Developing Silvicultural Tools for Managing Mixed Forest Structures in Patagonia

Abstract

Leaf area is an important ecophysiological and silvicultural variable for quantifying the potential production of trees, since it can represent growing space occupancy. At the stand level in mixed forests, productivity is conditioned on how growing space is distributed among different components structure, such as species and strata. In complex structures, traditional forest variables (i.e., basal area) do not allow a good representation of the occupied growing space, whereas leaf area appears as a better indicator. Andean cypress and coihue beech are species of the Andean-Patagonian forests that grow in either pure or mixed stands, presenting high productive potential. The aim of this study was to develop, for each species, leaf area prediction functions through allometric relations and to evaluate the relation between leaf area, volume increment and growing space occupancy. For this purpose, we carried out destructive sampling of individuals of both species in mixed Andean cypress-coihue forests. Results for these species show that leaf area can be reliably estimated by using the models developed in this study. These models, based on sapwood area, tree diameter, and/or height measurements, explain at least 90 percent of variation in leaf area. The functions fitted are a fundamental tool to study the distribution of growth and to formulate management guidelines for mixed forests through the control of growing space occupancy using leaf area index.

leaf area, sapwood area, growing space efficiency, Austrocedrus chilensis, Nothofagus dombeyi

Management and Policy Implications

In this study, we developed leaf area models (LAMs) for determining their usefulness as simple tools for stocking control in either pure or mixed Andean cypress and coihue beech stands grown in Patagonia. These LAM allowed the growth space occupied at individual, stratum, and stand level to be determined, resulting in an improved tool to define target structures for maximizing resilience and productivity of mixed Andean cypress—coihue forests as compared to other stock variables traditionally used. In this way, the use of LAM will help in facing the challenges of forest management imposed by the greater complexity of forest structures that have resulted from incorporating coihue into disease Andean cypress stands. Development of these tools may also be of interest for other regions of the world with similar species and/or forest structure complexity.

The structure, function, and behavior of mixed forests are research topics with increasing international relevance (del Río et al. 2018), particularly regarding the consequences that mixing tree species has on the stability and productivity of forest systems (Coll et al. 2018). Mixed forests present a higher biodiversity, productivity, and resilience, and provide more ecosystem services and capacity to adapt to climate change than monospecific forests (Jactel et al. 2009, Scherer-Lorenzen et al. 2010, Kolstrom et al. 2011). Thus, knowledge about the structure and dynamics of mixed forests is essential for their conservation and sustainable management.

Trees in a stand develop by making use of the growing space. The growing space is the set of all resources necessary for tree growth. In monospecific and even-aged forests, characterized by simple structures, trees occupy the vertical space in a more or less homogeneous way, making use of resources of the same canopy layer (Pretzsch and Schütze 2015). In these simple structures, forest-management decisions are based on the control of parameters of the horizontal portion of the structure (i.e., basal area, relative density indices, etc.). In mixed and/or uneven-aged forests, which present more complex structures than pure-even-aged ones, species vary in their shade tolerance and in their height growth rates, and include the existence of two or more canopy layers. The vertical space occupation is also important to understand and manipulate stand growth (O’Hara et al. 1999), mainly because trees growth is the result of their capacity of occupying the available growing space. This aspect is particularly important in designing management schemes for relative complex and complex forests, where the different components of the stand (species, ages, and trees in different social positions) use site resources in differential ways.

The leaf area index (LAI) is a biometric variable that represents the ratio of projected total leaf area to ground surface area (Larcher 1983). The leaf area of a plant is considered the most appropriate biological variable to model growth, since essential processes such as photosynthesis, respiration, transpiration, and light absorption depend on it (Waring 1983). Although LAI has been widely used in ecological and ecophysiological studies, it has been less used in silvicultural studies focused on maximizing productive variables (Kollenberg and O’Hara 1999, O’Hara et al. 2001, O’Hara and Gersonde 2004). During the development of a stand, LAI reaches a maximum that depends on the site quality, and has a direct consequence on stand production (Waring 1983, Long and Smith 1984). Tree growth in relation to leaf area is a measure of the efficiency about how they occupy the growing space. Knowing the distribution of LAI among different components of the stand is then an essential tool to describe its structure and to design silvicultural practices for improving productivity.

Estimating LAI using individual tree allometries is a method that can be used to easily estimate LAI by individual trees, species, age classes, or canopy levels (Jones et al. 2015), especially useful in complex structures. LAI can also be estimated by several other methods, for example through hemispheric photographs or with optical instruments developed for indirect measurements of leaf area (i.e., LICOR LAI 2200). However, these methods are only useful at stand level in regular monospecific structures, since they do not allow the determination of individual leaf area in more complex structures, and they are also expensive and time-consuming (Jones et al. 2015). Allometric models usually include predictive variables such as sapwood area at the base of the live crown or at 1.3 m height, the diameter at breast height (dbh), and tree height. The pipe model proposed by Shinozaki et al. (1964a, b) explains the relation between leaf area and sapwood area at the base of the live crown. Sapwood area at the base of the live crown has in turn a strong relation with sapwood area at breast height, allowing an easier estimation of leaf area (Long et al. 1981, Waring et al. 1982, O’Hara et al. 2001). A high correlation between ​​sapwood area and leaf area has been reported for several hardwood (Shinozaki et al. 1964a, b, Waring et al. 1977, Bartelink 1997) and conifer species (Long et al. 1981, Waring et al. 1982, O’Hara and Valappil 1995, Stancioiu and O’Hara 2005). On the other hand, dbh and height tend to appear as complementary variables, since their relation with leaf area is less strong (Kendall and Brown 1978). Variables that characterize tree-growing environments, such as relative dominance, are less frequently included in leaf area estimations (Forrester et al. 2017). Knowing the way in which leaf area and the mentioned variables are related for species of interest allows predictive models to be developed to assess the LAI distribution, even in complex structures.

In the Andean-Patagonian region of Argentina, there are native species with timber importance that naturally grow in either pure or mixed forest structures. This is the case of the Andean cypress (Austrocedrus chilensis [D. Don] Pic. Ser. Et Bizzarri) conifer and the coihue beech (Nothofagus dombeyi [Mirb.] Oerst) hardwood, both perennials (Dezzotti 1996). One important natural process is occurring more and more frequently in pure Andean cypress stands when a disease that begins at the root level, caused by a pseudofungus named Phytophthora austrocedri (Greslebin and Hansen (2009), infects them. This disease, locally named “mal del ciprés” (cypress declining disease), reduces growth and causes high Andean cypress mortality (Loguercio et al. 2018b). During its evolution, this disease produces the decay and death of Andean cypress trees, liberating growing space that is occupied by Andean cypress regeneration and by coihue seedlings if nearby seed sources are available (Loguercio 1997, Amoroso et al. 2012). Adding coihue to these stands may improve the stability and increase the productivity of these newly established mixed stands (Loguercio et al. 2018b). This may be mainly because coihue is not affected by the “mal del ciprés” disease and grows at higher rates than Andean cypress (Veblen and Lorenz 1987, Dezzotti 1996, Caselli et al. 2018, Loguercio et al. 2018a). This natural process implies an opportunity to expand the possibilities of applying silvicultural management in unhealthy monospecific Andean cypress stands. The current challenge is to learn and develop silvicultural tools on how to manage the more complex, resilient, and productive forest structures that will be generated by adding coihue to unhealthy Andean cypress pure stands.

To achieve these goals, it is essential first to generate knowledge about growing dynamics of healthy mixed forests of Andean cypress and coihue, which is still very scarce in Patagonia (Veblen and Lorenz 1987, Dezzotti 1996, Loguercio et al. 2018a). In these multistrata structures, understanding leaf area distribution by species and canopy layer, and their relations with growth, is important for making management decisions at stand level. Therefore, the aims of this study were: (1) to develop leaf area prediction models for Andean cypress and coihue, based on simple measurement variables; (2) to analyze the leaf area–individual volume increment relations, and (3) to determine the growing space efficiency (stem volume increment/leaf area) on trees of different social positions for each species, and their possible implications for forest management. The generated knowledge will be crucial for developing management schemes to convert unhealthy monospecific Andean cypress stands into more resilient and productive mixed Andean cypress—coihue stands.

Methodology

Field Methodology and Data Processing

We studied tree-level relation of leaf area to other easy-to-measure important variables in trees of different mixed Andean cypress—coihue stands. The selected stands can be considered representative of their area of distribution in Patagonia and were located near Río Manso village (71°30′45ʺW, 41°34′24ʺS) and in Loma del Medio Forest Reserve (71°32′44ʺW, 41°56′25ʺS), in Río Negro province, Argentina. We carried out a destructive sampling on 18 coihue trees and on 20 Andean cypress trees, covering a range of dbh (1.30 m) between 8 and 52 cm, in stands with basal areas of 4 to 64 m²/ha (measured with angular plot, factor 4). Sampled trees were selected primarily based on their crown position (dominant, codominant, intermediate and suppressed, sensu Oliver and Larson 1990). We then divided the canopy in two layers, upper and lower, by separating trees that received direct light (dominant and codominant) from those growing under the mean canopy (intermediate and suppressed), which mainly received indirect light.

From each selected tree (sample tree), we recorded the species, crown position, dbh, total height, and height at the base of the live crown (defined as the height at the lowest living branch of the crown). In addition, depending on the size of the crown, we measured between four and eight radii of the horizontal crown projection of each tree. We made the same measurements on the three to five closest competitors to each sample tree, considering competitors those trees whose crowns were at a horizontal distance less than 2 m from the crown of the sample tree. With the competitor’s data, we calculated the degree of diametric dominance (Ui), the degree of mixture of species (Mi), and the relative height (RH). The degree of diametric dominance and the degree of mixture of species are indices that compare the diameter and species, respectively, of the sample tree with respect to its nearby competitors (von Gadow et al. 2007). Their values range from 0 (Ui: if the sample tree dbh < competitors dbh, Mi: if all trees are the same species as the sample tree) to 1 (Ui: if the sample tree dbh > competitors dbh; Mi: if the sample tree species ≠ competitors species). The relative height is the height of the sample tree divided by the average height of the nearby competitors (Forrester et al. 2017). In addition, we calculated the live crown ratio of each tree by dividing the length of the live crown by the total height, expressed as a percentage.

Sample trees were carefully felled to minimize any damage to the crown and neighboring trees. We cut each stem at 1.30 m and at the base of the live crown, and we took cross-sectional disks to determine the sapwood area using digital images. We took images using a Nikon Coolpix P100 camera (resolution 96 ppi) and processed them with the software ImageJ version 1.47v (Rasband 2013), with a precision level of 0.001 cm². We calculated the mean annual ring area in the sapwood (RAS) by dividing the sapwood area measured at breast height by the number of annual rings (average of four radii) within the sapwood.

We adapted the leaf area estimation methodology for from O’Hara and Valappil (1995). We divided the crown into three sections of equal length. Trees with crown length less than or equal to 2 m were processed in a single section. We cut and weighed all live branches of each section in the field, trying to obtain the highest precision (0.1 kg). In addition, we sampled a representative branch from each section and weighed in the field, with the highest accuracy (2 g). We separated all twigs with leaves from each representative branch, conditioned and stored them in a cold place, and took them to the lab. We separated leaves from twigs, and after oven-drying at 103° C for 48 h, we weighed the leaves (0.01 g). Then, we determined the relation between the fresh weight of the representative branch and the dry weight of its leaves. With these data and the fresh weight of the section, we estimated the dry weight of all the leaves of the section.

In the field, we randomly took a sample of about 50 g of leaves from each section. These were then transferred to the lab, and then three random samples of 40–50 leaves were selected, to determine the specific leaf area (cm²/g). The three leaf samples were independently scanned, when still fresh, to obtain TIFF images. We then oven-dried these leaves to determine their dry weight with precision scales (0.0001 g). We processed the leaf images using ImageJ software to determine the leaf area with a precision of 0.001 cm². The specific leaf area of the section was obtained as the average of the quotients between leaf area and dry weights of the samples. We calculated the leaf area of each section by multiplying the dry weight of leaves and the specific leaf area of the section, and the total leaf area of the tree as the sum of the leaf area of all sections.

We obtained cross-section disk samples of the stem by cutting each sample tree at 0.3 m in height, at 1.3 m and then every 2 m until the apex reached 7 cm in diameter. We determined the total area of each disk and the 5-years-ago disk area. The 5-years-ago disk area was determined by subtracting the average radial growth of the last 5 years in four radii. The current volume and 5-years-ago volume from each log were calculated using the Smalian formula. Smalian’s formula states that the volume of a log can be closely estimated by multiplying the average of the areas of the two log ends by the log’s length. The current annual stem volume increment was calculated as the difference between the current volume and the volume 5 years ago, divided by the 5 years of the period.

We calculated the growing space efficiency over the previous 5 years for each tree by dividing the stem volume increment by the leaf area (O’Hara 1988).

Evaluated Models

For both species and canopy layers, we evaluated the linear and nonlinear models shown in Table 1. We performed a Pearson correlation analysis to select the candidate variables (related to leaf area) for fitting linear models using Infostat statistical software (Di Rienzo et al. 2017). In addition, we graphically analyzed the leaf area relations with all the candidate variables to detect nonlinear trends.

Table 1.

Candidate leaf area models.

Model	Reference
${\beta }_1$ x ^ ${\beta }_2$	Jones et al. 2015
${\beta }_1$ + ${\beta }_2$ x + ${\beta }_3$x ^ 2	Quadratic
${\beta }_1$ + ${\beta }_2$x ${\beta }_3$z ^ 2	Quadratic
${\beta }_1$ + ${\beta }_2$ x + ${\beta }_3$ z ^ 2 + ${\beta }_4$ w ^ 2	Propose in this study
${\beta }_1$ + ${\beta }_2$ x + ${\beta }_3$ z + ${\beta }_4$ w ^ 2	Propose in this stud + y
${\beta }_1$ + ${\beta }_2$x	O’Hara & Valappil 1995
${\beta }_1$ + ${\beta }_2$ x + ${\beta }_3$ z	O’Hara & Valappil 1995
${\beta }_1$+ ${\beta }_2$ x + ${\beta }_3$ z + ${\beta }_4$ w	O’Hara & Valappil 1995
${\beta }_1$ + ${\beta }_2$x + ${\beta }_3$ z + ${\beta }_4$ w + ${\beta }_5$ v	Propose in this study
${\beta }_1$x / (⁠${\beta }_2$+ x)	Jones et al. 2015
e ^ (⁠${\beta }_1$ ln (x))	Bancalari et al. 1987
e ^ (–${\beta }_1$ e ^ (–${\beta }_2$(x − ${\beta }_3$⁠)))	Gompertz
${\beta }_1$/(1 + e ^ (⁠${\beta }_2$ + ${\beta }_3$x))	Sigmoide
${\beta }_1$x (1 – e ^ (–x))	Jones et al. 2015

R Studio software version 1.0.143 (RStudio Inc. 2009–2016) was used for model fit, regression assumptions verification (normality, homoscedasticity, residue independence), and checking possible collinearity between independent variables (by calculating the variance inflation factor, package “car”). The comparison between models was made using the adjusted determination coefficient (r² adj.) and the Akaike information criterion (AIC, package “stats”) with the R Studio software. In those cases in which these criteria did not differ, we used analysis of variance (ANOVA). We also used ANOVA to compare estimates of models with and without separation by canopy layers. We used Infostat to perform all ANOVAs.

In turn, we performed estimates of leaf area using the leaf area–sapwood area at breast height ratio (Dean et al. 1988). and we compared these with estimates obtain from the models with and without separation by layer, by ANOVA (with Infostat) and graphically with the observed values.

We analyzed annual current stem volume increment of each species by leaf area with linear and nonlinear models (Chapman–Richards, Weibull, and potential, cited by Gersonde and O’Hara 2005). We use R Studio for models fitting and for regression assumptions verification.

We validated the models using K-fold cross-validation prediction error (LOOV, package “boot”, with K = n) (Arlot and Celisse 2010, Forrester et al. 2017). We calculated model precision using the residual standard error (RSE, Equation 1), model efficiency (Ef, package “Validation”, Equation 2) (Tedeschi 2006, Ablan et al. 2011), and mean absolute percentage error (MAPE, package “Validation”, Equation 3) (Mayer and Butler 1993, Ablan et al. 2011):

$${\displaystyle \begin{array}{l}{\displaystyle \mathrm{R}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{n}{\displaystyle \underset{i=1}{{\displaystyle \sum ^n}}}{(P_i-O_i)}^2}}\end{array}}$$

(1)

$$\begin{array}{l}\text{Ef}=1-\frac{{\displaystyle {\sum }_{i=1}^n{(P_i-O_i)}^2}}{{\displaystyle {\sum }_{i=1}^n{(O_i-\overline{O})}^2}}\hfill \end{array}$$

(2)

$${\displaystyle \begin{array}{l}{\displaystyle \mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}=\frac{100}{n}{\displaystyle \underset{i=1}{{\displaystyle \sum ^n}}}\frac{|O_i-P_i|}{{\displaystyle \overline{O}}}}\end{array}}$$

(3)

where O is the observed value, Ō is the observed mean value, and P is the predicted value.

Results

Sampled Trees Attributes and Variables Selection

Sampled tree attributes are shown in Table 2. Sampled trees varied from a wide range of sizes: from 9 to 45 cm of dbh in Andean cypress and from 8 to 52 cm of dbh in coihue. The age of the sampled trees varied from 58 to 94 years in Andean cypress and from 18 to 101 years in coihue (Table 2). Coihue presented average sizes similar to Andean cypress despite being younger, which shows its greater growth. The rest of the attributes measured are shown in Table 2.

Table 2.

Sample tree attributes by species and canopy layer: mean (range).

	Andean cypress			Coihue beech
	All	Superior	Inferior	All	Superior	Inferior
N	20	11	9	18	10	8
Age at 0.3 m	83	88 (81–94)	79 (58–92)	48	61 (25–101)	32 (18–46)
dbh (cm)	26.1	33.4 (16–45)	17.2 (9–24)	24.1	33.2 (23–52)	12.7 (8–22)
BA (cm2)	636.4	943.0 (201–1626)	261.8 (59–468)	578,0	926.1 (415–2099)	142.9 (45–387)
Height (m)	18.1	21.0 (16–25)	14.7 (8–22)	18.3	22.5 (16–26)	13.2 (8–18)
HBC (m)	7.6	7.9 (4–12)	7.2 (2–15)	7.4	9.3 (3–15)	5.2 (0–8)
HMC (m)	12.9	14.4 (12–19)	11 (5–19)	12.9	15.9 (10–20)	9.2 (4–11)
SABH (cm2)	233.6	331.4 (129–584)	114.1 (14–233)	375.2	591.4 (304–984)	104.9 (25–271)
SABC (cm2)	182.9	260.4 (74–570)	88.3 (21–183)	252.5	382.0 (154–569)	90.7 (16–276)
CL (m)	10.5	13.0 (8–18)	7.5 (5–12)	10.9	13.2 (9–18)	8.0 (5–15)
LCR (percent)	58.0	62.0 (48–80)	53.2 (22–80)	60.6	59.8 (38–86)	61.6 (46–95)
CA (m2)	9.4	13.4 (2–28)	4.6 (1–9)	16.8	24.8 (7–39)	6.9 (2–19)
Ui	0.38	0.57 (0–1)	0.14 (0–0.5)	0.36	0.59 (0–1)	0.07 (0–0.3)
Mi	0.30	0.21 (0–0.7)	0.42 (0–0.7)	0.47	0.49 (0–0.8)	0.45 (0–0.8)
RH	1.00	1.18 (1.0–2.5)	0.77 (0.4–1.0)	0.89	1.01 (0.2–1.6)	0.73 (0.5–0.9)
LA (m2)	63.1	93.0 (18–181)	26.5 (5–54)	83.4	132.3 (75–311)	22.2 (8–48)
RAS (cm2)	7.3	10.5 (2.9–20.0)	3.4 (0.7–7.2)	17.1	26.2 (12.3–51.3)	8.1 (2.3–14.9)
SV (m3)	0.57	0.87 (0.1–1.7)	0.21 (0.02–0.5)	0.58	0.98 (0.4–1.9)	0.09 (0.01–0.3)
ISV (m3/year])	0.009	0.015 (.005-.03)	0.003 (.0004-.01)	0.023	0.037 (.01-.07)	0.005 (.001-.01)

Note: CA, crown projected area; CL, crown length; dbh, diameter at breast height; HBC, height to the base of the crown; HMC, height to the middle of the crown; ISV, annual stem volume increment over previous 5 years; LA, leaf area; LCR, live crown ratio; Mi, species mixture grade; RAS, mean annual ring area in the sapwood; RH, relative height; SABC, sapwood area at base of the crown; SABH, sapwood area at breast height; SV, stem volume; Ui, diameter dominance grade.

The Pearson correlation analysis showed that the most correlated variables with leaf area were the sapwood area at 1.3 m (SABH) and at the base of the live crown (SABC), the mean annual RAS and the degree of dominance (Ui), for both species. For Andean cypress, the most correlated variables with leaf area were the dbh, the basal area (BA), the total height (H), the crown area (CA), the crown length (CL), dbh/H, and dbh²/H (Table 3).

Table 3.

Candidate independent variables for leaf area models, correlation coefficient and P-value for Andean cypress (n = 20) and coihue beech (n = 18).

Acronym	Variable	Andean cypress		Coihue beech
		Correlation coefficient	P-value	Correlation coefficient	P-value
SABH	Sapwood cross-sectional area at 1.30 m	.95	<.0001	.91	<.0001
SABC	Sapwood cross-sectional area at base of live crown	.88	<.0001	.87	<.0001
RAS	Mean annual ring area in the sapwood	.95	<.0001	.89	<.0001
dbh	Diameter at breast height	.95	<.0001	.73	.0006
BA	Basal area	.96	<.0001	.66	.0029
H	Total tree height	.80	<.0001	.65	.0038
HBC	Height to base of the live crown	.20	.4079	.27	.2816
HMC	Height to middle of the live crown	.62	.0038	.52	.0263
CL	Crown length	.78	<.0001	.67	.0025
CA	Crown area	.81	<.0001	.71	.0009
LCR	Live crown ratio	.31	.1868	.12	.6353
	dbh/H	.86	<.0001	.65	.0033
	H/HMC	.29	.2129	.08	.7457
	dbh2/H	.96	<.0001	.65	.0032
	CA/H	.58	.0110	.63	.0054
Ui	Dominancy grade	.85	<.0001	.78	<.0001
Mi	Species mix grade	–.30	.2038	–.08	.7482
A	Age at 0.3 m	.56	.0097	.25	.3157
RH	Relative height	.63	.0029	.51	.0311

Leaf Area Prediction Models

Coihue leaf area showed more dispersion as its dbh, height, and sapwood area at breast height increased, whereas for Andean cypress the dispersion was homogeneous in the entire range of these variables (Figure 1).

Figure 1.

Leaf area (m²) for Andean cypress (left) and coihue beech (right) as a function of diameter at breast height (dbh, cm), total height (m), and sapwood area at breast height (SABH, cm²).

Satisfactory fits were achieved for all trees (without differentiating trees by canopy layers) for both Andean cypress (Equations 1–4, Table 4) and coihue (Equations 11–13, Table 4), explaining at least 90 percent of the variability of leaf area. Models that included aspects of the horizontal (degree of diametric dominance) and vertical (RH) structure of the tree environment had only satisfactory fits for Andean cypress (Equation 2, Table 4). The models that included tree age had satisfactory fits for both Andean cypress (Equations 3, 6 and 9, Table 4) and coihue (Equations 13 and 17, Table 4). Models that included RH or degree of diametric dominance, as well as models that included age, presented problems of underestimation (negative values) in some small suppressed trees. The best models fit without differentiating canopy layer of both species use the predictive variables SABH and dbh. For Andean cypress, Equation 1 gave the best model, and for coihue Equations 11 and 12 (Table 4).

Table 4.

Species-specific regression and statistics of leaf area (m²) for Andean cypress and coihue beech as a function of dbh (cm), SABH (cm²), SABC (cm²), Ui, HMC (m), RH (m), CL (m), and H (m).

Strata	No.	Equation	N	r2 adj	AIC	LOOV	RSE	Ef	MAPE
Andean cypress
All	1	0.1303 SABH + 0.0417 dbh^2	20	0.98	95	132	10.4	0.96	12.2
All	2	44.8024 + 0.3280 SABH − 24.0295 RH + 48.8417 Ui − 2.9130 H	20	0.97	151	122	9.0	0.97	10.0
All	3	0.1556 SABH + 2.3593 dbh − 0.4229 Age	20	0.98	158	158	11.1	0.95	13.0
All	4	–47.1097 + 0.2177 SABH + 42.8231 dbh / H	20	0.94	101	193	11.7	0.95	14.4
Inf	5	13.1029 + 0.2665 SABH − 1.5520 HMC	9	0.97	24	17	3.3	0.97	8.6
Inf	6	0.2599 SABH − 1.9885 HMC + 0.2361 Age	9	0.99	53	22	3.6	0.97	9.0
Sup	7	0.1332 SABH + 0.0417 dbh^2	11	0.98	58	209	12.8	0.93	10.1
Sup	8	–45.3888 + 2.5715 dbh + 0.1582 SABH	11	0.92	59	240	13.1	0.94	9.8
Sup	9	0.1576 SABH + 2.7173 dbh − 0.5716 Age	11	0.98	92	232	13.0	0.94	10.0
Sup	10	103.7884 + 0.2048 SABH − 117.7964 H / dbh	11	0.92	59	312	12.9	0.94	9.6
Coihue beech
All	11	0.2732 SABH − 0.0548 dbh^2 + 0.0001 SABC ^2	17	0.97	93	376	14.2	0.91	16.3
All	12	0.2797 SABH − 0.0630 dbh^2 + 11.8514 (dbh / H)^2	17	0.97	93	365	14.4	0.86	18.8
All	13	42.0114 + 0.3499 SABH − 17.8353 (dbh / H)^2 − 1.2289 Age	18	0.95	159	496	17.1	0.96	15.0
Inf	14	0.1344 SABH + 5.7549 H / HMC	8	0.96	28	36	5.0	0.87	16.9
Inf	15	8.6356 + 0.1494 SABC	8	0.90	25	37	4.2	0.91	13.6
Sup	16	0.4708 SABH − 5.9025 dbh + 0.0957 H^2	10	0.97	69	1024	27.8	0.89	15.1
Sup	17	0.2686 SABH + 0.1937 H^2 − 2.0795 Age	10	0.99	91	447	18.0	0.95	9.0
Sup	18	0.4732 SABH − 5.3694 dbh + 43.5097 H / dbh	10	0.97	69	1115	27.3	0.89	14.7
Sup	19	0.4453 SABH − 5.4278 dbh + 3.7071 CL	10	0.97	69	1096	27.6	0.89	14.0
Sup	20	0.3752 SABH − 0.0621 dbh^2 − 5.0310 (dbh / H)^2	10	0.95	73	3023	33.2	0.84	16.7

Note: Values shown in bold correspond to the best models fitted. AIC, Akaike information criterion; CL, crown length; dbh, diameter at breast height; Ef, model efficiency; H, total height; HMC, height to the middle of the crown; MAPE, mean absolute percentage error; RH, relative height; RSE, residual standard error; SABC, sapwood area at base of the crown; SABH, sapwood area at breast height; Ui, diameter dominance grade.

Sapwood area at the base of the live crown (SABC) was a significant parameter for coihue, in Equation 11 (Table 4), whereas for Andean cypress, SABC was only significant on a linear model without an intercept with a r² adj. = .91 but biased and with low predictive capacity (not shown, LOOV > 4000, RSE = 23, Ef = 77). As SABC determination is difficult, two models were adjusted to estimate SABC in coihue from other variables of simpler measurement (r² adj > .98, RSE < 29). One model uses SABH, CA, and H, and the other uses dbh, SABH, and height at the base of live crown (HBC). However, predicted means from the models in Equations 11 and 12 (Table 4) were similar (P = .29).

The models had better fits with different variables when trees were separated by a canopy layer. Those of the upper canopy of both species had dbh and SABH as predictors (Equations 7–10, 16 and 18–20, Table 4). For the lower canopy of both species, the best model included SABH and height at the middle of the live crown (HMC) (Equations 5 and 14, Table 4).

For both species, the predicted means of the best models fitted with and without separation by canopy layer were similar (Andean cypress: Equation 1 [all] versus Equation 5 [inf.] P = .80 and Equation 1 versus Equation 7 [sup.] P = .67; coihue: Equation 12 [all] versus Equation 14 [inf.] P = .48 and Equation 12 versus Equation 16 [sup.] P = .67) (Table 4). The plot of predicted versus measured leaf area in both species shows less dispersion for models fitted with trees of the lower canopy than models fitted without a differentiating canopy layer (Figure 2), whereas models fitted for the upper canopy showed a similar dispersion in Andean cypress and greater dispersion in coihue. Despite this, the model fitted with the upper canopy of coihue showed less biased estimates than that of the model without a differentiating canopy layer (see Figure 2).

Figure 2.

Measured leaf area as a function of predicted leaf area from models fit with all trees (Equations 1 and 12) and for canopy layer (Equations 5, 7, 14, and 16) (see Table 4) for Andean cypress (left) and coihue beech (right). Black line corresponds to one to one line.

The ratio between leaf area and sapwood area (LA:SABH) was similar for both species, with a value of 0.27 m²/cm² (_s = 0.02) for Andean cypress and 0.23 m²/cm² (_s = 0.02) for coihue (P = .13). This relation was also similar in both species for the upper and lower canopy (P > .74). The ratio between leaf area and sapwood area at the base of the live crown (LA:SABC) had the same behavior as LA:SABH ratio for the species, with a value of 0.33 m²/cm² (_s = 0.02 in Andean cypress and 0.03 in coihue, P = .95) and the canopy layer within the species (P > .31). For both species, the LA:SABC ratio was different to LA:SABH in the upper canopy (P < .04) and was similar in the lower canopy (P > .21).

The estimated LA means per canopy layer with LA:SABH constant ratio and with the models with and without separation by canopy layer did not differ statistically from each other or with the observed mean (coihue P > .79, Andean cypress P > .95). However, predictions with the LA:SABH ratio for coihue showed a trend of less bias than the prediction with models fitted without a differentiating canopy layer and greater bias than models by canopy layer (see Table 4, Figure 2), whereas for Andean cypress they showed a greater bias than for models with and without canopy layer separation (Figure 3).

Figure 3.

Measured leaf area as a function of predicted leaf area from canopy layer LA:SABH ratio for Andean cypress (left) and coihue beech (right). Black line corresponds to one to one line.

Stem Volume Increment and Leaf Area

The relation between leaf area and stem volume increment of the last 5 years was linear for both species. Coihue showed a greater increase than Andean cypress for the same value of leaf area (Figure 4).

Figure 4.

Stem volume increment over previous 5 years (m³) versus leaf area (m²) for Andean cypress (left) and coihue beech (right).

Satisfactory fits were achieved between stem annual volume increment and LA for both Andean cypress and coihue, explaining 93 percent of the variability in the first species and 97 percent in the second (see Figure 4 and Table 5). Estimated means of models fitted with and without differentiation of canopy layer were similar to each other, and both did not differ significantly from the observed means (P > .64 for Andean cypress and P > .95 for coihue).

Table 5.

Equations to predict tree volume annual increment (m³/year) over previous 5 years from leaf area (LA, m²).

Species	Strata	Equation	N	r2 adj	AIC	LOOV	RSE	Ef	MAPE
Andean cypress	All	0.0001522 LA	20	0.93	-103	0.0003	0.02	0.84	99.9
	Sup	0.00015462 LA	11	0.93	-50	0.0006	0.02	0.67	99.9
	Inf	0.0001174 LA	9	0.90	-64	0.00004	0.006	0.75	99.9
Coihue beech	All	0.000264 LA	18	0.97	-77	0.0007	0.03	0.94	99.9
	Sup	0.0002612 LA	9	0.97	-32	0.001	0.03	0.86	99.9
	Inf	0.000301 LA	9	0.96	-50	0.0001	0.013	0.94	99.8

Note: AIC, Akaike information criterion; Ef, model efficiency; MAPE, mean absolute percentage error; RSE, residual standard error.

Growing Space Efficiency

The growing space efficiency (GSE) of Andean cypress and coihue represented as a function of leaf area showed a peak in relatively low leaf areas and then a decrease for greater leaf areas (Figure 5). For Andean cypress, the estimated maximum GSE was 0.82 dm³/m²/5 years, and this was reached with 98 m² of leaf area. Coihue has an estimated maximum GSE of 1.55 dm³/m²/5 years, and this was reached with 102 m² of leaf area. If the behavior of GSE is analyzed according to social class, codominant and intermediate coihue plants are among the most efficient, whereas in Andean cypress the highest efficiency occurred among dominants and codominants (Figure 5). For both species, the dominant trees were less efficient as leaf area increased, and the less efficient plants corresponded to the suppressed ones.

Figure 5.

Growing space efficiency (dm³/m²/5 years) as a function of leaf area (m²) for dominant (squares), codominant (diamond), intermediate (triangle) and suppressed (circles) trees of Andean cypress (filled), and coihue beech (open). Black line corresponds to Ricker models fitted to the data (Ricker 1975).

Discussion

Relation between Leaf Area and Selected Variables

The leaf area of both Andean cypress and coihue correlates with variables of biological importance. SABH, RAS, SABC, and Ui showed a high correlation with leaf area in both species, whereas dbh, BAs, H, CA, CL, dbh / H, and dbh² / H were more correlated with the leaf area of ​​ Andean cypress. CA and CL show a good correlation with leaf area because they represent the size of the crown, resulting in a greater leaf area for larger crown sizes. The height and degree of dominance help to quantify the occupied growing space; trees in higher social positions are able to develop a greater leaf area than those of the lower canopy. The high correlation of RAS with the leaf area coincides with the trend reported for leaf biomass of Pinus sylvestris (Albrektson 1984).

Pearson correlation analysis confirmed the strong correlation between the area of ​​sapwood and leaf area for both species, as has been observed in conifers (Shinozaki et al. 1964a, b, Long et al. 1981, Waring et al. 1982, O’Hara and Valappil 1995, Stancioiu and O’Hara 2005) and hardwoods (Shinozaki et al. 1964a, b, Waring et al. 1977, Bartelink 1997). The sapwood conducts water and nutrients to the foliage and also stores water (Waring and Running 1978). It is then functionally related to the leaf area more directly than with external measurement variables such as BA and dbh, which include both sapwood and heartwood (Whitehead 1978). For large trees, the sapwood area needed to supply water to the transpiring foliage is insufficient to provide necessary mechanical support, and it must be compensated with a greater BA. Therefore, in developing trees, the difference between sapwood and BA increases as tree size increases, making the relation between the BA and the leaf area weaker (Long et al. 1981, Long and Smith 1984). In Andean cypress, sapwood area at breast height usually represents a small proportion with respect to the BA (less than 35 percent). Thus, a variation in sapwood (because of the amount of foliage to supply) has a small effect on basal area, and so it maintains a strong BA–LA relation. A strong BA–LA relation was also reported by Jones et al. (2015) for other conifer species. In coihue, sapwood area occupies on average more than 60 percent of the BA, so BA correlates less with LA. On the other hand, leaf area correlation with SABC is strong too, but less than with SABH.

It is interesting that, considering the pipe model (Shinozaki et al. 1964a, b), our species leaf area is more correlated with SABH than with SACB. Bancalari et al. (1987) observed that SACB is a better predictor of LA than SABH in fast-growing trees, whereas both variables are good predictors in slow-growing trees. In that study, a sapwood taper was observed from breast height to the base of the crown, which was reported also by Waring et al. (1982) and Brix and Mitchell (1983), as in our study for coihue (27 percent) and Andean cypress (11 percent). However, SABH and SACB means did not differ significantly from each other (P > .15), although these varaiables were different in coihue for dominant and codominant trees (P = .03 and P = .006). In addition, when comparing LA:SABH and LA:SACB ratios, we found differences only for dominant trees of both species (P < .04). These were the trees that grew the most compared to the other social classes and those that presented greater areas at the base of the crown. This coincides with the tendency indicated for Pseudotsuga menziesii by Brix and Michell (1983), which attributed this difference to variations in conductivity of sapwood between both points. These results do not indicate a contradiction with the pipe model, since it is evident that there are functional relations between sapwood area and leaf area. However, these results suggest that there may be other physiological aspects involved in the variation of the relation between leaf area and sapwood area at different tree heights.

Leaf Area Estimation

Although the number of sample trees was not very high, limited by the high costs and efforts associated with destructive sampling, especially for large trees, the homogenous coverage of the range of sizes, social positions and crown development, allow us to consider it as adequate. Statistics indicated that the fitting of leaf area allometric functions was satisfactory for both species when using all trees and when separating trees by canopy layer (see Table 4). Developed models explain in all cases more than 90 percent of the variability and include the sapwood area on the estimation. These fits are similar to those obtained in studies with other species in the Northern Hemisphere (O’Hara and Valappil 1995, O’Hara et al. 2001, Stancioiu and O’Hara 2005, Forrester et al. 2017). The statistical results indicate that separation by canopy layer would not be necessary in the species evaluated growing in mixed forest, although graphical results show a better prediction of large leaf areas with the upper canopy model for coihue.

A constant leaf area–sapwood area relation between trees of different social positions such as those found here was also reported for other species. These species are Pinus ponderosa (O’Hara and Valappil 1995, Monserud and Marshall 1999), Tsuga canadensis (Kenefic and Seymour 1999), Pinus taeda (Shelburne et al. 1993), Abies balsamea (Gilmore and Seymour 1996), Pseudotsuga menziesii, and Pinus monticola (Monserud and Marshall 1999). O’Hara and Valappil (1995) have explained these results by proposing that trees of the lower canopy tend to have less evaporative demands because they are not so exposed to the drying factors. In this case, they do not seem to need less conductive tissue to support a given unit of leaf area than trees of the upper canopy. The slight difference detected for large leaf areas of coihue would indeed show that very large trees of the upper canopy need more conduction tissue per unit of leaf area than the medium and small trees of the lower canopy. This is probably due to problems of sapwood functionality that require compensation with more tissue (Whitehead et al. 1984). However, as mentioned earlier, this difference (0.22 m²/cm² versus 0.23 m²/cm²) is not significant in the range of sizes studied, so sampling of larger trees may be necessary to corroborate this hypothesis.

The shape of the sapwood area–leaf area relation has been studied for several species and under different growth conditions. For Dean and Long (1986), the relation of sapwood area to leaf area may seem linear under relatively narrow ranges of sapwood area because the average of tree size, stand density, and site quality are correlated (Long and Smith 1984). However, there is evidence of linear sapwood area–leaf area relations (Marchand 1984, Schuler and Smith 1988, Coyea and Margolis 1992, Robichaud and Methven 1992, O’Hara and Valapill 1995, Forrester et al. 2017) and nonlinear relations (Dean and Long 1986, Long and Smith 1988, 1989, Thompson 1989). In this sense, our results coincide with those reported by the first authors, since the models that best fit for Andean cypress and coihue are linear.

Incorporation of dbh improved the predictions of the functions without separation by canopy layer (Equations 1, 11, and 12, Table 4) and those of the upper canopy (Equations 7 and 16, Table 4). Diameter at breast height indirectly provides information on the history of the tree that has led to the development of its current leaf area (Forrester et al. 2017), and it had already been indicated as a good predictor of LA by several authors (Kendall Snell and Brown 1978, Schönenberger 1984, Bancalari et al. 1987). In addition, leaf area models of the lower canopy of Andean cypress and those of coihue with and without separation by canopy layers included H and/or HMC. HMC improves the estimates of leaf area in sites of different density and site quality according to Dean and Long (1986) and Long and Smith (1988), since this variable represents the structure of the forest.

Incorporation of stand structure variables gives greater versatility to the leaf area prediction models to apply them to more variety of stands (Forrester et al. 2017), although they may complicate data collection in providing estimates. In this study, most of the functions with structure variables (CA, density, mixing degree, degree of dominance, CL, RH) did not give better predictions. This could be due to the fact that the sampled stands did not show a great variation of site conditions, but at the same time they corresponded to the limited range in which this type of mixed forest develops. Also, it could be due to the need for a greater sample size, in order to capture more variability within the studied ranges. On the other hand, the functions that included age, considering the reported variation of leaf area with respect to this variable (Porté et al. 2000, Forrester et al. 2017), did not improve the estimations with respect to the functions with simpler variables (Equations 1 and 12, Table 4), although they had good results. In addition, functions that included RAS did not improve the leaf area estimates in relation to the sapwood area as well as for Pseudotsuga menziesii (Bancalari et al. 1987). The best models for estimating leaf area obtained in our study, which explained most of the variability, used expedited measurement variables. These expedited variables allowed faster and less expensive leaf area estimation, which is consistent with the findings of Jones et al. (2015).

Leaf area estimation with a constant LA:SABH ratio has been widely used (Waring 1983, Dean et al. 1988, O’Hara et al. 1999), although it has been shown that it can vary with density of the stand and between trees (Keane and Weetman 1987). In our study, it shows good results (see Figure 3), but it is no better than that of models with separation of canopy layers. The mean leaf area estimated with the models with and without separation by canopy layers and the estimate with LA:SABH ratio do not differ significantly from each other or with the observed means, but tree-to-tree variations show that it is better to use models with differentiation by canopy layers to obtain better estimates, especially in coihue.

Stem Volume Increment and Leaf Area

As expected, leaf area was highly correlated with stem volume increment in both species. These results coincide with those reported by Gilmore and Seymour (1996), Seymour and Kenefic (2002) and Gersonde and O’Hara (2005), among others, although, unlike in our study, relations were nonlinear. It is expected that volume increment presents an asymptote in ​​higher values of leaf area than those sampled, since it is unlikely to grow indefinitely when LA increases, as described by the adjusted model. However, in the sampled size ranges, all adjusted linear models explained more than 90 percent of the variability of the stem volume annual increment in relation to LA, and the separation by canopy layers did not present any advantages.

GSE

GSE provides a conceptual link between physiological aspects of tree growth and tangible measurements of wood production (Webster and Lorimer 2003). The efficiency of coihue is practically twice that of Andean cypress, which implies that for the same unit of occupied growing space, coihue produces almost twice as much wood in the stem as Andean cypress. This fact, plus its higher capacity to produce more foliar area, constitutes a competitive advantage of coihue concerning Andean cypress. This is particularly important in Andean cypress stands, because liberations of growing space occur after a disturbance (i.e., produced by mal del ciprés). This free space is then occupied by coihue, and it explains the greater productivity of mixed Andean cypress–coihue stands than of pure Andean cypress forests (Loguercio et al. 2018a).

In addition, sociological position has an effect on the efficiency of Andean cypress and coihue trees, as has been reported for other species too (Waring et al. 1980, O’Hara 1988). Below 50 m², a great GSE increase is observed as leaf area increases, and after reaching the maximum, it declines. This behavior has also been reported by other authors (Roberts et al. 1993, Gilmore and Seymour 1996, Seymour and Kenefic 2002). Suppressed trees have the lowest efficiency because they assign a greater proportion of carbon to respiration than that assigned to stem growth, compared to trees of the other social classes (Gilmore and Seymour 1996). At the same time, as height growth increases in searching for light, a greater mechanical support tissue in the trunk is necessary (Cannell and Dewar 1994). This explains the high efficiency of trees of intermediate social positions (codominant and intermediate), especially observed in coihue. However, when trees have larger crowns, efficiency decreases because the proportion of foliage located in shaded and old portions of the crown increases, which increases the cost of respiration (Waring and Schlesinger 1985). The maintenance of these leaves is done at the expense of stem growth (O’Hara 1988, Long and Smith 1989). In addition, photosynthetic capacity decreases with age (Yoder et al. 1994, Ryan et al. 1997, Seymour and Kenefic 2002), decreasing the amount of carbon allocated to the trunk. On the other hand, when comparing the efficiency of these species with that of conifers (Gersonde and O’Hara 2005), we observed that the maximum of Andean cypress and coihue is reached at a low leaf area, following the trend of the most shade-intolerant species.

Conclusion

In this study, we developed a tool for determining the leaf area of ​​coihue and Andean cypress at the individual level and at both canopy layer and stand level. This knowledge was gathered and estimated using allometric relations that included sapwood area, diameter at breast height, and tree-height measurements. The high correlation between leaf area and volume increment allowed the study of the GSE of different forest structures, which is essential to determine the conditions to achieve different forest-management objectives. Coihue grows more than Andean cypress, and it is more efficient in the use of the growing space. For this reason, we expect that the higher participation of coihue in the LAI of the stand would generate a higher productivity by making more efficient use of available resources. On the other hand, both species showed the maximum growth efficiency during their early stages of development, when individual leaf area is still relatively low. For this reason, we propose the elimination of their competitors during the juvenile stage of development. Although the upper canopy of coihue trees may show a low efficiency, their abundant leaf area compensates for this low efficiency, producing a higher stem growth. If the main objective were to produce lumber of large dimensions, the silvicultural treatment should consider increasing undergrowth thinning to allow remaining coihue trees to accumulate more leaf area. On the other hand, if the objective is to maintain Andean cypress trees in the upper canopy (Andean cypress show lower growth rates than coihue), some competing coihue trees should be cut to assign them some growing space and allow a better Andean cypress growth. However, these silvicultural proposals should be validated in the field through specific experiments at the stand level. This study not only presents essential information for designing forest management schemes for mixed Andean cypress–coihue forests but also may be of interest for other regions of the world that have similar species and/or forest structure complexity.

Acknowledgments

We thank the owners and administrators of Estancia Cacique Foyel, members of Campo Forestal General San Martín del INTA and responsible for the Loma del Medio Forest Reserve—Río Azul, Province of Río Negro, Argentina, and the Forestry Undersecretary of the Province of Río Negro, for allowing the sampling to be carried out; to Tania Figueroa, Cristian Huisca, Cristian Muñoz, Stefano Gianolini, Julieta Sandoval, Ariel Neri, and Ramiro Gorosito for their invaluable help in the samplings, and Tania Figueroa and Julieta Sandoval for their help in the processing of the samples; and to Kevin O’Hara for his advice in sampling and data analysis. Finally, we thank Melisa Rago for her comments on the final version of the manuscript, and the anonymous reviewers for their detailed comments and suggestions that helped to improve the manuscript.

Funding: This work was supported by grant P4-A2-013 from Patagonian Andean Forestry Research and Extension Center (CIEFAP), by grant Applied Research Project (PIA) 14067 from Forestry Sustainability and Competitiveness Program of the Unit for Rural Change (UCAR, Argentina), and by 22920160100128CO PUE Project from CIEFAP-CONICET. This research was carried out within the frame of a Postgraduate fellow from National Scientific and Technical Research Council (CONICET, Argentina).