## 2 Materials and Methods  
This research was conducted in the Nurzec Forest District (Regional Directorate of State Forests in Bialystok) from 14 March to 12 April 2019. The empirical material was obtained from trees growing in the area of 3 forest units with different forest site types. These were mixed coniferous forest (unit: 50 A-f), mixed broadleaved forest (unit: 58 d), and broadleaved forest (unit: 12 d). The ages of the stands were similar and amounted to 78 years, 74 years, and 88 years, respectively. [PERSON]'s method was used to designate sample trees representing the stand (in each site, 9 trees). This method is based on taking trees ordered by increasing DBH values and categorizing them into three classes in the same cross-sectional area [32]. Then, three sample trees of the average DBH value from each class were selected: \"thin\", \"medium\", and \"thick\" (hereinafter referred to as THN1-3, MED1-3, and TCK1-3). For the mixed coniferous forest site, these values were 30.5 cm, 35.5 cm, and 42.5 cm; for mixed broadleaved forest, they were 23.5 cm, 31.5 cm, and 40.5 cm; and for broadleaved forest, they were 27.0 cm, 34.5 cm, and 42.5 cm. Then, measurements of the sample trees' heights and crown heights were taken using a SUNTO PM-5/1520 height gauge (Suunto Oy, Vantaa, Finland). A 50 mm deep, 12 mm diameter hole was made in the trunk of each tree on the north side, at a height of 100 cm, which was then cleaned and rinsed with distilled water. A tube with an internal diameter of 10 mm and an external diameter of 12 mm, made of plastic, approved for contact with food, was placed tightly in each hole. Before installation, each tube was disinfected with 70% ethyl alcohol and washed twice with distilled water. Birch sap was collected in airtight containers of 10 L to 30 L, made of plastic, approved for contact with food (Figure 1). The containers were disinfected similarly to the tubes. The amount of leaking birch sap was measured over 29 days, starting from 15 March 2019. Sap was taken every day at the same time--from each tree and in each habitat--rounded to 10 mL. The containers and tubes were washed with 70% alcohol and distilled water after each measurement. The sap collection phase has not been precisely defined in the literature so far. A definition has been proposed that includes the following:  
Phase 1--the period when the leakage intensity is below average (initial);  
Phase 2--the period when the leakage intensity is above average (main);  
Phase 3--the period when the leakage intensity is again below average (final). The amount of birch sap obtained, both daily and seasonally, was characterized statistically, using descriptive statistics measures. The efficiency of sap extracted from individual trees was compared using multifactorial analysis of variance, making the average value of this feature dependent on qualitative variables, which included forest site type, sap collection phase, and tree thickness class in the stand. Hypotheses regarding the influence of these factors and their interactions in the average daily sap efficiency were verified. A linear model with fixed and random effects was used to model the relationship between the amount of sap obtained and the biometric features of trees and site characteristics. Among the biometric features, the modeling included the following as explanatory variables: tree diameter category within the stand, total height, crown base, crown length, relative crown length, and slenderness. The site characteristic was the forest site type, which, within the classification used in Poland, considers the site's humidity and fertility. The last variable used in the modeling was the feature related to the date of sap collection, which was assumed to be the sap collection phase. The daily volumes of obtained birch sap were modeled; these variables were explained in the constructed models. The maximum likelihood method, designated ML, was used to search for model parameters.