The constant stress cantilever model has however had some criticism (Niklas and
Spatz 2000; Slater 2016), even though model simplifications might explain some of
the deviations between the model developed by Niklas and Spatz (2000) and the
cantilever model (Mattheck 2000). Moreover, the effect of wind on the movement of
a tree is complex, where the branches act as a damping mass thus reducing mechanical loads on the stem (James et al. 2006; Eloy 2011). Nevertheless, models based on
the “d3” law and its variants are able to reproduce observed variations in stem taper
(Dean et al. 2002) and other ecological observations such as the self-thinning rule
(Dean and Baldwin 1996). On a broader scale, plant biomechanics have been used to
explain tree and plant development (e.g. King et al. 2009; Niklas 2013).
5 Empirical Evidences of Changes in Stem Form
5.1 Literature Review
The first studies on stem form were interested in determining the principal factors
influencing stem form (see Larson 1963 for review), and very early the relation
between crown size and taper was established (Pressler 1865). Trees with large
crowns have more taper than trees with shorter crowns, whereby the addition of such
variables in taper equations greatly increases their precision (Leites and Robinson
2004). Crown dimensions are not usually measured in national inventories, and thus
equations have sought to include proxies for crown dimensions such as stand density
and/or basal area. Thus, trees in denser stands will have less taper (Morris and Parker
1992; Muhairwe 1999; Sharma and Zhang 2004; Schneider et al. 2013), as their
crowns are shorter (Ducey 2009). Other stand-level variables also influence the tree
shape, such as site index (Newberry and Burkhart 1986; Schneider et al. 2013).
Silvicultural interventions can also play a role in determining tree form. Commercial thinning increases the growth of the tree at its base, thus increasing tree taper
(Karlsson 2000; Mäkinen and Isomäki 2004). The effect of reducing stand density
on stem form is however species dependant, and most probably site dependant. No
changes were observed in the form of black spruce trees after commercial thinning,
whereas changes were observed for jack pine (Goudiaby et al. 2012). In fact, radial
growth of black spruce was constant throughout the stem, and maximum at tree base
for jack pine. These observations were explained by the foliage biomass distribution.
Finally, fertilization also changes stem taper (Groot et al. 1984; Wiklund et al. 1995;
Karlsson 2000; Younger et al. 2008).
The effect of climatic effects on stem form, although studied very early
(e.g. Schwarz 1899), has not seen a lot of research in recent years, even if these
effects could have very important repercussions on reconstructing long-term
dendrochonologies using either dead or subfossilized trees (Autin et al. 2015).
Larger changes in tree form with climatic variables were observed for conifers
when compared to broadleaved species (Franceschini et al. 2016). Changes in
tree shape between ecozones are also observed across large tracks of land
Understanding the Factors Influencing Stem Form with Modelling Tools
305
Spatz 2000; Slater 2016), even though model simplifications might explain some of
the deviations between the model developed by Niklas and Spatz (2000) and the
cantilever model (Mattheck 2000). Moreover, the effect of wind on the movement of
a tree is complex, where the branches act as a damping mass thus reducing mechanical loads on the stem (James et al. 2006; Eloy 2011). Nevertheless, models based on
the “d3” law and its variants are able to reproduce observed variations in stem taper
(Dean et al. 2002) and other ecological observations such as the self-thinning rule
(Dean and Baldwin 1996). On a broader scale, plant biomechanics have been used to
explain tree and plant development (e.g. King et al. 2009; Niklas 2013).
5 Empirical Evidences of Changes in Stem Form
5.1 Literature Review
The first studies on stem form were interested in determining the principal factors
influencing stem form (see Larson 1963 for review), and very early the relation
between crown size and taper was established (Pressler 1865). Trees with large
crowns have more taper than trees with shorter crowns, whereby the addition of such
variables in taper equations greatly increases their precision (Leites and Robinson
2004). Crown dimensions are not usually measured in national inventories, and thus
equations have sought to include proxies for crown dimensions such as stand density
and/or basal area. Thus, trees in denser stands will have less taper (Morris and Parker
1992; Muhairwe 1999; Sharma and Zhang 2004; Schneider et al. 2013), as their
crowns are shorter (Ducey 2009). Other stand-level variables also influence the tree
shape, such as site index (Newberry and Burkhart 1986; Schneider et al. 2013).
Silvicultural interventions can also play a role in determining tree form. Commercial thinning increases the growth of the tree at its base, thus increasing tree taper
(Karlsson 2000; Mäkinen and Isomäki 2004). The effect of reducing stand density
on stem form is however species dependant, and most probably site dependant. No
changes were observed in the form of black spruce trees after commercial thinning,
whereas changes were observed for jack pine (Goudiaby et al. 2012). In fact, radial
growth of black spruce was constant throughout the stem, and maximum at tree base
for jack pine. These observations were explained by the foliage biomass distribution.
Finally, fertilization also changes stem taper (Groot et al. 1984; Wiklund et al. 1995;
Karlsson 2000; Younger et al. 2008).
The effect of climatic effects on stem form, although studied very early
(e.g. Schwarz 1899), has not seen a lot of research in recent years, even if these
effects could have very important repercussions on reconstructing long-term
dendrochonologies using either dead or subfossilized trees (Autin et al. 2015).
Larger changes in tree form with climatic variables were observed for conifers
when compared to broadleaved species (Franceschini et al. 2016). Changes in
tree shape between ecozones are also observed across large tracks of land
Understanding the Factors Influencing Stem Form with Modelling Tools
305