# A phylogenetic analysis of galaxies in the Coma Cluster and the field: a new
approach to galaxy evolution

M. Martínez-Marín1, R. Demarco1, G. Cabrera-Vives2,3, P. Cerulo2, N. W. C.
Leigh1,4 and R. Herrera-Camus1
1 Department of Astronomy, Facultad de Ciencias Físicas y Matemáticas,
Universidad de Concepción, Concepción, Chile
2 Department of Computer Science, Universidad de Concepción, Concepción, Chile
3Millennium Institute of Astrophysics, Chile
4Department of Astrophysics, American Museum of Natural History, New York, NY
10024, USA E-mail<EMAIL_ADDRESS>
(Accepted October 2020. Received June 2020)

###### Abstract

We propose a phylogenetic approach (PA) as a novel and robust tool to detect
galaxy populations (GPs) based on their chemical composition. The branches of
the tree are interpreted as different GPs and the length between nodes as the
internal chemical variation along a branch. We apply the PA using 30 abundance
indices from the Sloan Digital Sky Survey to 475 galaxies in the Coma Cluster
and 438 galaxies in the field. We find that a dense environment, such as Coma,
shows several GPs, which indicates that the environment is promoting galaxy
evolution. Each population shares common properties that can be identified in
colour–magnitude space, in addition to minor structures inside the red
sequence. The field is more homogeneous, presenting one main GP. We also apply
a principal component analysis (PCA) to both samples, and find that the PCA
does not have the same power in identifying GPs.

###### keywords:

Galaxies – Clusters – Evolution – Abundances – stellar content

††pubyear: 2020††pagerange: A phylogenetic analysis of galaxies in the Coma
Cluster and the field: a new approach to galaxy evolution–A phylogenetic
analysis of galaxies in the Coma Cluster and the field: a new approach to
galaxy evolution

##  1 Introduction

In recent years, phyloinformatic studies have been used in astronomy to help
understand different processes that could involve evolution. These studies
were based either on discrete character states (DCs) or distance matrices of
pairwise dissimilarities (Dm). Their main objective is to study the
evolutionary history and relationships among individual or groups of
astronomical objects. Astrocladistic utilizes DC, by either qualitative (e.g.
morphology) or quantitative (e.g. luminosity, stellar mass, chemical
composition) properties of galaxies to compare states of evolution in a
cladogram. Astrocladistics has been used to study different astronomical
objects like dwarf galaxies of the Local Group (Fraix-Burnet et al. 2006),
globular clusters and their classification (Fraix-Burnet et al. 2006), and
stellar populations (SPs) in $\omega$ Centauri (Fraix-Burnet & Davoust 2015).

On the other hand, studies based on Dm are proper of Phylogenetics. This
method takes as input the abundances of chemical elements of astronomical
objects as a proxy for DNA in order to analyze their evolutionary history
through their chemical compositions. This generates a branching diagram known
as a phylogenetic tree. The branches of this tree are interpreted as different
populations, and the position on the tree as a parameter to measure the mean
rate of chemical enrichment of the population. This method has been employed
as an attempt to reconstruct the chemical history of stars in the solar
neighbourhood (Jofré et al. 2017) and to retrieve stars from an open cluster
(Blanco-Cuaresma & Fraix-Burnet 2018).

Galaxies are complex systems made up of stars, gas, dust and dark matter.
Understanding their formation and evolution is one of the key problems in
modern astrophysics. Galaxy evolution is the result of several complex
physical processes that involve the various galaxy components in different
ways through cosmic epochs. These mechanisms bring galaxies to transition from
one physical state to another and to change their observed properties.

Morphology is the most immediate way to classify galaxies since it is based on
a visual assessment. Following Hubble (1926), galaxies are classified as
ellipticals, lenticulars or S0s, and spirals. A class of irregular galaxies is
added to take into account objects that cannot be classified either as
elliptical, S0 or spiral. Ellipticals and S0s are commonly said early-type
galaxies (ETGs), while spirals and irregulars are commonly grouped together as
late-type galaxies (LTGs).

Morphology is related to the underlying structural distribution of the stellar
populations and interstellar medium. ETGs tend to be red and with no or little
star-formation, while LTGs tend to be blue and star-forming (see Baldry et al.
2004, Cassata et al. 2008, Taylor et al. 2015). Up to $z\sim 6$, the star
formation in galaxies is observed to be related to their stellar mass: massive
galaxies are less star-forming than their low-mass counterparts (Cowie et al.,
1996). The stellar mass of galaxies is finally related to their metallicity:
more massive galaxies are also metal-richer (Lequeux et al. 1979; Tremonti et
al. 2004; Gallazzi et al. 2005)

Regardless of the environment where galaxies reside, they show a bimodal
colour distribution. Three main populations can be defined from this color-
magnitude distribution: (1) a Red Sequence of quiescent galaxies; (2) a Green
Valley as an "intermediate" population; and (3) a diffuse cloud of blue star-
forming galaxies. Thus, in principle, the evolution of a galaxy population can
be investigated by looking at the gradual build-up of the Red Sequence as a
function of redshift (Tanaka et al. 2010; Gobat et al. 2011; Muzzin et al.
2012; Lidman et al. 2004; Snyder et al. 2012).

Nevertheless, we can obtain more detailed information by studying galaxy
spectra. Spectra of galaxies contain information about the properties of both
gas and stellar populations. These contain a preserved record of the host
galaxy’s formation and evolution. Emission lines are used to study the
physical state of the ionized gas, so we can trace black hole accretion,
derive gas kinematics and star formation activity (Kauffmann et al. 2003a;
Schawinski et al. 2007). Absorption lines provide information about the
properties of stellar populations and can be used to derive ages,
metallicities, star formation histories and elemental abundances.(Davies et
al. 1993; Fisher et al. 1996; J’́orgensen 1999; Kuntschner 2000; Thomas et al.
2010a). The most common sets of optical absorption line indices are the Lick
index system (Burstein et al. 1984; Faber et al. 1985; Worthey 1994; Worthey &
Ottaviani 1997), and the [OIII] indices (González 1993). These indices group
different absorption lines together. Therefore, they measure the compositions
of various chemical elements. However, the abundance derivations for
individual elements is non-trivial.

Studies use absorption lines to compare morphology with chemical abundances
and other properties of the host galaxy such as velocity dispersion (Davies et
al. 1987, Burstein et al. 1988), B-band absolute magnitude ( Faber 1973;
Terlevich & Melnick 1981), or effective radius (Parikh et al. 2018).

In this work, we propose a new technique to study galaxy evolution, analyzing
galaxies according to their chemical composition through a phylogenetic
approach. This approach generates a phylogenetic tree that gives a graphical
visualization of the chemical diversification between galaxies through a
branching process. Each branch gathers galaxies with similar chemical
composition, and their hierarchical structure can be related to common
properties of galaxies like stellar mass ($M_{*}$), specific star formation
rate (sSFR; $SFR/M_{*}$), metallicity and morphology. The main characteristic
of this schema is that it allows us to hypothesise how developmental changes
are mediated by tracing branching points to a physical process or galaxy
property. This is critical for understanding the mechanisms that take part in
the evolution of galaxies and, overall, finding common ancestors within a
group of chemically related galaxies allows us to think about galaxy evolution
and their possible morphological change as a non-linear process.

For this, we analyze the chemical composition of stellar populations in
galaxies that reside in different environments. We consider 475 galaxies in
the Coma cluster with redshifts in the range $0.015<z<0.033$, and 438 field
galaxies at $0.035<z<0.054$. We use a set of 30 abundance indices from the
value added catalogs of the Sloan Digital Sky Survey data release 14 (SDSS
DR14) (Abolfathi et al. 2018). We generate a phylogenetic tree based on a
distance matrix from the pairwise differences of these indices using the
Neighbor Joining algorithm (NJ; Saitou & Nei 1987; Studier & Keppler 1988). NJ
allows us to find hierarchical relationships that can be used to uncover
possible evolutionary paths of the observed galaxies. We interpret the
branches of the phylogenetic tree as different galaxy populations (GP), and
the length between the nodes of these branches as a gradient of chemical
difference in the stellar population content of these galaxies. In this way we
can see how properties like morphology, stellar mass, sSFR or metallicity
([Z/H]) relate with the galaxy populations found with this phylogenetic
approach at different environments.

##  2 Data

Previous phyloinformatic studies in astronomy, have utilized abundance ratios
of several elements as a proxy for DNA. In our case study, we will use instead
absorption line indices, which measure different individual element abundances
giving us information about the stellar population properties of our galaxies.
On the other hand, in order to understand which physical properties of
galaxies are involved in the hierarchical structure of the phylogenetic trees,
we will use information about their stellar mass, specific star formation rate
(sSFR), metallicity (Z/H) and stellar ages.

###  2.1 Phylogenetic Study

For the phylogentic study on the Coma cluster we use the membership of
Beijersbergen et al. 2002, obtaining 475 galaxies with redshifts between
$0.015$ and $0.033$. For the field, we select galaxies that do not belong to
galaxy groups (Tempel et al. 2012) nor filaments (Tempel et al. 2014), however
the galaxies that meet this criterion and have information of abundance
indices are too small to use as a sample comparable to that of the Coma
cluster. Therefore, we select a sample of galaxies that meets the above
criteria but at a slightly larger redshift. Thus obtaining a sample of 438
galaxies with redshifts between $0.035$ to $0.054$. For both samples we obtain
the spectroscopic data from the seventh data release (DR7 Abazajian et al.
2009) of the Sloan Digital Sky Survey (SDSS;York et al. 2000 ). We use the
spectral line strength measurement database provided by the OSSY group (Oh et
al. 2011), considering the stellar absorption-line measurements for this
galaxy sample.

###  2.2 Ancillary Data

The stellar mass is based on fits to the photometry following (Kauffmann et
al. 2003a), and (Salim et al. 2007) from the SDSS DR7. The galaxy sample of
the Coma cluster presents a stellar mass distribution characterized by a mean
value of $\log(M_{*}/M_{\odot})=9.98$ and a 1-$\sigma$ dispersion of
$\log(M_{*}/M_{\odot})=0.58$. For the field sample, we have a stellar mass
distribution centered at $\log(M_{*}/M_{\odot})=9.99$ with a 1-$\sigma$
dispersion of $log(M_{*}/M_{\odot})=0.50$. The $sSFR$ estimates are based on
the technique discussed in Brinchmann et al. 2004, with a slight modification
for non-star-forming galaxies. Here, the likelihood distribution of the sSFR
is constructed as a function of D4000 using the star-forming sample, also from
the SDSS DR7. Our sample of cluster galaxies in Coma presents a sSFR
distribution centered at $\log{(sSFR/yr^{-1})}=-10.28$ with a 1-$\sigma$
dispersion $\log{(sSFR/yr^{-1})}=0.53$, on the other hand, the Field presents
a sSFR distribution centered at $\log{(sSFR/yr^{-1})}=-9.39$ with a 1-$\sigma$
dispersion of $\log{(sSFR/yr^{-1})}=0.6$) (see Figure 2). We calculate the
ages and metallicities of the galaxies in the GPs found by the PA following
the procedure from Cardiel et al. 2003. We interpolate our model with the
simple stellar population predictions of Thomas et al. 2010b for the
$H_{\beta}$ and $C4668$ indices.

Finally, we utilize the visual morphological classification from Beijersbergen
et al. (2002) and two parameters of the morphological classification from
Domínguez Sánchez et al. 2018, obtained with deep learning algorithms
implementing convolutional neural networks (CNNs). Domínguez Sánchez et al.
2018 used T Types (see de Vaucouleurs 1959) to separate ETGs from LTGs and
gives the probability $P_{S0}$ of being $S0$ versus a pure elliptical in order
to have three galaxy classes: Elliptical, Spiral and S0. Elliptical galaxies
are defined such that they have TType values ranging from $-3$ to $0$ and
$P_{S0}$ values lower than $0.5$. S0 galaxies have TType values between $-1$
and $3$, and $P_{S0}$ values higher than $0.5$. Finally, spiral galaxies have
a TType value between $3$ and $8$, independent of their $P_{S}0$ value. For
galaxies in the sample that do not have information on TType and $P_{S0}$, the
visual morphological classification from Beijersbergen et al. (2002) is
assigned.

##  3 The method

We perform a phylogenetic study based on a distance matrix with the NJ
algorithm, utilizing the open-source Scikit-bio python package. In our case
study, the distance matrix elements are obtained by the summation of chemical
distance differences for a given abundance index ($X_{k}$) ($k$ is the
specific absorption index) between every pair of galaxies ($i$ and $j$) in our
sample. Therefore, each element of our distance matrix is the total chemical
distance $D_{i,j}$ from our set of abundance indices between our galaxies:

$D_{i,j}=\sum^{N}_{k=1}|[X_{k}]_{i}-[X_{k}]_{j}|.$

Where N is the number of end nodes. For example, let us consider the following
distance matrix:

$\begin{bmatrix}&G_{A}&G_{B}&G_{C}&G_{D}&G_{E}&G_{F}\\\ G_{A}&0&5&4&7&6&8\\\
G_{B}&5&0&7&10&9&11\\\ G_{C}&4&7&0&7&6&8\\\ G_{D}&7&10&7&0&5&9\\\
G_{E}&6&9&6&5&0&8\\\ G_{F}&8&11&8&9&8&0\\\ \end{bmatrix}$

A clustering method would group galaxies A and C as the most similar galaxies,
because their total chemical distance $D_{i,j}$ is the smallest. This assume
that the elements under study evolve in a clock-like behavior. Therefore, the
samples obtained at the same calendar time would have experienced the same
number of generations since their common ancestor, maintaining a constant rate
of change per generation. Nevertheless, in galaxies there are several internal
and external processes, especially in large and dense cosmic structures where
they may undergo interactions with the surrounding environment that make them
deviate their course from a linear evolution. The main characteristic of NJ is
that it takes into account the development of evolution at different rates.
For that, the NJ defines a new corrected distance $D^{{}^{\prime}}_{i,j}$
which subtracts the divergence $r_{i}$ and $r_{j}$.

$D^{{}^{\prime}}_{i,j}=D_{i,j}-(r_{i}+r_{j})$

The divergences, correspond to the mean over the total chemical distance
$D_{i,j}$ of each possible pair of galaxies and the other galaxies:

$r_{j}=\frac{\sum_{i\leq j}D_{i,j}}{N-2}.$

With this new rate-corrected distance, we create a new distance matrix that
will show us how to obtain our first node $U_{1}$ that joins the most similar
galaxies, which in our example are galaxies A and E, for which
$D^{{}^{\prime}}_{i,j}$ is minimal. However, we could also choose galaxies D
and E. The decision of selecting one or the other node will define the zero
point of our tree. We can calculate the length of the branches from each
galaxy to this node:

$S_{i,j}=\frac{D_{i,j}+(r_{i}-r_{j})}{N-2}\cdot\frac{1}{2},$

where $N$ is the number of end-nodes. In order to get the fully resolved
topology of our tree, we now repeat the process until we have no galaxies left
(see Figure 1).

Figure 1: Final star representation of the galaxy distribution in our example.
Red branches represent known distances. Each galaxy is at the end of a
respective branch. The U letters represent the nodes that join our galaxies.
Numbers indicate the chemical distance between galaxies and nodes or between
nodes. We have a topology that shows two different galaxy populations: A, B
and C versus E and D. Galaxy F does not belong to any galaxy population.

With this algorithm galaxies that have similar chemical composition, such as A
and B, belong to the same node at the top of the tree. Their next closest
neighbour in stellar content is galaxy C. Galaxies A, B and C belong to the
same branch which we interpret as the same GP. In contrast, galaxies E and D
belong to another branch separated by node $U_{4}$ and, therefore, to a
different GP. On the other hand, galaxy F does not belong to any GP. The
distance between nodes $U_{1}$ and $U_{3}$ works as a chemical index that will
allow us to differentiate galaxies A and B from galaxy C, even when they
belong to the same population. Finally, galaxies that are in the tree canopy
are the galaxies whose chemical composition are most similar, and, therefore,
they have the longest distance to the root. Galaxies at the top of the tree
end up being actually chemically different from galaxies at the root of the
tree, even when they belong to the same population. Therefore the length
between the nodes (Hereafter: NodeLength) along the tree, will help us
understand which parameters can promote the chemical diversification of
galaxies from the top of the tree down to the root.

In order to obtain a consistent hierarchical structure for the phylogenetic
tree, we calculate 1,000 trees utilizing Monte Carlo sampling from a normal
distribution where the center of the distribution is the value of the
absorption index and the width the error of the measurement from SDSS DR14
(Abolfathi et al. 2018). Also, we make bootstrapping with replacement so that
every time we calculate our distance matrix with Monte Carlo sampling we will
have a different combination of 29 or 30 absorption indices to generate our
tree. Finally, we make a majority rule consensus, which considers structures
in the tree that repeat at least $50\%$ of the time in the trees that we
calculate. This procedure allows us to eliminate branches that are not
statistically significant.

##  4 Analysis

Table 1: Galaxy distribution of different structures in the consensus phylogenetic tree of the Coma Cluster Population | No. of members
---|---
`Branch 1` | 10
`Branch 2` | 18
`Branch 3` | 67
`Branch with 1 node` | 90
`Branch with 2 node` | 39
`Branch with 3 node` | 18
`Branch without nodes` | 233

###  4.1 The Coma Cluster

We calculate a phylogenetic tree for our galaxy sample of the Coma cluster.
Our tree presents three main branches that we arbitrarily named branch one
(B1), branch two (B2) and branch three (B3). From the majority consensus rule
of 1,000 trees, they appear in 683, 694 and 655 trees, respectively. Several
other minor branches are found that appear at least 50$\%$ of the times and
whose complete description is shown in Table 1.

Each of our branches represents a GP and they are differentiated by their
chemical content. In what follows, we will focus on the three main GPs, namely
B1, B2 and B3. In order to prove that our GPs are different, we plot them in
Color-Magnitude space, indicating also galaxy morphology.

Figure 2: Color-Magnitude diagram of the Coma Cluster with photometric filters
Johnson B and Sloan r. Triangles, circles and squares represent galaxies
belonging to branch 1 (B1), branch 2 (B2) and branch 3 (B3), respectively. The
colors indicate galaxy morphology where red corresponds to elliptical
galaxies, blue to spiral galaxies, and yellow to S0 galaxies. Grey dots
represent galaxies from the Coma cluster that not appear in the main branches
of the consensus phylogenetic tree.

Figure 2 shows that, branches B1 and B2 belong to the bright-end of the Red
Sequence, and B3 belongs to the blue cloud of the cluster. This shows us that
at least populations B1 and B2 are different from population B3, as we see
they belong to different areas in the Color-Magnitude diagram. From the
consensus morphology, we see that B1 has 3 elliptical galaxies and 7 S0
galaxies; B2 has 15 elliptical galaxies and 3 S0 galaxies; whereas B3 has 50
spiral galaxies and 17 S0 galaxies. In order to have a better visualization of
this GP’S, we plot each population as a single tree with an image of they
morphology. (See Figures 3, 4 and 5).

Figure 3: Branch B1 of the phylogenetic tree of the Coma Cluster that
represents our first galaxy population. Each galaxy has its ID number from the
SDSS DR7, and its image from the SkyServer DR15. The number between the nodes
is the chemical length of their separation. Figure 4: Branch B2 of the
phylogenetic tree of the Coma Cluster that represents our second galaxy
population. Each galaxy has its ID number from the SDSS DR7, and its image
from the SkyServer DR15. The number between the nodes is the chemical length
of their separation. Figure 5: Branch B3 of the phylogenetic tree of the Coma
Cluster that represents our third galaxy population. Each galaxy has its ID
number from the SDSS DR7, and its image from the SkyServer DR15. The number
between the nodes is the chemical length of their separation.

We plot our GP’s in a sky projection of the galaxy cluster in Figure 6. This
shows us that, 1) galaxies in the B1 population have lenticular morphology at
the outskirts of the cluster and elliptical morphology in the cluster core; 2)
galaxies in the B2 population are distributed in two clumps in the cluster,
one in the centre and the other near the galaxy NCG 4839 which is associated
with a subgroup of galaxies in-falling into the Coma Cluster. This population
includes the two brightest cluster galaxies (BCG) NGC4874 and NGC4889 of the
Coma cluster (Neumann et al. 2001); and 3) galaxies in the B3 population do
not show any preferential distribution in the cluster.

Figure 6: Projected sky distribution of galaxies in the Coma Cluster belonging
to different branches of the phylogenetic tree. Triangles, circles and
inverted triangles represent galaxies belonging to branch 1 (B1), branch 2
(B2) and branch 3 (B3), respectively. The colors indicate the morphology of
the galaxy where red corresponds to elliptical galaxies, black to spiral
galaxies, and magenta to S0 galaxies. The color scale shows the number count
of galaxies by degree squared in the sky for the Coma Cluster. The white star
points out the galaxy NGC4839.

In order to characterize the common properties of the GP’s, we compare their
stellar masses, sSFRS, metallicities and ages in Figure 7. B1 galaxies are
quiescent with a high stellar mass with a mean value of
$log(M/M_{\odot})=10.66$ and 1 $\sigma$ dispersion of $log(M/M_{\odot})=0.21$,
high metallicity with a distribution centered at $[Z/H]=0.38$ and $1-\sigma$
dispersion of $[Z/H]=0.1)$, low sSFR with a mean value of
$10^{-10.75}[yr^{-1}]$ and 1-$\sigma$ dispersion of $0.13yr^{-1}$, but of
predominantly S0 morphology and with a distribution of young-to-intermediate
age stellar populations centered at $3.82Gyr$ and 1-$\sigma$ dispersion of
$1.15Gyr$. On the other hand, B2 galaxies correspond to quiescent galaxies
with high stellar mass with a mean value of $log(M/M_{\odot})=11.08$ and
$1-\sigma$ dispersion of $log(M/M_{\odot})=0.33$, high metallicity with a
distribution centered at $[Z/H]=0.37$ and 1-$\sigma$ dispersion of
$[Z/H]=0.07$), low sSFR with a mean value of $10^{-10.95}yr^{-1}$ and 1
$\sigma$ dispersion of $0.18yr^{-1}$, intermediate-to-old-age stellar
populations with a distribution centered at $9.0Gyr$ with 1 $\sigma$
dispersion of $2.85Gyr$ and mostly elliptical morphology. B3 galaxies have low
stellar mass with a mean value of $log(M/M_{\odot})=9.47$ and 1-$\sigma$
dispersion of $log(M/M_{\odot})=0.51$, with low metallicity distribution
centered at $[Z/H]=-0.33$ and 1-$\sigma$ dispersion of $log(M/M_{\odot})=0.49$
and high sSFR centered at $10^{-9.64}yr^{-1}$ with 1-$\sigma$ dispersion of
$1.8yr^{-1}$, have predominantly spiral morphology and contain stellar
populations having a wide range of ages $2.62Gyr$ with 1-$\sigma$ dispersion
of $2.41Gyr$). From this comparison we see that although branches B1 and B2
reside in the red sequence of the cluster, they have different distributions
of ages and mass. Therefore from this comparison we can conclude that B1, B2
and B3 are indeed three different GPs.

Figure 7: The histograms A, B, C and D show the distribution of galaxies from
the three different branches (B1, B2 and B3) with respect to stellar mass,
metallicity, age and sSFR. The yellow, red and blue colors represent galaxies
from branches B1, B2 and B3, respectively. Each branch sample have a gaussian
function, where the mean is indicated with a vertical line of the corresponded
color sample.

Now we analyze each branch’s hierarchical structure. As we show in section 3,
the NodeLength works as a chemical index. This chemical index characterizes
the variation in the chemical composition of galaxies. In order to see how the
general properties of mass, sSFR, ages and $[Z/H]$ relate internally in our
GP, we add the node length from the root of the tree to the leaves where each
galaxy is.

Table 2: Statistical Results between Nodelenght and galaxy properties for the Coma cluster main populations. We show the slope and y-intercept, with the 1-$\sigma$ uncertainties for a OLS fitting, as well as the 1-$\sigma$ dispersion for the WLS and the value for the chi squared forced to unity. Branch | Slope | $y_{intercept}$ | $\overline{X}_{OLS}$ | $\sigma_{OLS}$ | $\sigma_{WLS}$ | $X_{i}^{2}$
---|---|---|---|---|---|---
`Mass` |  |  |  |  |  |
`B1` | 0.14 | 10.58 | 10.66 | 0.04 | 3.62 | 22.68
`B2` | 0.31 | 10.95 | 11.08 | 0.11 | 5.56 | 50.48
`B3` | -0.16 | 9.63 | 9.47 | 0.13 | 4.91 | 36.73
`[Z/H]` |  |  |  |  |  |
`B1` | 0.25 | 0.23 | 0.39 | 0.07 | 0.17 | 0.01
`B2` | 0.06 | -0.39 | 0.37 | 0.02 | 0.23 | 0.07
`B3` | -0.17 | -0.21 | -0.37 | 0.13 | 0.29 | 0.03
`Age` |  |  |  |  |  |
`B1` | -3.58 | 6.03 | 3.83 | 1.06 | 1.0 | 7.32
`B2` | 3.65 | 7.48 | 9.02 | 1.31 | 5.56 | 24.33
`B3` | 1.38 | 1.21 | 2.55 | 1.08 | 2.68 | 3.17
`sSFR` |  |  |  |  |  |
`B1` | -0.22 | -10.62 | -10.75 | 0.06 | 4.73 | 22.62
`B2H` | 0.06 | -10.98 | -10.95 | 0.02 | 5.06 | 51.02
`B3` | 0.32 | -9.67 | -9.36 | 0.25 | 4.74 | 36.9

We investigated the variations in stellar mass, metallicity, stellar age and
sSFR as a function of NodeLength to establish whether one of these physical
properties is driving the differences in chemical composition along a branch.
For that we use a bootstrap methodology generating 1,000 fake data sets with
replacement to sample stellar mass, sSFR, metallicity and stellar age
distributions. Then we use an ordinary least squares regression (OLS) to get
the slope and y-intercept in order to report the standard deviation of the
distribution. We also perform a weighted least squares (WLS) in order to
assess the error in our absorption indices, setting the uncertainties equal to
some intrinsic dispersion term $\sigma_{int}$ and the evaluating the value of
this $\sigma_{int}$ term by forcing the reduced chi-squared of your fit to be
unity. We report the value that gives $X_{i}^{2}=1$, and the $\sigma_{int}$
for the WLS fit in Table 2

We find from Table 2 that our Nodelength parameter have a good fit with the
metallicities of our populations. Therefore the metallicity plays an important
roll in the formation of the hierarchical structures of the different branches
of our phylogenetic tree. Population B3 has different metallicity content than
populations B1 and B2, while populations B3 and B1 share similar ages,
although stellar mass and sSFR are not relevant for their hierarchical
relationships.

Figure 8: Color-magnitude diagram of our Coma Cluster galaxy sample with the photometric filters Johnson B and Sloan r. Panels A, B, C, D, and E show a recalculated phylogenetic tree without a negative response to $\alpha/Fe$ enhancement, insensitive response to $\alpha/Fe$ enhancement, positive response to $\alpha/Fe$ enhancement, absorption Balmer lines, and Emission Line $[OIII]\alpha 5007$ indices $[OIII]$. The black plus represent the galaxies that appear in the branches of each recalculated tree. Table 3: Remaining galaxy populations for the recalculated phylogenetic trees without a specific set of line indices  Index Class | Branches
---|---
`Blamer Lines` | B2
`Positive response to alpha/Fe enhancement` | B3 B2 B1
`Negative response to alpha/Fe enhancement` | BE B3 B1
`Insensitive to alpha/Fe` | B3 B2
`Emission Line $[OIII] \alpha 5007$` | B2 B3

Studying general or average properties such as metallicity, sSFR, age and mass
is not enough to fully understand what are the physical differences and/or
common characteristics of galaxies in our GPs. These are what determine the
hierarchical structures we observe. Therefore we separate our abundance
indices into five classes according to Thomas et al. 2003: (1) absorption,
age-sensitive Balmer lines including $H\delta_{A}$, $H\delta_{F}$,
$H\gamma_{A}$, $H\gamma_{F}$, $H\beta$ and $H\beta_{G}$; (2) positive
responses to $\alpha/Fe$ enhancement, including $CN_{1}$, $CN_{2}$, $Mg_{1}$,
$Mg_{2}$, $Mg_{b}$, $Ca4227$ and $G4300$; (3) negative responses to
$\alpha/Fe$ enhancement, including $Fe4383$, $Fe4531$, $Fe4930$, $Fe5015$,
$Fe5270$, $Fe5270S$, $Fe5335$, $Fe5406$ and $Fe5709$; (4) emission Line
$[OIII]\alpha 5007$, with $[OIII_{1}]$ and $[OIII_{2}]$ (Gonzalez et al.
2005); and (5) insensitive to $\alpha/Fe$, comprising $NaD$, $C4668$,
$Fe5782$, $Ca4455$, $TiO_{1}$ and $TiO_{2}$ .

Next, we recalculate the phylogenetic tree for the Coma cluster with the same
sample of galaxies but without one of these classes of abundance lines. We
obtain five new consensus trees, so we can analyze how these classes influence
the presence of our GPs in the phylogenetic tree. For this we analyze our re-
calculated consensus tree, by plotting color-magnitude diagrams. We graph the
distribution of galaxies from our original tree, and that of the galaxies that
appear in our re-calculated trees (see Figure 8). We summarize the results in
Table 3.

Table 4:  Statistical Results between Nodelenght and absorption indices for the Coma cluster main populations. We show the slope and y-intercept, with the 1-$\sigma$ uncertainties for a OLS fitting, as well as the 1-$\sigma$ dispersion for the WLS and the value for the chi squared forced to unity.  Branch | Slope | $y_{intercept}$ | $\overline{X}_{OLS}$ | $\sigma_{OLS}$ | $\sigma_{WLS}$ | $X_{i}^{2}$
---|---|---|---|---|---|---
$H_{\delta}A$ |  |  |  |  |  |
`B1` | 1.3 | -1.39 | -0.59 | 0.37 | 0.11 | 0.35
`B2` | -0.39 | -2.2 | -2.36 | 0.14 | 1.51 | 2.23
`B3` | 1.56 | 3\. 35 | 4.87 | 1.22 | 2.52 | 4.69
$H_{\delta}F$ |  |  |  |  |  |
`B1` | 0.57 | 0.42 | 0.77 | 0.16 | 0.33 | 0.03
`B2` | -0.38 | 0.2 | 0.04 | 0.13 | 0.12 | 0.03
`B3` | 0.9 | 2.74 | 3.62 | 0.7 | 1.8 | 3.11
$H_{\gamma}A$ |  |  |  |  |  |
`B1` | 0.62 | -5.18 | -4.79 | 0.18 | 1.63 | 4.79
`B2` | -0.39 | -6.13 | -6.29 | 0.14 | 3.16 | 15.81
`B3` | 2.21 | 0.68 | 2.83 | 1.72 | 1.93 | 0.23
$H_{\gamma}F$ |  |  |  |  |  |
`B1` | 0.74 | -1.34 | -0.88 | 0.21 | 0.23 | 0.34
`B2` | -0.22 | -1.64 | -1.73 | 0.08 | 0.95 | 1.14
`B3` | 1.11 | 2.07 | 3.14 | 0.86 | 1.7 | 1.76
$H_{\beta}$ |  |  |  |  |  |
`B1` | 0.5 | 1.78 | 2.09 | 0.14 | 0.77 | 0.57
`B2` | -0.24 | 1.75 | 1.65 | 0.09 | 0.79 | 1.29
`B3` | 0.64 | 3.14 | 3.76 | 0.5 | 1.89 | 3.93
$H_{\beta}G$ |  |  |  |  |  |
`B1` | 0.44 | 2.03 | 2.31 | 0.13 | 0.87 | 0.72
`B2` | -0.16 | 2.02 | 1.95 | 0.06 | 0 .98 | 1.72
`B3` | 0.55 | 3.2 | 3.73 | 0.43 | 1.84 | 4.09
$CN_{1}$ |  |  |  |  |  |
`B1` | 0.07 | 0.05 | 0.09 | 0.02 | 0.07 | 0.01
`B2` | 0.05 | 0.09 | 0.11 | 0.02 | 0.07 | 0
`B3` | -0.03 | -0.08 | -0.11 | 0.02 | 0.06 | 0
$CN_{2}$ |  |  |  |  |  |
`B1` | 0.05 | 0.06 | 0.09 | 0.02 | 0.04 | 0
`B2` | 0.07 | 0.13 | 0.16 | 0.02 | 0.1 | 0.01
`B3` | -0.03 | -0.04 | -0.07 | 0.02 | 0.04 | 0
$M{\gamma}_{1}$ |  |  |  |  |  |
`B1` | 0.03 | 0.1 | 0.11 | 0.01 | 0.04 | 0
`B2` | 0.03 | 0.13 | 0.15 | 0.01 | 0.08 | 0.01
`B3` | 0 | 0.03 | 0.03 | 0 | 0.01 | 0
$M{\gamma}_{2}$ |  |  |  |  |  |
`B1` | 0.03 | 0.23 | 0.25 | 0.01 | 0.09 | 0.01
`B2` | 0.04 | 0.28 | 0.3 | 0.02 | 0.16 | 0.03
`B3` | -0.03 | 0.11 | 0.08 | 0.02 | 0.03 | 0

Now that we can see which classes of indices influence our GP, we can study in
more detail their internal structure. Therefore we analyze the relations
between each index and the NodeLength, with the same methodology used with the
general galaxy properties but for each abundance index in our input sample.
See Table 4, 5 and 6.

Table 5: Same as in table 4, but for a different set of indices. Branch | Slope | $y_{intercept}$ | $\overline{X}_{OLS}$ | $\sigma_{OLS}$ | $\sigma_{WLS}$ | $X_{i}^{2}$
---|---|---|---|---|---|---
$M{\gamma}_{B}$ |  |  |  |  |  |
`B1` | 0.15 | 3.81 | 3.9 | 0.04 | 1.4 | 2.57
`B2` | 0.6 | 4.45 | 4.7 | 0.21 | 2.38 | 8.34
`B3` | -0.03 | 0.11 | 0.08 | 0.02 | 0.03 | 0
`Ca4227` |  |  |  |  |  |
`B1` | -0.13 | 1.21 | 1.13 | 0.04 | 0.4 | 0.26
`B2` | -0.03 | 1.28 | 1.27 | 0.01 | 0.76 | 0.73
`B3` | -0.11 | 0.59 | 0.48 | 0.09 | 0.18 | 0.14
`G4300` |  |  |  |  |  |
`B1` | -0.27 | 5.1 | 4.93 | 0.08 | 1.91 | 4.54
`B2` | 0.02 | 5.53 | 5.54 | 0.01 | 2.98 | 13.0
`B3` | -1.08 | 2.25 | 1.2 | 0.84 | 0.2 | 2
`Fe4383` |  |  |  |  |  |
`B1` | 0.5 | 4.23 | 4.54 | 0.14 | 1.89 | 3.24
`B2` | -0.01 | 5.2 | 5.2 | 0 | 3.26 | 12.54
`B3` | -1.12 | 2.75 | 1.67 | 0.87 | 0.29 | 3.07
`Fe4531` |  |  |  |  |  |
`B1` | -0.28 | 3.43 | 3.25 | 0.08 | 1.31 | 2.09
`B2` | 0.02 | 3.52 | 3.53 | 0.01 | 1.84 | 5.25
`B3` | -0.62 | 2.65 | 2.04 | 0.49 | 0.84 | 2.76
`Fe4930` |  |  |  |  |  |
`B1` | 0.31 | 1.73 | 1.93 | 0.09 | 0.84 | 0.57
`B2` | 0.11 | 1.89 | 1.93 | 0.04 | 1.08 | 1.53
`B3` | -0.21 | 1.31 | 1.11 | 0.16 | 0.29 | 0.76
`Fe5015` |  |  |  |  |  |
`B1` | 0.23 | 4.46 | 4.6 | 0.06 | 1.58 | 3.63
`B2` | 0.19 | 5.13 | 5.22 | 0.07 | 2.68 | 11.11
`B3` | -0.74 | 3.28 | 2.56 | 0.57 | 0.54 | 4.81
`Fe5270` |  |  |  |  |  |
`B1` | 0.17 | 2.78 | 2.88 | 0.05 | 1.24 | 1.45
`B2` | 0 | 3.0 | 3.0 | 0 | 1.71 | 3.92
`B3` | -0.46 | 1.97 | 1.52 | 0.36 | 0.44 | 1.58
`Fe5270S` |  |  |  |  |  |
`B1` | 0.03 | 2.19 | 2.21 | 0.01 | 0.85 | 0.83
`B2` | -0.03 | 2.31 | 2.3 | 0.01 | 1.3 | 2.32
`B3` | -0.36 | 1.57 | 1.22 | 0.28 | 0.39 | 1.0
`FE5335` |  |  |  |  |  |
`B1` | 0.63 | 2.15 | 2.54 | 0.18 | 1.19 | 1.02
`B2` | 0.1 | 2.71 | 2.75 | 0.03 | 1.5 | 3.13
`B3` | -0.38 | 1.62 | 1.25 | 0.3 | 0.39 | 1.06

If an absorption index has a good fit with NodeLength and, at the same time,
has a different range of values for each GP, we conclude that this index is
relevant for the hierarchical structure of our branches.

Table 6:  Same as in table 4, but for a different set of indices. Branch | Slope | $y_{intercept}$ | $\overline{X}_{OLS}$ | $\sigma_{OLS}$ | $\sigma_{WLS}$ | $X_{i}^{2}$
---|---|---|---|---|---|---
`Fe5406` |  |  |  |  |  |
`B1` | 0.33 | 1.45 | 1.66 | 0.1 | 0.79 | 0.49
`B2` | 0.03 | 1.8 | 1.82 | 0.01 | 0.99 | 1.39
`B3` | -0.24 | 1.06 | 0.83 | 0.19 | 0.2 | 0.48
`FE5709` |  |  |  |  |  |
`B1` | -0.1 | 0.93 | 0.86 | 0.03 | 0.32 | 0.15
`B2` | -0.05 | 0.87 | 0.85 | 0.02 | 0.48 | 0.33
`B3` | 0.01 | 0.47 | 0.48 | 0.01 | 0.25 | 0.09
$OIII_{1}$ |  |  |  |  |  |
`B1` | -0.13 | -0.69 | -0.77 | 0.04 | 0.29 | 0.08
`B2` | 0.07 | -0.96 | -0.93 | 0.02 | 0.4 | 0.39
`B3` | 0.13 | -0.92 | -0.8 | 0.1 | 0.34 | 0.34
$OIII_{2}$ |  |  |  |  |  |
`B1` | 0.11 | 0.97 | 1.04 | 0.03 | 0.43 | 0.17
`B2` | -0.02 | 1.14 | 1.13 | 0.01 | 0.66 | 0.57
`B3` | -0.09 | 0.38 | 0.29 | 0.07 | 0.63 | 1.5
$Na_{D}$ |  |  |  |  |  |
`B1` | 1.15 | 3.23 | 3.94 | 0.33 | 1.7 | 1.94
`B2` | 1.06 | 4.42 | 4.86 | 0.38 | 2.45 | 8.25
`B3` | -0.36 | 1.5 | 1.15 | 0.28 | 0.39 | 0.9
`C4668` |  |  |  |  |  |
`B1` | 0.23 | 6.98 | 7.12 | 0.06 | 2.55 | 8.61
`B2` | 0.9 | 7.49 | 7.87 | 0.32 | 4.39 | 23.94
`B3` | -1.12 | 3.0 | 1.92 | 0.87 | 0.33 | 3.72
`Fe5782` |  |  |  |  |  |
`B1` | 0.29 | 0.59 | 0.77 | 0.08 | 0.31 | 0.06
`B2` | 0.02 | 0.84 | 0.85 | 0.01 | 0.53 | 0.33
`B3` | -0.11 | 0.55 | 0.44 | 0.09 | 0.12 | 0.13
`Ca4455` |  |  |  |  |  |
`B1` | 0.21 | 1.06 | 1.19 | 0.06 | 0.52 | 0.22
`B2` | 0.08 | 1.34 | 1.37 | 0.03 | 0.74 | 0.76
`B3` | -0.17 | 0.7 | 0.53 | 0.13 | 0.16 | 0.2
$TIO_{1}$ |  |  |  |  |  |
`B1` | 0 | 0.04 | 0.04 | 0 | 0.01 | 0
`B2` | 0.01 | 0.04 | 0.04 | 0 | 0.01 | 0
`B3` | 0 | 0.01 | 0.01 | 0 | 0.01 | 0
$TIO_{2}$ |  |  |  |  |  |
`B1` | 0 | 0.08 | 0.08 | 0 | 0.03 | 0
`B2` | 0 | 0.09 | 0.09 | 0 | 0.04 | 0
`B3` | -0.01 | 0.04 | 0.03 | 0.01 | 0.01 | 0

Our main findings are:

$\bullet$ Absorption Balmer lines: from table 3 we see that only the B2
population remains in our tree. Balmer lines decrease in strength as stellar
populations get older, which is reflected in their influence on populations B1
and B3. This reinforce that population B1 and B2 are different, although both
belong to the red sequence of the Coma cluster. From Table 4 we see that
Balmer lines have a good fit for each galaxy population, however $H_{\gamma
F}$ is an index that have different range of values for each galaxy population
independent of the possible error influence ($\sigma_{wls}$). Therefore this
index is important for breaking the degeneracy between age and horizontal
branch morphology (in agreement with Schiavon et al. 2004).

$\bullet$ Insensitive to $\alpha/Fe$ enhancement: this abundance indices are
relevant for the B1 population. This is because, as seen in Table 3 and figure
8-B, the B1 population is not present in our recalculated tree. Analyzing
individual abundance indices, the $NaD$ index (see 6) shows a good fit with a
different value for each GP, although values for population B2 can be
influenced by errors in our data. This absorption index measures Carbon,
Magnesium and Sodium, elements that are produced and released through stellar
winds to the interstellar medium by massive stars. This tells us that galaxies
in B1 have undergone a recent period of star formation, and this is the reason
for showing up in our phylogenetic tree as a separated GP.

$\bullet$ Negative Response to $\alpha/Fe$ enhancement: at first glance from
Table 3, we see that the re-calculated tree has tree main GPs. But if we look
at figure 8-A, we notice that the B3 population is missing its reddest
galaxies, mostly of lenticular morphology. Nevertheless B1 population that
also have mostly lenticular galaxies remains in our re-calculated tree. From
Table 5 and Table 6 the abundance indices show a good fit for populations B1
and B3, although this results can be affected by the uncertainties in our
sample. Populations B1 and B3 have different abundances of $Fe5270S$ index, in
spite of the uncertainties. This index measures Carbon, Iron and Magnesium,
elements that are produced in Type Ia supernovae. Therefore the hierarchical
structure of S0 galaxies from B3 depends on the presence of Type Ia
supernovae, unlike S0 galaxies in B1.

$\bullet$ Positive Response to $\alpha/Fe$ enhancement: from figure 8-C) we
see that the presence of these lines is not relevant for the identification of
hierarchical structures in our GP, as we obtain the same galaxy populations
without these absorption indices.

$\bullet$ Emission Line $[OIII]\alpha 5007$, with $[OIII_{1}]$ and
$[OIII_{2}]$ (Gonzalez et al. 2005): the re-calculated tree without this index
shows a few galaxies from B2 and B3 and does not show B1 population. This
reinforce that our GPs are different. These indices present a good fit (see
Table 6 ), but all the GPs have similar abundances. Therefore we can not
evaluate their influence in the internal structures of our GPs.

From this analysis we can infer that the minimum amount of indices needed to
perform a successful and consistent phylogenetic study is 12 see Table 4, 5
and 6, and those include the following: $H\delta_{A}$,$H\delta_{F}$,
$H\gamma_{A}$ , $H\gamma_{F}$, $Fe4383$, $C4668$, $H_{\beta}$, $Fe5270$,
$Fe5270S$, $Fe5709$, $Fe5782$, $NaD$. We have investigated the possibility of
carrying out such an analysis with fewer indices. The results showed
inconsistencies in the sense that the MC trials with bootstrapping delivered
different outcomes in terms of tree structures. Hence, we do not necessarily
recommend applying such a phylogenetic method with indices other than those
indicated above.

####  4.1.1 Field

The environment of the cosmic structures in which galaxies reside affects
their evolution (Kauffmann et al. 2003b, Kauffmann et al. 2003a, Baldry et al.
2006, Peng et al. 2010). Therefore, in order to assess the differential
effects between high and low density environments, we generate a phylogenetic
tree with 438 field galaxies homogeneously distributed across the sky (see
figure 10), at redshifts range of $0.034-0.054$. From our consensus tree, we
obtain a main branch with 46 galaxies that appears 561 times from 1,000 tree
samples, and several minor structures (220 branches with 1, 2, 3, or 4 nodes
and 172 in single branches without nodes). We interpret the main branch as our
main GP.

Figure 9: Galaxy population obtained in the field, plotted as a single tree.
Each galaxy has its ID number from the SDSS DR7, and its image is from the
SkyServer DR15. Figure 10: Spatial distribution of our field galaxy sample
across the sky. Grey circles represent all galaxies in our sample, whereas
triangles represent our main galaxy population. Red, yellow, and blue colors
indicates, correspondingly, elliptical, S0 and spiral galaxies. Grey dots are
galaxies from Coma that do not appear in the main GP.

This population presents galaxies predominantly of lenticular morphology, that
we can observe in more detail in Figure 9. Also show distributions
characterized by high stellar masses with a mean value of
$log(M/M_{\odot})=10.63$ and 1-$\sigma$ dispersion of $log(M/M_{\odot})=0.31$.
For the sSFR the distribution is centered at $10^{-10.4}yr^{-1}$, with
1-$\sigma$ dispersion of $0.42yr^{-1}$, for the age the distribution is
centered at $6.6(Gyr)$ with 1-$\sigma$ dispersion of $3.52Gyr$ and the
distribution of the metallicity is centered at $[Z/H]=0.01$ with 1-$\sigma$
dispersion of $0.23$. In order to analyze the internal structure of our field
GP, we follow the same procedure as in section 4.1, comparing the lengths
between nodes with common galaxy properties (see figure 7) with a bootstrap
methodology generating 1000 fake data sets with replacement and performing a
OLS fit. We also perform a WLS in order to assess the error in our absorption
indices, setting the uncertainties equal to some intrinsic dispersion term
$\sigma_{i}nt$ and the evaluating the value of this $\sigma_{i}nt$ term by
forcing the reduced chi-squared of your fit to be unity. We report the value
that gives $X_{i}^{2}=1$, and the $\sigma_{i}nt$ for the WLS fit. 7.

Table 7: Statistical Results between Nodelenght and galaxy properties for the field main population. We show the slope and y-intercept, with the 1-$\sigma$ uncertainties for a OLS fitting, as well as the 1-$\sigma$ dispersion for the WLS and the value for the chi squared forced to unity. Branch | Slope | $y_{intercept}$ | $\overline{X}_{OLS}$ | $\sigma_{OLS}$ | $\sigma_{WLS}$ | $X_{i}^{2}=1$
---|---|---|---|---|---|---
`Mass` | 0.03 | 10.53 | 10.63 | 0.03 | 3.27 | 11.41
`[Z/H]` | 0.12 | -0.32 | 0.01 | 0.11 | 0.02 | 0.01
`Age` | -0.63 | 8.37 | 6.6 | 0.6 | 2.23 | 8.03
`SSFR` | -0.27 | -9.64 | -10.4 | 0.26 | 3.26 | 9.6

The internal structure of the main branch of our phylogenetic tree, shows a
good fit with metallicity. In order to see whether a specific class of
absorption indices influences the detection of this GP, we calculate a new
phylogenetic tree, but excluding different classes of absorption lines, as we
can see in figure 12. We notice that no particular class influences the
outcome of our GP in the tree. We analyze the internal structure of our main
GP, comparing the relation of the NodeLenght with respect to each absorption
index. In order to know how the error in our data can affect our fit between
absorption indices and the NodeLengthWe, we perform a OLS fit and a WLS fit
with an intrinsic dispersion term to estimate its value by forcing the reduced
chi-squared of our fit to be unity. We summarized the results in Table 8. The
NodeLength have good fit for all the abundance indices. This shows that our GP
is does not depend on any specific absorption line.

Table 8: Statistical Results of OLS and WLS fit between Nodelenght and specific abundance lines for the main population of the Field sample. We show the slope and y-intercept, with the 1-$\sigma$ uncertainties for a OLS fitting, as well as the 1-$\sigma$ dispersion for the WLS and the value for the chi squared forced to unity. Branch | Slope | $y_{intercept}$ | $\overline{X}_{OLS}$ | $\sigma_{OLS}$ | $\sigma_{WLS}$ | $X_{i}^{2}$
---|---|---|---|---|---|---
$H_{\delta}A$ | -0.84 | 1.83 | -0.53 | 0.8 | 0.07 | 0.65
$H_{\delta}F$ | -0.33 | 1.84 | 0.9 | 0.32 | 0.41 | 0.61
$H_{\gamma}A$ | -1.26 | -1.19 | -4.75 | 1.2 | 1.57 | 0.14
$H_{\gamma}F$ | -0.61 | 0.89 | -0.84 | 0.58 | 0.32 | 0.08
$H_{\beta}$ | -0.08 | 2.2 | 1.98 | 0.07 | 0.61 | 0.5
$H_{\beta}G$ | -0.14 | 2.6 | 2.21 | 0.13 | 0.64 | 0.7
$CN_{1}$ | 0.02 | -0.05 | 0.01 | 0.02 | 0.01 | 0
$CN_{2}$ | 0 | 0.05 | 0.06 | 0 | 0.03 | 0
$MG_{1}$ | 0.01 | 0.05 | 0.08 | 0.01 | 0.03 | 0
$MG_{2}$ | 0.02 | 0.15 | 0.21 | 0.02 | 0.06 | 0
$MG_{B}$ | 0.4 | 2.28 | 3.41 | 0.38 | 1.04 | 0.54
$Ca4227$ | 0.05 | 0.77 | 0.92 | 0.05 | 0.17 | 0.2
$G4300$ | 0.57 | 3.41 | 5.03 | 0.55 | 1.68 | 1.28
$Fe4383$ | 0.47 | 2.96 | 4.28 | 0.44 | 1.3 | 0.91
$Fe4531$ | 0.14 | 2.75 | 3.14 | 0.13 | 0.96 | 0.78
$Fe4930$ | 0 | 1.78 | 1.78 | 0 | 0.46 | 0.38
$Fe5015$ | 0.12 | 4.41 | 4.75 | 0.12 | 1.3 | 2.21
$Fe5270$ | 0.26 | 1.96 | 2.68 | 0.25 | 0.83 | 0.39
$Fe5270S$ | 0.1 | 1.77 | 2.05 | 0.1 | 0.61 | 0.32
$Fe5335$ | 0.07 | 2.2 | 2.41 | 0.07 | 0.6 | 0.68
$Fe5406$ | 0.06 | 1.38 | 1.54 | 0.05 | 0.42 | 0.23
$Fe5709$ | -0.05 | 1.02 | 0.88 | 0.05 | 0.29 | 0.11
$OIII_{1}$ | 0.05 | -0.75 | -0.6 | 0.05 | 0.1 | 0.12
$OIII_{2}$ | 0.05 | 0.99 | 1.13 | 0.05 | 0.32 | 0.11
$Ca4455$ | 0.14 | 0.76 | 1.15 | 0.13 | 0.39 | 0.07
$C4668$ | 0.62 | 3.56 | 5.3 | 0.59 | 1.49 | 1.6
$Fe5782$ | 0.06 | 0.5 | 0.68 | 0.06 | 0.2 | 0.03
$Na_{D}$ | 0.32 | 2.13 | 3.03 | 0.3 | 0.96 | 0.47
$TIO_{1}$ | 0 | 0.03 | 0.04 | 0 | 0.01 | 0
$TIO_{2}$ | 0.01 | 0.06 | 0.07 | 0.01 | 0.02 | 0
Figure 11: Color-magnitude diagram of our field galaxy sample, where panels A,
B, C, D, and E show a recalculated phylogenetic tree excluding absorption
Balmer lines, lines insensitive to $\alpha/Fe$, lines with negative response
to $\alpha/Fe$ enhancement, lines with positive response to $\alpha/Fe$
enhancement, and Emission Line $[OIII]\alpha 5007$, with $[OIII_{1}]$ and
$[OIII_{2}]$ respectively. The cyan diamonds represent the galaxies that
appear in branches of each recalculated tree. Grey dots represent galaxies
from the field that do not appear ih the main GP.

###  4.2 Discussion

The phylogenetic analysis performed in this work takes as input information on
the galaxy stellar population content in the form of a pairwise distance
matrix whose components are the total difference between absorption indices
for a given pair of galaxies. The NJ generates hierarchical structures that
retrieve the evolutionary history of galaxies. The branches of the trees
represent different GPs, and the NodeLength the chemical variation from one
galaxy to another within the corresponding GP or branch. The phylogenetic
analysis of galaxies is a better tool to identify GP because it allows us to
detect them regardless of the morphology, stellar mass, sSFR, metallicity or
stellar population properties of the galaxies.

####  4.2.1 Comparison with other methods

Chemical tagging is the closest method to our phylogenetic approach.
Therefore, we make this in an unsupervised manner by performing a principal
component analysis (PCA) of the same dataset of 30 abundance indices for the
Coma Cluster and field samples. Then we apply K-means clustering (Hartigan &
Wong 1979), an unsupervised machine learning algorithm, to categorize our data
into groups according to centroids. In order to obtain the centroids for the
Coma Cluster we define 4 groups, so we can compare the result that we get with
the phylogenetic approach. Then we also used the elbow method (Joshi & Nalwade
2013) to define the ideal number of groups, that in this case is 8 for both
samples.

We calculate 10 principal components for the Coma Cluster and the field.
Figure 12 shows the combinations of principal components 1 and 2, and also
principal components 1 and 4, which were the only combinations that showed
class differentiation in both samples.

Figure 12:  We compare a PCA of 30 abundance indices with the phylogenetic
approach, for our galaxy samples of the Coma Cluster and the field. Panel A
presents the principal components 1 and 2, and panel B presents the principal
components 1 and 4 for the Coma Cluster. Red, blue and yellow dots indicate
the GP1, GP2 and GP3 of the Coma Cluster found by our consensus phylogenetic
tree. Magenta and cyan diamonds indicate the 4 and 8 centroids for the PCA
decomposition of the Coma cluster. Panel C presents the principal components 1
and 2, and panel D presents the principal components 1 and 4 for the field.
Yellow dots indicate the main GP found by our phylogenetic tree. Cyan diamonds
indicate the 2 centroids for the PCA decomposition of the Field.

For the Coma Cluster, the PCA method at a first glance is able to separate two
populations, with the combination of principal components 1 and 2. We
calculate the centroids for 4 groups, and 8 groups based on the 10 components
originally calculated. We see that the centroids are not able to differentiate
the three main GPs obtained with the phylogenetic approach. On the other hand,
the combination of principal components 1 and 4 shows three possible groups.
Nevertheless, by calculating the centroids for 4 and 8 groups we see that the
centroids are unable to differentiate the GP obtained by our phylogenetic
tree.

PCA decomposition is able at first glance to separate our sample into groups,
but does not recover the GP obtained from the phylogenetic approach in the
Coma Cluster. Furthermore, PCA lacks the extra parameter given by the
phylogenetic approach that is the length between nodes. This new parameter can
be used to explore correlations between specific absorption lines in order to
understand the physical processes that are occurring in our GP. Also, the
determination of groups depends on a K-means analysis which needs, as an
input, a predefined number of groups in order to compute the centroids that
separate our GP.

####  4.2.2 Minor Structures

Our phylogenetic analysis shows the presence of our GPs in both the Coma
Cluster and the field. Nevertheless, for the Coma Cluster $30\%$ of our
galaxies can be found in structures with one, two or three nodes, which we
name minor structures, and $49\%$ in branches without nodes. In a similar way,
$50\%$ of field galaxy are found in minor structures and $39\%$ in branches
without nodes.

For the Coma Cluster, the phylogenetic analysis shows three different GPs,
represented by the three main branches of the tree. The NJ algorithm, in
principle, is able to retrieve evolutionary information about their input
taxa. Nevertheless, the input information can be incomplete, and thus the
consensus tree restricts the possibility of further exploring structures with
low statistical significance as our minor structures.

In order to explore the minor structures of our consensus phylogenetic tree,
we divide them into branches without nodes, and structures with 1, 2 or 3
nodes. We plot them in color-magnitude space and in the PCA analysis (see
figure 12). From figure 12-A we see that these minor structures belong to the
red sequence of the Coma Cluster. Nevertheless both samples of minor
structures of the Coma Cluster do not show a clear disentanglement from each
other. From figure 12-B the PCA decomposition is also unable to separate these
minor structures as different groups. Therefore for the Coma Cluster we can
conclude that the red sequence is not homogeneous, it has small groups of
galaxies in color-magnitude space belonging to small substructures that appear
in our consensus phylogenetic tree. For the field sample we make the same
division for minor structures and from figure 12 we can see that PCA
decomposition is also unable to separate these minor structures in different
groups.

It is interesting to note that red sequence galaxies at intermediate and low
stellar masses do not belong to any of the three main galaxy populations. This
is interesting because at these masses most of the build-up of the red
sequence should occur. The red sequence at intermediate and low stellar masses
should in fact be a mixture of old galaxies and recently quenched galaxies.
This probably reflects the difficulty in identifying more significant GP’s.
Furthermore, the signal-to-noise of the spectra is lower for faint galaxies
with respect to bright ones, which may share part of the responsibility in not
identifying definite structures. Larger samples of galaxies may help to
resolve structures in the faint region of the red sequence.

Figure 13:  Comparison of minor structures of the phylogenetic approach with
the PCA. Panel A shows a PCA of the Coma Cluster. Red, blue and yellow dots
represent GP1, GP2 and GP3 respectively. Panel B shows a PCA decomposition of
the field. Yellow dots represent galaxies that belong to the main GP found in
the field. Panel C shows a Color-Magnitude diagram of the Coma Cluster with
the photometric filters Johnson B and Sloan r. For all Panels grey dots
indicate galaxies that belong to structures with 1, 2 and 3 nodes and black
dots represent galaxies in a single branch.

##  5 Summary and Conclusions

In this paper, we study the chemical properties of galaxies applying for the
first time a phylogenetic techniques based on a distance matrix between
absorption indices. This novel method gives us a graphical visualization of
the chemical diversification among galaxies in the form of the hierarchical
structure of a phylogenetic tree.

This structure connects galaxies through features that we call "nodes".
Branches in the consensus phylogenetic tree are interpreted as GPs, and the
length between nodes (NodeLength) as the internal chemical variation along a
branch. The NodeLength acts as a chemical index, by relating galaxy stellar
populations to various structural and environmental properties, both in galaxy
groups or clusters and in the field.

We apply the phylogenetic method to 475 galaxies in the Coma cluster
($0.015<z<0.033$) and 438 galaxies in the field ($0.035<z<0.054$) using 30
abundance indices from the Sloan Digital Sky Survey.

The three main branches in the Coma Cluster are named B1, B2, and B3. Galaxies
belonging to B1 are quiescent with high stellar mass with a mean value of
$log(M/M_{\odot})=10.66$ and 1 $\sigma$ dispersion of $log(M/M_{\odot})=0.21$.
Also this GP show high metallicity with a distribution centered at
$[Z/H]=0.38$ and 1-$\sigma$ dispersion of $[Z/H]=0.1)$. On the other hand this
GP present a low sSFR with a distribution centered at a value of
$10^{-10.75}[yr^{-1}]$ and 1-$\sigma$ dispersion of $0.13yr^{-1}$. This GP
shows of predominant S0 morphology with a distribution of young-to-
intermediate age stellar populations centered at $3.82Gyr$ and 1-$\sigma$
dispersion of $1.15Gyr$. On the other hand, B2 galaxies correspond to
quiescent galaxies with high stellar mass with a mean value of
$log(M/M_{\odot})=11.08$ and 1-$\sigma$ dispersion of $log(M/M_{\odot})=0.33$.
This GP has high metallicity with a distribution centered at $[Z/H]=0.37$ and
1-$\sigma$ dispersion of $[Z/H]=0.07$), low sSFR with a mean value of
$10^{-10.95}yr^{-1}$ and 1-$\sigma$ dispersion of $0.18yr^{-1}$. B2 GP present
intermediate-to-old-age stellar populations with a distribution centered at
$9.0Gyr$ with 1-$\sigma$ dispersion of $2.85Gyr$ and mostly elliptical
morphology. B3 galaxies have low stellar mass with a mean value of
$log(M/M_{\odot})=9.47$ and 1-$\sigma$ dispersion of $log(M/M_{\odot})=0.51$,
with low metallicity distribution centered at $[Z/H]=-0.33$ and 1-$\sigma$
dispersion of $log(M/M_{\odot})=0.49$ and high sSFR centered at
$10^{-9.64}yr^{-1}$ with 1-$\sigma$ dispersion of $1.8yr^{-1}$. This GP have
predominantly spiral morphology and contain stellar populations having a wide
range of ages $2.62Gyr$ with 1-$\sigma$ dispersion of $2.41Gyr$. B2 is
distributed in two clumps in the cluster, one in the centre including both
BCGs NGC4874 and NGC4889 and the other near the galaxy NCG 4839 which is
associated with a subgroup of galaxies falling into Coma (Neumann et al.
2001). Although the B1 and B2 populations reside in the red sequence they have
different ranges of stellar ages and mass. Minor structures in the Coma
cluster belong to the red sequence. Therefore, this one is not homogeneously
distributed in color-magnitude space.

The metallicity plays an important role in the formation of the hierarchical
structures of the different branches of our phylogenetic tree (see Table 2,
Table 7).

B3 comprises a portion of galaxies with lenticular morphology (see figure 8)
that are chemically different (negative response to $\alpha/Fe$ enhancement,
Fe5270S) to lenticular galaxies in B1 (insensitive response to$\alpha/Fe$
enhancement, $Na_{D}$), suggesting that galaxies with lenticular morphology in
Coma follow different chemical paths. These can be interpreted as B1
lenticulars having undergone a recent period of star formation, while B3
lenticulars being abundant in type I SNe.

The galaxy population in the field is too homogeneous for us to be able to
differentiate more than one population. The field presents a main branch with
galaxies that we interpret as our main GP. This one has objects of
predominantly lenticular morphology (see figure 9), with distributions
characterized by high stellar masses with a mean value of
$log(M/M_{\odot})=10.63$ and 1-$\sigma$ dispersion of $log(M/M_{\odot})=0.31$.
For the sSFR the distribution is centered at $10^{-10.4}yr^{-1}$, with
1-$\sigma$ dispersion of $0.42yr^{-1}$, for the age the distribution is
centered at $6.6Gyr)$ with 1-$\sigma$ dispersion of $3.52Gyr$ and the
distribution of the metallicity is centered at $[Z/H]=0.01$) with $1-\sigma$
dispersion of $0.23$. The metallicity plays an important role in the
hirarchical structure of the main populations (see table 7), as seen in the
hirerarchical structures of the different GPs of the Coma cluster. The main
population of the field shows no dependence of any specific absorption lines
(see table 8), in contrast with what we observe in the GPs of the Coma
cluster.

Our phylogenetic approach introduces a new index that reflects the chemical
distance between galaxies in a GP. This index is given by the NodeLength and
allows us to study the hierarchical structures within the tree in terms of
general properties of galaxies and specific abundance indices.

From the analysis of the NodeLength values and specific absorption indices in
both the field and the Coma Cluster, we find that just 12 indices are relevant
to find GPs with this phylogenetic approach (see Table 4), Table 5 and Table
6, and those include the following: $H\delta_{A}$, $H\delta_{F}$,
$H\gamma_{A}$ , $H\gamma_{F}$, $Fe4383$, $C4668$, $H_{\beta}$, $Fe5270$,
$Fe5270S$, $Fe5709$, $Fe5782$, $NaD$.

As an overall conclusion of this work, we find that phylogenetics is a
promising method to identify and study GPs in different environments. This is
due to the fact that it is directly based on chemical information that is
determined by the stellar population content in galaxies themselves. Our
results indicate that, at least in the case of the Coma Cluster, galaxies in
that high density region are chemically more heterogeneous than their
counterparts in the field.

We also notice that the hierarchical structure of the phylogenetic tree does
not depend on the presence of positive response to $\alpha/Fe$ enhancement
abundance indices. We speculate that these differences and the independence of
$\alpha/Fe$ enhancement may be a consequence of environmental processes that
drive the evolution of galaxies at different local densities.

The main advantage of the phylogenetic approach is that, by being exclusively
based on chemical information, it allows us to perform robust analyses and
interpretations without introducing biases by first selecting samples based on
a specific characteristic such as stellar mass, morphology, sSFR or
metallicity, as done with more traditional techniques. We caution, however,
that more studies with more cluster and field samples at higher redshifts are
needed to firmly establish the validity of the results obtained in this work.
The samples used in the phylogenetic analysis of galaxy spectra could suffer
biases due to the spectroscopic selection function (completeness in flux,
colour, morphological type, etc.).

## Data Availability Statement

There are no new data associated with this article. Please refer to the text
for the references where the data were obtained from.

## Acknowledgements

The authors thank Inger Jørgensen for useful discussions on the analyses of
this work.

We acknowledge support by CONICYT Programa de Astronomía Fondo ALMA-CONICYT
2017 31170002. R.D. gratefully acknowledges support from the Chilean Centro de
Excelencia en Astrofísica y Tecnologías Afines (CATA) BASAL grant AFB-170002.
P.C. acknowledges the support from the ALMA-CONICYT grant no 31180051. NWCL
gratefully acknowledges support from a Fondecyt Iniciacion grant 11180005.
G.C.V. acknowledges support from CONICYT through the FONDECYT Initiation grant
No. 11191130 and the Ministry of Economy, Development, and Tourism’s
Millennium Science Initiative through grant IC120009, awarded to The
Millennium Institute of Astrophysics (MAS).

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