Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain

Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Student: Narangarav Dugarsuren Co-advisors: Prof. Felipe Oviedo Bravo Ing. Cristobal Ordonez Alonso July, 2019 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 2 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 3 INDEX LIST OF FIGURES ............................................................................................................................... 4 LIST OF TABLES ................................................................................................................................. 4 RESUMEN ......................................................................................................................................... 5 ABSTRACT ......................................................................................................................................... 5 1. - INTRODUCTION .......................................................................................................................... 6 2. - OBJECTIVES................................................................................................................................. 8 3. - MATERIAL AND METHODS ......................................................................................................... 8 3.1. Study site ............................................................................................................................... 8 3.2. Biomass estimation ............................................................................................................. 10 3.3. Tree species diversity estimation ....................................................................................... 11 3.3.1. Species richness indices ............................................................................................... 11 3.3.1.1. Simpson Diversity index (1-D) ............................................................................... 11 3.3.1.2. Shannon index ....................................................................................................... 11 3.3.1.3. Berker-Parker index (D) ......................................................................................... 12 3.3.1.4. Evenness index (E) ................................................................................................. 12 3.3.2. Species intermingling ................................................................................................... 12 3.3.2.1. Species segregation (S) index ................................................................................ 12 3.3.2.2. Mingling (Mi) index ............................................................................................... 13 3.3.2.3. Spatial diversity status (MS) .................................................................................. 14 3.3.3. Spatial structural indices .............................................................................................. 15 3.3.3.1. Uniform Angle Index (W)....................................................................................... 16 3.3.3.2. Aggregation index R ............................................................................................. 16 3.3.3.3. Height Differentiation index (TH) .......................................................................... 16 3.3.3.4. Vertical species profile (A)..................................................................................... 17 3.4. Statistical analysis ............................................................................................................ 17 4. - RESULTS .................................................................................................................................... 19 5. - DISCUSSION .............................................................................................................................. 23 6. - CONCLUSIONS .......................................................................................................................... 24 7. - AKNOWLEDGEMENTS .............................................................................................................. 24 8. - REFERENCES ............................................................................................................................. 25 ANNEX ............................................................................................................................................ 29 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 4 LIST OF FIGURES Figure 1.Study area location of Marteloscope of Llano de San Marugan (Valladolid, Spain) .............................................................................................................. 9 Figure 2. Workflow for the study of tree biomass and diversity relationship ..................... 9 Figure 3. Description and calculation of Mingling index (Mi), Spatial diversity status (MS) and Uniform Angle index (Wi) and corresponding likelihood values for structure unit of 4 neighbors around the reference i tree: a, b, c, d are the tree species types ; 𝜽 are angles between adjacent neighbor trees; 𝜽𝒔 is a standard angle (which is equal to 360/4 for 4 neighbor trees) (Adapted from Gadow & Hui, 2002) ............................................................................................................. 15 LIST OF TABLES Table 1. Biomass allometric equations by species ........................................................ 10 Table 2. Categorization of indices ................................................................................. 11 Table 3. Descriptions of variables for S index calculation .............................................. 13 Table 4. Fitting models and their predictor variable reference ....................................... 19 Table 5. Parameter estimates for biomass from selected models at community level ... 21 Table 6. Parameter estimates for biomass from selected models at species level ........ 22 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 5 RESUMEN La biomasa de árboles y su relación con la diversidad en bosques mixtos se ha convertido en uno de los temas de investigación más interesantes para los ecólogos en las últimas décadas debido a la importancia de los bosques mixtos para una mejor provisión de servicios ecosistémicos. La pregunta “¿Producen los bosques mixtos más a medida que aumenta la diversidad de árboles?” Ha sido objeto de muchos estudios que llevan a resultados no concluyentes. Este estudio se realizó para contrastar el resultado de estudios anteriores mediante la investigación de la biomasa de árboles y la relación de diversidad en un rodal mixto de bosque mediterráneo (Llano de San Marugan, España), tanto a nivel de masa como de árbol individual. Se analizaron diversos modelos que se ajustaron a partir de ecuaciones de regresión lineal y no lineal para determinar la relación entre la biomasa de los árboles y la diversidad. Se utilizaron 10 índices de diversidad que se pueden clasificar en 3 categorías: índices de riqueza de especies (Sm, Sn, D, E); Índices de composición / mezcla de especies (Mi, MS, S); Los índices estructurales verticales (W, A, TH) como variables predictoras de los modelos con el objeto de caracterizar diferentes estructuras de diversidad en el rodal. Nuestro resultado reveló que la relación entre la biomasa y la diversidad de árboles varía entre las especies. Una combinación de la relación negativa del índice D-Berker-Parker (abundancia de especies dominantes) y la relación positiva de TH (heterogeneidad de la altura) explica la variación de la biomasa a nivel rodal y para Pinus pinea. La biomasa de las especies de Quercus (Quercus faginea y Quercus ilex) se relaciona positivamente con la proporción de especies en área basimétrica (Gp); los índices de diversidad probados no mostraron ninguna relación con la biomasa de las especies del género Quercus. Palabras clave: diversidad de especies arbóreas, índices de diversidad, riqueza específica, composición específica, estructura vertical del rodal. ABSTRACT Tree biomass and diversity relationship in mixed forest has become one of the attractive research subjects for ecologist in recent decades due to an importance of multicultural mixed forest for better provision of goods and services than monoculture. The questions “Does mixed forest produce more productive and the productivity increase as tree diversity increases?” have been subject of many researches that lead to two contrast results. This study was conducted to contrast the result of previous studies by investigating the tree biomass and diversity relation in Mediterreanean multicultural mixed stand, Llano de San Marugan, Spain, at stand and individual species level. A variety of models that developed from linear and nonlinear regression equations were employed to reveal tree biomass and diversity relation. 10 diversity indices that falls in 3 categories: species richness indices (Sm, Sn, D, E); species compositional/mingling indices (Mi, MS, S); vertical structural indices (W, A, TH) were used as predictor variables for the models to characterize different structure of diversity in the stand. Our result revealed that tree biomass and diversity relation varies among species. A combination of negative relation of DBerker-Parker index (abundance of dominant species) and positive relation of TH (height heterogeneity) explains the variation of biomass at community level and for Pinus pinea. Biomass of Quercus species (Quercus faginea and Quercus ilex) was positively related with basal area proportion of species (Gp); the tested diversity indices didn’t show any relation with biomass of Quercus species and Juniperus thurifera as concerned by metrics and models in this study. Key words: tree biomass, tree diversity, mixed forest, diversity indices, species richness, species composition, stand vertical structure. Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 6 1. - INTRODUCTION Mediterranean forests are characterized by a remarkable set of features that make them naturally and aesthetically attractive, but also quite fragile (ScarasciaMugnozza et al., 2000). Mediterranean forest is a multi-functional, providing a wide range of goods and services for society ranging from products with high market value (fuelwood, cork, mushroom, pinecones etc) and non-market value ecosystem services (soil and landscape protection, water regulation, biodiversity conservation, carbon dioxide fixation, recreation, aesthetic view etc). The latter is more significant than their productive value, especially their significant role for carbon sequestration (del Río et al., 2017). One of notable characteristics of Mediterranean forests is its rich biodiversity, reflected by high genetic variability, exemplified by the large number of tree species in comparison to Nordic forests resulting from the survival of many conifer and broadleaf species during the glacial periods. Long-term exploitation (manipulation) of trees and forestland since ancient times is another feature of Mediterranean forest which results in the dispersion of species as Pinus pinea, Castanea sativa, and Quercus suber all over the Mediterranean basin (Scarascia-Mugnozza et al., 2000). Dry, hot, harsh climate along with long lasting and frequent droughts, pest and decease, increasing the risk of large-scale fires and severe water scarcity are main challenges for the Mediterranean forests which largely impact on forest health, growth and productivity. The role of mixed forest for promoting forest productivity while coping with these challenges has been increased in Mediterranean region in recent decades. Multicultural mixed forest have been taken a great attention in recent decades due to its greater provision of goods and services, high ecological value in comparison to monoculture forest (Pretzsch & Schütze, 2014; Riofrío, et al., 2017). Mixed forest is defined as a forest unit of at least 0.5 ha that composes at least two tree species at any developmental stage, shares common resources (water, light, soil nutrients) and its structure and component species are altered over the time (Bravo-Oviedo et al., 2014). Main characterizations of mixed forests are described not only by better protection, preservation, maintaining and monitoring of biodiversity but also have high resistance capacity against both natural and anthropogenic disturbances such as climate change, storm, pest and decease, air pollution and its consequences. Economic importance of mixed forest is un-negligible because of its multi-use, multi-source than pure stands (Knoke et al., 2005). The loss of biodiversity imposed by anthropogenic and climatic change has brought the importance of diversity under the control worldwide over the past 25 years (Hooper et al., 2012; J. Liang et al., 2016; Szwagrzyk et al., 2007) after the Earth Summit of world governments in Rio de Janeiro in 1992 (Evans, 2016). Since that time, scientists have been taken into account the importance of biodiversity on many ecosystem functioning and service such as productivity, stability, sustainability, sinking carbon dioxide, preserving soil fertility, controlling pest outbreaks, retaining water, and so on (Baskin, 1994). Among them, the importance of tree species diversity on biomass productivity has been studied based on the variety of genes, species, or functional traits of organisms in hundreds of types of ecological communities (Fraser et al., 2015; Jingjing Liang et al., 2016). A series of biodiversity-ecosystem functioning studies have revealed that biodiversity (including taxonomic, functional and phylogenetic diversity) promotes the functionality of ecosystems such as primary production, decomposition, nutrient cycling, trophic interactions and so on) and consequently supports a broad Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 7 range of ecosystem services (e.g. food production, climate regulation, pest control, pollination (Gamfeldt et al., 2013; Mori et al., 2017). However, contradictory results have been documented in the findings of previous researchers focused on relationship between species diversity and biomass: biomass decrease (Szwagrzyk et al., 2007) or doesn’t change (Grace et al., 2016) with species diversity. In addition, numerous researches justified on loss of biodiversity ranks among the most pronounced changes to environment (Sala et al., 2000), reduction of diversity along with species composition changes alter fluxes of energy and essential services that ecosystem provide to human such as production of food, pest and disease control, water purification and so on (Daily, 1997). Biodiversity are largely and irreversibly being degraded and lost globally due to direct drivers; i.e. habitat disturbance, habitat fragmentation, land use change, overexploitation and the spread of alien species and indirect drivers; i.e. climate change, population growth, economic growth and increasing demand for food, materials, water and energy (Iranah et al., 2018). The loss of biodiversity weakens species connections and impairs the ecosystems, leading to extinction of species and local populations, which will disrupt the capacity of ecosystem to contribute to human well-being and sustain future generations. Tree diversity plays a fundamental role for forest diversity because it is often linked with major properties of forest ecosystem, leading to the possible enhancement of diversity of other forest assembles (Mori et al., 2017) and providing required resources and suitable habitat for other forest species (Ozcelik, 2009). Diversity is generally defined by the variety of organisms including micro-organisms, plants, and animals in different ecosystems, i.e. deserts, grassland, forests etc. The most commonly used representation of ecological diversity is species diversity, which is defined by the number of species and abundance of each species living within a certain area (Liu et al., 2018). The species coexisting in a certain area are interconnected and dependent on one another for survival, while doing so; they perform important ecosystem functions and offer different ecosystem services for human life and society: provisional service (products obtained from ecosystem: many different type of food, fresh water etc); regulating services (the benefits obtained from the regulation of ecosystem processes: air quality and pollination); cultural service (the non-material benefits that people obtain: spiritual enrichment, recreation and aesthetic experiences); supporting service needed to maintain other services (i.e photosynthesis and nutrient recycling). The provision of ecosystem for such goods and service depends basically on functions performed by living plants (Tilman et al., 1997). Two main mechanisms explain the reasons that biodiversity influence on productivity: selection effects and complementary effects. Different plant species in a mixture have different physiologies, morphologies and life history traits might allow them to fully utilize limiting resources at different space and time than a monoculture of any species (Tilman 1997). For instance, some tree species have more ability to adapt and grow better in cooler and wetter environmental condition while others grow better in hotter and drier environment. If these species grow together in a mixture, these complementary characteristics of both species lead to greater productivity across the whole grown season than either species grows alone. Similarly, tree species that have different root morphologies occupy different soil profile which potentially allowing them to exploit soil resources from different soil depth. However it should be noted that these complementary occur solely when co-existing species exhibits various forms of niche differentiation that allow them to capture resources in different space or time (Cardinale Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 8 et al., 2007; David Tilman, 1999). Another mechanism that diversity effects on productivity is selection effect (sampling effect) which describes species specific effect on biomass: a greater productivity in more diverse communities is due to the most productive species which become dominant in the community due to competition. The likelihood of becoming a high productive species increases as diversity increases. Thus this causes in the increment of the total productivity of the community. Such considerations have led to the general perception of having higher productivity in an area where more plant species co-exist. Forest is 3-dimensional system whose structure is a key element in ecosystem functioning and biological diversity by regulating resource related forest functioning (light, water, soil nutrients supply, capture, use), intra and inter specific interactions (Brockerhoff et al., 2017a; del Río et al., 2018), regeneration pattern, consequent selfthinning and past and present disturbance events (Bohn & Huth, 2017; Zhang et al., 2018). Stand structural diversity leads to increase species richness and contributes to forest stability and integrity (Wang et al., 2016). Stand structural diversity combines the concepts of species richness (diversity), species composition (mixture), and spatial diversity (tree positioning) and size differentiation (Bravo & Guerra, 2002). Accordingly three distinct types of stand structural indices and methods have frequently been purposed in preceding literature for explaining the influence of stand structural diversity on productivity and functioning of forest stand: i) species richness - Simpson index (1949), Shannon index (1948), Berger-Parker index (Berger et al., 1970) and Evenness index (Kohn, 1977); ii) species composition indices – Mingling index (Füldner, 1995), Spatial diversity status (Gadow & Hui, 2002) and Segregation index (Pielou, 1977); iii) tree distributional indices including horizontal and vertical patterns and size differentiation - Aggregation Index (Clark et al., 1954), Uniform Angle Index (Gadow et al., 1998), Vertical Species Profile (Pretzch 1995b), Height differentiation index (Gadow 1993). Since forest structure is determined in 3 dimensions, it is appropriate to analyze the effect of tree diversity on biomass by the metrics that can fully address 3dimensionality of mixed forest structures. 2. - OBJECTIVES In this study, we addressed the question “Does stand diversity impact on biomass?” by examining the relationship between tree biomass and diversity indices (species richness, species compositional, horizontal and vertical structural indices) in the Mediterranean multi-species mixed forest, Llano de San Marugan, Valladolid, Spain. The specific aims were: - To calculate biomass of individual trees by different compartments (stem, thin branches + needles, medium and thick branches) and in total - To compute the tree diversity indices to represent the diversity of the stand - To determine the relationship between tree biomass and diversity. 3. - MATERIAL AND METHODS 3.1. Study site The study was conducted in a Mediterranean mixed forest stand, located in Llano de San Marugan, Valladolid, Castile and Leon, Spain. Valladolid has a continental Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 9 Mediterranean climate with cold winters and hot summers. The average annual temperature ranges between 11 and 12ºC. Fog is frequent in the long, cold winter, while summers are dry and hot with average temperature around 30ºC. Precipitation falls irregularly throughout the year with a minimum in the summer and a maximum in spring and autumn, with maximum of 400 mm. In a mixed forest stand, a marteloscope was installed in 2015 covering 1 hectare (ha). The marteloscope (a square of 100 by 100 m) was divided into 16 subplots (hereafter referred as quadrants), 25 x 25 m length, as shown in Figure 1. Within each quadrant, locations of all trees were recorded in 4.55728º W and 41.43948º N geographic coordinates and their species were identified and corresponding diameter at breast height (dbh, in cm) and, total height (in m). The diameter at breast height and total height were measured from trees whose diameters were greater than 5 cm. The study workflow is shown in Figure 2 and detailed explanations are given in following sub-sections. Figure 1. Study area location of Marteloscope of Llano de San Marugan (Valladolid, Spain) Figure 2. Workflow for the study of tree biomass and diversity relationship Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 16 vertical or horizontal axis (del Río et al., 2018). The horizontal spatial distribution gives an idea of the variation of tree positioning (Bravo & Guerra, 2002). The indices that measure the horizontal spatial distribution quantifies the degree of regularity of the trees which are typically classified into regular, random, and clustered patterns and linked to processes of tree mortality, competitive interaction, regeneration and gap creation and so on. Vertical spatial distribution is most commonly described in terms of layers that refer to distinct classes or stratification of the canopy corresponding to height-related differentiation between trees. 3.3.3.1. Uniform Angle Index (W) The Uniform Angle Index (W) formulates the degree of spatial dispersion of nearest neighbors around the reference tree based on angles between adjusting nearest neighbor trees defined as vectors from reference tree to each neighbors as shown in Figure 3 (Gadow et al., 1998). W is determined as the proportion of the angles that are smaller than the standard angle 𝛼0 (360/ 𝑛) and calculated as (Eq. 9): 𝑊𝑖=1 𝑛∑𝑣𝑗 where 𝑣𝑗={1,𝛼𝑗<𝛼0 0,otherwise 𝑛 𝑗=1 Eq. 9 where 𝑛 is number of nearest neighbours 0 ≤ W ≤ 1; If {𝑊<0.5, 𝑟𝑒𝑔𝑢𝑙𝑎𝑟 𝑡𝑟𝑒𝑒 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑜𝑖𝑛 0.5<𝑊<0.6, 𝑟𝑎𝑛𝑑𝑜𝑚 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑊>0.6, 𝑐𝑙𝑢𝑚𝑝𝑒𝑑 The value of W ranges from 0 to 1. The value of W increases from regular to clumped pattern (regular < random < clumped). 3.3.3.2. Aggregation index R Aggregation index (R) by Clark & Evans (1954) is a single value index that is designed to describe aspects of variability of tree locations in forest stands (Eq. 10). 𝑅=𝑟𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝐸(𝑟) where 𝐸(𝑟)=√𝐴 𝑁 Eq. 10 Where 𝑟𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 is an average distance to their nearest neighbours in a given forest stand while E(r) is an average nearest neighbor distance when trees completely random distributed, A is area of the plot, N is the total number of trees in the plot. The edge effect arising from the spatial limitations of experiment plots has minimized by applying the boundary correction factor by Donnelly (1978). Interpretation of R values is as follows: 0≤𝑅≤2.149: 𝑅 {<1; 𝑡ℎ𝑒𝑛 𝑝𝑎𝑡𝑡𝑒𝑟𝑛 𝑠ℎ𝑜𝑤𝑠 𝑐𝑙𝑢𝑠𝑡𝑒𝑟𝑖𝑛𝑔 ≈1;𝑡ℎ𝑒𝑛 𝑝𝑎𝑡𝑡𝑒𝑟𝑛 𝑖𝑠 𝑟𝑎𝑛𝑑𝑜𝑚 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 >1;𝑡ℎ𝑒𝑛 𝑝𝑎𝑡𝑡𝑒𝑟𝑛 𝑖𝑠 𝑟𝑒𝑔𝑢𝑙𝑎𝑟 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 3.3.3.3. Height Differentiation index (TH) Height differentiation index (TH) is size differentiation index, developed by Gadow (1993) which measures the variability in height between 𝑖-th reference tree to each neighboring trees (j-1…n) and describes vertical distribution of tree height (Eq. 11). Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 17 𝑇𝐻𝑖𝑗 =1−𝑀𝐼𝑁(𝐻𝑖, 𝐻𝑗) 𝑀𝐴𝑋(𝐻𝑖, 𝐻𝑗) Eq. 11 where 𝐻𝑖,& 𝐻𝑗 are the height of reference tree and neighbor tree respectively. 0 ≤ TH ≤ 1. If {𝑇𝐻=1, 𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑢𝑟 𝑡𝑟𝑒𝑒𝑠 ℎ𝑎𝑣𝑒 ℎ𝑖𝑔ℎ 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑡𝑖𝑜𝑛 𝑖𝑛 ℎ𝑒𝑖𝑔ℎ𝑡 𝑇𝐻=0, 𝑛𝑒𝑖𝑔ℎ𝑡𝑏𝑜𝑢𝑟 𝑡𝑟𝑒𝑒𝑠 ℎ𝑎𝑣𝑒 𝑒𝑞𝑢𝑎𝑙 ℎ𝑒𝑖𝑔ℎ𝑡 3.3.3.4. Vertical species profile (A) Vertical species profile (A) (Pretzsch, 1995) is outlined in Eq. 12. Calculation is based on the Shannon and Weaver (Shannon, 1948) diversity index. A considers both proportion of the species within a stand and the presence of each species in different height zones (Eq. 12). Height zones were determined as a same way as Pretzsch (2009). 𝐴=−∑∑𝑝𝑖𝑗×ln(𝑝𝑖𝑗) 𝑍 𝑖=1 𝑆 𝑖=1 Eq. 12 where S represents the number of species present, Z is the number of height zones (three in this case), 𝑝𝑖𝑗 is the proportion of a species in the height zone 𝑝𝑖𝑗 =𝑛𝑖𝑗 𝑁, N is the total number of individuals, 𝑛𝑖𝑗 is the number of individuals of the species i in the zone j. Standardization of A can be done by dividing A value by the maximum value of the A index, i.e. 𝐴𝑚𝑎𝑥 =𝑙𝑛(𝑆×𝑍). Its value is greater than 0. For a pure stand with single layer, A equals to 0. Its value is increases as heterogeneous the vertical profile increases. 3.4. Statistical analysis We used multiple linear regressions to evaluate the relationship between tree biomass and diversity indices in the stand, where total biomass (B) per tree was the dependent variable, and species richness, composition and species distribution indices were covariates of interest. Following previous researches that have developed a various regression models for estimating total-tree and tree compartment biomass, we utilized following three general forms of linear and non-linear regression equations (Eq. 13 to Eq. 15) for development of different forms of prediction models. 𝑌= 𝛽0+𝛽1𝑥1+⋯+𝛽𝑘𝑥𝑗+𝜀 Eq. 13 𝑌=𝛽0𝑥1𝛽1𝑥2𝛽2…𝑥𝑗𝛽𝑘+𝜀 Eq. 14 𝑌=𝛽0𝜋(𝑥𝑖𝑥𝑗)𝛽𝑘 Eq. 15 Two different approaches of regression analysis were used to find the coefficients: the first approach was to apply, whenever possible, multiple linear regressions to the original equations; the second approach was to transform the above equations to the logarithmical form and then apply multiple linear regressions to the transformed equations. Eq. 13 used to develop multiple linear regressions that can be fitted by standard least squares estimation. Non-linear models (Eq. 14 and Eq. 15) were transformed into linear models (Eq. 16 and Eq. 17) by taking the logarithm of both sides of the equation. In this form, the equation parameters can easily be estimated by least squares procedures. Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 18 ln𝑌=ln𝛽0+𝛽1ln𝑥𝑖+⋯𝛽2ln𝑥𝑗 +𝜀 Eq. 16 ln𝑌=ln𝛽0+𝛽1ln(𝑥𝑖∗𝑥𝑗)+𝜀 Eq. 17 where ln is the natural logarithm. 𝜀 is the random error term which is assumed to be normally distributed with mean zero and variance constant. The models structures and their corresponding predictor variables are given in Table 4. 11 predictor variables: four species richness indices (Sm, Sn, D, E), three species composition indices (Mi, MS, S), four spatial distribution indices: A, TH, W and G were used as predictor variables for fitting models. Several different ways were implemented in variable selection process for the fitting models in order to avoid a problem of collinearity. First, all the variables were used as a single predictor variable for the models with single term. Second, basal area, species richness indices and species composition indices were utilized as state variables individually and each one of the spatial distribution indices were added into the multivariable models with two terms as secondary predictor variable. Third, we tested G, TH or A as a second, other individual indices as a third predictor variable for the multivariable models with three terms. Finally all possible combinations of indices are examined for multivariable models as well. In total, 537 alternative models were examined for each individual species and community level. For the community level analyze, basal area per quadrant G (m2/ha), for the species level analyze, species proportion of basal area 𝐺𝑝 per quadrant were explored. For the best models selection, four criteria were employed: i) significance of variables (in the ANOVA analysis, an effect is concerned to be significant when its coefficients have a probability less than or equal to the significant probability (𝑃 < 0.05), ii) biological meaning of parameters, iii) the normality of the residuals with Q-Q plots and iv) Akaike Information Criteria (AIC). Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 19 Table 4. Fitting models and their predictor variable reference # Fitted models Predictor variable 𝑥1 𝑥2 𝑥3 Single predictor (33 alternative models) 1. 𝐵=𝛽0+𝛽1𝑥1 G, Sm, Sn, D, E, Mi, MS, S, A, TH, W 2. ln𝐵=𝛽0+ 𝛽1ln𝑥1 3. ln𝐵=𝛽0+𝛽1ln𝑥1+𝛽2ln(𝑥12) Multivariate models with 2 predictors (360 alternative models) 4. 𝐵=𝛽0+𝛽1𝑥1+ 𝛽2𝑥2 G, Gp Mi, MS, S, A, TH, W 5. 𝐵=𝛽0+𝛽1𝑥12+𝛽2𝑥22 Sm 6 𝐵=𝛽0+𝛽1𝑥1+𝛽2𝑥2+𝛽3𝑥3 Sn 7 𝐵=𝛽0+𝛽1(𝑥1∗𝑥2) D 8 ln𝐵=𝛽0+𝛽1ln𝑥1+𝛽2ln𝑥2 E 9 ln𝐵=𝛽0+𝛽1ln(𝑥12)+𝛽2ln(𝑥22) Mi A, TH, W 10 ln𝐵=𝛽0 +𝛽1ln(𝑥1∗𝑥2) MS 11 ln𝐵=𝛽0+𝛽1ln(𝑥12∗𝑥2) S Multivariate models with 3 predictors (144 alternative models) 12 𝐵=𝛽0+𝛽1𝑥1+𝛽2𝑥2+𝛽3𝑥3 G TH Sm, Sn, D, E, Mi, MS, S, A, W 13 ln𝐵=𝛽0+𝛽1ln𝑥1+𝛽2ln𝑥2+𝛽3ln𝑥3 A 14 ln𝐵=𝛽0+ 𝛽1 ln(𝑥1∗𝑥2∗𝑥3) D, E, A, Sm, S, TH, MS, S, TH, S, W, where 𝐵 represents total biomass; 𝑥1, 𝑥2, 𝑥3 represent the predictor variables; 𝛽0, 𝛽1, 𝛽2, 𝛽3 are the parameters of the models; For the species level analyze, basal area proportion of each species in each quadrant, for the whole community level analyze, basal area of each quadrant (m2/ha) were explored along with other indices. Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 20 4. - RESULTS From the result of 537 investigated models, 11 significant models for community level are summarized in Table 5. Parameters of all models were statistically significant at (𝑝< 0.01). TH alone or in combination with species richness or composition indices i.e Sm+TH, Sm*TH, Sn*TH, D+TH, E+TH, E*TH, Mi+TH, MS+TH, S+TH, G+TH+Sm, G+TH+MS was a main explanatory variable in all models except model 10 demonstrating the importance of vertical structural on tree biomass. According to parameter estimation, negative parameters were associated to species richness and compositional indices (Sm in model 1 and 4; MS in model 2 and 10; Mi in model 9; S in model 11 in logarithmic form) while positive parameters were correspond to TH in all the models excluding models 5 and 8 which implies that biomass increases as species richness or species composition decreases and height heterogeneity increases. From the selected 11 models, model 6 (Eq. 18) was found to be the best model for predicting community level tree biomass, showing negatively influence of D and positively influence of TH on tree biomass of the stand. Ln𝐵=6.594−1.349ln𝐷+0.841ln𝑇𝐻 Eq. 18 Where B is total biomass per tree (kg), D is Berker-Parker index, TH is height differentiation index. Table 6 showed that the parameter estimates of selected models by species based on models in Table 4. Similar trend that had observed at community level occur for Pinus pinea: TH alone or in combination with species richness or composition indices such as Sm+TH; Sm*TH; Sn+TH; Sn*TH; D+TH; D*TH; E*TH, Mi*TH was a main explanatory variable for all the models. The strength of the relationship ranges from 0.02 to 0.16 (0.16 < R2 < 0.2). The highest statistically significant and the lowest AIC value belong to Eq. 19 (model 6, Table 6). The same form of model as community level analysis has been chosen as a best model for Pinus pinea as well. The reciprocal interactive effect of D and TH had the best prediction power on biomass. 𝐺𝑝 has been shown to be the best explanatory variable for the biomass for both Quercus faginea (Eq. 20) and Quercus ilex (Eq. 21). None of the model was significant for Juniperus thurifera as concerned by models in this study. ln𝐵=7.249−0.935ln𝐷+0.988ln𝑇𝐻 Eq. 19 ln𝐵=4.278+0.156ln𝐺𝑝 Eq. 20 ln𝐵= 4.241+ 0.168ln𝐺𝑝 Eq. 21 Table 5. Parameter estimates for biomass from selected models at community level Intercept logG logD logTH logSm logMS log(Sm*TH) logE logMi logS log(E*TH) 1 2.929*** (0.638) 0.812*** (0.217) 0.763*** (0.098) -11.142*** (2.953) 437 0.20 1264.2 1.02 37.809*** 2 4.426*** (0.594) 0.706*** (0.213) 0.990*** (0.097) -2.028*** (0.465) 437 0.21 1259.6 1.02 39.746*** 3 5.684*** (0.137) 0.883*** (0.096) 437 0.16 1283.9 1.05 84.958*** 4 5.191*** (0.207) 0.797*** (0.099) -9.264*** (2.954) 437 0.18 1276.1 1.04 48.260*** 5 5.717*** (0.142) 0.881*** (0.097) 437 0.16 1285.8 1.05 82.659*** 6 6.594*** (0.218) -1.349*** (0.257) 0.841*** (0.093) 437 0.21 1258.9 1.02 58.877*** 7 6.149*** (0.185) 0.894*** (0.095) 32.906*** (8.965) 437 0.19 1272.5 1.03 50.434*** 8 5.701*** (0.138) 0.887*** (0.096) 437 0.16 1283.2 1.05 85.791*** 9 6.466*** (0.217) 1.038*** (0.100) -1.319*** (0.288) 437 0.20 1265.2 1.02 54.926*** 10 6.288*** (0.197) 1.001*** (0.098) -1.973*** (0.470) 437 0.19 1268.5 1.03 52.898*** 11 5.963*** (0.146) 0.710*** (0.101) -2.125*** (0.452) 437 0.20 1264.2 1.02 55.575*** ***p<0.01 F.value Model Explainatory variable N Adj.R2 AIC RSE Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 22 Table 6. Parameter estimates for biomass from selected models at species level Intercept logTH logSm log(Sm*TH) logSn log(Sn*TH) logD log(D*TH) log(E*TH) log(Mi*TH+1) logG log(E+1) log(E+1)^2 log(D+1) log(D+1)^2 1 6.575*** (0.191) 0.937*** (0.163) 177 0.16 488.5 0.95 33.191*** 2 6.158*** (0.249) 0.926*** (0.160) -8.738** (3.391) 177 0.18 483.8 0.94 20.452*** 3 6.596*** (0.199) 0.917*** (0.163) 177 0.15 489.9 0.96 31.494*** 4 7.986*** (0.662) 0.923*** (0.161) -1.230** (0.553) 177 0.17 485.5 0.94 19.444*** 5 5.500*** (0.074) 0.774*** (0.162) 177 0.11 497.5 0.98 22.873*** 6 7.249*** (0.289) 0.988*** (0.160) -0.935*** (0.306) 177 0.19 481.2 0.93 22.060*** 7 5.782*** (0.098) 0.532*** (0.145) 177 0.07 506.2 1.00 13.398*** 8 6.594*** (0.193) 0.943*** (0.163) 177 0.16 488.1 0.95 33.613*** 9 5.004*** (0.129) 2.864*** (0.556) 177 0.13 494.3 0.97 26.489*** 1 4.278*** (0.170) 0.156** (0.072) 157 0.023 183.2 0.43 4.632** 1 4.241*** (0.126) 0.168*** (0.045) 69 0.157 74.3 0.403 13.702*** **p < 0.05; ***p < 0.01 F.value Pinus pinea Quercus ilex Quercus faginea Model Explanotory variable N Adj.R2 AIC RSE 5. - DISCUSSION Our finding revealed that the variation of tree biomass can be accounted by negative influence of D and positive influence of TH indicating that specific dominance in the stand influenced negatively and height heterogeneity influenced positively on biomass at community level. For the species level analysis, the variation of biomass of Pinus pinea can be explained by the same model as community level analysis which highlighted the negative impact of D and the positive impact of TH on biomass. This results is agreement with Bohn & Huth, (2017) who examined an influence of species diversity and forest structure on aboveground biomass over a broad range of forest stands and found out a positive relation between forest structural diversity and forest productivity. The same result was found in Riofrío et al., (2017). Size heterogeneity enables bigger trees to obtain greater amount of a certain resource and use them more efficiently than small trees (Brockerhoff et al., 2017b). In our stand, mixture of the Pine, Quercus faginea, Quercus ilex and Juniperus thurifera might create a different canopy strata; top layer occupied by Pinus pinea, enabling the light-demanding species – Pine - to capture more light and grow better than other species and become dominant in the stand. The variation of biomass for Quercus faginea and Quercus ilex were predicted by basal area proportion of species (Gp). The examined diversity indices such as Sm, Sn, D, E, Mi, MS, S, W, A, TH were found not significant relation with biomass of Quercus. This might be explained by abundance of Pinus pinea. The abundance of Pine have an strong inhibitory effect on the abundance and richness of understory species through light, water, and soil nutrients and thus reversely influences on biomass productivity of understory species (Laughlin & Grace, 2006). Moreover, biomass of individual tree in a given stand is not only the reflection of diversity (species richness, composition and structure) but also various internal and external factors such as age, stand density, site productivity, competition at the tree level, climate, soil (texture, moisture content), geographical location, and length of grown season (Con et al., 2013; Poudel & Hailemariam, 2015) which might not be reflected by the available metrics or models that we are considered in this study. One notable thing is that almost all the predictor variables of significant models (except model 1 in Table 6) for Pinus pinea were identical with the community level models in Table 5. This might be fact that community level analysis may be influenced by characteristic of Pinus pinea due to its dominance in the stand. This can be explained by “selection effect” which describes the impact of the most productive species on relationship between species richness and productivity. Positive relation between productivity (biomass accumulation) and tree diversity largely depends on presenting highly productivity species in multi-cultural communities (Tilman, 1999). However, in our case the proportion of the most productive, dominant species (Pinus pinea) showed a negative effect on biomass stand as represented by D in Eq. 18 & Eq. 19. As stresstolerant and pioneer species, Pinus has the ability to become a dominant tree species in the mixed forest and accumulate biomass in a short time and it is considered as a strong competitor species with relatively high production due to its prolonged photosynthetic activity (coniferous evergreen tree) and high nutrient uptake through the rapid turnover of nutrients (Li, Su, Lang, Liu, & Ou, 2018). In old growth stand, Pinus with large diameter have a greater contribution to the stand biomass than small diameter trees (Baishya & Barik, 2011). In terms of complementarity of the species in this stand, Pinus pinea may facilitate development of Quercus by increasing seed protections, enhancing habitat condition which promote the recruitment of Quercus (Sheffer, 2012). Nevertheless, the facilitation of Pine for Quercus colonization depends on many factors such as stand density, development stage of Quercus, and environmental conditions. Pine forests with intermediate density enhance the site conditions for successful colonization of Quercus by reducing light intensity, creating partial shading and Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 24 improving the soil moisture status for Quercus seedlings. However, there is an opposition between suitable condition for recruitment and suitable condition for further growth and development of Quercus species that after seedlings and saplings stages (Puerta-Piñero, Gómez, & Valladares, 2007). In dense forest with poor environmental condition, although Pinus improved soil properties during a short period (a decade), it causes in decrement of soil moisture which may reduce recruitment of Quercus in their subcanopy. Low light interception levels and competition for water with Pinus reduces Quercus colonization in poor environmental condition. Maestre & Cortina, (2004) emphasized that Pine plantation in semi-arid environment don’t facilitate the establishment of Quercus and causes in reduction of species richness and all plant cover. Therefore, based on these reviews, we can say that Pinus pinea might be a main contributor for biomass of the stand whereas its abundance has negatively impact on biomass of coexisting species i.e Quercus faginea, Quercus ilex and Juniperus thurifera. 6. - CONCLUSIONS In this study, we examined the relationship between tree biomass and diversity in Llano de San Marugan, Valladolid, Spain at stand and individual species level by a various linear and non-linear models. After thoughtful examination of 537 models with 11 predictor tree diversity indices, we found out that there is a relation between tree biomass and diversity although this relation varies among the species. A stand level analyze revealed that tree biomass-diversity relation can be explained by an interaction of negative affect of abundance of dominant species and positive effect of tree’ height heterogeneity which indicates that tree biomass increases as abundance of dominant species decreases and height heterogeneity increases. This result was identical for Pinus pinea. For Quercus faginea and Quercus ilex, only the species proportion of basal area (𝐺𝑝) has a positive relation with biomass. The examined diversity indices were found not to have significant explanatory power for the explanation of biomass variation for Quercus species and Juniperus thurifera. Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 25 7. - AKNOWLEDGEMENTS The author would like to greatly appreciate and acknowledge the following people for their help and support for success of this study: - For supervisor Prof. Felipe Oviedo Bravo and co-supervisor Cristobal Ordonez Alonso for their enormous amount of contribution, guidance, critical comments, suggestion and helpful instructions from the initial to final stages which truly permits to successful completion of this work. - For all the professors, staffs at University of Valladolid and University of Padova for sharing their valuable knowledge, skills and experiences which helped me a lot to strengthen my knowledge and experience in this science. - For MEDfOR program for not only for the financial support but also letting us to build international network of friendship and living and experiencing in different countries with different culture. - For all wonderful friends, labmates, postdoctoral students who are studying in the Department of Agriculture and Forestry at UVA for assisting and supporting me in many ways. Without their assistance and motivation, this work would not have been accomplished. Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 32 Annex 3. Main attributes of tree by quadrant. Quadrant number Number of trees Tree variables Stand variables B d h v g Mi MS A W S TH G Sm Sn D E R 1 26 110.4 14.1 5.4 0.18 0.027 0.55 0.25 2.29 0.47 0.21 0.29 11.06 0.96 3.18 2.60 0.98 1.02 2 31 127.5 16.0 5.7 0.14 0.030 0.65 0.27 2.56 0.52 0.21 0.29 14.73 0.97 3.40 1.94 0.99 1.27 3 21 152.0 16.5 6.0 0.19 0.034 0.73 0.35 2.25 0.48 0.22 0.36 11.36 0.95 2.97 2.33 0.97 1.00 4 34 132.8 16.4 5.6 0.18 0.032 0.71 0.34 2.57 0.54 0.22 0.30 16.81 0.97 3.41 2.29 0.98 0.92 5 12 272.9 25.8 7.5 0.38 0.065 0.50 0.18 1.59 0.52 0.17 0.41 12.55 0.91 2.47 1.33 0.99 0.99 6 29 130.3 16.5 5.6 0.25 0.031 0.59 0.26 2.62 0.45 0.18 0.33 14.27 0.96 3.33 1.93 0.99 1.15 7 28 140.6 17.5 5.9 0.11 0.033 0.65 0.29 2.41 0.54 0.24 0.33 14.80 0.96 3.29 2.15 0.99 1.00 8 53 83.4 13.1 5.0 0.07 0.020 0.53 0.24 3.35 0.53 0.39 0.21 16.63 0.98 3.94 2.21 0.99 1.06 9 26 93.5 12.9 5.0 0.17 0.021 0.64 0.29 2.52 0.49 0.21 0.28 8.76 0.96 3.20 2.17 0.98 1.12 10 13 353.7 28.6 8.0 0.21 0.081 0.31 0.12 1.56 0.38 0.18 0.36 16.89 0.92 2.54 1.18 0.99 1.08 11 23 173.9 17.8 6.0 0.04 0.038 0.60 0.30 2.42 0.38 0.29 0.33 14.14 0.95 3.08 2.30 0.98 0.89 12 36 66.7 12.6 5.0 0.09 0.016 0.39 0.18 2.81 0.53 0.53 0.22 9.46 0.97 3.52 1.89 0.98 0.97 13 11 365.9 29.9 8.3 0.36 0.085 0.55 0.22 1.54 0.45 0.16 0.37 14.93 0.91 2.38 1.38 0.99 1.21 14 25 175.8 20.8 7.1 0.18 0.044 0.41 0.16 2.13 0.49 0.29 0.31 17.48 0.96 3.18 1.47 0.99 1.03 15 31 105.5 14.8 5.3 0.01 0.025 0.60 0.29 2.71 0.36 0.34 0.33 12.46 0.97 3.40 2.58 0.99 1.02 16 38 131.3 17.1 6.2 0.02 0.032 0.62 0.32 2.61 0.51 0.28 0.30 19.44 0.97 3.60 2.11 0.99 1.22 Average values are presented for the tree stand variables: Babove-ground biomass (kg); d – tree diameter at breast height (cm); htotal height (m); v – volume (m3); g – Basal area per tree (m2), Mi - mingling index; MS – spatial diversity status; A – vertical profile Index; W – uniform angle index; S – segregation index; TH – height differentiate index; G – basal area per quadrant (m2/ha); Sm – simpson index; Sn - shannon index; DBerker-Parker index; E – evennes index; R – aggregation index, respectively. Annex 4. R scripts Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 34 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 35 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 36 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 37 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 38 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 39 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 40 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 41 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 48 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 49 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 50 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 51 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 52 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 53 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 54 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 55 Tree biomass and biodiversity relationship in a mixed Mediterranean forest in Spain Narangarav Dugarsuren Master Erasmus Mundus in Mediterranean Forestry and Natural Resources (MEDFOR) 56