, and the DBHStum p15 and DBHTo p10 are the DBH at the stump height of 15 cm and top height at the DIB of 10 cm, respectively. 2.4. Data analysis Eq. (1) was used to calculate the real value recovery for each individually measured tree, and the summation of all the value recoveries was used as the real value for the plot’s value creation potential, VReal. The statistical procedure of volume recovery estimate was applied to the plot data by obtaining the mean values of DBH, H, and T, and then Eq. (1) was used to calculate mean value recovery of all the individual trees in the plot, and the plot’s value creation potential, VMean, is obtained by multiplying by the number of trees. The estimate of the percentage of biased value recovery from the true value recovery, B, by using the mean values of DBH, H, and T was calculated as: V Mean V Real B¼ 100% V Real
(3)
A sensitivity analysis was also carried out by individually varying the mean values of measured variables by 10% increments, and then calculating the relative contributions of the variables to the bias estimation. 3. Results Table 1 shows the true lumber value recovery of the trees in the test plot dataset and the one estimated using the simplified statistical procedure. The value from the simplified procedure 1 The Optitek software package was developed by the Forintek Division of the FPInnovations, Canada for sawmills to optimize log cutting pattern for maximizing the percentage of lumber volume recovery.
underestimated the true value by 27.6%. Therefore, the hypothesis that there is no significant difference between the estimated lumber value recovery from the simplified statistical procedure and the true value did not hold in this case. Table 2 shows the relative contribution to the biased lumber value recovery from DBH, H, and T. Our sensitivity analysis results in Table 2 suggests that among these three variables DBH contributed the most (74%), and followed by H (17%), and T (9%). Therefore, more attention should be paid to DBH and its distribution within a stand. Fig. 2 is the results of applying the test procedure to all the inventory plots that contain a black spruce component (499 plots in total). The distribution of the biased estimates was very scattered along the stand age, with 17.8% underestimate the true value in average. The range of the bias was from a 73.5% underestimate to a 3.5% overestimate. 4. Discussion 4.1. Forest valuation—forest product options Forest valuation provides useful information for forest manager’s decision-making on whether a harvest operation should be performed and what to do with it when trees are harvested. From the forest economics perspective, the harvest operation should probably be performed only when that operation could result in a certain level of benefits, which is determined by the net or marginal value (based on either current or future value) of the forest, i.e., the difference between forest value and the costs associated with the product production. Our discussion is focused on forest valuation (or the value creation potential of the forest) with fixed costs for simplification. A number of product options could be available for each of the forests from a forest manager’s perspective, and the determination of an optimal wood utilization from the forest is perhaps the best way to maximize the value creation potential. Consequently, the information required for this
C. Li et al. / Ecological Complexity 7 (2010) 208–211
determination will be the value creation potential estimates for various product options. We focused on the lumber product option in this study because of its likely higher expectation in economic return from harvested trees than that of other forest product options. It is also because they are relatively straightforward to account for because they are priced goods and services from the forests. However, our results suggested that the valuation of this product option could still be complicated by different statistical procedures. Nevertheless, this complication could be resolved through application of correct statistical procedure, i.e., to calculate lumber value recovery for each individual tree first, and then sum them up to obtain plot level lumber value recovery. In other words, one needs to reconstruct the stand structure before estimating lumber value recovery of the stand. Forest valuation can be complicated by other factors, such as changes in industry structure, mill infrastructure, forest policy, and fluctuations in market conditions. It can also be complicated by the complex, hierarchical, and adaptive dynamics of forest ecosystems (Costanza and Jørgensen, 2002), coupled with human systems (Liu et al., 2007). Human behaviour as another important aspect in decision-making has also gained increasing attention in bioeconomics research (Clark, 2007; Breda et al., 2008; Brede and Boschetti, 2009). However, they are beyond the scope of this paper and will be discussed elsewhere. 4.2. Information flow across scales Information flow across scales has been one of the central concerns in ecology in the past couple of decades (Makarieva et al., 2004). It concerns whether the research results or observations made at a lower level of hierarchical structure can be appropriately used in the next higher level of ecosystem structures. For instance, can observations made at the individual tree level be appropriately used in the presentations of stand level research results? With this information scaling-up process, detailed presentation of variables measured at the individual tree level could be lost. However, this information is represented in frequency distributions of the variables and species composition within the stand. Whether this loss of detailed information is acceptable for the purpose of information presentation and whether the detailed information can be reconstructed from the aggregated presentation of information are probably the most important issues facing forest managers. Considering that it is not feasible or desirable to measure every individual tree and/or stand, certain kinds of approximation must be made and this is perhaps one of the main focuses in the study of information flow across scales. Our case study is aimed at addressing a practical question of whether the simplified statistical procedure in volume estimation can be directly used for the estimation of lumber value recovery. Our results from a single plot dataset suggest that about a 27% bias in underestimating black spruce lumber value recovery could occur when the simplified procedure is used. A wider range of biases were found when the same statistical procedure applied to all the plot data in the study area with a black spruce component. Though the results are a surprise, it is still understandable from a sampling theory perspective since the bias was probably caused by the nonlinear nature of the lumber value recovery function (Eq. (1)), together with the fact that the sampled distributions of
211
DBH and H do not follow the normal probability distribution. The overall results suggest that the simplified statistical procedure should be avoided. Computer simulations based on the reconstruction of stand structure could provide a solution to reduce the possible population level estimates, which will be discussed in a separate article. 4.3. Management application Our recommendations from the results of this study include: (1) due to the loss of detailed information in aggregated presentation, simplifications in analytical procedures should be avoided whenever it is possible to ensure the accuracy in estimation; (2) forest managers and researchers can take advantage of fast developing information technology and increasing computing power, to test simplifications and assumptions carefully before applying them widely; and (3) reconstruction of stand structure through computer simulations could improve the accuracy of population estimates, and achieve the goal of information flow across multiple scales without losing accuracy significantly. 5. Conclusions Simplified statistical procedures could bring about a wide range of biases in population estimation, specifically in lumber value recovery estimates from the forest inventory plot data of Manitoba, Canada. Improved understanding of stand structure and its reconstruction could be essential in reducing the bias. References Brede, M., Boschetti, F., 2009. Commons and anticommons in a simple renewable resource harvest model. Ecological Complexity 6, 56–63. Breda, M., Boschetti, F., McDonald, D., 2008. Strategies for resource exploitation. Ecological Complexity 5, 22–29. Clark, C.W., 2007. The Worldwide Crisis in Fisheries: Economic Models and Human Behavior. Cambridge University Press. Costanza, R., Jørgensen, S.E. (Eds.), 2002. Understanding and Solving Environmental Problems in the 21st Century: Toward a New, Integrated Hard Problem Science. Elsevier. Guthrie, G., Kumareswaran, D., 2009. Carbon subsidies, taxes and optimal forest management. Environmental and Resource Economics 43, 257–293. Holt, R.D., 1987. Population dynamics and evolutionary processes: the manifold roles of habitat selection. Evolutionary Ecology 1, 331–347. Klos, R.J., Wang, G., Dang, Q.L., East, E.W., 2007. Taper equations for five major commercial tree species in Manitoba, Canada. Western Journal of Applied Forestry 22, 163–170. Li, C., 2009. Toward full, multiple, and optimal wood fibre utilization: a modeling perspective. Forestry Chronicle 85, 377–381. Li, C., Liu, J., Lafortezza, R., Chen, J., 2010. Managing forest landscapes under changing global scenarios. In: Li, C., Lafortezza, R., Chen, J. (Eds.), Landscape Ecology and Forest Management: Challenges and Solutions in a Changing Globe. HEP-Springer, in press. Liu, J., Dietz, T., Carpenter, S.R., Alberti, M., Folke, C., Moran, E., Pell, A.N., Deadman, P., Kratz, T., Lubchenco, J., Ostrom, E., Ouyang, Z., Provencher, W., Redman, C.L., Schneider, S.H., Taylor, W.W., 2007. Complexity of coupled human and natural systems. Science 317, 1513–1516. Makarieva, A.M., Gorshkov, V.G., Li, B.L., 2004. Body size, energy consumption and allometric scaling: a new dimension in the diversity–stability debate. Ecological Complexity 1, 139–175. Manitoba Conservation, 2006. Wood supply report for forest management licence area #1.