Predictive analytics of tree growth based on complex networks of tree competition

Abstract Competition between individual trees is a major factor influencing the development of forests. However, due to the complexity of such interactions, that span over vast geographic areas, systematic analysis of competition has only recently become possible through the concepts of so-called predictive analytics. The rationale behind the utilised approach is that a prediction model, which is capable of forecasting future increments of tree development parameters accurately, contains knowledge about the underlying relationships that govern them. The analysis of such model, therefore, holds the potential to reveal new insights into the critical factors that influence forest developments. Within this study, we utilise an Evolutionary Algorithm in order to enable predictive analytics based on a complex-network representation of competition. This allowed us to study the patterns related to spatial distribution of individual trees. We discovered that triplets of competing trees, and their betweenness centralities, have significantly greater influence on the development of each individual tree than traditionally observed parameters like the number of a tree’s competitors and distances between them. While this indicates preferable spatial patterns for optimal forest development, the introduced methodology proved to be an efficient predictive analytics tool that allows for their discovery.

[1]  Bruno Fady,et al.  Relationships between climate and radial growth in black pine (Pinus nigra Arnold ssp. salzmannii (Dunal) Franco) from the south of France , 2012, Annals of Forest Science.

[2]  Steven J. Cooke,et al.  Integrating network analysis, sensor tags, and observation to understand shark ecology and behavior , 2015 .

[3]  Yoshiaki Nakagawa,et al.  Complex network analysis reveals novel essential properties of competition among individuals in an even-aged plant population , 2016 .

[4]  E. Tomppo National Forest Inventories : pathways for common reporting , 2010 .

[5]  Isabel Cañellas,et al.  Growth response to climate and drought in Pinus nigra Arn. trees of different crown classes , 2008, Trees.

[6]  Roberta E. Martin,et al.  A Tale of Two “Forests”: Random Forest Machine Learning Aids Tropical Forest Carbon Mapping , 2014, PloS one.

[7]  Ulrich Kohnle,et al.  Combining Tree- and Stand-Level Models: A New Approach to Growth Prediction , 2008, Forest Science.

[8]  Rodrigo Ramos-Jiliberto,et al.  A conceptual framework for studying the strength of plant-animal mutualistic interactions. , 2015, Ecology letters.

[9]  Woodam Chung,et al.  Evaluating tree competition indices as predictors of basal area increment in western Montana forests , 2011 .

[10]  Erik E. Westlund,et al.  Ecological Networks over the Edge: Hypergraph Trait-Mediated Indirect Interaction (TMII) Structure. , 2016, Trends in ecology & evolution.

[11]  David W. Sims,et al.  Sex and social networking: the influence of male presence on social structure of female shark groups , 2010 .

[12]  Jean-Philippe Schütz,et al.  Comparing close-to-naturesilviculture with processes in pristine forests: lessons from Central Europe , 2016, Annals of Forest Science.

[13]  L. Duponchel,et al.  Support vector machines (SVM) in near infrared (NIR) spectroscopy: Focus on parameters optimization and model interpretation , 2009 .

[14]  Neo D. Martinez,et al.  Scaling up keystone effects from simple to complex ecological networks , 2005 .

[15]  Jordi Bascompte,et al.  Habitat loss and the structure of plant-animal mutualistic networks. , 2006, Ecology letters.

[16]  Giorgio Alberti,et al.  Airborne Laser Scanning - the Status and Perspectives for the Application in the South-East European Forestry , 2013 .

[17]  Kevin L. O'Hara,et al.  What is close-to-nature silviculture in a changing world? , 2016 .

[18]  L. Freeman Centrality in social networks conceptual clarification , 1978 .

[19]  Julian C. Fox,et al.  Stochastic structure and individual-tree growth models , 2001 .

[20]  Stephen Muggleton,et al.  Towards Machine Learning of Predictive Models from Ecological Data , 2014, ILP.

[21]  Domen Mongus,et al.  Two-level evolutionary algorithm for discovering relations between nodes' features in a complex network , 2017, Appl. Soft Comput..

[22]  H. Groeneveld,et al.  Predicting the growth in tree height and crown size of three street tree species in the City of Tshwane, South Africa , 2008 .

[23]  Jacob Weiner,et al.  Size symmetry of competition alters biomass–density relationships , 2002, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[24]  Petri Nokelainen,et al.  Investigating the Number of Non-linear and Multi-modal Relationships Between Observed Variables Measuring Growth-oriented Atmosphere , 2007 .

[25]  Pedro Jordano,et al.  Evolution and Coevolution in Mutualistic Networks , 2022 .

[26]  Gert Jan Reinds,et al.  Intensive monitoring of forest ecosystems in Europe: 1. Objectives, set-up and evaluation strategy , 2003 .

[27]  Robert A. Monserud,et al.  Do individual-tree growth models correctly represent height:diameter ratios of Norway spruce and Scots pine? , 2010, Forest ecology and management.

[28]  Robin Freeman,et al.  Emerging Network-Based Tools in Movement Ecology. , 2016, Trends in ecology & evolution.

[29]  R. Brooker,et al.  Importance versus intensity of ecological effects: why context matters. , 2011, Trends in ecology & evolution.

[30]  Sorin Draghici,et al.  Machine Learning and Its Applications to Biology , 2007, PLoS Comput. Biol..

[31]  Trevor Hastie,et al.  Generalized linear and generalized additive models in studies of species distributions: setting the scene , 2002 .

[32]  Michael J. O. Pocock,et al.  The robustness of a network of ecological networks to habitat loss. , 2013, Ecology letters.

[33]  Dominique Gravel,et al.  The dissimilarity of species interaction networks. , 2012, Ecology letters.

[34]  Jari Hynynen,et al.  Impact of plot size on individual-tree competition measures for growth and yield simulators , 2003 .

[35]  R. LarocqueGuy,et al.  Competition theory — science and application in mixed forest stands: review of experimental and modelling methods and suggestions for future research , 2013 .

[36]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[37]  Xin Zhou,et al.  Networking Our Way to Better Ecosystem Service Provision. , 2016, Trends in ecology & evolution.

[38]  J. Bellot,et al.  Assessing components of a competition index to predict growth in an even-aged Pinus nigra stand , 1998, New Forests.

[39]  M. Yokozawa,et al.  Competition among plants can lead to an increase in aggregation of smaller plants around larger ones , 2015 .

[40]  James S. Clark,et al.  Tree growth prediction using size and exposed crown area , 2005 .

[41]  Gregor Božič,et al.  30 years of Forest monitoring in Slovenia , 2015 .

[42]  F. Lieutier,et al.  Entomological Research in Mediterranean Forest Ecosystems , 2005 .

[43]  F. Houllier,et al.  Prediction of stem profile of Picea abies using a process-based tree growth model. , 1995, Tree physiology.

[44]  B. Žalik,et al.  An efficient approach to 3D single tree-crown delineation in LiDAR data , 2015 .

[45]  Mike J Jeger,et al.  Modelling disease spread and control in networks: implications for plant sciences. , 2007, The New phytologist.

[46]  Boris Rewald,et al.  Belowground competition in a broad-leaved temperate mixed forest: pattern analysis and experiments in a four-species stand , 2009, European Journal of Forest Research.

[47]  Markus Hollaus,et al.  A Benchmark of Lidar-Based Single Tree Detection Methods Using Heterogeneous Forest Data from the Alpine Space , 2015 .

[48]  Stefano Allesina,et al.  The dimensionality of ecological networks. , 2013, Ecology letters.

[49]  Carlos J. Melián,et al.  The nested assembly of plant–animal mutualistic networks , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[50]  Bernard Zenko,et al.  Gut Microbiota Patterns Associated with Colonization of Different Clostridium difficile Ribotypes , 2013, PloS one.

[51]  Marie-Josée Fortin,et al.  From Graphs to Spatial Graphs , 2010 .

[52]  Matteo Dainese,et al.  Growth prediction for five tree species in an Italian urban forest , 2011 .

[53]  Patrick C Phillips,et al.  Network thinking in ecology and evolution. , 2005, Trends in ecology & evolution.

[54]  J. Mª. Gonzalez,et al.  Evolución del crecimiento radial en un rodal adulto de Pinus nigra Arn. de la provincia de Lleida , 2001 .

[55]  Serge Planes,et al.  Evidence of social communities in a spatially structured network of a free-ranging shark species , 2012, Animal Behaviour.

[56]  Harald Vacik,et al.  A decision support tool to improve forestry extension services for small private landowners in southern Austria , 2005 .

[57]  Jens Krause,et al.  The evolutionary and ecological consequences of animal social networks: emerging issues. , 2014, Trends in ecology & evolution.

[58]  S L Warner,et al.  Randomized response: a survey technique for eliminating evasive answer bias. , 1965, Journal of the American Statistical Association.

[59]  Robert S Schick,et al.  Graph models of habitat mosaics. , 2009, Ecology letters.

[60]  Nicolas Loeuille,et al.  The ecological and evolutionary implications of merging different types of networks. , 2011, Ecology letters.

[61]  Jurij Diaci,et al.  Gap size and position influence variable response of Fagus sylvatica L. and Abies alba Mill. , 2014 .

[62]  Harold E. Burkhart,et al.  Indices of Individual-Tree Competition , 2012 .

[63]  Olaf Sporns,et al.  Complex network measures of brain connectivity: Uses and interpretations , 2010, NeuroImage.

[64]  Galit Shmueli,et al.  Predictive Analytics in Information Systems Research , 2010, MIS Q..

[65]  M. Begon,et al.  Ecology: Individuals, Populations and Communities , 1986 .

[66]  James S. Clark,et al.  Tree growth inference and prediction from diameter censuses and ring widths. , 2007, Ecological applications : a publication of the Ecological Society of America.

[67]  Jens Krause,et al.  Novel Acoustic Technology for Studying Free-Ranging Shark Social Behaviour by Recording Individuals' Interactions , 2010, PloS one.

[68]  Hans Pretzsch,et al.  Simulation tools for decision support to adaptive forest management in Europe , 2011 .