169
7.5.2 The More of the Tree of Life That Is Sampled, the More
Complex Models Will (or Should) Be
Most of the models of evolution and phylogenetic signal statistics we saw here are
actually rather simple. For example, a Brownian motion model has two parameters,
the trait value at the root (mean) and the rate of evolution (variance). The single-rate
Brownian motion model may reasonably describe the evolution of leaf water content in dogwoods (Cornus), but it would probably do a terrible job if you were
analyzing all flowering plants because of the sheer heterogeneity and diversity that
they possess (Felsenstein 2008; O’Meara 2012; Cornwell et al. 2014).
There is a trade-off: the most realistic model would have a different set of parameters at every time point on every branch but would have far more parameters to
estimate than the data could support; a simple model of one set of parameters across
all the time periods and species examined is clearly unrealistic. Most applications
have used the simplest approach, but there are ways to allow for more complex
models. Some of them test a priori hypotheses about heterogeneity in models of
evolution: Biologists propose particular models linking sets of parameters on different parts of the tree (e.g., gymnosperms and angiosperms having different rates of
evolution), and then the methods select between the possible models (Butler and
King 2004; O’Meara et al. 2006). There are also methods that can automatically
search across possible mappings to find the ones that fit best (Uyeda and Harmon
2014). In the case of multiple characters, such as reflectance at different wavelengths of light, there is also the question of whether different characters are
evolving under the same or different models, and there are models to test that, as
well (Adams and Otárola-Castillo 2013).
Early attempts to analyze spectra in an evolutionary context (Cavender-Bares
et al. 2016; McManus et al. 2016; Meireles et al. in review) have used models that
are maximally simple for each character (a single model applying for all taxa and
times) and are nearly maximally complex between characters (each trait evolves
independently of all others on the same common tree). Those approaches are computationally cheap but are at odds with our understanding of biology (i.e., models of
evolution do vary among lineages) and physics (i.e., spectral bands do covary).
Other ways of segregating complexity, such as models that incorporate heterogeneity among lineages and account for the covariance among spectral bands, remain
potentially more fruitful ways of examining the diversity in leaf spectra.
7.5.3 Spectra Do not Evolve
∗
, Leaves Do!
{
∗
except when they do}
One could estimate the pace of evolution of the beaks of Darwin’s finches from
their photographs. But the photographs didn’t evolve. Leaf spectra do capture many
different aspects of the complex phenotype, and, we have seen in this chapter, each
7 Linking Leaf Spectra to the Plant Tree of Life
7.5.2 The More of the Tree of Life That Is Sampled, the More
Complex Models Will (or Should) Be
Most of the models of evolution and phylogenetic signal statistics we saw here are
actually rather simple. For example, a Brownian motion model has two parameters,
the trait value at the root (mean) and the rate of evolution (variance). The single-rate
Brownian motion model may reasonably describe the evolution of leaf water content in dogwoods (Cornus), but it would probably do a terrible job if you were
analyzing all flowering plants because of the sheer heterogeneity and diversity that
they possess (Felsenstein 2008; O’Meara 2012; Cornwell et al. 2014).
There is a trade-off: the most realistic model would have a different set of parameters at every time point on every branch but would have far more parameters to
estimate than the data could support; a simple model of one set of parameters across
all the time periods and species examined is clearly unrealistic. Most applications
have used the simplest approach, but there are ways to allow for more complex
models. Some of them test a priori hypotheses about heterogeneity in models of
evolution: Biologists propose particular models linking sets of parameters on different parts of the tree (e.g., gymnosperms and angiosperms having different rates of
evolution), and then the methods select between the possible models (Butler and
King 2004; O’Meara et al. 2006). There are also methods that can automatically
search across possible mappings to find the ones that fit best (Uyeda and Harmon
2014). In the case of multiple characters, such as reflectance at different wavelengths of light, there is also the question of whether different characters are
evolving under the same or different models, and there are models to test that, as
well (Adams and Otárola-Castillo 2013).
Early attempts to analyze spectra in an evolutionary context (Cavender-Bares
et al. 2016; McManus et al. 2016; Meireles et al. in review) have used models that
are maximally simple for each character (a single model applying for all taxa and
times) and are nearly maximally complex between characters (each trait evolves
independently of all others on the same common tree). Those approaches are computationally cheap but are at odds with our understanding of biology (i.e., models of
evolution do vary among lineages) and physics (i.e., spectral bands do covary).
Other ways of segregating complexity, such as models that incorporate heterogeneity among lineages and account for the covariance among spectral bands, remain
potentially more fruitful ways of examining the diversity in leaf spectra.
7.5.3 Spectra Do not Evolve
∗
, Leaves Do!
{
∗
except when they do}
One could estimate the pace of evolution of the beaks of Darwin’s finches from
their photographs. But the photographs didn’t evolve. Leaf spectra do capture many
different aspects of the complex phenotype, and, we have seen in this chapter, each
7 Linking Leaf Spectra to the Plant Tree of Life