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photosynthetic capacity and derive the optimum fruit number for each individual tree, in order to achieve a defined fruit size, which is named as the fruit bearing capacity of the tree. The estimation of fruit bearing capacity was carried out considering the total leaf area per tree as measured with a 2-D LiDAR laser scanner, LALiDAR, and key carbon-related variables of the trees including leaf gas exchange, fruit growth and respiration, in two commercial apple orchards. The range between LALiDAR and LALiDAR was found to be 2.4 m2 on Pinova and 4.3 m2 on RoHo 3615 at fully developed canopy. The daily C requirement of the growing fruit and the associated leaf area demand, necessary to meet the average daily fruit C requirements showed seasonal variation, with maximum values in the middle of the growing period. The estimated fruit bearing capacity ranged from 33-95 fruit tree and 45-121 fruit tree on the trees of Pinova and RoHo 3615, respectively. This finding demonstrates sub-optimal crop load at harvest time in both orchards, above or below the fruit bearing capacity for individual trees. In conclusion, the LiDAR measurements of the leaf area combined with a carbon balance model allows for the estimation of fruit bearing capacity for individual trees for precise crop load management. K e y w o r d s: fruit growth rate, fruit respiration, leaf area, LiDAR, precision horticulture INTRODUCTION As a perennial plant, the production of premium size apples requires a balance of crop level and the ability of the tree to support the crop as well as flower bud development for the following year. Crop load management (CLM) targets the fruit number per tree to enable the growth to optimal fruit sizes by optimizing the carbon supply to demand balance for economically desirable fruit growth. Also, when performed less than 30 days after full bloom, CLM avoids a reduction in flower bud development to prevent alternate bearing on susceptible cultivars (Kofler et al., 2019). CLM may include pruning to reduce flower-bud numbers per branch (Breen et al., 2015), mechanical (Penzel et al., 2021) or chemical thinning of flowers (Janoudi and Flore, 2005) or fruitlets (Penzel and Kröling, 2020), and frequently corrective hand thinning after fruit drop. In order to optimize CLM for the quantity of profitable fruit size, it is crucial to define the optimum fruit number per tree, which should be considered as the target fruit number for the purposes of making an accurate determination of the intensity of each individual management practice (Treder, 2008; Robinson et al., 2017). The optimum fruit number per tree depends on the economically desirable fruit size at harvest, the daily C demand of growing fruit required to achieve this fruit size and the individual photosynthetic capacity of each tree to support fruit growth versus vegetative growth and flower bud development. ©2020Institute of Agrophysics, Polish Academy of Sciences M. PENZEL et al. 410 The photosynthetic capacity of fruit trees is associated with the extent of their generative and vegetative growth, both directly and indirectly determined by interacting factors of intra-plant competition. Furthermore, external factors such as light availability and interception, temperature, mineral nutrition, soil properties and water availability affect the photosynthetic capacity (Monteith, 1977; Xia et al., 2009; Lakso and Goffinet, 2017; Lopez et al., 2018). Physiological crop models can quantify cumulative effects of several factors on the magnitude of vegetative and generative growth of fruit trees (Lakso et al., 2001; Mirás-Avalos et al., 2011; Pallas et al., 2016). Therefore, physiological crop models are helpful in understanding the seasonal growth patterns of fruit trees or they may be used to determine the tree’s photosynthetic capacity and they can also be applied as a tool for decision support for precise orchard management (Lakso and Robinson, 2014). Furthermore, physiological and decision support models may be utilized to predict the optimum timing for the application of thinning agents (Robinson et al., 2017; Yoder et al., 2013), the thinning response (Greene et al., 2013), flower bud formation, fruit mass at harvest (Iwanami et al., 2018) and to estimate the target fruit number per tree (Handschack and Schmidt, 1990). In practice, the target fruit number per tree is, however, often estimated from the average yields of the previous years considering the mean of the entire orchard, divided by the number of trees in the orchard and the targeted fruit fresh mass. This approach leads to one level of treatment for all of the trees. This empirical method is not based on the natural variance in the capacity of each tree to support fruit of an economically desired size, namely the fruit bearing capacity (FBC), which can be highly variable within orchards (Manfrini et al., 2009). Therefore, the individual FBC of a certain number of trees is potentially over or underestimated by the established method. Overestimation of the FBC will lead to excessively high crop levels, poor fruit quality and reduced flower bud induction, while underestimation leads to too few fruits, a loss of crop value, reduced storability and an increased risk of storage disorders (Wójcik et al., 2001; Mussachi and Serra, 2018). As individual trees require a variable intensity of CLM, it is assumed that lack of treespecific CLM is an important cause of heterogeneity in fruit size, quality, and value. In order to observe the variability in the growth habits of trees, data from a large quantity of trees is required. Recent approaches used to detect flower clusters and the fruit of individual trees (Tsoulias et al., 2020) or to estimate other canopy parameters such as canopy height, volume or total leaf area, have shown promising results (Bresilla et al., 2019; Tsoulias et al., 2019; Hobart et al., 2020; Vanbrabant et al., 2020). When these techniques are implemented within existing physiological models, the data generated can potentially be applied to estimate the photosynthetic capacity of individual trees, the optimum and target fruit number per tree, their variability within an orchard, and the required variable intensity for precise CLM practice. The estimation of leaf area may be of outstanding importance, since the photosynthetic capacity of a tree relies on the total leaf area, especially from the exposed leaves, the quantity of light intercepted by the leaves and the photosynthetic conversion to fixed carbon. The percentage of leaf-assimilated carbohydrates partitioned to fruit, Cpart (%), is dynamic during the whole season, with significant changes in the first weeks after bloom (Hansen, 1967; Corelli-Grappadelli et al., 1994; Pallas et al., 2016). The magnitude of Cpart for a specific date is determined by the C supply to demand balance of the tree, which is influenced by the quantity and actual sink activity of all organs including shoots, fruit, leaves, branches, roots, and stem. Cpart can range from 0% on non-bearing trees to 85% on fruiting trees with a low leaf area to fruit ratio (LA:F) (Hansen, 1969; Palmer, 1992; Lakso, unpublished data). In periods showing C demand exceeding the supply in a particular apple tree, there is a prioritization in C partitioning among the sink organs, with the highest priority assigned to growing shoots (Bepete and Lakso, 1998). When shoot and leaf growth is complete, the highest priority for C partitioning is the fruit (Wagenmakers, 1996). When integrated over the whole season, Cpart is defined as the harvest index (HI). For fruiting trees of different cultivars, varying HI were reported in previous studies, ranging from 50% 85% (Koike et al., 1990; Palmer et al., 2002; Glenn, 2016; Lakso, unpublished data). They were typically grown on dwarfing rootstocks including M.9, M.26 and M.27. The HI is negatively correlated to the N supply of the tree, which positively affects the LA:F (Xia et al., 2009). The C supply to the individual fruit may limit fruit growth at different times during the season (Lakso and Goffinet, 2017) and, therefore, determine the fruit size at harvest time. Hence, assuming the total leaf area per tree is closely related to light interception, the fruit size at harvest is positively correlated to LA:F (Palmer, 1992) and can be further described as a hyperbolic function of the exposed LA:F of healthy LA, not affected by external stress. The effective LA required to produce a specific fruit size from a cultivar varies depending on the exposed versus shaded LA as demonstrated by earlier studies. Hansen (1969) reviewed several early studies concerning the relationship between LA:F and fruit size, pointing out that 300-500 cm2 LA:F, or 20-30 leaves per fruit, is the minimum requirement to achieve a marketable fruit size. The required LA:F in contemporary orchards may be different, because it may be assumed that at the time when the studies were carried out, the trees were probably not as optimally supplied with nutrients and water as in present day orchards. Other factors which affect the required LA:F are cultivar, rootstock, growing system and seasonal climate, all affecting the light interception of the trees and the HI. FRUIT BEARING CAPACITY IN APPLE 411 Previous studies have in common that the LA:F was determined at full canopy or at harvest. However, the fruit growth rate and related C consumption of individual fruit underlies seasonal changes (Schechter et al., 1993; Pavel and DeJong, 1995; Lakso and Robinson, 2014). As a consequence, since seasonal leaf area and fruit development occur with different patterns, it may be assumed that the LA:F required for fulfilling the fruit’s C requirement varies during fruit development. Additionally, the total LA per tree changes continuously during the season, as does the LA:F, until fruit drop and shoot growth have ended. Schumacher (1962) pointed out the negative effect of temporarily variable LA:F in or

Carbon consumption of developing fruit and the fruit bearing capacity of individual RoHo 3615 and Pinova apple trees