Two-stage ingrowth models for four major tree species in Alberta

Abstract

A two-stage modelling approach was used for developing ingrowth models for four major tree species in Alberta: aspen, lodgepole pine, black spruce and white spruce. The probability of ingrowth presence was modelled first, followed by the modelling of annual amount of ingrowth conditional on ingrowth being present. To handle variable measurement intervals and plot sizes typical of repeatedly measured forestry data, two generalized logistic models were evaluated at the first stage: a traditional model with measurement interval length and plot size factor incorporated as an exponent of a standard logistic function and an alternative model with measurement interval length and plot size factor incorporated as a denominator. Two criteria were evaluated for defining optimal threshold values for plot classification: criterion 1 to maximize the summation of sensitivity and specificity and criterion 2 to maximize the overall rate of correct plot classification. It was found that criterion 1 was superior to criterion 2 for providing better plot classifications. The two ingrowth probability models behaved similarly based on model fitting and model validation results. Annual amount of ingrowth was modelled at the second stage by exponential functions.

Development of ingrowth models for forest types in South Korea

“…where p i is the ingrowth occurrence probability, and b is the regression coefficient to estimate. In the first stage, each model used the same form of logistic regression for the common goal of ingrowth probability estimation (Table 2); however, different independent variables were applied based on the data characteristics to develop the estimation equation (Vanclay 1989;Qin 1998;Brovo et al 2008;Adame et al 2010;Li et al 2011;Yang and Huang 2015). We used the Nlin Procedure module of SAS program for this purpose (SAS Institute Inc 2004).…”

“…In the second stage, the ingrowth amount was estimated through a regression analysis of only the sampling plots where ingrowth occurred (Table 3). This study modified a previous ingrowth amount estimation equation by using the number of trees ha À1 as the dependent variable and obtained (Qin 1998;Shin et al 2003;Adame et al 2010;Yang and Huang 2015) a total of seven candidate models.…”

“…In such cases, ingrowth model can be developed in two stages: in the first stage, a logistic can be used to estimate the probability that the ingrowth of the target species will occur, and in the second stage, a regression equation can be used to develop a model for estimating the ingrowth rate under the conditions in which the ingrowth occurs. Various studies have been carried out so far by considering the ingrowth as a stochastic event for the two outcomes and applying a two-stage model development approach (Qin 1998;Brovo et al 2008;Adame et al 2010;Li et al 2011;Klopcic and Boncina 2012;Yang and Huang 2015). Previous researches on the development of the ingrowth model were mainly based on permanent sample plots or National Forest Inventory (NFI) sample plots where the survey data were accumulated over a long period of time.…”

Modelling natural regeneration of European beech in Saxony, Germany: identifying factors influencing the occurrence and density of regeneration

“…In this study, we successfully created complex ZANB spatial models with various covariates stemming from both the plot and the surrounding stand. In contrast to many earlier studies that followed a frequentist approach (Zhang et al 2012;Klopcic et al 2012;Yang and Huang 2015;Shen and Nelson 2018;Monteiro-Henriques and Fernandes 2018;Zell et al 2019), a Bayesian approach was applied. Although maximum likelihood methods and Bayesian methods with weakly informative priors provide the same results for fixed effect models (Rue et al 2009;Zuur et al 2018), the great advantage of using Bayesian methods in R-INLA is the userfriendly integration of spatial random effects.…”

“…First, the probability of occurrence is modelled based on a set of covariates. Second, another equation estimates the density of regeneration based on the same or a different set of covariates (Vanclay 1992;Sterba et al 1997;Qin 1998;Klopcic et al 2012;Yang and Huang 2015). Recent papers used a one-step modelling approach by combining two separate estimation processes into a joint distribution of probabilities (Shive et al 2018;Shen and Nelson 2018;Monteiro-Henriques and Fernandes 2018;Zell et al 2019).…”