Methods to model natural tree mortality

VANCLAY (1994) classifies tree mortality that influences forest growth into two groups:

natural mortality and anthropogenic mortality. Further, natural mortality is split into regular mortality that refers to ageing, suppression and competition as well as normal incidence of pests, diseases, and weather conditions. Catastrophic mortality includes wildfire, occasional but severe losses from "abnormal" weather conditions, and major pest and disease outbreaks. Anthropogenic mortality refers to planned harvesting, silvicultural treatment and damage from silvicultural activities. BIGLER & BUGMANN (2003) and OZOLINČIUS et al. (2005)

separate growth dependent mortality (related to competition for growing space between trees) and growth independent mortality (related to ageing of trees, diseases, pest outbreaks, wildfire and weather conditions). This study focuses only on growth dependent mortality.

Modelling of growth dependent mortality is implemented by applying deterministic or stochastic models (HAWKES 2000). EK (1980) and WEBER et al. (1986) found no difference

between the results of deterministic and averaged stochastic projections. Yet, deterministic models are applied to model mortality in stand level and stochastic models are very useful to model the probability of natural mortality of each tree in the stand. Some authors as WOOLLONS (1998), EID &ØYEN (2003) and ZHAO et al. (2007) combine these two methods.

Deterministic models. Cumulative probability distributions are appropriate models for mortality in even-aged stands due to their ability to describe the development of stem numbers over time. The Weibull distribution, gamma distribution, negative binomial distribution, and a distribution derived from the Richards function showed comparably good fits to cumulative mortality data (BUFORD &HAFLEY 1985). GLOVER &HOOL (1979), SOMERS

CHAPTER 2: SCIENTIFIC BACKGROUND

25 et al. (1980) and WOOLLONS &HAYWARD (1985) also reported Weibull distribution models to

be compatible with analysed data.

Other modelling approaches are based on stand density rule proposed by REINEKE (1933) (for

description see subsection 3.7.3) or the -3/2 power rule developed by YODA et al. (1963). The

stand density rule describes the relationship between quadratic mean diameter and stem number per hectare in a fully stocked, unmanaged, pure even aged stand. With slope coefficient b=-1.605, an increase in quadratic mean diameter by 1% results in a decrease of tree numbers by 1.605% (PRETZSCH 2009). Stand density rule in modelling natural mortality

was applied by CLUTTER et al. (1992), HYNYNEN (1993), TANG et al. (1994), AMATEIS et al.

(1997), VANCLAY &SANDS (2009) and others. The power rule developed by Yoda et al. 1963

describes the relationship between the mean shoot weight and plant number per hectare. This rule could be simply reformulated in the form where number of growing trees per hectare equals to quadratic mean diameter raised to the power by minus 2 (PRETZSCH 2009). This

concept in modelling natural mortality was applied by DREW &FLEWELLING (1977), DREW &

FLEWELLING (1979), VANCLAY &SANDS (2009) and others.

Stochastic models predict the probability of natural mortality of each tree in the stand. For this purpose MONSERUD (1976) tested discriminant, probit and logit functions and concludes that

the logistic equation provides the greatest discriminating power for predicting live and dead trees. During recent decades many logistic models to predict natural mortality have been developed. AVILA & BURKHART (1992), DURSKY (1997) and DOBBERTIN & BRANG (2001)

argue that prediction accuracy is a valuable criterion for comparing logistic models of tree mortality. CROW &HICKS’model(1990) correctly classified 78% dead and 64% of live trees;

EID & TUHUS’ model (2001) correctly classified 75.9% of dead trees and BIGLER &

BUGMANN’S model(2003) correctly classified 79.6% of dead and alive trees.

MONSERUD (1976) contends the probability of survival is exceedingly well defined by

function of tree size and CI. HAMILTON (1986) complements these findings by stating that

variation in mortality could be explained by a measure of tree size, stand density, individual tree competition and growth rate. Most of the authors that have investigated the probability of natural tree mortality expressed tree size by tree diameter at breast height (MONSERUD 1976,

HAMILTON & EDWARDS 1976, WYKOFF et al. 1982, BUCHMAN 1983, HAMILTON 1986,

WYKOFF 1986, HANN &WANG 1990, CROW &HICKS 1990, VANCLAY 1991b, DURSKY 1997,

MURPHY & GRANEY 1998, MONSERUD &STERBA 1999, JURKONIS 2004, YANG et al. 2003,

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26 2006, SCHRÖDER et al. 2007, SIMS et al. 2009 and ADAME et al. 2010) or by tree height

(HAMILTON &EDWARDS 1976, DURSKY 1997, SCHRÖDER et al. 2007, SIMS et al. 2009).

Individual tree competition is mainly expressed by distance independent CI basal area of larger trees (BAL) (see HANN & WANG 1990, MURPHY & GRANEY 1998, MONSERUD &

STERBA 1999, YANG et al. 2003, TEMESGEN &MITCHELL 2005, BRAVO-OVIEDO et al. 2006,

and SIMS et al. 2009). Also individual tree competition is estimated by tree diameter and

quadratic mean diameter ratio (see HAMILTON 1986, WYKOFF 1986, BURGMAN et al. 1994,

SIMS et al. 2009) or vice versa quadratic mean diameter and tree diameter ratio (see AVILA &

BURKHART 1992, LYNCH et al. 1998). In the same manner the competitive situation of trees

could be expressed by tree height and mean stand height ratio (see AVILA &BURKHART 1992,

SIMS et al. 2009, ADAME et al. 2010). The other expressions of tree competitive situation are

area overlap index (MONSERUD 1976), relative size (SIMS et al. 2009), and relative basal area

CIs (ZHAO et al. 2004, SIMS et al. 2009).

Various researchers express tree vigour by predicted diameter growth (MONSERUD 1976) or

by diameter increment in a previous period (BUCHMAN 1983, HAMILTON 1986, WYKOFF

1986). Additionally, basal area increment in the last period is used to express tree vigour (see DURSKY 1997, and SCHRÖDER et al. (2007). Independent variables like crown ratio (HANN &

WANG 1990, AVILA &BURKHART 1992, MONSERUD &STERBA 1999), tree diameter at breast

height and tree height ratio (SCHRÖDER et al. 2007), tree defoliation (DOBBERTIN &BRANG

2001, JURKONIS 2004 and JUKNYS et al. 2006) or crown class (ZHAO et al. 2004) are also used

to define tree vigour status.

The most widely used stand level independent variable is stand basal area (HAMILTON 1986,

LYNCH et al. 1998, MURPHY &GRANEY 1998, YANG et al. 2003, ZHAO et al. 2004, TEMESGEN

&MITCHELL 2005, BRAVO-OVIEDO et al. 2006). Stand site quality or site index is the second

most important stand level independent variable (HANN &WANG 1990, BURGMAN et al. 1994,

DURSKY 1997, MURPHY &GRANEY 1998, BRAVO-OVIEDO et al. 2006) and MSA was the third

most important stand level independent variable (BURGMAN et al. 1994, MURPHY &GRANEY

1998, JURKONIS 2004, JUKNYS et al. 2006). The other stand level independent variables like

quadratic mean diameter (BURGMAN et al. 1994, MURPHY &GRANEY 1998 ZHAO et al. 2004),

mean stand height (LYNCH et al. 1998) or stocking (BURGMAN et al. 1994) are also used to

model the probability of natural tree mortality.

Mortality likelihood (ML) functions modify the values of probability of natural tree mortality ranging from 0 to 1 into likelihood values generating mortality as observed in the field for

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27 given intervals of probability of natural tree mortality (SCHRÖDER et al. 2007). Some authors

check the third step by comparing ML values with the equally distributed random values (MR). If the value of ML is greater than MR, the tree is classified as dead (DURSKY 1997).

To conclude, deterministic models are applied to model mortality at stand level and stochastic models are very useful to model the probability of the natural mortality of each tree. Thus, stochastic models are recommended. Due to possessing the greatest discriminating power, stochastic logit functions should be used. The most appropriate independent variables used to model natural tree mortality are tree diameter at breast height, tree height, distance independent CIs, tree diameter and quadratic mean diameter ratio, diameter or basal area increment in previous period, MSA, site index and stand basal area.

In document Single Tree Level Simulator for Lituanian Pine Forests (Page 42-45)