Growth and carbon sequestration in biomass of Cordia alliodora in Andean agroforestry systems with coffee

Timber production and carbon sequestration in trees in agroforestry systems (AFS) are key to productivity and climate change mitigation. There are no studies about dynamics of growth and carbon sequestration of Cordia alliodora during all plantation cycle. The objective of this study was to develop models for diametric growth and carbon sequestration in aboveground biomass of C. alliodora in AFS with coffee in Líbano, Tolima, Colombia. Nonlinear models of growth and carbon sequestration in aboveground biomass of C. alliodora in AFS with coffee were developed. A total of 90 trees, ranging in age from 1 to 19 years, were randomly selected in farms and measured (diameter at breast height -dbh- and total height -h) in AFS with a basal area of C. alliodora between 0.22 and 17.8 m2/ha. Timber volume and aboveground biomass were estimated with allometric models, while carbon was estimated by multiplying aboveground biomass by 0.47. The best-fit models were selected according to the coefficient of determination (R2), Akaike's information criterion (AIC), predicted residual error sum of squares (PRESS), biological logic and a residual analysis. The highest growth rate of this species was reached at 4–6 years for dbh and h (3.6 cm/year and 2.9 m/year, respectively) and at 20 years for timber and carbon (0.60 m3/tree/year and 88.9 kg C/tree/year, respectively). In 20 years, a C. alliodora tree would store 1.1 Mg C and a AFS with 60 trees/ha would sequester between 260 Mg CO2/ha in aboveground biomass. The results show that C. alliodora trees could be maintained in the field for more than 20 years, thus increasing the volume per individual and carbon sequestration for a longer time. This demonstrates the importance of this species mainly when timber production and carbon sequestration are priorities for its profitability.

Abstract Timber production and carbon sequestration in trees in agroforestry systems (AFS) are key to productivity and climate change mitigation.There are no studies about dynamics of growth and carbon sequestration of Cordia alliodora during all plantation cycle.The objective of this study was to develop models for diametric growth and carbon sequestration in aboveground biomass of C. alliodora in AFS with coffee in Líbano, Tolima, Colombia.Nonlinear models of growth and carbon sequestration in aboveground biomass of C. alliodora in AFS with coffee were developed.A total of 90 trees, ranging in age from 1 to 19 years, were randomly selected in farms and measured (diameter at breast height -dbhand total height -h) in AFS with a basal area of C. alliodora between 0.22 and 17.8 m 2 /ha.Timber volume and aboveground biomass were estimated with allometric models, while carbon was estimated by multiplying aboveground biomass by 0.47.The bestfit models were selected according to the coefficient of determination (R 2 ), Akaike's information criterion (AIC), predicted residual error sum of squares (PRESS), biological logic and a residual analysis.The highest growth rate of this species was reached at 4-6 years for dbh and h (3.6 cm/year and 2.9 m/year, respectively) and at 20 years for timber and carbon (0.60 m 3 /tree/year and 88.9 kg C/tree/year, respectively).In 20 years, a C. alliodora tree would store 1.1 Mg C and a AFS with 60 trees/ha would sequester between 260 Mg CO 2 /ha in aboveground biomass.The results show that C. alliodora trees could be maintained in the field for more than 20 years, thus increasing the volume per individual and carbon sequestration for a longer time.This demonstrates the importance of this species mainly when timber production and carbon sequestration are priorities for its profitability.

Introduction
Agroforestry systems (AFS), commonly understood as the interactive association of woody species with agricultural production systems (Somarriba 1992;Nair 1993), are one of the key mechanisms for climate change mitigation given their potential for carbon (C) sequestration in biomass and soil (Albrecht and Kandji 2003;Beer et al. 2003;Montagnini and Nair 2004;Oelbermann et al. 2004;Swamy and Puri 2005;Andrade et al. 2008;Soto-Pinto et al. 2010).In addition, AFS represent a sustainable alternative that favors agricultural production, timber production and the provision of environmental services (Beer et al. 2003;Montagnini et al. 2004;Farfán 2014;Detlefsen and Somarriba 2015), which contributes to reducing pressure on natural forests, who are the largest terrestrial C sinks (Montagnini and Nair 2004).It is estimated that AFS can store between 12 and 228 Mg C/ ha in biomass (Winjum et al. 1992;Schroeder 1994;Dixon 1995;Beer et al. 2003).Authors such as Montagnini and Nair (2004), consider that 400 million hectares of AFS have the potential to sequester one million tons of carbon by 2040.
In Central America, AFS cover between 27 and 50% of the agricultural area (Detlefsen and Somarriba 2012).One of the best traditional models is Cordia alliodora in association with coffee crops (Somarriba and Beer 1987), which is widely used in the 920 thousand hectares of coffee production systems in Colombia (Farfán 2012).One of the reasons for implementing this type of system is the production of commercial timber, which provides an alternative source of income to the producer in the medium and long term, allowing to mitigate income loss due to fluctuating coffee prices (Beer et al. 1998;Detlefsen and Somarriba 2015;Montagnini et al. 2015).Dzib (2003) states that revenues amount to U$6410 from timber sales (123 m 3 /ha) of C. alliodora in AFS in Costa Rica.
C. alliodora, also known as coffee walnut or laurel, is a fast-growing forest species widely distributed in tropical America (Graves and McCarter 1990).In Colombia, it is distributed along the three mountain ranges and the Sierra Nevada de Santa Marta, from 0 to 1900 m altitude (Ospina et al. 2010).According to Holdridge (1967), this species is found in dry to humid tropical and humid and very humid premontane forests ( Van der Poel 1988).Given its silvicultural characteristics, C. alliodora is an ideal component to be implemented in AFS (Valdivieso et al. 1998), since it produces high quality timber, is selfpruning, has a straight trunk free of branches for 50-60% of its height, a compact crown and is easy to regenerate naturally on cleared sites (Graves and McCarter 1990;Valdivieso et al. 1998).
The density of this species is continuously controlled to adjust to the shade needs of the agricultural species (Somarriba 1990).In coffee AFS, it is recommended to maintain densities between 100 and 180 trees/ha of C. alliodora, so as not to significantly affect crop productivity (Hernández et al. 1997;Ospina et al. 2010).Shading is considered to strengthen the resilience of coffee to climatic or economic disturbances that providing a microclimate suitable for coffee production and improve the productivity of the system (Ospina et al. 2010;Salgado 2012;Andrade et al. 2014a;Chait 2015;Rapidel et al. 2015).Some authors have found that crop production can be reduced by 22-50% under C. alliodora shade (Glover 1981;Detlefsen 1988;Farfán and Urrego 2004); however, other researchers have found an incremented productivity and C sequestration at 30-65% of shade, including legume trees (Beer et al. 1998;Staver et al. 2001;Righi et al. 2007;Andrade et al. 2014a).
Multiple studies on the growth in diameter, height and volume of Cordia alliodora have been conducted in Central America, mainly in Costa Rica (Rosero and Gewald 1979;Somarriba 1990;Hernández et al. 1997;Somarriba et al. 2001;Aristizábal et al. 2002;Farfán and Urrego 2004;Parresol and Devall 2013).Somarriba et al. (2001) suggest that the growth of the species is greater in AFS than in pure plantations.The objective of this study is to quantify the growth and carbon sequestration of individual trees of C. alliodora in AFS with coffee in the municipality of Líbano, Tolima, Colombia, by developing growth models.Additionally, the results will allow estimating the rate of growth and carbon sequestration at any age of this tree species, which can contribute to determine the tree density necessary to reach a certain level of carbon sequestration.This would allow Vol.: (0123456789) achieving climate change mitigation objectives and reaching carbon neutrality in coffee production.The novelty of this research is the tool to estimate the rates of growth and carbon sequestration of C. alliodora in AFS with coffee during all plantation cycle, so that management can be optimized to maximize wood production or carbon sequestration.Although the results are focused on the department of Tolima in Colombia, the findings could be used in a wider region: the Colombian coffee-growing zone, located in the Andean region of the country and others Andeans zones of the tropics.

Study area
The study was carried out in the municipality of Líbano, located in the north of the department of Tolima (Colombia), in a very humid premontane forest (Holdridge 1967).The area is located at an altitude of 1565 m, 2235 mm of annual precipitation and an average temperature of 19.1 °C (Instituto de Hidrología, Meteorología y Estudios Ambientales [IDEAM] 2010).The soils in the study area are classified as Andisols, with good physical characteristics, high fertility, and slopes between 25 and 60%.Líbano contains a high variety of coffee production systems ranging from monoculture plantations and AFS with musaceae, rubber (Hevea brasiliensis) and C. alliodora (Andrade et al. 2014b).

Measurement of trees and estimation of volume, biomass and carbon
Eleven coffee farms with AFS with C. alliodora larger than 1 ha and with shades between 20 and 60%, a basal area between 0.22 and 17.8 m 2 /ha and trees between 1 and 19 years old were selected.These systems are managed conventionally, except for shade regulation through thinning of C. alliodora, which is a self-pruning species.All AFS were established planting C. alliodora trees at the same time, having just one cohort.These producers were selected with the support of extension agents from the Comité de Cafeteros del Líbano (Tolima).Among these, 90 individuals of this species were randomly selected, which were typical and representative of those found in the system.The age of each individual tree was consulted with the coffee growers, whose answers were verified with those extension agents who have been familiar with these production systems since their establishment.The diameter of the trunk at breast height (dbh) was measured with a diametric tape (varying between 4.0 and 76.4 cm) and the total height (h) was estimated with a metric tape and clinometer (ranging from 2.4 to 36.3 m).
The total volume of timber with bark (overbark) was estimated using the model of Somarriba and Beer (1987) (Eq. 1) developed for C. alliodora trees less than 41 years old in cocoa, coffee, sugarcane and pasture plantations in Costa Rica.
where V: total volume of timber with bark (m 3 /tree), dbh: trunk diameter at breast height (cm), Ln: natural logarithm Total aboveground biomass was estimated using the allometric model developed by Andrade et al. (2022) for individual C. alliodora trees with dbh between 3.9 and 102 cm in AFS with cocoa in Talamanca, Costa Rica (Eq.2).Total aboveground carbon per tree was obtained using a carbon fraction of 0.47, which is recommended by Intergovernmental Panel on Climate Change [IPCC] (2006).

Model development
Nine nonlinear regression models were tested to describe the growth in height, diameter, volume, aboveground biomass and carbon of C. alliodora trees as a function of age (Table 1).These models are some of the most commonly used for the development of growth curves (Sit and Poulin-Costello 1994;Adesuyi et al. 2020;Yang et al. 2021).In selecting the best fitting model, the three models with the highest coefficient of determination (R 2 ) value and the lowest Akaike Information Criterion (AIC) and predicted residual error sum of squares (PRESS) values were considered.The three best models per dependent variable were plotted in order to select the one with (1) V = e (−9.62+2.697* Ln(dbh)) (2) B = e (−2.70+2.49* Ln(dbh)) the best fit in terms of biological logic and finally, a residual analysis was carried out to corroborate this selection.All statistical analyses were performed in Past4 version 4.11 (Hammer et al. 2001).

Estimation of growth and carbon sequestration rates
Growth and carbon sequestration rates were estimated as the current annual increment (CAI) and mean annual increment (MAI), using Eqs. 3 and 4. A simulation was carried out to estimate the carbon sequestration rate in aboveground biomass at the agroforestry system level, using densities of 60 trees/ha of C. alliodora.
where CAI: current annual increment (cm/tree/year, m/tree/year, m 3 /tree/year or kg tree/year), V t+1 and V t : value of the variable in the year t + 1 and t (cm/ tree, m/tree, m. 3 /tree or kg tree/tree) MAI: mean annual increment (cm/tree/year, m/ tree/year, m 3 /tree/year or kg/tree/year) V t : value of the variable in year t (cm/tree, m/tree, m 3 /tree, or kg/tree). (3) A: age of the tree (years)

Fitting of growth models
Three nonlinear growth models were developed for each of the variables under study: dbh, h, V, B and C (Table 2).These models presented the best statisticians (R 2 , AIC and PRESS), and the first of them also presented the best biological logic, being the most recommended to study the growth of this species under the mentioned conditions (Hill model for dbh, B and C, logistic for h and exponential for V).These models were selected to develop the growth and carbon sequestration curves.Likewise, the selected models presented a random distribution of the residuals (Figs. 1 and 2), whose variance increases slightly in large trees (age > 13 years).The Hill model proved to be the best fit for three of the five growth variables analyzed (dbh, B and C); while the logistic and potential models were the best fit for total height and total timber volume, respectively (Table 2).In all cases, the R 2 was higher than 0.61, being the highest in dbh and h (0.77 and 0.75, respectively).

Growth of diameter and total height
During the ages analyzed (1 to 19 years), C. alliodora trees grew an average of 3.0 cm/year in dbh and 1.3 m/year in h (Fig. 1).The highest growth rate of the species was reached between 4 and 6 years of age (3.6 cm/year in dbh and 2.9 m/year in h).After 6 years, growth in these two variables had different trends, since while dbh continues to grow at a slower rate (up to 2.1 cm at 20 years), growth in height stagnated and stopped at 20 years (Fig. 2b).The dispersion of the data could indicate differences in growth between sampling sites, which were more noticeable at h than at dbh.The 20-year-old C. alliodora trees would reach, on average, 63.6 cm in dbh and 26.2 m in h.

Volumetric growth
C. alliodora trees grew, on average, at a rate of 0.30 m 3 /tree/year during the measurement period, showing an increasing trend with age, i.e., the highest rate of Vol.: (0123456789) accumulation of total timber volume was reached at 20 years of age (0.60 m 3 /tree/year) (Fig. 2a).As with dbh, and as expected, a high variability in volume was found, mainly at high ages (Fig. 2a).Total aboveground biomass showed a similar trend to volume, with an average of 118.2 kg/tree/year and a maximum at 20 years of 177.8 kg/tree/year (Fig. 2b).Each 20-year-old C. alliodora tree would reach, on average, 5.4 m 3 of total timber volume and 2203.8 kg of total aboveground biomass (Fig. 2b).

Rate of carbon sequestration in biomass
C. alliodora trees sequestered, on average, 59.1 kg C/tree/year (217.0 kg CO 2 /tree/year) in aboveground biomass up to 20 years of age.The maximum carbon sequestration was reached at 20 years of age, being 88.9 kg C/tree/year (Fig. 2c).During the entire study period, a tree of this species would have sequestered 1.1 Mg C, equivalent to 4.0 Mg CO 2 (Fig. 2c).

Discussion
The models developed present a good fit and allow predictions of C. alliodora growth in coffee AFS in the study area.Other authors have developed growth models for forest species using nonlinear regressions with similar fit statistics (Adesuyi et al. 2020;Doyog et al. 2021;Yang et al. 2021).Parresol and Devall (2013) found that the growth of C. alliodora trees in forests mostly follow a sigmoid (sigmoidal) pattern, which is similar to that found in this study.These  (Houllier et al. 1995;Somarriba et al. 2001;Jaimez et al. 2013).The peak growth of these two variables was reached at year 4-6, which coincides with Hernández et al. (1997), who found that the increase in diameter and height of C. alliodora in AFS with coffee decreases progressively over the seventh year, possibly due to increased competition between canopies.Parresol and Devall (2013) also found a reduction in the growth of C. alliodora in Panamá forests at seven years of age.The dimensions reached by trees in this area at 20 years of age (63.6 cm in dbh and 26.2 m in h) are much higher than data reported by Liegel and Stead (1990) Beer (1987) reported diameters up to 66 cm of around 32 years in the same type of production system in the region of Turrialba, Costa Rica.These studies confirm that C. alliodora continues to grow at an age greater than 20 years, although at a lower rate, which has implications for management and profitability of this production system.
The growth of C. alliodora varies depending on the site and the management of the associated crop, differing between production systems such as forests, pure plantations or agroforestry systems (Somarriba and Beer 1987;Current et al. 1998;Valdivieso et al. 1998;Somarriba et al. 2001;Parresol and Devall 2013).Current and mean annual increases in dbh and total height obtained by this study were also higher than those reported in plantations of C. alliodora in Colombia ( Van der Poel 1988), and in AFS with cacao, coffee, sugarcane and pastures in Costa Rica (Somarriba and Beer 1987).Somarriba et al. (1995) report increases of 6.4 cm/year and 4.5 m/year at 2.4 years in cocoa Fig. 2 Best-fit models of volumetric growth and accumulation of aboveground biomass and carbon, with corresponding residual plots, for Cordia alliodora in agroforestry systems with coffee in Líbano, Tolima, Colombia.a V: total timber volume; b B: total aboveground biomass; c C: carbon in total aboveground biomass; A: age (years); R 2 : coefficient of determination; AIC: Akaike's Information Criterion; PRESS: predicted residual error sum of squares AFS in Puerto Viejo, Talamanca, Costa Rica; while Rosero and Gewald (1979) estimated increases of 0.9 cm/year and 0.2 m/year in 15 to 17-years-old trees in associations with coffee cultivation in the Atlantic zone of Costa Rica.Peak growth occurs at an age slightly higher than the findings of Montero and Mellink (1987) and Somarriba et al. (2001), who consider that the greatest increases of the species are obtained mainly in the first four years.The higher growth and carbon sequestration rates in this study may be due to the high fertility of these Andisol soils.
Volumetric growth was maximized in trees close to 20 years of age (0.60 m 3 /tree/year), which indicates the feasibility of maintaining the trees in the field for a longer period, so that larger sawlog dimensions can be produced (Somarriba and Beer 1987).These increases exceed those reported by Rosero andGewald (1979), Glover (1981) and Hernández et al. (1997) in Colombia andCosta Rica. Valdivieso et al. (1998) estimated that C. alliodora (68 trees/ha) can reach 0.87 m 3 /tree at 6 years (59.2 m 3 / ha and MAI = 9.6 m 3 /ha/year) in AFS with cocoa and banana.Somarriba et al. (2008) reported in AFS with 56 trees/ha in Talamanca (Costa Rica) a value of 59.3 m 3 /ha in cacao plantations, while for 51 trees/ ha it was 54.1 m 3 /ha in banana plantations (with a periodic annual increment of 4.0 and 6.3 m 3 /ha/year, respectively).These values that are largely surpassed by the timber stocks achieved at those same densities in the present study (276-303 m 3 /ha, with a MAI of 13.8-15.1 m 3 /ha/year).Somarriba and Beer (1987) state that this species can be maintained longer in the field and achieve total volumes of 298 to 690 m 3 /ha for densities of 68 to 290 trees/ha of C. alliodora at 34 years in AFS (MAI of 8.8 and 20.4 m 3 /ha/year, respectively).Although comparisons are difficult due to differences in climate, soils and management, the volumetric growth of C. alliodora in Líbano is high, but within the estimates of other authors at higher tree densities.Larger logs usually command higher market prices per cubic meter (Ramírez et al. 2020;Wanneng et al. 2021), which represents a high advantage of this species.
As with volumetric growth, carbon sequestration was maximized in trees of older age (20 years) and size (dbh = 62.6 cm) (88.9 kg/tree/year).This indicates the possibility of maintaining individuals of this species longer in the AFS, so that more carbon is sequestered, the permanence of carbon in the biomass is increased, and more emission reduction credits, and greater profitability are achieved (Waldén et al. 2020).This practice would bring positive impacts, as Andrade et al. (2014b) state that timber species contribute approximately 66% of carbon sequestration in AFS with coffee in this same study area.
By modeling carbon sequestration, it was estimated that C. alliodora, at a density of 60 trees/ha, can sequester 260 Mg CO 2 /ha over the 20 years (a mean sequestration of 13.0 Mg CO 2 /ha/year = 3.5 Mg C/ ha/year), without considering below-ground biomass (additional 18-21%).Pocomucha and Alegre (2013) state, as do these findings, that the age of the AFS and tree density significantly affect the carbon stock potential.In this same study area (Tolima, Colombia), carbon sequestration rates have been estimated for C. alliodora in the order of 1.1 to 4.9 Mg C/ha/year in cocoa plantations and 4.4 Mg C/ha/year in coffee plantations; while in plantations 1.2 Mg C/ha/year is reported (Andrade et al. 2013(Andrade et al. , 2014b;;Patiño et al. 2018).In contrast, Aristizábal et al. (2002) found lower values in Caldas, Colombia in AFS with cocoa and banana and densities of 200 trees/ha (4.3 Mg C/ ha/year).The same occurs in Costa Rican AFS: Segura (2005) estimated 2.1 and 2.8 Mg C/ha/year in cocoa plantations with 100 and 150 trees/ha, respectively; while Ávila et al. (2001) estimated between 0.3 and 2.2 Mg C/ha/year in cocoa AFS with 156 trees/ha and wooded pastures with 370 trees/ha, respectively.The inclusion of C. alliodora in coffee plantations would change the magnitude of the carbon footprint in this production system, transforming them from net GHG (greenhouse gases) emitters (− 5.7 Mg CO 2 /ha/ year) to net CO 2 sequesters (14.2 Mg CO 2 /ha/year) (Andrade et al. 2014b), achieving carbon neutrality (Birkenberg and Birner 2018) and its economic and market benefits (Birkenberg et al. 2021).This means that the potential carbon offset by C. alliodora was 19.9 Mg CO 2 /ha/year (Andrade et al. 2014b) compared to 13.0 Mg CO 2 /ha/year in this study, whose differences are explained by tree densities.

Conclusions
The non-linear regression models obtained in this study allowed us to evaluate the growth and carbon sequestration of C. alliodora in coffee plantations in the municipality of Líbano, Tolima.These models are a tool for the silvicultural management of these agroforestry systems and are a support to maximize timber production and atmospheric CO 2 sequestration.
The maximum volumetric, biomass and carbon growth at 20 years would indicate that it is possible to maintain these trees in these agroforestry systems for longer, so that they achieve larger logs, sequester more carbon for longer and achieve a greater permanence of carbon in the biomass.This would mean a very important win-win strategy for the promotion of these production systems.
The high carbon sequestration rates (2.7 to 8.0 Mg C/ha/year), for more than 20 years, are an indicator of the importance of these production systems for climate change mitigation.In the same way, the inclusion of C. alliodora would make a conversion in the carbon footprint, from being a net emitter of GHG to a net fixer of atmospheric CO 2 .This species could be used in emission reduction projects or in carbon neutral coffee production.

Fig. 1
Fig. 1 Best-fit diameter and height growth models and their corresponding residual plots for Cordia alliodora in agroforestry systems with coffee in Líbano, Tolima, Colombia.dbh: diameter of trunk at breast height; h: total height; A: age

Fig. 3
Fig. 3 Carbon sequestration rate (current annual increment) a of individual trees and b stands at a density of 60 trees/ha of Cordia alliodora in agroforestry systems with coffee in Líbano, Tolima, Colombia

Table 1
Generic non-linear models tested for the development of growth curves and biomass and carbon accumulation in Cordia alliodora growing in agroforestry systems with coffee in Líbano, Tolima, Colombia y Dependent variable (diameter at breast height -dbh-, total height -h-, total volume of timber with bark -V-, aboveground biomass -B or carbon in aboveground biomass -C); a, b, c and d: model parameters; x: age.