ecologists can help real ecologists

Summary 1. Tree growth and mortality are key elements of forest dynamics, and thus are of great concern for forest managers. It is widely accepted that tree mortality can be predicted using tree growth data. Several approaches have been proposed for modelling the growth-mortality relationship, differing in terms of data sources and model flexibility. However, little is known about their ability to reliably reconstruct the shape of the real growth-mortality relationship due to a lack of long-term data. 2. We adopted a 'virtual ecology' approach to this problem, simulating forests with either of two a priori specified growth-mortality relationships. Different sampling regimes in these virtual forests resulted in virtual tree-ring data, forest inventory data, or a combination of both. We used eight existing or newly developed models of different structural flexibility to analyse the growth-mortality relationship. The accuracy of the different model outputs, i.e. the deviation from the a priori specified growth-mortality relationships, was quantified with the Kullback-Leibler distance. 3. For all data sources, reliable growth-mortality models could be identified. The highest accuracies were found for tree-ring based models, which require only a small sample size (60 dead trees). High model accuracies were also found for forest inventory based models, starting at sample sizes of 500 trees. 4. Flexible statistical approaches turned out to be superior to less flexible models only for large sample sizes (totally 2000 trees). The additional use of Bayesian statistics, specifically designed for small sample sizes, led to high model accuracies only when model flexibility was constrained. 5. Synthesis. Our study shows that simulated experiments are a powerful tool for selecting reliable approaches to analyse ecological processes such as tree mortality. Reliable models are fundamental for gaining novel ecological insights into the growth-mortality relationship of tree species. The use of more accurate growth-mortality relationships in forest succession models would allow for strongly improved projections of past and future forest dynamics. Our study provides the theoretical basis for a sound estimation of such growth-mortality models, and it also provides guidelines for efficient sampling schemes in real forests.

[1]  Matthias Dobbertin,et al.  Tree growth as indicator of tree vitality and of tree reaction to environmental stress: a review , 2005, European Journal of Forest Research.

[2]  J. Battles,et al.  The relationship between tree growth patterns and likelihood of mortality: a study of two tree species in the Sierra Nevada , 2007 .

[3]  R. Motta,et al.  Long‐term investigations in a strict forest reserve in the eastern Italian Alps: spatio‐temporal origin and development in two multi‐layered subalpine stands , 2002 .

[4]  B. Reineking,et al.  Constrain to perform: Regularization of habitat models , 2006 .

[5]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[6]  H. Mäkinen,et al.  Predicting the decomposition of Scots pine, Norway spruce, and birch stems in Finland. , 2006, Ecological applications : a publication of the Ecological Society of America.

[7]  David A. Coomes,et al.  Mortality and tree‐size distributions in natural mixed‐age forests , 2007 .

[8]  Roderick Hunt,et al.  Comparative Plant Ecology: A Functional Approach to Common British Species , 1989 .

[9]  A. Hirzel,et al.  Assessing habitat-suitability models with a virtual species , 2001 .

[10]  H. Bugmann,et al.  Decay of Picea abies snag stands on steep mountain slopes , 2003 .

[11]  Ricardo Villalba,et al.  INFLUENCES OF LARGE-SCALE CLIMATIC VARIABILITY ON EPISODIC TREE MORTALITY IN NORTHERN PATAGONIA , 1998 .

[12]  D. Faber-Langendoen,et al.  Diameter distributions and structural sustainability in forests , 2006 .

[13]  T. Kitzberger,et al.  Factors predisposing episodic drought‐induced tree mortality in Nothofagus– site, climatic sensitivity and growth trends , 2004 .

[14]  D. Burslem,et al.  The interpretation and misinterpretation of mortality rate measures , 1995 .

[15]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[16]  Ü. Niinemets,et al.  Tolerance to shade, drought, and waterlogging of temperate northern hemisphere trees and shrubs , 2006 .

[17]  C. Bigler,et al.  PREDICTING THE TIME OF TREE DEATH USING DENDROCHRONOLOGICAL DATA , 2004 .

[18]  J. B. Faliński.  Vegetation Dynamics in Temperate Lowland Primeval Forests: Ecological Studies in Białowieza Forest , 1986 .

[19]  D. Lindenmayer,et al.  INFERRING PROCESS FROM PATTERN: CAN TERRITORY OCCUPANCY PROVIDE INFORMATION ABOUT LIFE HISTORY PARAMETERS? , 2001 .

[20]  Robert M. May,et al.  MORTALITY AND RECRUITMENT RATE EVALUATIONS IN HETEROGENEOUS TROPICAL FORESTS , 1996 .

[21]  H. Bugmann.  A Review of Forest Gap Models , 2001 .

[22]  Boris Zeide,et al.  Intrinsic units in growth modeling , 2004 .

[23]  A. Watt,et al.  Pattern and process in the plant community , 1947 .

[24]  Fritz H. Schweingruber,et al.  Tree rings and environment dendroecology , 1997 .

[25]  J. R. Wallis,et al.  Some ecological consequences of a computer model of forest growth , 1972 .

[26]  Volker Grimm,et al.  Individual-based modelling and ecological theory: synthesis of a workshop , 1999 .

[27]  J. Rolstad,et al.  How long do Norway spruce snags stand? Evaluating four estimation methods , 2004 .

[28]  F. Bravo,et al.  Competition-induced mortality for Mediterranean Pinus pinaster Ait. and P. sylvestris L. , 2006 .

[29]  G. Weetman,et al.  Age and size structure of gap-dynamic, old-growth boreal forest stands in Newfoundland , 2006 .

[30]  Christopher B. Field,et al.  Tree Mortality in Gap Models: Application to Climate Change , 2001 .

[31]  Stephen P. Hubbell,et al.  Local neighborhood effects on long-term survival of individual trees in a neotropical forest , 2001, Ecological Research.

[32]  C. Bigler,et al.  Growth patterns as indicators of impending tree death in silver fir , 2004 .

[33]  K. Woods.  Intermediate disturbance in a late‐successional hemlock‐northern hardwood forest , 2004 .

[34]  Thomas M. Smith,et al.  Plant functional types : their relevance to ecosystem properties and global change , 1998 .

[35]  G. Ståhl,et al.  A Three-step Approach for Modelling Tree Mortality in Swedish Forests , 2001 .

[36]  H. Remmert,et al.  The Mosaic-Cycle Concept of Ecosystems , 1991, Ecological Studies.

[37]  John A. Silander,et al.  Juvenile Tree Survivorship as a Component of Shade Tolerance , 1995 .

[38]  Richard H. Waring,et al.  Modifying Lodgepole Pine Stands to Change Susceptibility to Mountain Pine Beetle Attack , 1985 .

[39]  James S. Clark,et al.  Predicting tree mortality from diameter growth : a comparison of maximum likelihood and Bayesian approaches , 2000 .

[40]  John Harte,et al.  Dead wood biomass and turnover time, measured by radiocarbon, along a subalpine elevation gradient , 2004, Oecologia.

[41]  Sunil J Rao,et al.  Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis , 2003 .

[42]  K. Beven,et al.  A hydraulic model to predict drought-induced mortality in woody plants: an application to climate change in the Mediterranean. , 2002 .

[43]  C. Bigler,et al.  Predicting tree death for Fagus sylvatica and Abies alba using permanent plot data , 2007 .

[44]  C. Loehle.  Strategy Space and the Disturbance Spectrum: A Life‐History Model for Tree Species Coexistence , 2000, The American Naturalist.

[45]  O. Zackrisson,et al.  Stand structure and successional trends in virgin boreal forest reserves in Sweden , 1997 .

[46]  Phillip B. Gibbons,et al.  Forest and woodland stand structural complexity: Its definition and measurement , 2005 .

[47]  B. Pedersen,et al.  THE ROLE OF STRESS IN THE MORTALITY OF MIDWESTERN OAKS AS INDICATED BY GROWTH PRIOR TO DEATH , 1998 .

[48]  Trevor Hastie,et al.  Polynomial splines and their tensor products in extended linear modeling. Discussion and rejoinder , 1997 .

[49]  J. Kouki,et al.  Spatiotemporal Availability of Dead Wood in Protected Old-growth Forests: A Case Study from Boreal Forests in Eastern Finland , 2002 .

[50]  C. Bigler,et al.  Optimisation of tree mortality models based on growth patterns , 2006 .

[51]  James S. Clark,et al.  The relationship between growth and mortality for seven co‐occurring tree species in the southern Appalachian Mountains , 2002 .