Simplifying the decision matrix for estimating fine root production by the sequential soil coring approach

Acta Oecologica 48 (2013) 54e61

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Original article

Simplifying the decision matrix for estimating fine root production by the sequential soil coring approach Z.Y. Yuan, Han Y.H. Chen* Faculty of Natural Resources Management, Lakehead University, 955 Oliver Rd, Thunder Bay, Ontario P7B 5E1, Canada

a r t i c l e i n f o

a b s t r a c t

Article history: Received 4 September 2012 Accepted 16 January 2013 Available online 5 March 2013

Sequential soil coring is a commonly used approach to measure seasonal root biomass and necromass, from which root production can be estimated by maximumeminimum, sum of changes, compartmentflow model, and/or decision matrix methods. Among these methods, decision matrix is the most frequently used. However, the decision matrix, often underestimating fine root production, is frequently misused in research due to inadequate documentation of its underlying logic. In this paper, we reviewed the decision matrix method and provided mathematical logic for the development of the matrix, by which not only root production but also mortality and decomposition rates can be calculated. To ease its use for large datasets, we developed simplified equations to facilitate computation of root production, mortality and decomposition to be used in MS Excel or R. We also presented results from calculations by an example using empirical data from boreal forests to show proper calculations of root production, mortality and decomposition. The simplified decision matrix presented here shall promote its application in ecology, especially for large datasets. Ó 2013 Elsevier Masson SAS. All rights reserved.

Keywords: Belowground production Decision matrix Decomposition Fine roots Mortality Sequential soil coring

1. Introduction Net primary production (NPP) is an essential component for energy, carbon and nutrient budget models in terrestrial ecosystems (Field et al., 1995; Jackson et al., 1997; Cramer et al., 1999; Fahey and Knapp, 2007). Although there is a long history of NPP studies in the ecological literature, current understanding of ecosystem-level production is biased to aboveground NPP (ANPP). Despite its importance in nutrient cycling and resource acquisition, belowground NPP (BNPP), which is often greater than ANPP (Gower et al., 2001; Yuan et al., 2006), is seldom measured, mainly due to methodological difficulties associated with collecting belowground data. For natural ecosystems, direct measurement of NPP, especially BNPP, is difficult and often impossible (Clark et al., 2001; Tierney et al., 2007). Indirect methods, therefore, are commonly used to estimate BNPP (Fahey et al., 1999; Lauenroth, 2000). Because the production of fine roots (<2 mm in diameter) (FRP) can account for up to 80% BNPP (Nadelhoffer and Raich, 1992), FRP is generally used as an analog for BNPP (Yuan et al., 2011). Of all indirect methods, sequential soil coring has been most commonly used in the published literature (Vogt et al., 1998; Hendricks et al., 2006; Yuan and Chen, 2012a). This method is based on the changes in biomass and necromass among

* Corresponding author. Tel.: þ1 807 343 8342; fax: þ1 807 8116. E-mail address: [email protected] (H.Y.H. Chen). 1146-609X/$ e see front matter Ó 2013 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.actao.2013.01.009

multiple sampling dates during a period of one year or longer. From sequential soil cores, FRP can be estimated by one of the following procedures: 1) “maximumeminimum method”, which is based on differences between the maximum and minimum root biomass measured during a year, 2) “sum of changes methods”, which is mostly based on all statistically significant positive differences in root biomass between successive sampling dates, 3) “compartment-flow model” technique, which includes two compartments (live and dead) and three flows (production, mortality and decomposition). 4)“decision matrix” method, or “balancing transfer” calculations, which consider significant changes in both live and dead roots between sample dates (Santantonio and Grace, 1987; Publicover and Vogt, 1993; Vogt et al., 1998). The decision matrix, a multi-compartment model, is widely used in a broad literature in mathematics and other fields. In ecology, it was first developed by Singh and Yadava (1974) and modified by Pettersson and Hansson (1990) for estimating ANPP. For FRP estimation, the decision matrix was first developed by McClaugherty et al. (1982) and modified by Fairley and Alexander (1985). This approach is further improved by Publicover and Vogt (1993) and Murach et al. (2009), but it appears to underestimate fine root dynamics (Osawa and Aizawa, 2012). However, the matrices developed by these authors differ from one another. As a result, various adapted and complex matrices have been used in the published literature. These matrices frequently confuses researchers and may be one important contributing factor to the variations in FRP

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55

estimates among studies since the same coring data can result in different estimates from different and often misused matrices. Unfortunately, no logical reasoning has been provided in the original and later relevant literatures for the use of a specific matrix. In this paper, we provide the underlying mathematical logic for the development of decision matrix. We also provide a simplified decision matrix to make it to be more used friendly. To ease the difficulty to assess the decision matrix individually for each sample, especially when large datasets are involved, we developed simplified equations in a MS Excel format and codes in R. Lastly, we presented an example to show how to calculate root production, mortality and decomposition in boreal forest stands from northwestern Ontario, Canada. 2. The models for decision matrix BNPP/FRP based on sequential soil cores could be described by a pool-flux model in a single pool system (Fig. 1). This pool-flux model for the studied system could be viewed as a reservoir (or pool) with mass X and fluxes of input and output associated with time t. This system can be a single leaf, whole plant, community, or ecosystem. The function of X is:

Z f ðtÞ ¼

½IðtÞ  OðtÞdt

(1)

where I(t) and O(t) are the input and output rate of X in the system, respectively. The change of pool X within a period of t2  t1 is:

DX ¼ f ðt2 Þ  f ðt1 Þ ¼

Zt2

Zt2 ½IðtÞ  OðtÞdt ¼

t1

Zt2 IðtÞdt 

t1

OðtÞdt t1

¼ Xin  Xout

ð2Þ

where Xin and Xout are the integral functions of I(t) and O(t), respectively. For a root system, the pool-flux model comprises two pools (live and dead root mass, units: Mg ha1) and three fluxes (root production, mortality and decomposition, units: Mg ha1 year1) (Fig. 2). Therefore, if L(t), D(t), p(t),m(t) and c(t)represent biomass, necromass and rates of production, mortality and decomposition, respectively, the biomass and necromass at any time t are:

Z Root biomass : LðtÞ ¼

½pðtÞ  mðtÞdt

(3)

Z Root necromass : DðtÞ ¼

½mðtÞ  cðtÞdt

(4)

From time t1 to t2, the change in biomass and necromass are:

Change in biomass : DL ¼ Lðt2 Þ  Lðt1 Þ ¼

Fig. 2. The model system for estimating root production, mortality and decomposition based on sequential cores. p(t), m(t) and c(t) are rates of root production, mortality and decomposition with time t, respectively. t1 and t2 represent time. Pools are represented by circles (biomass) and ellipses (necromass); fluxes by heavy arrows (closed and dashed represent influx and efflux, respectively). Narrow arrows represent root mass at time t1 and t2. Root production (P), mortality (M) and decomposition (C) from time t1 to t2 are represented by cylinders. L and D are live and dead root mass, respectively. DL and DD, the changes in live root mass (biomass) and dead root mass (necromass) between two consecutive measurements, respectively, are represent by dashed cylinder and cube, respectively. The dashed shade outside the circle (biomass) and the ellipse (necromass) represent the changes in root biomass and necromass at time t2, respectively. Note that DL and DD can be positive, negative or zero.

Change in necromass : DD ¼ Dðt2 Þ  Dðt1 Þ Zt2 ½mðtÞ  cðtÞdt

¼ t1

In natural ecosystems, the rates of production, mortality and decomposition, i.e., p(t),m(t) and c(t), vary with time. Consequently, from a mathematical perspective, it is unrealistic to know their instantaneous rates and to get the integration from these functions. However, when we assume p(t),m(t) and c(t) to be constant within a short period of sampling intervals such as a week or month, then

Root production : pðtÞ ¼ P

(7)

Root mortality : mðtÞ ¼ M

(8)

Root decomposition : cðtÞ ¼ C

(9)

where P, M and C are constants. The equations (5) and (6) can then be changed into:

Change in biomass : DL ¼

Zt2

ðP  MÞdt ¼ ðP  MÞtjtt21

t1

Zt2 ½pðtÞ  mðtÞdt

(5)

(6)

(10)

¼ ðP  MÞðt2  t1 Þ

t1

Change in necromass : DD ¼

Zt2

ðM  CÞdt ¼ ðM  CÞtjtt21

t1

Input

the ‘black box’

X

¼ ðM  CÞðt2  t1 Þ Output

Fig. 1. A simple model showing pool (X), influx (input) and efflux (output) rate in a dynamic system. Pools are represented by ellipses; fluxes by arrows (closed and dashed represent influx and efflux, respectively).

ð11Þ

If sampling interval is one unit (month or week), t2t1 ¼ 1. Then,

Change in biomass : DL ¼ P  M

(12)

Change in necromass : DD ¼ M  C

(13)

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Z.Y. Yuan, H.Y.H. Chen / Acta Oecologica 48 (2013) 54e61

From sequential soil cores, the DL and DD are known variables (calculated as differences in root mass between successive sampling dates). However, there are three unknown variables (P, M and C) in Equations (12) and (13) and thus it is impossible to calculate those unknown variables from a mathematic point of view. Based on the pool-flux model (Fig. 2) and Equations (12) and (13), P, M and C could be calculated as:

Root production : P ¼ DL þ M ¼ DL þ DD þ C

(14)

Root mortality : M ¼ DD þ C ¼ P  DL

(15)

Root decomposition : C ¼ M  DD ¼ P  ðDL þ DDÞ

(16)

Because there are fewer known variables than unknown variables in the set of equations, we need an additional assumption to solve the above equations: let the smallest unknown variable of P, M and C be equal to zero. The rest two variables can be calculated according to the Equations (14)e(16). Therefore, the process to develop the decision matrix is dependent upon whether the changes in biomass are equal to zero. In other words, first, we need to figure out which variable is the smallest and then assume this variable to be zero. Second, the other two remaining variables can be calculated according to the Equations (14)e(16). Here, we discuss the calculations based on the changes in biomass firstly and in necromass secondly as below. 1. When DL > 0, i.e., P > M. We need to calculate P, M and C based on the sign of changes in necromass. 1) When DD>0, i.e., M > C. Then P > M > C. In this case, C is assumed to be zero. From the Equations (14)e(16), P and M can be calculated as: 2) When DD ¼ 0, i.e., M ¼ C. Then P > M ¼ C. So both M and C in this case are assumed to be zero, then P ¼ DL 3) When DD < 0, i.e., M < C. Then P > M < C. M is assumed to be zero, then P ¼ DL. In this case, C is a positive value that is larger than M. It equals to absolute value of the change in root necromass (negative value), i.e.,

C ¼ DD ¼ jDDj 2. When DL ¼ 0, i.e., P ¼ M. 1) When DD > 0, i.e., M > C. Then P ¼ M > C. We need to assume C equals to zero, then P ¼ DL þ DD ¼ DD, M ¼ DD 2) When DD ¼ 0, i.e., M ¼ C. In this case, P, M and C are all zero. 3) When DD < 0, i.e., M < C. Then P ¼ M < C. In this case, we need to assume P ¼ M ¼ 0. Therefore, C ¼ DD ¼ jDDj

3. When DL < 0, i.e., P < M. 1) When DD > 0, i.e., M > C. Then P < M > C. At this condition, we still do not know the smallest variable among P and C. So, further discussion is needed. a) if jDLj > jDDj. Thus M  P > M  C because DL < 0 and DD > 0. Then P < C, P < M. Therefore, assuming P ¼ 0, then M ¼ DL ¼ jDLj; C ¼ DL  DD ¼ jDL þ DDj b) if jDLj ¼ jDDj, i.e., M  P ¼ M  C. Then P ¼ C < M, Therefore, let P ¼ C ¼ 0, then M ¼ jDLj ¼ jDDj c) if jDLj < jDDj, i.e., M  P < M  C. Then M > P > C. Therefore, let C ¼ 0, then P ¼ DL þ DD; M ¼ jDDj 2) When DD ¼ 0, i.e., M ¼ C. Then P < M ¼ C. Let P ¼ 0, thenM ¼ DL ¼ jDLj; C ¼ DL  DD ¼ jDL þ DDj 3) When DD < 0, i.e., M < C. Then P < M < C. Let P ¼ 0, then M ¼ DL ¼ jDLj; C ¼ DL  DD ¼ jDL þ DDj Based on the above logic, a decision matrix is given in Table 1. By summing weekly or monthly P, M and C from each sampling interval, annual root production, mortality and decomposition can be obtained. The matrix as shown in Table 1, however, is complete and it is tedious to be used in research, especially for a large dataset. Table 1 can be simplified into Table 2A and simplified equations can be developed for use in MS Excel or R:

P ¼ if ðsignðDL þ DDÞ > ¼ 0; DL þ DD*signð1 þ signðDDÞÞ; if ðDL > ¼ 0; DL; 0ÞÞ

ð17Þ

M ¼ if ðsignðDL þ DDÞ > ¼ 0; DD*signð1 þ signðDDÞÞ; if ðDL < ¼ 0; DL; 0ÞÞ

ð18Þ

C ¼ if ðsignðDL þ DDÞ > ¼ 0; DD*ðsignð1 þ signðDDÞÞ  1Þ; if ðDL < ¼ 0; DL  DD; DDÞÞ ð19Þ where the If function returns one value if a specified condition is TRUE, or another value if it is FALSE; the sign function returns the sign of a number (1 if positive, 0 if 0, 1 if negative). Equations from 17 to 19 for Table 2a can be applied to data in MS Excel (see the XLSX file in the Appendix). By summing weekly or monthly P, M and C calculated from Equations (17)e(19), we can get the annual P, M and C. The R codes are given in Table 3. First, the data is read from a CSV file. Then the data are sorted by sampling month, stand age, soil layer and replicates and so on. Second, the monthly changes in root biomass (RdL) and necromass (RdD) can be calculated. Third, the monthly production, mortality, and decomposition can be calculated by a loop with ‘if else’ statements in R. In this table, we need to know if RdL or RdD in a cell is negative or positive in value or whether it equals to zero. From the above monthly production,

Table 1 The decision matrix for calculating root production, mortality and decomposition based on sequential soil cores. D ¼ changes in fine root biomass or necromass, L ¼ biomass, D ¼ necromass, P ¼ production, M ¼ mortality, C ¼ decomposition. The two vertical bars after equal sign indicate the absolute values. Inequalities in the top rows and in the first left column indicate conditions on the values of changes in fine root biomass and necromass, on which the suggested equations in the Table are given to calculate fine root production, mortality and decomposition based. If

DL > 0

DL ¼ 0

DD > 0

P ¼ DL + DD M ¼ DD C¼0 P ¼ DL M ¼ DD ¼ 0 C ¼ DD ¼ 0 P ¼ DL M¼0 C ¼ jDDj

P ¼ DL + DD ¼ DD M ¼ DD C¼0 P¼0 M ¼ DD ¼ 0 C ¼ DD ¼ 0 P¼0 M ¼ jDLj ¼ 0 C ¼ jDDj

DD ¼ 0 DD < 0

DL < 0 jDLj > jDDj

jDLj ¼ jDDj

jDLj < jDDj

P¼0 M ¼ jDLj C ¼ jDL + DDj P¼0 M ¼ jDLj C ¼ jDL + DDj ¼ jDLj P¼0 M ¼ jDLj C ¼ jDL + DDj

P ¼ jDL + DDj ¼ 0 M ¼ jDLj C¼0 ∕

P ¼ DL + DD M ¼ DD C¼0 ∕

P¼0 M ¼ jDLj C ¼ jDL + DDj ¼ 0

P¼0 M ¼ jDLj C ¼ jDL + DDj

Z.Y. Yuan, H.Y.H. Chen / Acta Oecologica 48 (2013) 54e61 Table 2 Two simplified decision matrices (A and B) for calculating root production, mortality and decomposition based on sequential soil cores. D ¼ changes in fine root biomass or necromass, L ¼ Live mass, D ¼ dead mass, P ¼ production, M ¼ mortality, C ¼ decomposition. Vertical bars indicate the absolute values. Inequalities in the first left column indicate conditions on the values of changes in fine root biomass and necromass, on which the suggested equations in the Table are given to calculate fine root production, mortality and decomposition based. (A) If

DL + DD  0 DD  0 DD < 0 DL + DD < 0 DL  0 DL < 0

P

M

C

DL + DD DL

DD 0

0 jDDj

DL

0 jDLj

DD jDL + DDj

0

(B) If

P

M

C

DL + DD  0 & DD  0 DL  0 & DD  0 DL  0 & DL + DD  0

DL + DD DL

DD

0 jDDj jDL + DDj

0

0 jDLj

mortality and decomposition, we can get the annual values for those three variables accordingly (see how to run R codes with running results in the pdf file in the Appendix). Alternatively, based on the assumption that the smallest unknown variable of P, M and C is equal to zero, another simplified decision matrix can be developed as below. 1) If C is the smallest among P, M and C, then let C ¼ 0, from the Equations (14)e(16), P, M and C can be calculated as:

P ¼ DL þ DD M ¼ DD 2) If M is the smallest among P, M and C, then let M ¼ 0. then

P ¼ DL C ¼ DD 3) If P is the smallest among P, M and C, then let P ¼ 0. then

M ¼ DL C ¼ DL  DD ¼ ðDL þ DDÞ ¼ jDL þ DDj This decision matrix is given in Table 2B. Similarly, simplified equations can be derived:

P ¼ if ðandðDL > ¼ 0; DD < ¼ 0Þ; DL; if ðandðDL < ¼ 0; DL þ DD < ¼ 0Þ; 0; DL þ DDÞÞ

ð20Þ

M ¼ if ðandðDL > ¼ 0; DD < ¼ 0Þ; 0; if ðandðDL < ¼ 0; DL þ DD < ¼ 0Þ; DL; DDÞÞ ð21Þ C ¼ if ðandðDL > ¼ 0; DD < ¼ 0Þ; DD; if ðandðDD > ¼ 0; DL þ DD > ¼ 0Þ; 0; ðDL þ DDÞÞÞ

(22)

where the and function returns TRUE if all conditions are met, otherwise it returns FALSE. Equations from 20 to 22 for Table 2B can

57

be also applied to data in Excel format (see the xlsx file in the Appendix). Similarly, we can get the annual P, M and C by summing weekly or monthly P, M and C calculated from Equations (20)e(22). The corresponding R codes are provided in Table 3. Equations (17)e(22) rely on two additional assumptions. First, only two pools and three fluxes are considered (Fig. 2) because only root biomass and necromass are known from sequential cores. Thus the decision matrix does not consider mass losses through herbivory. Moreover, growth from fine roots into coarse roots is not considered. This method considers root decomposition but does not measure it, therefore differing from the method by Osawa and Aizawa (2012) who evaluated decomposition with a root litter bag experiment. Second, all fluxes are assumed to be constant between two successive sampling times: This is unrealistic for natural ecosystems, especially for fine roots of fast-growing species and in young stands during the growing season. To minimize potential errors associated with these assumptions, the period between two successive sampling times should not be too long. Although we do not know the accurate period, monthly sampling is recommended at least for natural ecosystems to balance the destructive nature of soil coring and reduction of errors associated with constant flux rate assumption. The above two assumptions and the assumption to let the smallest of P, M and C ¼ 0 may lead to underestimation of root production associated with decision matrix approach (Osawa and Aizawa, 2012). It is urgently needed to understand the extent of underestimation associated with these assumptions in various natural ecosystems. Albeit many ‘new’ approaches have been proposed in the past several decades (Hertel and Leuschner, 2002; Hendricks et al., 2006), there is no technique to date that can ‘measure’ directly belowground processes, including fine root production. In the first developed decision matrix for estimating root production, mortality and decomposition (McClaugherty et al., 1982), the authors calculated both production and mortality as the change in biomass (i.e., P ¼ M ¼ DL) when DL  0 and DD  0. In that case, P  M ¼ 0 s DL, which differs from the Equation (12). The equation for M in their matrix, therefore, should be corrected as M ¼ 0. In the later modified and most cited decision matrix (Fairley and Alexander, 1985), the authors let M ¼ DL when DL < 0, DD > 0 and DL > DD. However, since DL < 0 but DD > 0, it is impossible to have DL > DD. The formulation in their matrix, therefore, should be changed into jDLj > jDDj, as shown in our Table 1. Murach et al. (2009) provided a corrected, but highly complicated decision matrix, and they did not give the logic, either. Next, by a case study, we applied our simplified equations in MS Excel and R codes to a boreal forest system and showed how to calculate fine root production, mortality and decomposition based on a decision matrix derived from sequential soil coring data. 3. An example from boreal forests To test our decision matrix and simplified equations, a case study was conducted in a boreal mixed-wood forest north of Lake Superior and west of Lake Nipigon in the Spruce River Forest and Black Sturgeon Forest, ca. 100 km west of Armstrong, Ontario, Canada between 49 270 N to 49 380 N and 89 290 W to 89 540 W with 350e370 m elevation. This region is characterized by warm summers and cold, snowy winters. Mean annual temperature is 0.4  C and mean annual precipitation is 716 mm. The vegetation of the study area is dominated by trembling aspen (Populus tremuloides Michx.), jack pine (Pinus banksiana Lamb.), black spruce (Picea mariana [Mill.] B.S.P), and paper birch (Betula papyrifera Marsh.). Wildfire is the most common natural disturbance in the study area, with an average wildfire return interval of approximately 100 years for the past century (Senici et al., 2010;

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Table 3 R codes (in Italic) for calculating fine root production, mortality and decomposition. Notes: 1. DL & DD represent monthly changes in root biomass and necromass, respectively. They are named as RdL or RdD in R, respectively. n is the row number to write the first RdL or RdD. n shall be equal to the total number of samples per month. In our case, n is 24. 2. RmP, RmM and RmC represent monthly production, mortality and decomposition, respectively. The number (1 or 2) after RmP, RmM and RmC refer to the calculations based on Equations (17)e(19) (Table 2A) or based on Equations (20)e(22) (Table 2B). 3. rP, rM and rC represent annual production, mortality and decomposition, respectively. The number (1 or 2) after rP, rM and rC refer to the calculations based on Equations (17)e(19) (Table 2A) or based on Equations (20)e(22) (Table 2B). The number of 121 is the row number to write the first production, mortality and decomposition. The number of 24, 48, 72 and 96 represent the row numbers for monthly production, mortality and decomposition from same treatment, respectively.

Step Read data Sort data ΔL & ΔD1

R code mydata<-read.csv(file.choose()) mydata[order(mydata$month,mydata$age,mydata$layer,mydata$replicate),] for (i in (n+1):nrow(mydata)) { mydata$RdL[i]<-mydata$L[i]-mydata$L[i-n] mydata$RdD[i]<-mydata$D[i]-mydata$D[i-n)] } Monthly P, M & C2 RmP1 for(i in 1:nrow(mydata)) {if(sign(mydata$RdL[i]+mydata$RdD[i])>=0) {mydata$RmP1[i]=0) {mydata$RmP1[i]<-mydata$RdL[i]} else {mydata$RmP1[i]<-0} } RmP2 for(i in 1:nrow(mydata)) { if(mydata$RdL[i]>=0 & mydata$RdD[i]<=0) {mydata$RmP2[i]<-mydata$RdL[i]} else if(mydata$RdL[i]+mydata$RdD[i]>=0 & mydata$RdD[i]>=0) {mydata$RmP2[i]<-mydata$RdL[i]+mydata$RdD[i] } else {mydata$RmP2[i]<-0} } RmM1 for(i in 1:nrow(mydata)) { if(sign(mydata$RdL[i]+mydata$RdD[i])>=0) {mydata$RmM1[i]<-mydata$RdD[i]*sign(1+sign(mydata$RdD[i]))} else if(sign(mydata$RdL[i]+mydata$RdD[i])<0 & mydata$RdL[i]<=0) {mydata$RmM1[i]<-(-1)*mydata$RdL[i]} else {mydata$RmM1[i]<-0} } RmM2 for(i in 1:nrow(mydata)) { if(mydata$RdL[i]+mydata$RdD[i]>=0 & mydata$RdD[i]>=0) { mydata$RmM2[i]<-mydata$RdD[i] } else if(mydata$RdL[i]+mydata$RdD[i]<=0 & mydata$RdL[i]<=0) { mydata$RmM2[i]<-(-1)*mydata$RdL[i] } else {mydata$RmM2[i]<-0} } RmC1

RmC2

for(i in 1:nrow(mydata)) { if(sign(mydata$RdL[i]+mydata$RdD[i])>=0) {mydata$RmC1[i]<-mydata$RdD[i]*(sign(1+sign(mydata$RdD[i]))-1)} else if(sign(mydata$RdL[i]+mydata$RdD[i])<0 & mydata$RdL[i]<=0) {mydata$RmC1[i]<-(-1)*(mydata$RdL[i]+mydata$RdD[i])} else {mydata$RmC1[i]<-0} } for(i in 1:nrow(mydata)) { if(mydata$RdL[i]>=0 & mydata$RdD[i]<=0) { mydata$RmC2[i]<-(-1)*mydata$RdD[i] } if(mydata$RdL[i]+mydata$RdD[i]<=0 & mydata$RdD[i]<=0) { mydata$RmC2[i]<-(-1)*(mydata$RdL[i]+mydata$RdD[i])} else {mydata$RmC2[i]<-0} }

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59

Table 3 (Continued)

Annual P, M & C3 Table 2A for (i in 121:nrow(mydata)) { mydata$rP1[i]<-mydata$RmP1[i]+mydata$RmP1[i-24]+mydata$RmP1[i48]+mydata$RmP1[i-72]+mydata$RmP1[i-96] mydata$rM1[i]<-mydata$RmM1[i]+mydata$RmM1[i-24]+mydata$RmM1[i48]+mydata$RmM1[i-72]+mydata$RmM1[i-96] mydata$rC1[i]<-mydata$RmC1[i]+mydata$RmC1[i-24]+mydata$RmC1[i48]+mydata$RmC1[i-72]+mydata$RmC1[i-96] } Table 2B mydata$rP2<-0; mydata$rM2<-0; mydata$rC2<-0 for (i in 121:nrow(mydata)) { mydata$rP2[i]<-mydata$RmP2[i]+mydata$RmP2[i-24]+mydata$RmP2[i48]+mydata$RmP2[i-72]+mydata$RmP2[i-96] mydata$rM2[i]<-mydata$RmM2[i]+mydata$RmM2[i-24]+mydata$RmM2[i48]+mydata$RmM2[i-72]+mydata$RmM2[i-96] mydata$rC2[i]<-mydata$RmC2[i]+mydata$RmC2[i-24]+mydata$RmC2[i48]+mydata$RmC2[i-72]+mydata$RmC2[i-96] }

Yuan and Chen, 2012a). Two stand age classes, i.e., 11 and 205 years since wildfire, respectively, were sampled, each randomly replicated by three spatially interspersed stands about 5 km apart. Sequential soil cores were used to obtain fine root data monthly from July to October in 2008 and from May to June in 2009 from a 20  20 m plot at each sampled stand. Therefore, an additional assumption in our case study was that there was no significant root growth in winter when soils were frozen. This assumption does not change the application of our proposed equations and codes to sequential (monthly or weekly) data. Eleven soil cores from each stand were extracted with a soil corer (6.6 cm in inner diameter) from the forest floor surface to 30 cm depth in the mineral soil using a power auger. The extracted cores were separated into forest floor layer (FF) and two mineral soil sections: 0e15 cm (MS1) and 15e30 cm (MS2). In the laboratory, fine roots (2 mm in diameter), by pooling all species together (including ground vegetation and trees of other species that might be growing there), were sorted according to vitality (live or dead). Fine roots were considered ‘live’ if they were pale-colored on the exterior, elastic and flexible, and free of decay with a whitish cortex, while fine roots were classified as ‘dead’ if they were brown or black in color, rigid and inflexible, in various stages of decay, and had a dark colored cortex (Brassard et al., 2011). After sorting, fine roots were oven-dried to a constant mass at 65  C and weighed. We first calculated monthly changes in fine root biomass (DL) and necromass (DD). Second, we calculated monthly fine root production, mortality and decomposition according to our simplified decision matrix (Table 2) both in Excel by using Equations (17)e(19) (Table 2A), Equations (20)e(22) (Table 2B) and in R by using the R codes (Table 3). Annual fine root production, mortality and decomposition were derived by summing the monthly values accordingly (see details in the Appendix). We did not include data from November to April because we had no data available for this winter period. However, fine root growth was expected to be slow in winter and therefore might be ignored. Since root mass samples, taken monthly from the same stand, were not independent, the sampling date was treated as a repeated measure in analysis of fine root biomass and necromass (Hicks and Turner, 1993). Log10 transformations were used when needed, to meet assumptions of normality and homogeneity of variance with the shapiro.test and bartlett.test functions in R.

Fine root biomass (Fig. 3A and B) and necromass (Fig. 3C and D) varied significantly among sampling dates (Table 4). The necromass was not significantly different among sampling dates in MS1 and MS2 (P > 0.01), and the biomass was significantly different between sampling ages in all layers (P < 0.01). According to our decision matrix, fine root production for all soil layers combined in young and old stands was 7.5 and 6.9 Mg ha1 year1, respectively (Fig. 4.). Fine root mortality and decomposition rates in young vs. old stands were 7.2 vs. 7.8 Mg ha1 year1 and 5.5 vs. 7.6 Mg ha1 year1, respectively. Young 11-year-old stands have higher fine root production but lower mortality and decomposition than 205-year-old stands, consistent with other boreal studies (Finér et al., 1997; Makkonen and Helmisaari, 2001; Helmisaari et al., 2002; Borja et al., 2008). The greater fine root production in young stands can be attributed to rapid vegetation colonization and species composition differences such as a higher proportion of deciduous Populus tremuloides, woody shrubs and herbaceous plants in young stands but more coniferous Abies balsamea and Picea spp. in old stands (Yuan and Chen, 2012a). The greater proportion of fast-growing Populus tremuloides, woody shrubs and herbaceous plants in young stands might have contributed to greater production in those stands. Furthermore, the N:P ratio in forest floor and mineral soils was higher in young stands than old stands (Shrestha and Chen, 2010; Yuan and Chen, 2010a), likely contributing to the observed differences between young and old stands. The greater mortality and decomposition in old stands could be attributed to senescence of pioneer trees in old stands (Chen and Taylor, 2012). In this paper, we demonstrate the calculation of fine root production, mortality and decomposition from our simplified equations in both MS Excel and R environments. Our values of boreal forests derived from the equations fell in the range of those reported for other boreal forest studies (Vogt et al., 1998; Hendricks et al., 2006; Yuan and Chen, 2010b; 2012b). Methodological errors in estimating fine root production have previously been discussed (Vogt et al., 1998; Hertel and Leuschner, 2002; Hendricks et al., 2006; Yuan and Chen, 2012c). However, no mathematical logic has so far been presented. Osawa and Aizawa (2012) developed a new approach similar to the ‘compartment-flow model’ as proposed by Santantonio and Grace (1987). They calculated fine root decomposition based on an assumption of “a linear first-order

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9 -1

Biomass (Mg ha )

A) 11-year old

FF MS1 MS2 Total

6

B) 205-year old

3

C) 11-year old

-1

Necromass (Mg ha )

0

D)

205-year old

0.75 0.50 0.25 0.00 Jul Aug Sep Oct May Jun

Jul Aug Sep Oct May Jun

2009

2008

2009

2008

Month

Month

Fig. 3. Seasonal variations in fine root biomass (A and B) and necromass (C and D) in boreal forest. Values are mean  1 SE (n ¼ 3). FF ¼ forest floor layer, MS1 ¼ 0e15 cm soil layer, MS2 ¼ 16e30 cm soil layer and Total ¼ necromass of all layers (FF þ MS1 þ MS2). Note the differences in y-axis scaling.

Table 4 Results (P and R2 values) of the repeated measure analysis of variance for the effects of stand age and sampling date on fine root biomass and necromass. FF ¼ forest floor layer, MS1 ¼ 0e15 cm soil layer, MS2 ¼ 15e30 cm soil layer and Total ¼ necromass of all layers (FF þ MS1 þ MS2). Source

Biomass FF MS1 MS2 Total Necromass FF MS1 MS2 Total

R2

Between subject

Within subject

Stand age (A)

Sampling date (D)

AD

<0.001 0.090 0.022 <0.001

<0.001 0.003 0.006 <0.001

0.542 0.591 0.810 0.582

10

A) 11-year-old FF MS1 MS2

8 6 -1

Rate of fine root proce ess (Mg ha year )

4

-1

differential equation”. Therefore, their proposed approach differs from decision matrix. To date, no approaches are available to ‘measure’ but to ‘estimate’ fine root production. New approaches that can ‘truly’ measure root processes are needed because of their importance in carbon and nutrient cycles. Also, it is important to recognize that every existing methodology has underlying assumptions, and it is necessary to assess errors and/or mistakes associated with these assumptions in diverse ecosystem conditions. For researchers who have not performed decomposition or minirhizotron studies, for instance, the decision matrix, especially with simplified equations and R codes we provided here, is useful in root studies. Our paper provided the mathematical logic for the development of decision matrix and developed a simplified matrix based on the logic, allowing a proper estimation of fine root production, mortality and decomposition rates from sequential cores. Due to the widely used computer technology of today, here, we also provide

2 0

B) 205-year-old 8 6 4 2

0.674 0.429 0.439 0.744 0.542 0.477 0.595 0.566

<0.001 0.001 0.002 <0.001

Bold indicates significant effects (P < 0.05).

0.004 0.057 0.604 0.018

0.049 0.512 0.716 0.436

0 Production

Mortality Decomposition

Fine root process Fig. 4. Sequential core-based estimates of fine root production, mortality and decomposition in boreal forest using the matrix in Table 1. FF ¼ forest floor layer, MS1 ¼ 0e15 cm soil layer, MS2 ¼ 15e30 cm soil layer. Process rate refers to the rates of fine root production, mortality and decomposition.

Z.Y. Yuan, H.Y.H. Chen / Acta Oecologica 48 (2013) 54e61

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