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Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

Exploiting the power of multivariate statistics for probing thecellular biology of environmentally challenged reef corals
Anderson B. Mayfield1,2
1Cooperative Institute for Marine and Atmospheric Studies, University of Miami, Miami, FL 33149, USA
2Atlantic Oceanographic and Meteorological Laboratory, National Oceanic and Atmospheric Administration, Miami, FL

33149, USA*Corresponding author. Email: abm64@miami.edu or anderson.mayfield@noaa.gov

Abstract
The coral reef research field has grown markedly in terms of both human power
and technological capacity in recent years, a fortuitous occurrence given the rapidly
diminishing nature of Earth’s reefs on account of climate change and otheranthropogenic stressors. Unfortunately, most coral biologists lack the statisticalbackground to realize the full analytical potential of “big” datasets emerging from (nonexhaustively) 1) expanding reef survey efforts, 2) satellite and in-water (e.g.,
photomosaic) coral reef imaging projects, and 3) “next-generation” molecularapproaches (i.e., ‘OMICs); statistical training has not advanced commensurately withdataset size, a significant short-coming when considering the utility of these data in
informing coral reef ecosystem management and conservation. One notably pervasive
issue in ‘OMICs research in particular is the general omission of multivariate statistical
approaches (MSA), which universally outperform the more commonly employed, lessstatistically conservative univariate alternatives when attempting to A) modelexperimental results and B) make predictions about reef coral health and fate. Herein I
have attempted to make a case for coral biologists to strongly re-evaluate the merit of
MSA, as well as explain why relying on univariate approaches alone may actually leadto spurious findings that do not advance our knowledge of corals and coral reefs.
Key words: Climate change, Coral reefs, Dinoflagellate, Molecular biology, Predictivemodeling, Upwelling Statistics

27

Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

Introduction

Pocillopora

Over the past 20 years, the collective

acuta

&

http://symbiont.iis.sinica.edu.tw/s_hystrix

research effort of the coral reef field has/static/html/ for Seriatopora hystrix).

grown immeasurably as more and more

In many such cases, though, “big”

young scientists in particular seek to study

datasets are generated (e.g., sequenced

and/or save these incredibly beautiful (Fig.

genomes or transcriptomes) and explored1), yet rapidly vanishing, ecosystems.

using “tried and true” (bio)informatics

Serendipitously, technological capacity

pipelines (e.g., Xiang et al., 2015), yet key

has also increased dramatically as offacets of the underlying biology arerecent, and many large-scale questions onnevertheless overlooked due to analyticalthe fundamental nature and persistence oferrors or oversights stemming from lack ofcoral-dinoflagellate endosymbioses cantraining in statistics. This arises not only

now be addressed in ways, and with levels

from poor data stewardship, but also fromof rigor and depth, that would have been

the “castles in the sky” phenomenon, in

unheard of even a decade ago (Mayfield etwhich a faulty script or statistical test isal., 2019b). It could be argued thatpublished in a respected, peer-reviewed

advances in molecular biology (Mayfield

journal,

et al., 2011) and high-level data analytics

ingratiated within the field’s Zeitgeist to(Mayfield & Chen, 2019) have benefited

where it is no longer questioned. For

the coral reef field (& certainly many

instance, failure to rigorously assess theothers) to greater degrees than any and all

validity of the ITS2 marker in the initial

other emerging discipline(s). As an

Symbiodiniaceae genotyping protocols

example,ondeveloped in the 1990s culminated in thescleractinian coral gene expression thatpublication of hundreds of articles on therequired 5-6 years of concerted field andimportance of endosymbiont diversity inlaboratory bench work (~60-70 hr/week;coral health (e.g., LaJeunesse, 2001) that

Mayfield, 2009; Mayfield et al., 2010) canwere later refuted through a series of

now be completed in several days given

simple,the existence of optimized protocols

experiments undertaken by a highly(Mayfield et al., 2009) and well curated

motivated

and annotated DNA/mRNA sequence

uncovereddatabases(e.g.,

heterogeneity of this gene within the

http://symbiont.iis.sinica.edu.tw/coral_pdl

Symbiodiniaceae genome (Apprill &

a

Ph.D.

dissertation

tte/static/html/index.html#homefor28

regularly

cited,

cloning-based
graduate
extensive

and

then

laboratory
student

who

sequencePlatax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

Fig. 1. A recent lava flow overtaken by several species of the reef-building coral genus
Acropora. “Lava Flow,” off Gunung Api (volcano), Banda Islands, Maluku, Indonesia.
Photo credit=Anderson Mayfield (a.k.a. 珊瑚醫生).
Gates, 2007); every ITS2 “type” can be

Entire careers and “paradigm-shifting”

found within a single cell, thereby

stories have been built off of a mistake that

invalidating all published research on thewas pointed out from data collected acrossuseonly several days of benchwork. Let us not

of

this

markerforassessingdinoflagellate diversity (Putnam et al.,allow

2017). Rather than go “back to the drawing

currently rife within the coral ‘OMICs

board” and admit defeat, the field has

literature (e.g., DeSalvo et al., 2008;

continued to build upon the ITS2-driven

Meron et al., 2019) invalidate thedinoflagellate diversity “castle” (e.g.,potentially immense value of the myriad

LaJeunesse et al., 2009), which sits atop acoral-dinoflagellate ‘OMICs datasets now

decidedly flimsy foundation (“the air”).

being generated by researchers across the29

sophomoricstatisticalerrorsPlatax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

globe. Before addressing this central

norm in the field (but see Mayfield, 2016.),

theme of this article, allow me to make onea researcher will be unable to demarcate aadditional conceptual recommendation forlevel of health or

those, like myself, interested in anthozoan

predictions regarding coral fate in this era

health and physiology (Mayfield et al.,of

2014a,c).

(Mayfield & Chen, this issue).

rapidlychanging

make confident
globalclimateMost studies of coral biology focus

With respect to ‘OMICs technologies

on only one member of the mutualism: thespecifically, in almost all cases, thecoral host (e.g., Palumbi et al., 2014) or the

microbial (including Symbiodiniaceae)

dinoflagellate endosymbionts. To be fair,data are collected alongside those of thesciencereductionistic,

host at no extra expense and with noparticularly molecular biology; if one isadditional need to undertake further

only interested in, for instance, coral genelaboratory benchwork; the only extraneous

expression,

why

need

one

concerneffort required to incorporate these data

his/herself

with

the

dinoflagellates’

would be in the time required to analyzetranscriptomes? This may indeed be athem (granted, this is not a trivial endeavor

valid question for those seeking toforelucidate coral thermo-biology, but forsuggestions outlined below apply to data

researchers (such as myself) interested infrom both the anthozoan and microbial

questions pertaining to coral health,fractions. Whether the coral and microbial

resilience, and persistence, it is decidedly

analytes are pooled or separated (e.g.,

myopic and overly simplistic to consider

Chen et al., 2017a) prior to statisticalthe biology only one of the plethora ofanalyses, however, is project-dependent,“compartments” within the holobiont

and health-informing, diagnostic findings(Cheng et al., 2016); only by probing the

could be garnered from either approach.

isinherently“big”

datasets.).

As

such,

all

biology of the anthozoan host (~60%), its

As did quality control fall to thegastrodermal symbionts (30%), and thewayside in early (& some more recent)diverse(10%)

works on Symbiodiniaceae genetics andcollectively comprising the holobiont

multi-compartmental coral molecular eco-

(Rosales et al., 2019) can we hope to paintphysiology, some common statisticala holistic picture of the health of a coral

mistakes that would not be accepted bypolyp or colony (Mayfield & Gates, 2007).

reviewers of traditional articles featuring

In

host

“small” datasets (e.g., Enochs et al., 2020)

physiology alone, which is the current

are often overlooked because, in many

microbial

contrast,byconsortium

characterizing

30Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

cases, those having undertaken “big data”

issues in datasets that have impressed inanalyses (e.g., transcriptomics) surely

their size, scope, and/or cost of acquisition,

spent a considerable amount of money andremains to be determined.

so could not readily redo the experiment(s)However, I would actually argue(e.g., Mayfield et al., 2018b); this could

against the latter excuse: were one topotentially assuage reviewers to be moreinvest heavily (in terms of funding, effort,

sympathetic. As an example, in the pursuit& time) in a study in which a massive,

of

the

potentially rich dataset was compiled, it

implications of global climate change

would be my hope that both authors and(GCC) on coral-dinoflagellate biology

reviewers would aim to ensure that it be(sensu Mayfield et al., 2013a-d, 2014a;

exploited to the fullest extent possible.

Putnam et al., 2013), there has been a focus

This idea is, in fact, another goal of thison uncovering differentially concentrated

article: to highlight the notion thatanalytes (DCAs; e.g., genes, proteins,insightful multivariate data exploration

lipids, etc.) in a “p-value-mining” fashion;algorithms, techniques, and presentation

althoughthese

responsestyles (beyond the few commonly adopted

analyses

(RSA)

are

discovery

rate

attemptingtounderstandscreeningtypicallyfalse

by coral biologists at present) exist and(FDR)-governed,

ifshould be more seriously incorporated,researchers fail to first uncover moreparticularly in the analysis of “big”

general multivariate patterns in the dataset,datasets. I envision this as a call to “up the

one could make a compelling argument(statistics) ante” and urge researchers tothat RSA are actually unsupported or

take advantage of both “time-tested” andinappropriate.

more

After

all,

an

articlecontemporary

data

analysispresenting post-hoc differences (e.g.,

approaches for making sense of the

Tukey’s tests) among means in the absence

evermoreof an overall ANOVA treatment effectgenerated nowadays. There will be awould be flagged by a competent reviewer.

particular focus on ‘OMICs research as theIn

complexdatasets

being‘OMICsresearch,however,

this

associated datasets are amongst the mostfundamental

statistical

flaw

oft

analytically daunting generated to date inoverlooked(i.e.,

univariate

the coral biology field, especially whencomparisons in the absence of a treatment

these data are mapped onto habitats (e.g.,effect). Whether this is more due toChen et al., 2017b, 2019) to attempt toreviewer ignorance of statistics or theunderstand the environmental drivers of

aforementioned willingness to overlook

variation in coral health and resilience

multipleis31

Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003(Mayfield et al., 2015, 2016a, 2017a-c,

has been an especially strong advocate of

2018c, 2019a, in prep.). My over-archingsuch ‘OMICs approaches (Wang et al.,hypothesis‘OMICs2013; Mayfield et al., 2014d; McRae et al.,researchers (not limited to coral biologists)

in review). In typical eco-physiologicalwould do well to familiarize themselves

experiments,

with the multivariate statistical approaches

Symbiodiniaceae(MSA) beyond the lone method commonly

experimental treatment(s) in the laboratory

found in the current literature: principal

for a pre-set period of time prior tocomponents analysis (PCA). Not only aresampling

these additional MSA more robust, but, as

macromolecular extraction (e.g., Mayfieldmentioned in the previous paragraph, it is

et al., 2011). Upon sequencing theactually statistically invalid to progress toresulting DNAs, mRNAs, proteins, lipids,

the far more commonly reported univariate

and/or metabolites via genomic (ampliconfindings unless the MSA provide strong

sequencing

or

support for doing so. This extra degree oftranscriptomic(RNA-Seq),

statistical conservation should not be seen(MS), lipidomic (MS), and metabolomic

as a barrier to publication, but instead as a(MS)means of tapping into the power of MSA

researcher must typically attempt to(& preferably MSA combined withdiscern patterns among tens of thousands,

information theory) while simultaneously

tens of thousands, thousands, hundreds,

limiting the possibility of type I statisticaland hundreds of molecules, respectively.

errors near-ubiquitous within p-value-

In very few cases are the number ofmining studies (Anderson et al., 2000).

analyzed samples greater than the number

is

that

most

coralsorarebiopsies

technologies,

cultured

exposed

for

to

later

meta-genomics),
proteomic

respectively,

theof analytes; even when profiling lipids, for

Materials & methods

which only 100-200 can typically be

As mentioned above, a plethora ofquantified in a single study, it is unlikely

studies have attempted to utilize cutting-that the researcher’s budget would lendedge molecular approaches like RNA-

itself to analyzing 100-200 samples atSequencing

mass

current rates of $200USD/sample (similar

spectrometry (MS)-based proteomics toto late-2020 prices for the other ‘OMICs

elucidate the implications of GCC andtechnologies). Although a dataset with 10-

other anthropogenic stressors on the

20 samples in total is publishable in evencellular biology of marine organisms

the(Monteiro et al., 2020); the coral reef field(assuming a robust experimental design &(RNA-Seq)

and

32

most

highlyrespected

journals

Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

preferably 3-5 replicates per treatment),

due to the aforementioned inability to use

what this signifies is that traditional MSA,

parametric statistical approaches (PSA) to

namely multivariate ANOVA (MANOVA),

uncover multivariate treatment effects. In

cannot be performed with such datasets

fact, there are a number of ways tobecause MANOVA generally necessitatesdocument multivariate treatment effects

that the number of analytes be less than thewith ‘OMICs datasets, and I 1) describe

number of samples. In other words,

them herein using a sample dataset and 2)

MANOVA cannot be used in >99% of

advocate for their more widely adopted‘OMICs studies.

use in future ‘OMICs analyses (not limited

It is for this reason, perhaps, thatto corals). Only when the approaches

MSA have fallen out of favor among

outlined below identify a treatment effect‘OMICs researchers. Additionally, many

should the more rudimentary, commonly

are only interested in uncovering DCAs

employed RSA be undertaken, preferably(e.g.,

using an FDR-adjusted alpha of no higher

differentiallyexpressed

genes[DEGs] & differentially concentrated

than 0.01.

proteins [DCPs] in their transcriptomic &PERMANOVA.

Permutational

proteomic projects, respectively), since,

MANOVA (PERMANOVA; Anderson eteven when using a FDR-controlled p-value,al., 2008) is likely the preferred means of

it is likely that at least several analytes willassessing multivariate differences withindiffer significantly in concentration across‘OMICs datasets because it can be carriedtreatments (i.e., results around which aout when there are more analytes thanmanuscript-sellingbesamples and is robust even when analyte

generated). However, as mentioned above,concentrations are collinear (a hallmark ofthis is analogous to proceeding directly to‘OMICs datasets; discussed in more detailinter-mean post-hoc tests without having

below). Furthermore, since it is based on

first carried out the requisite ANOVA; is it

assessment of inter-sample similarity, it isappropriate to search for univariate effects

also robust to datasets featuring numerous(i.e., on an analyte-by-analyte basis)

0s (i.e., analytes that went unsequenced inwithout having previously documented an

certain samples; Clarke et al., 2014).

overall multivariate treatment effect? The

PERMANOVA can be undertaken withgeneral consensus seems to be that no such

PRIMER (UK) or with open-access scripts

multivariate assessment is needed if one(e.g., R). In most cases, rows and columns

simply wants to search for DCAs acrossrepresent

samplestreatments, though this could simply berespectively,

and transformations

story

could

33

and

analytes,arePlatax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

critical since there may be large variation

critical (Levene’s test [or comparable],in mean analyte concentrations; somep>0.05 to justify use assuming a normal

analytes

distribution),

might

be

at

far

highermultivariate

dispersion

concentrations than others (& so would beshould ideally not vary significantly acrossover-weighted in the analysis). The

experimental treatments (i.e., PERMDISP

preferred means of accommodating inter-[PRIMER], p>0.05).

analytevariationisstandardization

As an example, please consider the(Mayfield, in review), whereby the data

“Seriatopora hystrix variable temperaturefor each analyte are transformed such thatstudy” (SHVTS) of Mayfield et al. (2012a),the mean is 0 and the standard deviation isin which we exposed corals from an

1. This then puts each analyte on an “evenupwelling site known as Houbihu (see Lee

playing field.”

et al., 1997; Ribas-Deulofeu et al., 2016; &Given that such standardized data

Liu et al., 2012 for oceanographic,

will inherently feature numerous negative

ecological,&

values, the Euclidean distance matrix

respectively.) or a non-upwelling site(EDM) is recommended over the Bray-(Houwan) to either upwelling-simulating

Curtis similarity matrix (BCSM), which(23-29°C over 6 hr) or stable-temperaturecannot be computed with negative values.

(26°C) conditions for a week and profiled

If a BCSM is preferred, then a “dummy”

thevariable can be added to the standardized

data,physiology ofcorals“transplanted”

(ex

to

foreigndata to where all values are positive.

temperatureenvironments(i.e.,

Alternatively, a fourth-root transformation

Houbihustable-temperatures&of the raw data might down-weigh high-Houwanvariable-temperatures) vs. non-concentration analytes sufficiently totransplanted controls (e.g., Houbihu corals

justify its use over standardization, in

exposedwhich case a BCSM could be constructed.

conditions). In this experiment, then, there

Ultimately,

andwere two fixed factors: site of origin (SO;distance matrix used may be justified byn=2) and temperature treatment (TT;determining

limitsstable vs. variable). We were particularly

heterogeneity in multivariate dispersion

interested in their interaction, since weacross2006);

hypothesizedthatalthough likely less critical than whendemonstratesuperior

undertaking parametric ANOVA, in which

performance when exposed to their “native”

homogeneity of (univariate) variance istemperature conditions. Although this wasthetransformation

which

treatments

best(Anderson,

34

molecular

human-impact

to

situ)

upwelling-simulatingcoralswould

physiologicalPlatax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

indeed documented to a certain extent

Symbiodiniaceae SHVTS transcriptome(Mayfield et al., 2012a), the Houwan

server referenced above, as well as NCBI.

corals actually appeared unstressed at theTohighly variable temperature regime (onePERMANOVA, I first standardized thethey never encounter in situ). It was later

data from a subset of ~93,000 contigs thatfound that all corals were of the same

passed all quality control. It is important togenotype

2014b),

note that, unlike virtually all RNA-Seq

signifying that all phenotypic plasticity

pipelines referenced in the literature (e.g.,

can be attributed to environmental, rather

Barshis et al., 2013), there was no

than

later

requirement that a contig must betranscriptomes

expressed by all samples; even those for(Mayfield et al., 2016c) and proteomes

which only 1 of the 12 samples expressed(Mayfield et al., 2016b, 2018a; Mayfield,

a particular gene were maintained in the2020) of a subset of 12 samples to makeanalysis. The omission of 0s from ‘OMICs

conjectures

how these corals

datasets likely stems from the early days ofacclimated to variable temperatures in thenext-generation technologies, in whichlaboratory, with the ultimate goal offew (if any) replicates were analyzed.

shedding light on the molecular basis of

When replication is limited, it is difficult

thermo-acclimatization and phenotypic

to discern whether a concentration of 0

plasticity in situ. In an effort to promote

actually reflects an absence of that analyte

datatransparency

in a sample or whether it was present but(discussed in more detail below), thesimply went unsequenced. Assuming

physiological and target gene expression

proper replication (n>2), if there is a genedata from Mayfield et al. (2012a, 2014b)

that is expressed by all replicates of one

from this same subset have been posted ontreatment and in none of the remainders,

JMP®

then this mRNA is likely to actually be the(Mayfield

genetic,

etal.,differences.

characterized

the

about

dissemination

and

We

Public:demonstratewithutilitymoste-of-corals-from-two-sites-to-sta/js-

developing

p/4blb_hY7xkwQ4srBMp55N.

describing the treatment effect (Mayfieldmechanistic

respectofhttps://public.jmp.com/packages/Respons

The transcriptome featuresinformative

the

to

hypotheses

over

et al., in review). If a second DEG is

125,000 contigs of both host coral andmeasured at 2-fold higher expression

Symbiodiniaceae

dinoflagellate

levels in one SO in the SHVTS, for(Cladocopium spp.) origin and can beinstance, it is unclear whether thisdownloaded

difference

from

the

S.

hystrix35

would

have

significant

Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

Fig. 2. A healthy Seriatopora hystrix colony (inset) and an actively bleaching, Seriatopora
spp.-dominated coral reef in the British Indian Ocean Territory (i.e., Chagos; May2016). The white scale bar in the inset is approximately 5 cm in length. Photo credits=珊瑚醫生.
implicationsforcellularbiology,the 2-fold-DEG.
especially given the well-establishedOf the ~93,000 contigs, I imported aabsence of congruency between generandom subset of 65,000 into PRIMER

expression and concentration of the(ver. 6) and created a EDM to assess inter-

respective protein in reef corals or

sampleSymbiodiniaceae (Mayfield et al., 2016c).

carried out because PRIMER currently

In contrast, if a gene is absent fromlimits analyses to 65,000 analytes (i.e.,

replicates of the stable TT, yet documented

columns). After generating a multi-

at high levels in those of the variable TT, it

dimensional scaling (MDS) plot (Fig. 3A)

is far more likely to play a role inand a PCA biplot (Fig. 3B), I then ran a 2-

acclimation to variable temperatures thanway PERMANOVA of SO, TT, and their

36

similarity.

Sub-selectionwasPlatax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

interaction. No random effects were

herein.) yet no TT or interaction (SO x TT)

considered. It is clear from Tab. 1 that alleffects (p>0.01). Given these findings, one

three simple random samples (SRS)

might question our treatise on TT-sensitive

yielded the same overall finding: strong

DCPs (Mayfield et al., 2016c); although

SO effect on the transcriptome (both coral

several genes were expressed only by

host & Symbiodiniaceae gene mRNAs

samples of one TT and in no replicates ofwere pooled in all analyses discussed

the other, the multivariate findings point toTab. 1. Permutational multivariate analysis of variance (PERMANOVA) of a partial Seriatopora
hystrix-Symbiodiniaceae transcriptome (Mayfield et al., 2016c). A type III sum of squares(SS) model (partial) with unrestricted permutation of raw data was run thrice (simple
random samples [SRS]1-3). Significant multivariate site of origin (SO; upwelling site
[Houbihu] vs. non-upwelling site [Houwan]) effects were documented in all three
iterations, and the mean SO effect p-value was 0.001. NA=not applicable. TT=temperature
treatment (stable vs. variable).
Sourcedf SS
Mean
Pseudo-F p#Permusquaretations
SRS1
SO
TT
SO x TT
Residual
Total
SRS2
SO
TT
SO x TT
Residual
Total
SRS3
SO
TT
SO x TT
Residual
Total
Average of three SRSSOTT
SO x TT
Residual
Total

1
1
1
8
11

1779
917.4
853.9
7375
10930

1779
917.4
853.9
921.9

1.930
0.99510.9263

0.001
0.444
0.668

992
989
985

1
1
1
8
11

1865
928.3
860.4
7412
11070

1865
928.3
860.4
926.5

2.013
1.002
0.9286

0.001
0.397
0.640

991
988
985

1
1
1
8
11

682.4
206.9
210.65
1965
3065

682.4
206.9
210.6
245.7

2.778
0.84200.8570

0.001
0.587
0.594

985
985
982

1
1
1
8
11

1442
684
642
5584
8355

1442
684
642
698

2.240
0.94570.9040

0.001
0.476
0.634

NA
NA
NA

37

Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

A)

Dimension 2

0.6

VV

stress=0.09
(6-D)

S

0.4

S

V

0.2
0.0

V

-0.2

S

-0.4

SS

-0.6
-1.0

-0.5

SV

B)
Component 2 (14%)

V
0.0
0.5
Dimension 1

S
100

1.0

VV

Houbihu

V

S

0

V

Houwan

S

V
V
S

-100

S=stable temperature-200 V=variable temperature
-400
-200
0
Component 1 (21.6%)

S

S

200

Fig. 3. MSA. Multi-dimensional scaling plot depicting similarity (Euclidean distance) among the
12 samples of the Seriatopora hystrix variable temperature study (A) and a principal
components analysis scoring plot (2-D) showing the same data (B). In both cases, data
were standardized prior to ordination. Biplot rays have not been shown in B since theywould obscure the 12 data points.
a more compelling SO effect, in whichconsequently guilty of data (p-value)-case we should have prioritized the SO

mining in a statistically unsupported

findings in the manuscript. We were

fashion.

38

Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

Non-parametric

MANOVAinherently fit a higher percentage of(NPMANOVA). When one is confident

variation within the dataset), the ability tothat the distance matrix robustly represents

detect an SO effect was inversely

similarity among samples (i.e., low MDS

correlated; statistically significant SO“stress” in the predicted vs. actual

effects were more likely to be documented

similarity

analysis),with only two dimensions. In this example,

permutation may be superfluous; the mean

the optimal dimensionality was six sincedistances within and among treatments inthis ordination is associated with ana EDM or BCSM may be sufficient for

acceptable stress (<0.2) and a highly

testing treatment effects. Although only

significant SO p-value. Please note that,two or three dimensions are normallyalthough the MDS plot in Fig. 3A wasportrayed in figs. (e.g., two dimensions incomputed across six dimensions, only theFig. 3), increasing dimensionality leads tofirst two have been presented.

[Shepard]

a better fit between predicted and actual
similarity (higher R

2

A PCA of the same dataset will give ain the Shepard

near-identical solution, and the ordination

diagram, or lower stress; Tab. 2). Instead,will actually be 100% identical if the data

the number of dimensions will likely be

are standardized prior to MDS (as was

dictated by the final NPMANOVA model.

conducted herein; Fig. 3B). Although PCA

In the example herein, there were 12 coralyields eigenvectors and eigenvalues thatsamples (3 in each of 4 interaction groups).

can be used to estimate treatment effects

However, since SO and TT have only 1 df

and the relative influence of various

each, the model’s residual term is 8. This

analytes, it cannot, in and of itself,means that the maximum number ofstatistically demarcate treatment effects

dimensions that can be included as Y terms(despite their being obvious in the case ofin the NPMANOVA is 8. For this reason, I

the SO effect shown in Fig. 3B). Therefore,

have computed the stress, the MANOVA

I recommend that ‘OMICs researchers

Wilks’ lambda for the entire model, and thestrongly consider MDS in place of (or, at

MANOVAforleast, in addition to) the far moredimensions ranging from 2 (the minimum)

commonly utilized PCA in presenting

to 8 (the maximum) in Tab. 2. It can be

multivariate ‘OMICs data simply because

seen that, although the predicted vs. actualof the direct link between the coordinates

similarity R (i.e., Shepard’s R ) increasedin the MDS plot and the corresponding

with

(as

PERMANOVA and/or NPMANOVA. In

expected since more complex models

contrast, PCA may better demonstrate theSO2increasing

effectp-values2

dimensionality

39Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

aforementioned high collinearity among(gen-reg) is superior to (& more robust

analytes (not evident in Fig. 3B sincethan)biplot rays were omitted), which would

penalizes against collinear model terms;

actually further invalidate the use of PSA

although the total number of DCAs may be(in addition to the #analytes>#samples

less than generated by RSA, the collective

issue raised above). Principal coordinates

DCA suite will be more informing (& lessordination (PCoA) could represent a

redundant) in model-building. Analytecompromise since it depicts inter-sample

clustering could also be considered.

similarity and features biplot rays showing

FDR-governed

Partial

least

RSA

since

squaresit(PLS).

relationships among response variables

PERMANOVA and NPMANOVA are notand experimental predictors (alongside thethe only means of depicting and analyzing

percent variation explained by each axis).

multivariate, highly collinear, “wide”

On the topic of inter-analyte collinearity, it

datasets in which there are many more

is worth noting here that, for thoseanalytes than samples (>92,000 vs. 12

interested in searching for DCAs in

herein); PLS is another such approach that

‘OMICs datasets, generalized regression

is rarely taken advantage of by coral

Tab. 2. Non-parametric multivariate analysis of variance (NPMANOVA) of a standardized coraltranscriptome. A Euclidean distance matrix was used in the multi-dimensional scaling
analysis with 2 to 8 dimensions. Please note that NPMANOVA cannot be undertaken with
>8 dimensions given the model’s degrees of freedom (df)- site of origin (SO; df=1) xtemperature treatment (TT; df=1)- and replication (n=3/SO x TT=12). Statisticallysignificant p-values (<0.01) have been highlighted in bold, as have typically publishable
stress levels (<0.1). No TT or interaction effects were documented for any model. Basedon these results, a similarity analysis with six dimensions represents the best compromise
in terms of limiting ordination stress while still enabling sufficient statistical power todetect a significant SO effect (see Fig. 3.).
#Dimensions

Shepard’s R2

StressWilks’ lambda (whole model) x 103

p-value (SO)80.79640.06050.2

0.1646

70.73570.07460.4

0.021860.67010.09042.7

0.004050.63740.11413.2

0.0004

40.61330.14524.4<0.0001

3

0.58310.197315.2<0.00012

0.5847

0.291356.9<0.000140

Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

biologists. In PLS, which bears similarity

21% of the variation in Y, it did clearlyto PCA in its data reduction approach,corroborate the aforementioned finding

latent variables (“projections to latentthat the transcriptome was more strongly

structures” being the original name) are

impacted by SO than TT (Tab. 3). It should

establishedmodel

be noted that the full PLS featuring 92,960

covariance between predictor (X) andgenes (standardized data) as Y and the SO,

response (Y) matrices (Cox & Gaudard,

TT, and SO x TT terms as X cannot be2013). In addition to the usual model

analyzed on a computer with 8 GB of

output terms (e.g., root mean square error),

RAM and a 1.7-Ghz Intel Core i7“variable importance” plots (VIP) areprocessor, though it is likely to yield agenerated such that users can best

similar finding: the SO effect on thedetermine which suites of analytes aretranscriptome >TT effect. When using themost influential in delineating treatment

SO, TT, and their interaction (threeeffects, as well as which treatment factors

separate models) as Y and the 92,960

drive the most variation across response

genes as predictors, a single latent factor invariables. PLS is widely used in marketing

each accommodated 47, 46, and 26% of

and has been more recently adopted in

the variation, respectively, and 43,903

metabolomic research, likely due to its(PRESS=0.64), 41,203 (PRESS=0.76),

accommodation

correlated

and 62,763 (PRESS=0.49) genes were

response (& even predictor) variables. It

characterized by VIP>0.8. Since nearly (oralso shines in response variable reduction

over in the case of SO x TT) 50% of theand so may be an alternative to gen-reg ingenes were included in the final models,robust DCA identification.

this suggests that PLS may not be thetosimultaneouslyofhighlyHerein several PLS models were built.

preferred means of reducing dataset

In the first, the six dimensions from thecomplexity (or identifying the most

MDS analysis (Fig. 3) were the Y terms

informative DCAs) in this particular(response variables), and the two treatment

example.

factors (SO & TT) were the predictors (X).

When using the 6D coordinates as Y

The resulting non-iterative PLS (NIPALS)

and SO alone as X, a PLS-basedalgorithm (KFold cross-validation of

discriminant analysis (DA) model could

seven) determined that the root mean

correctly predict the SO for 100% ofpredicted residual sum of squares (PRESS)

samples. When using all 92,960 genes asof 0.42 was minimized with a single latent

the Y in the PLS-DA, the misclassification

factor. Although the model explained only

rate was far higher: 5/12 (42%) called
41

Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

Data dissemination

incorrectly with respect to site. For TT
effects, 6D and 92,960-gene PLS-DA

Good data stewardship transcends

model misclassification rates were 2/12

simply identifying the best statistical(17%) and 6/12 (50%), respectively. In

approach for addressing the researchother words, the models had a greater

question at hand; it also hinges upon rapid

chance of correctly guessing the corals’ SO

and transparent data dissemination. Given(mean success rate of prediction=79%

thecorrect) than their experimental TT (67%scientists to “publish or perish,” data

correct); this is unsurprising given the

sharing typically occurs well after article

multivariate

ever-constantdemandonmosteffecttrend

publication, if at all. Although this indeed

PCA,

MDS,

limits data theft, in many cases such a

PERMANOVA, & NPMANOVA. Finally,significant amount of time passes between

the PLS-DA classification rates for the SOdata collection and data dissemination tox TT interaction group using the 6D andthe public that the coral(s) from which

92,960-gene data as Ys were the same assuch data were derived may no longer exist.

for SO: 100 and 58%, respectively

For instance, a coral may be sampled in(mean=79% correctly predicted).

May, used in an experiment in June, with

SO>TT

yielded/suggested

byTab. 3. Partial least squares variable importance plot (VIP) data generated upon using either themulti-dimensional scaling coordinates from six dimensions (“6D”) or the concentrationsof the 637 unique differentially expressed genes (“DEG”) as the Y and the two treatment
effects (& their interaction) as X. Model terms whose VIP were >0.8 (the commonly
accepted threshold for model inclusion; Cox & Gaudard, 2013) have been denoted byasterisks (*). Of the 762 DEGs whose FDRlogworths were >2, 558, 6, and 198 weresignificantly affected by site of origin (73.2%), temperature treatment (0.8%), and theirinteraction (26.0%), respectively (with 125 having been affected by more than one
experiment parameter, i.e., 637 unique DEGs).
X

VIP-6D

VIP-DEGsite of origin[Houbihu]

1.4132*

1.4680*site of origin[Houwan]

1.4132*

1.4680*site of origin[Houbihu] x temperature treatment[stable]

0.74160.9074*

site of origin[Houbihu] x temperature treatment[variable]

0.67150.9734*

site of origin[Houwan] x temperature treatment[stable]

0.76360.9295*site of origin[Houwan] x temperature treatment[variable]

0.64950.8602*42

Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

biopsies

analyzed

with‘OMICsboth publishable and of conservation

technologies in December. Then, the data

benefit may take months or even years

may be processed the next May, with thewith a team of dedicated researchers. For

article written the next December. After 6-

these reasons, there has been a push to

12 months of peer review and another 6-12

develop in situ diagnostic systems formonths of revisions, the data may finallycoral health (Mayfield & Chen, 2019). To

reach the public 2-3 years later. Although

use an example from work currently being

the article certainly benefits the authors’

conducted by scientists

careers, it does beg the question as toAtlantic

whether the data achieved what may, in

Meteorological Laboratory (AOML), if amany cases, have been the primary goal ofproteomic analysis of environmentallythe study: to aid in the ultimate

challenged corals reveals that certain

conservation of that coral (& the reef

proteins show spikes in concentration inframework in which it is embedded). Yes,

visibly healthy corals that later proceed tothe data may later be used to better manage

bleach, their concentrations could be

the same reef, even if the study corals havemeasured in “test” field samples todied, but the point is that the data

determine which colonies and reefs are atdissemination process is nearly always too

most risk of bleaching as seawater

slow to benefit the resident corals in atemperatures rise (univariate biomarker

timely fashion (Mayfield & Chen, 2019),

approach). Antibodies raised against suchand proactive endeavors are certainly

protein biomarkers could be incorporated

doomed to fail.

into microfluidic chips to where the data

Slow data dissemination can beat

NOAA’s

Oceanographic

andare obtained while still at sea, not months

combatted on at least two fronts: rapid

later like in the example above.

publishing of data online in open-accessIfacandidatebiomarker-basedformat before manuscript submission (Fig.

diagnostic approach is considered overly

4) and expediting data acquisition itself.

simplistic or lacks predictive power with

Regarding the latter, a typical ‘OMICs

respect

pipeline was used as the example in the

consuming

preceding paragraph; although extractions

could be undertaken; Fig. 5 presents one

can now be done in bulk, there is nearlyexample of how this could be achieved. As

always a bioinformatics bottleneck. Even

molecular biology and data analysis

if a well-established pipeline is employed,

technologies continue to improve, it is no

making sense of the data to where they are

longer inconceivable that a coral could be43

tohealth,the‘OMICs-scale

more

time-

alternative

Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

sampled on Monday, with the ‘OMICs-

we will soon know exactly whichscale data obtained by the end of the week.

molecules are most informative with

Given the concerted effort by the coral reef

respect to resilience by having analyzed

research field to elucidate the molecular

their concentrations in experiments inbiologyanthozoan-dinoflagellate

which common physiological benchmarks

endosymbioses (sensu Peng et al., 2011),

like growth and endosymbiont density (Fig.

ofFig. 4. JMP® Public. In addition to simply uploading data tables alongside manuscripts topromote data transparency, or posting data tables on public repositories (e.g., dryad,
Figshare, & Zenodo), data can be shared interactively by websites such as JMP® Public.
In this example, the MDS and PCA plots of Fig. 3 are shown above an effect size vs.
FDRLogworth (inverse log10 of p) volcano-like plot (logworth of 2=p of 0.01). Readers
can download the data table and plots to their devices, or, alternatively, directly manipulatethem on the website without the need for third party software. With this approach,interested readers can re-analyze data and attempt to reproduce findings from publishedmanuscripts. Green icons=Houbihu. Black icons=Houwan.
44

Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

6) are also measured (sensu Mayfield et al.,even cryopreservation (Lin & Tsai, thisin review). Although the health of the coralissue) represents the only means by which

would not be known while still on the divecorals and their genetic material willboat with this approach, the diagnostic

persist beyond 2100. These severe threats

speed might still be amenable to some sortalso signify that poor data and statisticalof proactive conservation measure, even if

stewardship not only thwart progress in theit simply amounts to “triage,” whereby

field, but they could actually detrimentallycolonies (or, more likely, reefs) are ranked

affect the very coral reef ecosystems theon a scale of 1 (highly likely to bleach) to

researchers intend to conserve; statistical

10 (the most resilient corals studies to

mistakes resulting in false positive resultsdate).

could, for instance, lead to management

Efforts are currently being made tointervention at reefs that should not havecompare these “bottom-up” (molecularbeen prioritized (i.e., resilient ones) at thebiology-derived) coral health predictions

expense of more stress-prone reefs (or viceagainst(global-scale)versa, i.e., inadvertently prioritizing reefs

analyses of satellite temperature data (vanwith so little ability to withstand climate

Hooidonk et al., 2020), which havechange and other anthropogenic stressors

projected most reefs to begin bleachingas to be beyond saving). By employing

annually by 2040. These analyses willmore statistically rigorous MSA prior toallow us to identify “refugia,” reefs that,the more commonly utilized univariate

either due to environmental forcing or theapproaches featured in most coral biology

unique physiologies of the resident corals

studies, not only will the dataset have been

(Brown et al., 2000), resist widespreadrealized to its full potential, but greater

bleaching. We had previously prioritizedinsight into the health of the experimental

upwelling reefs such as those discussed

or field corals will have been gained.

hereinenvironmental

Furthermore, MSA will allow us to makeconditions may “stress-harden” corals

predictions as to which corals may have

(Safaie et al., 2018; Storlazzi et al., 2020,

the physiological capacity to acclimatize

but

to

“top-down”

since

see

variable

Chollett

Unfortunately,etHoubihual.,2010.).

GCC

and

other

environmental

experienced

challenges, and which may only avoid

catastrophic bleaching in 2020, leading

extinction via cryopreservation and othersome to wonder whether ex situ husbandry

human-assisted preservation efforts (sensu(Lin et al., 2019; Mayfield et al., 2019b;

Lin & Tsai, this issue).

Chang et al., 2020; Huang et al., 2020) or
45

Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

Fig. 5. Similarity analysis of coral health. In this example, molecular signatures are defined withmulti-dimensional scaling (MDS) in at least two dimensions for healthy (i.e., resilient)corals (left image & “X’s” in MDS plot) and stress-susceptible (i.e., bleaching-prone)corals (right image & “Y’s” in MDS plot). “Test” samples “Z-Sample 1” (blue) and “AASample 2” (orange) are then collected from the field, analyzed, and, based on theirpositions on the MDS plot (i.e., proximity to experimental coral data points), hypothesized
to represent healthy and stressed corals, respectively. Each polyp is approximately 1 mm
in diameter.

46

Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

Fig. 6. Coral health diagnostics. Molecular techniques alongside traditional physiological benchmarks (e.g.,
growth) can be used to make conjectures about current coral health as well as future resilience toenvironmental change. Please see Mayfield & Chen (same issue) for details on undertaking predictivemodeling with ‘OMICs data. In this example, “Braindon” has demonstrated aberrant respiration withanomalously low endosymbiont densities; given these ailments, Dr. Coral (珊瑚醫生) recommends that hebe cooled off and consume large quantities of plankton under photosynthetically active radiation levels near
200 µmol m-2 s-1.

47

Platax 17: 27-52, 2020
doi: 10.29926/platax.202012_17.0003

Chen, T.Y., G.W. Hwang, H.J. Lin, A.B.
Mayfield & C.P. Chen. 2019. The
development of a habitat suitability
model for sub-tropical tidal flat fiddler
crabs. Ocean and Coastal Management,
182:104931.
Chen, T.Y., G.W. Hwang, A.B. Mayfield, C.P.
Chen & H.J. Lin. 2017b. The
relationship between intertidal soil
composition and fiddler crab burrow
depth. Environmental Engineering,
100:256-260.
Cheng, Y.R., P.J. Meng, A.B. Mayfield & C.F.
Dai. 2016. Copepods associated withscleractinian corals: a worldwide
checklist and a case study of their impact
on the reef-building coral Pocillopora
damicornis(Linnaeus,
1758)(Pocilloporidae). Zootaxa, 4174(1):291345.
Chollett, I., P.J. Mumby & J. Cortés. 2010.
Upwelling areas do not guarantee refuge
for coral reefs in a warming ocean.
Marine Ecology Progress Series, 416:4756.
Clarke, K.R., R.N. Gorley, P.J. Somerfield &R.M. Warwick. 2014. Change in marine
communities: an approach to statisticalanalysis and interpretation, 3rd edition.
PRIMER-E, Plymouth, UK.
Cox, I. & M. Gaudard. 2013. Discovering
partial least squares with JMP® . SAS
Institute, Inc., Cary, NC, USA.
Desalvo, M.K, C.R. Voolstra, S. Sunagawa,
J.A. Schwarz, J.H. Stillman, M.A.
Coffroth, A.M. Szmant & M. Medina.
2008. Differential gene expression
during thermal stress and bleaching in
the Caribbean coral Montastraea
faveolata. Molecular Ecology, 17(17):3952-3971.
Enochs, I.C., N. Formel, D.P. Manzello, J.
Morris, A.B. Mayfield, A. Boyd, et al.
2020. Coral persistence despite extreme
periodic pH fluctuations at a volcanicallyacidified Caribbean reef. Coral Reefs,
39:523-528.
Huang, Y.L., A.B. Mayfield & T.Y. Fan. 2020.

Acknowledgements
Thanks are given to the Fulbright and
MacArthur Foundations for funding thiswork. I would also like to thank Mr. John
Powell(JMP)

forassistancewithinteractive HTML. All opinions are myown and do not necessarily represent thoseof the United States government.

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