††thanks: These authors contributed equally.††thanks: These authors
contributed equally.

# Electrically empowered microcomb laser

Jingwei Ling  Department of Electrical and Computer Engineering, University of
Rochester, Rochester, NY 14627, USA  Zhengdong Gao  Department of Electrical
and Computer Engineering, University of Rochester, Rochester, NY 14627, USA
Shixin Xue  Department of Electrical and Computer Engineering, University of
Rochester, Rochester, NY 14627, USA  Qili Hu  Institute of Optics, University
of Rochester, Rochester, NY 14627, USA  Mingxiao Li  Department of Electrical
and Computer Engineering, University of Rochester, Rochester, NY 14627, USA
Kaibo Zhang  Institute of Optics, University of Rochester, Rochester, NY
14627, USA  Usman A. Javid  Institute of Optics, University of Rochester,
Rochester, NY 14627, USA  Raymond Lopez-Rios  Institute of Optics, University
of Rochester, Rochester, NY 14627, USA  Jeremy Staffa  Institute of Optics,
University of Rochester, Rochester, NY 14627, USA  Qiang Lin
<EMAIL_ADDRESS>Department of Electrical and Computer Engineering,
University of Rochester, Rochester, NY 14627, USA  Institute of Optics,
University of Rochester, Rochester, NY 14627, USA

###### Abstract

Optical frequency comb underpins a wide range of applications from
communication, metrology, to sensing. Its development on a chip-scale platform
– so called soliton microcomb – provides a promising path towards system
miniaturization and functionality integration via photonic integrated circuit
(PIC) technology. Although extensively explored in recent years, challenges
remain in key aspects of microcomb such as complex soliton initialization,
high threshold, low power efficiency, and limited comb reconfigurability. Here
we present an on-chip laser that directly outputs microcomb and resolves all
these challenges, with a distinctive mechanism created from synergetic
interaction among resonant electro-optic effect, optical Kerr effect, and
optical gain inside the laser cavity. Realized with integration between a
III-V gain chip and a thin-film lithium niobate (TFLN) PIC, the laser is able
to directly emit mode-locked microcomb on demand with robust turnkey operation
inherently built in, with individual comb linewidth down to 600 Hz, whole-comb
frequency tuning rate exceeding $\rm 2.4\times 10^{17}$ Hz/s, and 100%
utilization of optical power fully contributing to comb generation. The
demonstrated approach unifies architecture and operation simplicity, high-
speed reconfigurability, and multifunctional capability enabled by TFLN PIC,
opening up a great avenue towards on-demand generation of mode-locked
microcomb that is expected to have profound impact on broad applications.

Optical frequency comb is a coherent light source that consists of many highly
coherent single-frequency laser lines equally spaced in the frequency domain.
Its development has revolutionized many fields including metrology,
spectroscopy, and clock diddams2020optical . In recent years, significant
interest has been attracted to the generation of phase-locked optical
frequency comb in on-chip nonlinear microresonators kippenberg2018dissipative
; gaeta2019photonic ; chang2022integrated . The superior coherence offered by
these mode-locked microcombs has rendered a variety of important applications
including data communication marin2017microresonator , spectroscopic sensing
yang2017microresonator , optical computing xu202111 ; feldmann2021parallel ,
range measurement suh2018soliton ; trocha2018ultrafast ;
riemensberger2020massively ; liu2020monolithic , optical spencer2018optical
and microwave liang2015high  frequency synthesis, with many others expected in
the years to come.

Despite these great progresses, challenges remain in the development and
application of microcombs. The first is the difficulty in triggering comb
mode-locking due to the intrinsic device nonlinearities. Recently, self-
starting operation has been demonstrated to address this issue he2019self ;
shen2020integrated ; bai2021brillouin ; rowley2022self . Their
implementations, however, require sophisticated system pre-configuration and
careful balance of specific nonlinear dynamics, which are difficult to apply
in most practical devices. The second is the low power efficiency of soliton
microcomb generation due to the pump-laser-cavity frequency detuning induced
by soliton pulsing. Although pulse pumping obrzud2017temporal  or auxiliary-
resonator enhancement xue2019super ; bao2019laser  can improve the generation
efficiency, they require delicate synchronization in time or resonance
frequency and the difficulty of soliton initialization remains the same. The
third is the limitation in the comb controllability due to the monolithic
nature of the comb generator that is difficult to change after the device is
fabricated. Piezoelectric effect could be used to deform the comb resonator
liu2020monolithic , which, however, exhibits limited tuning speed and
efficiency due to its slow mechanical response. To date, the majority of comb
generators still have to rely on external laser control to adjust the
microcomb state.

Recently, there are significant advances in chip-scale integration of
semiconductor lasers and nonlinear comb generators shen2020integrated ;
stern2018battery ; raja2019electrically ; xiang2021laser , in which a diode
laser produces single-frequency laser emission to pump a hybridly or
heterogeneously integrated external nonlinear resonator to excite microcombs.
Such a fully integrated system shows great promise in improving the size,
weight, and power consumption. However, the nature of soliton comb generation
remains essentially the same, with all the above challenges persistent. Up to
now, the realization of an integrated comb source free from these challenges
remains elusive.

Figure 1:  Device concept of the integrated comb laser. a. Conceptual
illustration of the comb generation and mode-locking principle, in which
electro-optic (EO) comb generation, Kerr comb generation, and broadband
optical gain all work synergistically together inside a single laser cavity
for on-demand generation of mode-locked soliton comb. In addition, the laser
comb output is detected and fed back to the laser cavity for resonant EO
modulation to realize a self-sustained operation. b. Schematic of comb laser
cavity structure formed by hybrid integration between a RSOA chip and a LN
external cavity chip. Two different configurations are employed: A, cavity-
enhanced (CE) comb laser structure in which the LN external cavity is formed
mainly by an embedded high-Q racetrack resonator together with a broadband
Sagnacloop mirror; B, Fabry-Perot (FP) comb laser in which the LN external
cavity is formed by an EO phase modulation section together with an a
broadband Sagnac loop mirror. c. Photo of a CE comb laser, showing that the
RSOA is edge-coupled to the LN external cavity chip. d. Zoom-in photo showing
the edge-coupling region between the RSOA and the LN chip. e., Photo of the
racetrack resonator and the loop mirror in a CE comb laser. f. Photo of the EO
phase modulator and the loop mirror in an FP comb laser.

Here we present a fundamentally distinctive approach to resolve all these
challenges in a single device. Figure 1a shows the device concept. In contrast
to conventional approaches that rely solely on a single mechanism – either
optical Kerr or electro-optic effect – for comb generation while with external
pumping, we utilize the resonantly enhanced electro-optic (EO) modulation to
initiate the comb generation, the resonantly enhanced optical Kerr effect to
expand the comb bandwidth and phase-lock the comb lines, and the embedded
III-V optical gain to sustain and stabilize the comb operation. Moreover, the
resulting coherent microwave (via optical detection) is fed back to the EO
comb to further enhance the mode-locking, leading to unique self-sustained
comb operation.

We realize this approach by integrating a III-V gain element with a thin-film
lithium-niobate (LN) photonic integrated circuit (PIC) to produce a III-V/LN
comb laser (Fig. 1b). LN PIC has attracted significant interest recently
boes2018status ; lin2020advances ; zhu2021integrated ; boes2023lithium  for a
variety of applications including high-speed modulation wang2018integrated ;
he2019high , frequency conversion wang2018ultrahigh ; lu2020toward ;
mckenna2022ultra , optical frequency comb he2019self ; zhang2019broadband ;
gong2020near , and single-frequency lasers de2021iii ; han2021electrically ;
li2022integrated ; ling2023self . Here, we unite active EO modulation with
passive four-wave mixing (FWM) in a dispersion-engineered high-Q laser cavity
for the on-demand generation of mode-locked soliton microcomb, which naturally
leads to self-starting full turnkey operation simply by turning on/off either
the RF signal driving the comb resonator or the electric current driving the
gain element. As the comb modes extract energy directly from material gain,
100% of the optical power contributes directly to the comb generation.
Moreover, the strong electro-optic effect of the LN cavity enables high
tunability and reconfigurability of the produced microcomb. With this
approach, we are able to produce broadband highly coherent microcombs, with
individual comb linewidth down to 600 Hz, frequency tunability of over $\rm
2.4\times 10^{17}$ Hz/s for the entire microcomb, microwave phase noise down
to -115 dBc/Hz at 500 kHz frequency offset, and a wall-plug efficiency
exceeding 5.6%. The simplicity of the demonstrated approach opens up a new
path for on-demand generation of mode-locked microcombs that is expected to
have profound impact on the broad applications in high-precision metrology,
telecommunications, remote sensing, clocking, computing, and beyond.

Comb laser structure design

The III-V/LN microcomb laser is formed by integrating an InP reflective
semiconductor optical amplifier (RSOA) with an LN external cavity chip via
facet-to-facet coupling. We employ two types of laser cavity structures for
the purpose, as shown in Fig. 1b. Chip A laser structure is embedded with a
dispersion-engineered EO microresonator and Chip B laser structure consists of
a simple EO phase modulation waveguide section. The advantage of Chip-A
resonator-type structure is that the high-Q microresonator offers strong
cavity enhancement for comb generation and mode-locking, which we term as the
cavity-enhanced (CE) comb laser. The benefit of the Chip-B Fabry-Perot-type
structure is that it offers flexibility of mode-locking operation, which we
term as the Fabry-Perot (FP) comb laser.

Figure 2:  Lasing performance of a CE comb laser. a. Schematic of the
experimental setup for comb laser characterization. RSOA is powered by a
stable current source and an RF signal generator is used to drive the
racetrack resonator. OSA: optical spectrum analyzer; AC: autocorrelator; PD:
photo-detector; ESA: electrical spectrum analyzer; OSC: real-time
oscilloscope; PNA: phase noise analyzer. b. Optical spectrum of the comb laser
output. Off state: single mode lasing with the RF driving signal turned off.
On state: comb lasing when the RF driving signal is turned on. Inset:
Autocorrelation trace of the laser output pulses, in the ”comb on” state, in
which the blue curve shows the experimental data, dotted curves show the the
fitted autocorrelation profiles from individual ${\rm sech^{2}}$ pulses, and
the dashed curve show the overall fitted autocorrelation trace. The
autocorrelation is recorded directly from the laser output pulses without
dispersion compensation or pulse shaping. c. Electrical spectrum of the beat
note detected from the comb laser output. The red and blue curves show the
comb-on and comb-off (single-mode lasing) states, respectively, corresponding
to those in b. Gray curve shows the noise background of the optical detector,
as a comparison. The inset shows the detailed spectrum of the RF beat note at
39.58 GHz. d. Phase noise spectrum of the 39.58-GHz RF beat note (red) and the
RF driving signal (blue). e. Phase noise spectrum of the CE comb laser output
measured with a self-heterodyne method. Red and green curves show for two
different comb states, and blue curve shows for the comb-off (single-mode
lasing) state. Inset shows the corresponding frequency noise spectrum of the
three laser states. f. P-I-V curve of the CE comb laser, in which the red and
blue curves show the L-I and I-V curves, respectively. g - j. Turnkey
operation of the comb laser at two different speed of 2 Hz (g, h) and 200 Hz
(i, j), respectively. Red curve shows the normalized driving RF power and blue
curve shows the beating signal between the comb laser ouput and an external
reference laser at 1582 nm. h and j show the zoomed-in signal for the on/off
states, respectively.

In the CE comb laser, the group-velocity dispersion (GVD) of the racetrack
microresonator (intrinsic optical Q $\sim 1.6\times 10^{6}$) is engineered to
be small but slightly anomalous to support broadband comb generation. At the
same time, the pulley coupling regions are specially designed for uniform
close-to-critical coupling to the resonator over a broad telecom band. Such a
design ensures high loaded optical Q ($\rm\sim 5\times 10^{5}$) of the
resonator uniformly across a wide spectral range which is crucial both for
enhancing the comb generation and mode-locking and for efficient light
coupling into/out of the microresonator. Moreover, we also engineer the GVD of
straight waveguide sections outside the racetrack resonator to compensate for
that of the RSOA section so as to minimize the overall laser cavity GVD. At
the same time, the overall optical path length of the laser cavity is designed
to be an integer multiple of the racetrack resonator’s for matching their
resonance mode frequencies and round-trip group delay. The GVD of the FP comb
laser is engineered in a similar fashion. The free-spectral range (FSR) of the
racetrack resonator is designed to be around 40 GHz to better accommodate
bandwidths of RF filter and amplifier after detection of comb beating signal.
In contrast, the FP comb laser is designed to have a small FSR of around 10
GHz for easy operation of harmonic mode locking.

Figure 3:  Harmonic mode-locking of a FP comb laser with an FSR of 9.817 GHz.
Third harmonics (29.45 GHz) and fourth harmonics (39.27 GHz) are separately
used as driving signals. a. Schematic of the experimental setup for harmonic
mode-locking of the comb laser. b. Optical spectrum of the laser output with
third-harmonic mode-locking, by driving the phase modulator with a RF signal
at 29.45 GHz. c. Optical spectrum of the laser output with fourth-harmonic
mode-locking, by driving the phase modulator with a RF signal at 39.27 GHz. In
b and c, the left insets shows the electrical spectrum of the RF beat note
detected from the output laser comb, and the right insets show the
autocorrelation trace of the laser output pulses with dashed curve showing the
fitted individual pulses. Same as Fig. 2b, autocorrelation is recorded
directly from the laser output pulses without dispersion compensation or pulse
shaping.

To support the broadband operation, the Sagnac loop mirror employs an
adiabatic coupling design ramadan1998adiabatic  to achieve high reflection and
feedback with a reflectivity of $>$95% over a broad spectral band of 1500-1600
nm. On the other hand, a horn taper waveguide is designed on the LN chip to
minimize the coupling loss between the LN chip and the RSOA gain chip. The
RSOA exhibits a broadband gain in the telecom L-band, with a 3-dB bandwidth of
$>$40 nm. Fig. 1c-f show the device structures. Details about the design
parameters and the characterization of the laser structures are provided in
the Supplementary Information (SI).

Comb laser performance

To excite the mode-locked microcomb, we first launch a single-frequency RF
signal to drive the racetrack resonator of the CE comb laser (Fig. 2a), with a
frequency of 39.58 GHz that matches its FSR. Before the RF signal is applied,
the device exhibits single-mode or multi-mode lasing, with an example shown in
the blue curve of Fig. 2b. However, A microcomb is readily produced as soon as
the RF signal is applied, with an optical spectral bandwidth of about 20 nm
(Fig. 2b, red curve). Mode-locking of the comb is verified by the clean RF
tone at 39.58 GHz detected from the beating between comb lines (Fig. 2c), as
well as the autocorrelation trace from the laser output pulses (Fig. 2b,
inset). The 39.58-GHz RF tone exhibits a high signal-to-noise ratio of 79 dB
(Fig. 2c, inset), whose phase noise spectrum matches identically the driving
RF source (Fig. 2d), showing the preservation of the relative phase coherence
between comb lines via mode-locking. Mode-locking of the comb is also clearly
evident by the clean noise floor around the DC region in the RF spectrum (Fig.
2c. See SI for details), where the zero extra noise from the mode-locked comb
state infers that all the comb lines of the entire comb are phase-locked
together.

The underlying mechanism responsible for mode-locking dominantly contributes
from the combined resonant EO modulation and optical Kerr effect, in which the
EO modulation produces EO sidebands to initiate the comb generation while the
optical Kerr effect broadens the comb spectrum and phase-locks the comb lines
(Fig. 1a). Indeed, the laser is able to produce mode-locked soliton pulses in
the absence of EO modulation (while with a narrower spectrum), in which only
the optical Kerr effect is responsible for mode-locking. The detailed
theoretical modeling and testing results are provided in SI. In Fig. 2c, the
small RF tone around the half-harmonic at 19.79 GHz indicates certain comb
dynamics. It can be eliminated by reconfiguring the laser and one example is
shown in SI which exhibits a clean single RF beating tone and a well-defined
${\rm sech^{2}}$-shaped soliton pulse spectrum. The two lasers mainly differ
in their overall dispersion of the laser cavity, indicating that the device
dispersion plays an important role on the comb spectrum. The two-sidelobe
feature of the comb spectrum in Fig. 2b implies that the output pulses are
likely to be mode-locked two-color pulses in which the two color pulses bounds
with each other via certain interpulse interaction liao2020dual . Its exact
nature, however, will require further exploration. The comb spectrum can be
reconfigured by changing the power or frequency of the RF driving signal,
whose details are provided in the SI.

Figure 4:  Fast frequency tuning of the whole lasing comb. a. Left panel:
Schematic of the setup for comb frequency tuning, in which a triangular-
waveform electrical signal produced by an arbitrary waveform generator (AWG)
is used to drive the racetrack resonator of the CE comb laser together with
the 39.58-GHz mode-locking RF signal. Middle panel: Conceptual illustration of
the comb frequency tuning process, showing the laser frequencies of the comb
are tuned together as a whole. Right panel: Schematic showing the
corresponding sideband creation around the comb lines, introduced by
triangular-waveform frequency modulation. b, c, d. Time-frequency spectra of
the beatnote between the comb laser output and a referenced laser operatoing
at a fixed wavelength of 1582 nm, at the modulation speed of 1, 10, and 100
MHz, respectively. The dashed curves show the corresponding triangular-
waveform EO tuning signal. Bottom panels: Corresponding relative frequency
deviation at each modulation speed. e, f, g. Electrical spectrum of the
39.58-GHz beat note detected from the laser output comb, at modulation speed
of 1 MHz (e), 10 MHz (f), and 100 MHz (g), respectively. h. Laser frequency
tuning efficiency recorded at different modulation speeds.

In addition to the high coherence between the comb lines, the comb laser also
exhibits narrow linewidth on its individual comb lines. To show this feature,
we employ the correlated self-heterodyne method camatel2008narrow ;
yuan2022correlated  to characterize the overall linewidth of the whole comb
laser by launching the entire comb for linewidth measurement (rather than
characterizing individual comb lines themselves) (See SI for details). The
recorded phase noise spectrum is shown in Fig. 2e, which indicates a white
frequency-noise floor of $\sim$350 $\rm Hz^{2}/Hz$ (Fig. 2e, inset) that
corresponds to a laser linewidth of $\sim$2 kHz. The linewidth of the comb
lines can be decreased further and an example is shown in Fig. 2e for a
slightly different comb state produced from the same laser, which exhibits a
white frequency-noise floor of $\sim$100 $\rm Hz^{2}/Hz$ (Fig. 2e, inset) that
corresponds to a laser linewidth as low as $\sim$600 Hz. Note that these
values represent the overall linewidth contributed from the entire comb, which
indicates the upper limit of the intrinsic linewidth of individual comb lines.

Figure 2f shows the current-dependent characteristics of the comb laser, which
exhibits a low threshold current of 50 mA, indicating the low overall loss of
the integrated laser. The comb laser produces an optical output power of 11 mW
at a pumping current of 275 mA and a pumping voltage of 1.4 V, which
corresponds to a wall-plug efficiency of 2.8%. As the laser has two output
ports (Fig. 1b) that emit the same amount of optical power, the total wall-
plug efficiency of the laser is thus 5.6%. This level of wall-plug efficiency
is on par with other integrated external-cavity semiconductor lasers recently
developed xiang2021high ; porter2023hybrid . Intriguingly, the comb power
increases with increased driving RF power, whose details are provided in the
SI. Note that the total optical power contributes fully to the generated comb,
in strong contrast to conventional Kerr solitons or EO combs in which the
major optical power remains in the residual pump wave with low comb generation
efficiency.

A distinctive feature of the comb laser is that the produced comb can be
switched on/off on demand by simply switching on/off the driving RF signal. To
show this feature, we beat the comb with a reference single-frequency laser
operating at the wavelength of 1582 nm that is inside the comb spectrum, and
monitor the beating signal with the RF driving signal being turned on/off. As
shown in Fig. 2g and i, the beating signal follows faithfully the driving RF
signal. The coherent beating signal shows up readily when the RF driving is
on, indicating the generation of the mode-locked comb. The beating signal
disappears right after the RF driving is off, indicating the shutoff of the
comb state. Same phenomenon is observed when the reference laser is tuned to
other wavelengths within the comb spectrum.

Similar phenomena are observed in the FP comb laser, while generally with
smaller spectral extents due to the lack of cavity enhancement. The FP comb
laser, however, exhibits a distinctive feature in that it can be flexibly
mode-locked at higher harmonics of the laser cavity FSR. Fig. 3 shows this
feature. We are able to achieve third- and fourth-order harmonic mode-locking
by applying an RF signal to the phase modulation section of the FP comb laser,
with a frequency of 29.45 and 39.27 GHz, respectively, that are three and four
times of the laser FSR (9.817 GHz). Again, mode locking of the combs is
clearly verified by the detected RF beating signal from the combs with a SNR
of 77 dB, as well as by the autocorrelation traces from the laser output
pulses (Fig. 3b,c, insets).

Figure 5:  Self-sustained operation of the CE comb laser with feedback
locking. a. Schematic of self-feedback locking of the CE comb laser. b.
Optical spectrum of the comb laser output at a driving current of 285 mA. c -
e. Optical spectrum (d) and optical power (e) of the comb laser output as a
function of the RSOA driving current (c). f. Electrical spectrum of the
39.58-GHz beat note detected from the laser output comb, with a driving
current of 60 mA. g. Phase noise spectrum of the detected 39.58-GHz beat note.

High-speed frequency tuning of the comb laser

Another distinctive characteristic of the comb laser is that the laser
frequencies of the entire mode-locked comb can be tuned cohesively at an
extremely high speed. To show this feature, we apply a triangular-waveform
electric signal – together with the 39.58-GHz RF driving signal – to the
racetrack resonator of the CE comb laser as shown in Fig. 4a. While the
39.58-GHz RF driving signal supports the mode-locking process, the triangular-
waveform electric signal will adiabatically tune the resonance frequencies of
the racetrack resonator, thus tuning the laser frequencies of the entire mode-
locked comb together as a whole.

To show this feature, we beat the comb with a narrow-linewidth reference CW
laser at 1582 nm that is about 15 GHz away from a comb line, and monitor the
beating signal in real time. At the same time, we monitor the spectrum of the
recorded 39.58-GHz RF tone from the beating between the comb lines (See SI for
details of the setup). The frequency dynamics of the 15-GHz beating signal
with the reference laser show the frequency tuning of the comb line nearby
while the 39.58-GHz RF tone from the comb line beating indicates the quality
of mode locking during the frequency tuning. Fig. 4f-h show the temporal
variation of the 15-GHz beating signal at different modulation speeds of 1,
10, 100 MHz. They show clearly that the frequency tuning of the comb line
follows faithfully the waveform of the driving triangular-waveform electric
signal at all modulation speeds, with a deviation of no more than 5%. In
particular, the recorded 39.58-GHz RF tone from the comb line beating (Fig.
4e-g) remains unchanged during the frequency tuning, except with created
modulation sidebands that simply results from the laser frequency modulation
(see also Fig. 4a, right figure). This observation confirms that the phase-
locking between the comb modes is fully preserved during the high-speed
frequency tuning process, indicating that the entire mode-locked comb is tuned
in its frequencies as a whole, without any perturbation to the comb mode
spacing. This is in strong contrast to other comb modulation approaches
liu2020monolithic ; riemensberger2020massively ; he2023high  where the comb
mode spacing is seriously impacted by external modulation. The frequency
tuning range of 1.2 GHz at the modulation speed of 100 MHz (Fig. 4h)
corresponds to a frequency tuning rate as high as $\rm 2.4\times 10^{17}Hz/s$
for the comb. Both the frequency tuning rate and tuning speed are orders of
magnitudes higher than the piezoelectric tuning and the external pump
modulation approaches liu2020monolithic ; riemensberger2020massively , which
are constrained only by the photon lifetime of the high-Q racetrack resonator.
As shown in Fig. 4e, the device exhibits a frequency tuning efficiency of
about 0.2–0.8 GHz/V depending on the modulation speed, which is more than an
order of magnitude higher than the piezoelectric approach liu2020monolithic .
The tuning efficiency can be further doubled by employing both sets of driving
electrodes of the racetrack resonator (Fig. 4a).

Feedback mode-locking of the comb laser

So far, the comb laser utilizes an external RF signal to support the mode-
locking. This signal, however, can be removed by feeding the coherent
39.58-GHz RF tone detected from the comb mode beating directly back to the
comb laser cavity to sustain the mode-locking, resulting in unique stand-alone
self-sustained comb lasing operation. Figure 5a illustrates this approach. The
comb laser output is detected by a high-speed optical detector whose output RF
signal is amplified to an adequate amplitude, filtered to suppress excess low-
frequency noises, adjusted with appropriate phase, and then fed back to drive
the racetrack resonator of the CE comb laser.

As shown in Fig. 5b, a broadband microcomb with a spectrum covering about 50
nm and an optical power of 8.5 mW is produced on chip with a driving current
of 285 mA. Indeed, the microcomb is readily produced on demand as soon as the
driving current is turned on, with a driving current as low as 60 mA, as shown
in Fig. 5c-e. Mode locking of the comb is clearly evident by the clean
39.58-GHz RF tone detected from the comb mode beating (Fig. 5f), which
exhibits a SNR of 65 dB and a narrow 3-dB linewidth of 1.5 kHz. The phase
noise of the RF beating signal reaches a level of -90 dBc/Hz at an offset
frequency of 60 kHz, which is considerably lower than the laser heterodyne
beating approach xiang20233d  and is comparable to that of free-running
optical Kerr soliton microcombs liu2020photonic ; wang2021towards ; he2023high
. The optical spectral bandwidth and the output power of the comb laser
increase considerably with increased driving current (Fig. 5d). This is
expected since the increased optical power of the mode-locked comb inside the
high-Q racetrack resonator would significantly enhance the optical Kerr effect
and the resulting four-wave-mixing process to broaden the comb spectrum. No
saturation is observed on the comb spectral bandwidth as the current
increases.

Discussion

The attainable extent of the microcomb spectrum or soliton pulse width in
current devices is primarily limited by the available optical power inside the
cavity and the group delay mismatch between the enhancing resonator and the
main laser cavity. For the former, it can be improved by either reducing the
loss (_e.g._ , improving the RSOA-LN chip coupling efficiency) or increasing
the optical gain (_e.g._ , using a higher-power RSOA) inside the laser cavity.
For the latter, our theoretical modeling (see SI) shows that the formation of
ideal ultrashort soliton pulses would require that the roundtrip time of the
main laser cavity be integer times that of the enhancing racetrack resonator.
In current devices, however, there is a certain amount of mismatch which
limits the comb spectrum and the coherence of the mode-beating RF tone. This
problem can be resolved by further optimization of the roundtrip length of the
main laser cavity and introducing tunability, after which we expect that
ultra-broadband highly coherent soliton microcomb can be produced.

To conclude, we have introduced a new type of chip-scale microcomb laser that
can be flexibly mode-locked with either active-driving or passive-feedback
approaches and that can be tuned/reconfigured at an ultrafast speed, with
robust turnkey operation inherently built in. The demonstrated integrated comb
laser exhibits outstanding reconfigurability and performance significantly
beyond the reach of conventional on-chip mode-locked semiconductor lasers
wang2017iii ; davenport2018integrated ; malinowski2019towards ;
hermans2022chip . The demonstrated devices combine elegantly the simplicity of
integrated laser structure, robustness of mode-locking operation, and electro-
optically enhanced tunability and controllability, opening up a new avenue
towards on-demand generation of soliton microcombs with high power efficiency
that we envision to be of great promise for a wide range of applications
including ranging, communication, optical and microwave synthesis, sensing,
metrology, among many others.

Method
Device fabrication The device fabrication begins with a congruent x-cut thin
film lithium-niobate-on-insulator (LNOI) wafer, with a 600 nm LN layer on a
4.7 $\rm\mu m$ silica-coated silicon substrate. E-beam lithography (EBL) and
Ar-ion milling are used to etch the waveguide with ZEP-520A as mask. Etching
thickness ranges from 300 nm (CE comb laser) to 350 nm (FP comb laser) for
dispersion engineering. Second EBL is applied on PMMA for deposition of 400 nm
gold-evaporated electrodes, which are placed 2.5 $\rm\mu m$ from the
waveguide. The distance between the waveguide and electrode is chosen to
balance the EO modulation frequency with loss from metal absorption. Dicing
and polishing of LN chip are employed at last to acquire optimized fiber-to-
chip and amplifier-to-chip coupling, with both coupling losses around 6 dB.

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Acknowledgements

The authors would like to thank Lin Chang and William Renninger for helpful
discussions. This work is supported in part by the Defense Advanced Research
Projects Agency (DARPA) QuICC program under Agreement No. FA8650-23-C-7312 and
LUMOS program under Agreement No. HR001-20-2-0044, and the National Science
Foundation (NSF) under Grant No. OMA-2138174 and ECCS-2231036. This work was
performed in part at the Cornell NanoScale Facility, a member of the National
Nanotechnology Coordinated Infrastructure (National Science Foundation,
ECCS-1542081); and at the Cornell Center for Materials Research (National
Science Foundation, Grant No. DMR-1719875).

Author Contributions

J.L. and Z.G. designed and fabricated the devices. J.L. and Z.G. performed the
device characterization. S.X and Q.H. assisted in the device fabrication.
S.X.,M.L., K.Z., U.J., R.L. and J.S. assisted in experiments. J.L., Z.G., and
Q.L. wrote the manuscript with contributions from all authors. Q.L. supervised
the project. Q.L. conceived the concept.

Additional Informations
Supplementary information Supplementary Information is available for this
paper.
Competing interests. The authors declare no competing interests.
Correspondence and requests for materials should be sent to Q.L.
(qiang.lin@rochester.edu).
Reprints and permission. Reprints and permissions are available at
www.nature.com/reprints.


longtable captionstableheading

# Unification of species, gene, and cell trees for single-cell expression
analyses

Samuel H. Church, Jasmine L. Mah, Casey W. Dunn

Department of Ecology and Evolutionary Biology, Yale University, New Haven,
CT, 06511

##  1 Abstract

Comparisons of single-cell RNA sequencing (scRNA-seq) data across species can
reveal links between cellular gene expression and the evolution of cell
functions, features, and phenotypes. These comparisons invoke evolutionary
histories, as depicted with phylogenetic trees, that define relationships
between species, genes, and cells. Here we illustrate a tree-based framework
for comparing scRNA-seq data, and contrast this framework with existing
methods. We describe how we can use trees to identify homologous and
comparable groups of genes and cells, based on their predicted relationship to
genes and cells present in the common ancestor. We advocate for mapping data
to branches of phylogenetic trees to test hypotheses about the evolution of
cellular gene expression. We describe the kinds of data that can be compared,
and the types of questions that each comparison has the potential to address.
Finally, we reconcile species phylogenies, gene phylogenies, cell phylogenies,
and cell lineages as different representations of the same concept: the tree
of cellular life. By integrating phylogenetic approaches into scRNA-seq
analyses, we can overcome challenges for building informed comparisons across
species, and robustly test hypotheses about gene and cell evolution.

##  2 Introduction

Single-cell RNA sequencing (scRNA-seq) generates high-dimensional gene
expression data from thousands of cells from an organ, tissue, or body1.
Single-cell expression data are increasingly common, with new animal cell
atlases released every year2–6. The next step is to compare atlases across
species2, to identify the dimensions in which these results differ, and to
associate these differences with other features of interest7. Because all
cross-species comparisons are inherently evolutionary comparisons, there is an
opportunity to integrate approaches from the field of evolutionary biology,
and especially phylogenetic biology8. Drawing concepts, models, and methods
from these fields will overcome central challenges with comparative scRNA-seq,
especially in how to draw coherent comparisons over thousands of genes and
cells across species. In addition, this synthesis will help avoid the
unnecessary reinvention of analytical methods that have already been
rigorously tested in evolutionary biology for other types of data, such as
morphological and molecular data.

Comparative gene expression has been used for decades to answer evolutionary
questions (e.g.  _How are changes in gene expression associated with the
evolution of novel functions and phenotypes?_)9. Single-cell RNA sequencing
represents a massive increase in the scale of these experiments1, from working
with a few genes or a few tissues, to assays of the entire transcriptome,
across thousands of cells in a dissociation experiment. Comparative scRNA-seq
therefore allows us to scale up our evolutionary questions, for example:

  * •

_How has the genetic basis of differentiation evolved across cell populations
and over time?_

  * •

_What kinds of cells and gene expression patterns were likely present in the
most recent common ancestor?_

  * •

_What changes in cell transcriptomes are associated with the evolution of new
ecologies, life-histories, or other features?_

  * •

_How much variation in cellular gene expression do we observe over
evolutionary time? Which changes in gene expression are significant (i.e.
larger or smaller than we expect by chance)?_

  * •

_Which genes show patterns of correlated expression evolution? Can
evolutionary screens detect novel interactions between genes?_

For these comparisons, we seek to compare and analyze the results of
individual scRNA-seq experiments across species. These experiments generate
matrices of count data, with measurements along two axes: cells, and genes
(Figure 1). Comparative scRNA-seq adds a third axis: species. At first glance,
we might seek to align scRNA-seq matrices across species, creating a three-
dimensional tensor of cellular gene expression. But neither genes nor cells
are expected to share a one-to-one correspondence across species. In the case
of genes, gene duplication (leading to paralogous relationships) and gene loss
are rampant10. In the case of cells, there is rarely justification for
equating two individual cells across species, instead, we typically consider
similarity across populations of cells (“cell types”)11. Therefore to align
matrices, we must first find the appropriate system of grouping these
dimensions. This is essentially a question of homology12: which genes and cell
types are homologous, based on their relationship to predicted genes and cell
types in the common ancestor.

Figure 1: Single cell experiments generate count matrices, shown here with
columns as cells and rows as genes. Higher expression counts for a given gene
in a given cell are depicted with darker shading. In an idealized comparison,
count matrices across species would be aligned to form a three-dimensional
tensor of expression across cells, genes, and species. In reality we have no
expectation of one-to-one correspondence or independence for any the three
axes. Instead, relationships between species, genes, and cells are described
by their respective evolutionary histories, as depicted with phylogenies.

Questions about homology can be answered using phylogenies12. Species
relationships are defined by their shared ancestry, as depicted using a
phylogeny of speciation events (Figure 2). Gene homology is also defined by
shared ancestry, depicted using gene trees that contain nodes corresponding to
either speciation and gene duplication events. Cell homology inference
requires assessing the evolutionary relationships between cell types12,13,
defined here as populations of cells related via the process of cellular
differentiation, and distinguishable from one another e.g. using molecular
markers14. Relationships between cell types can be respresented with cell
phylogenies that, like gene trees, contain both speciation and duplication
nodes13. As with genes, the evolutionary relationships between cell types may
be complex, as differentiation trajectories drift, split, or are lost over
evolutionary time7,13,15.

In this paper we consider each of these axes: across species, genes, and
cells. In each case we lay out challenges and solutions derived from a
phylogenetic comparative approach. We relate these solutions to methods
previously proposed in the literature, including SAMap7 for pairwise alignment
of cellular dimensional reductions. Finally, we reconcile species trees, gene
trees, cell phylogenies and cell lineages as descriptions of the same
concept–the tree of cellular life.

Figure 2: Species phylogenies contain speciation events as nodes in a
bifurcating tree. Gene phylogenies contain both gene duplication events (black
hexagons) and speciation events (unmarked) at nodes. Cell phylogenies also
include both speciation and duplication events; here duplication events
represents a split in the program of cellular development that leads to
differentiated cell types13. Branches from the species phylogeny (numbered
branches) can be found within gene and cell phylogenies. Note that gene
families are strictly defined by ancestry, but cell types have historically
been defined by form, function, or patterns of gene expression15. This means
groups of cells identified as the same “type” across species may reflect
paraphyletic groups11, as depicted in the second cell type in this tree.

##  3 Comparing across species

Shared ancestry between species will impact the results of all cross-species
analyses, and should therefore influence our expectations and
interpretations16. For scRNA-seq data, this has several implications: First,
we expect species to be different from one another, given that they have
experienced evolutionary time since diverging from their common ancestor.
Therefore, by default we expect there to be many differences in cellular gene
expression across the thousands of measurements in an scRNA-seq dataset.
Second, we expect the degree of difference to be correlated with time since
the last common ancestor. Our null expectation is that more closely related
species will have more similar cellular gene expression than more distantly
related species. The structure of this similarity can be approximated with a
species phylogeny calibrated to time.

Methods for the evolutionary comparison of scRNA-seq data have already been
proposed in packages like SAMap7. These packages have overcome significant
challenges, such as how to account for non-orthologous genes (see the
description of gene comparisons below). However, up to now they have relied on
pairwise comparisons of species, rather than phylogenetic relationships. The
problems with pairwise comparisons have been well-described elsewhere17; in
summary, they result in pseudo-replication of evolutionary events. An
evolutionary comparative approach, on the other hand, maps evolutionary
changes to branches in the phylogeny8,10. In this approach:

  * •

data are assigned to tips of a tree;

  * •

ancestral states are reconstructed using an evolutionary model;

  * •

evolutionary changes are calculated as differences between ancestral and
descendant states;

  * •

the distribution of evolutionary changes along branches are analyzed and
compared18.

Shifting toward a phylogenetic approach to comparative scRNA-seq unlocks new
avenues of discovery, including tests of co-evolution of cellular gene
expression and other features of interest9, as well as evolutionary screens
for signatures of correlated gene and cell modules19. In phylogenetic
analyses, statistical power depends on the number of independent evolutionary
events rather the absolute number of taxa8. Therefore the choice of which
species to compare is critical, especially as we construct comparisons to
capture potential convergence.

One consideration when comparing species is the degree to which the history of
scientific study has favored certain organisms (e.g. model organisms)20. This
is especially relevant to single-cell comparisons, as we have a much deeper
knowledge about cell and gene function for some species (e.g. mice, humans)
than others. This creates a risk of bias toward observing described biological
phenomena, while missing the hidden biology in less well-studied organisms20.
Consider the identification of “novel” cell types based on the absence of
canonical marker genes. Because most canonical marker genes were originally
described in well-studied species, cell type definitions that rely on these
will be necessarily less useful in the context of other species2.

Technologies such as single-cell sequencing have great potential to even the
playing field by democratizing the types of data collected2. For example,
scRNA-seq allows us to assay all genes and thousands of cells, rather than a
curated list of candidates. To leverage this to full effect, we must
acknowledge the remaining filtering steps in our analyses, including how we
identify orthologous gene sequences and how we label cell types.

##  4 Comparing across genes

Due to gene duplication and loss, there is usually not a one-to-one
correspondence between genes across species21. Instead, evolutionary histories
of genes are depicted using gene trees (Figure 2). Pairs of tips in gene trees
may be labeled as “orthologs” or “paralogs” based on whether they descend from
a node corresponding to a speciation or gene duplication event22. Gene
duplication happens both at the individual gene level, or in bulk via whole or
partial genome duplication21. Gene loss means that comparative scRNA-seq
matrices may be sparse not only due to failure to detect, but also because
genes in one species don’t exist in another.

Many cross-species comparisons have confronted the challenge of finding
equivalent genes across species23. These often start by restricting analyses
to sets of one-to-one orthologs24. There are several problems with this
approach22: [1] One-to-one orthologs are only well-described for a small set
of very well annotated genomes23. [2] The number of one-to-one orthologs
decreases rapidly as we both add species to our comparison, and as we compare
across deeper evolutionary distances7. [3] The subset of genes that can be
described by one-to-one orthologs is not randomly drawn from across the
genome, they are enriched for indispensable genes under single-copy control25.

New tools like SAMap7 expand the analytical approach beyond one-to-one
orthologs to the set of all homologs across species7. Homolog groups are
identified with a clustering algorithm by which gene separated into groups
with strong sequence or expression similarity. These may include more than one
representative gene per species. Gene trees can be inferred for these gene
families, and duplication events can be mapped to individual nodes in the gene
tree.

How can we compare cellular expression measures across groups of homologous
genes? One option is to use summary statistics, such as the sum or average
expression per species for genes within a homology group26. However these
statistics might obscure or average over real biological variation in
expression that arose subsequent to a duplication event (among paralogs)19. An
alternative is to connect genes via a similarity matrix, and then make all-by-
all comparisons that are weighted based on putative homology, as in the
approach in SAMap7.

A third approach is to reconstruct changes in cellular expression along gene
trees, rather than the species tree10,27. Here evolutionary changes are
associated with branches descending from either speciation or duplication
events. Such an approach has been demonstrated by Munro _et. al._ for bulk
RNA-sequencing27, as follows:

  * •

cellular expression data are assigned to tips of a gene tree;

  * •

ancestral states and evolutionary changes are calculated, as above;

  * •

equivalent branches between trees are identified using “species branch
filtering”27. Branches between speciation events can be unambiguously equated
across trees based on the composition of their descendant tips (see numbered
branches in Figure 2);

  * •

changes across equivalent branches of a cell tree are analyzed (e.g. to
identify significant changes, signatures of correlation, etc).

Mapping cellular gene expression data to branches of a gene tree sidesteps the
problem of finding sets of orthologs by incorporating the history of gene
duplication and loss into the analytical framework.

##  5 Comparing across cells

Like with genes, there is usually not an expectation of a one-to-one
correspondence between cells across species. We can rarely equate individual
cells across species, with notable exceptions such as the zygote, or the cells
of certain eutelic species, with an invariant number of cellular divisions.
Instead we typically consider the homology of groups of cells (cell types),
with the hypothesis that the cell developmental programs that give rise to
these groups are derived from a program present in the shared ancestor11.

We also don’t expect a one-to-one correspondence between cell types across
species. As with genes, cell types may be gained or lost over evolutionary
time. The relationships between cell types across species can been described
using phylogenetic trees. These cell phylogenies are distinct from cell
lineages–the bifurcating trees that describe cellular divisions within an
individual developmental history. Nodes in cell lineages represent cell
divisions, while nodes in cell phylogenies represent either speciation events
or splits in differentiation programs leading to novel cell types (Figure 2).

The term cell “type” has been used for several distinct concepts15, including
cells defined and distinguished by their position in a tissue, their form,
function, or in the case of scRNA-seq, their relative expression profiles that
fall into distinct clusters14. Homology of structures across species is often
inferred using many of the same criteria: position, form, function, and gene
expression patterns28. The fact that the same principles are used for
inferring cell types and cell homologies presents both an opportunity and an
obstacle for comparative scRNA-seq. We can potentially leverage the same
methods we use for identifying clusters of cells within species to identify
clusters of cells across species. This could be done simultaneously, inferring
a joint cell atlas in a shared expression space7, or it could be done
individually for each species and subsequently merged2,23. In either case,
this inference requires contending with the complex evolutionary histories
between genes and species described above.

One obstacle is that, because cell types are not typically defined according
to evolutionary relationships15, cells labeled as the same type across species
may constitute paraphyletic groups11. A solution is to use methods for
reconstructing evolutionary relationships to infer the cell tree15,29 (Figure
2). This method is robust to complex evolutionary histories (e.g. duplication
and loss), and has the additional advantage of generating a tree, comparable
to a species or gene tree, onto which cellular characters can be mapped and
their evolution described15. As described in Mah and Dunn, 202330, tools for
tree building based on character data can be applied to the high-dimensional
data of gene expression to successfully reconstruct a cell tree. In this
approach:

  * •

cell trees are inferred;

  * •

gene expression data are assigned to tips of the cell tree;

  * •

ancestral states and evolutionary changes are calculated, as above;

  * •

changes along branches are analyzed (e.g. to identify changes in gene
expression associated with the evolution of novel cell types)

Another obstacle is that there are reported batch effects26 across single-cell
experiments which may need to be accounted for via integration23. However our
null expectation is that species are different from one another. Naive batch
integration practices have no method for distinguishing technical effects from
the real biological differences that are the target of study in comparative
scRNA-seq23. Other approaches (e.g. LIGER31, Seurat32) have been reported as
able to distinguish and characterize species-specific differences23. Given
that we are still developing null hypotheses16 for how much variation in
expression we expect to observe across species19, we hold that cross-species
integration should be treated with caution until elucidation of the approach
can robustly target and strictly remove technical batch effects.

A final obstacle is that cell identities and homologies may be more complex
than can be accurately captured by categorizations into discrete clusters or
“types”14,15. Single-cell experiments that include both progenitor and
differentiated cells can highlight the limits of clustering algorithms33. In
experiments that capture cells along a differentiation trajectory, there may
or may not be obvious boundaries for distinguishing cell populations. In cases
where boundaries are arbitrary, the number of clusters, and therefore the
abundance of cells within a cluster will depend on technical and not
biological inputs, such as the resolution parameter that the user
predetermines for the clustering algorithm.

A solution is to define homology for the entire differentiation trajectory,
rather than individual clusters of cells26. This may be accomplished by
defining anchor points where trajectories overlap in the expression of
homologous genes, while allowing for trajectories to have drifted or split
over evolutionary time, such that sections of the trajectories no longer
overlap15. Cellular homologies within a trajectory may be more difficult to
infer, as this requires contending with potential heterochronic changes to
differentiation (e.g. as cell differentiation evolves, genes may become
expressed relatively earlier or later in the process)26.

##  6 scRNA-seq data

Single-cell comparisons potentially draw on a broad range of phylogenetic
comparative methods for different data types, including binary, discrete,
continuous, and categorical data34 (Figure 3). The primary data structure of
scRNA-seq is a matrix of integers, representing counts of transcripts or
unique molecular identifiers for a given gene within a given cell35. In a
typical scRNA-seq analysis, this count matrix is passed through a pipeline of
normalization, transformation, dimensional reduction, and clustering36,37. The
decisions of when during this pipeline to draw a comparison determines data
type, questions we can address, and caveats we must consider.

Figure 3: Types of scRNA-seq data that can be mapped onto a tree, with example
questions that can be addressed and caveats to be considered.

###  6.1 Gene expression

Unlike bulk RNA-sequencing, where counts are typically distributed across a
few to dozens of samples, scRNA-seq counts are distributed across thousands of
cells. The result is that scRNA-seq count matrices are often shallow and
sparse38. In our recent paper35, we highlighted that the vast majority of UMI
counts in standard scRNA-seq datasets (often >95%) are either 0, 1, or 2.
These values are discrete, low-integer numbers, and not continuous
measurements. The high-dimensionality and sparse nature of single-cell data
present a unique challenge when considering cross-species comparisons2.

In a standard scRNA-seq approach, expression values are analyzed following
depth normalization and other transformations. With depth normalization,
counts are converted from discrete, absolute measures to continuous, relative
ones, though our instruments don’t actually quantify relative expression.
There is a growing concern that this and other transformations are inadequate
for the sparse and shallow sequencing data introduced here39,40. Further
transformations of the data, such as log-transformation or variance rescaling,
introduce additional distortions that may obscure real biological differences
between species.

Alternatively, counts can be compared across species directly, without
normalization or transformation35. There are two potential drawbacks to this
approach: First, count values are influenced by stochasticity, due to the
shallow nature of sequencing, resulting in uncertainty around integer values.
Second, cells are not sequenced to a standard depth. Comparing raw counts does
not take this heterogeneity into account, though our recently published
approach35 describes how this might be accomplished using a restricted algebra
to analyze counts.

An alternative is to transform count values to a binary or categorical
trait41, for example, binning counts into “on” and “off” based on a threshold
value, and then model the evolution of these states on a tree. Analyzing
expression as a binary or categorical trait eliminates some of the
quantitative power of scRNA-seq, but still allows us to address interesting
questions about the evolution of expression dynamics within and across cell
types.

###  6.2 Models of expression

A promising avenue for scRNA-seq is using generalized linear models to analyze
expression40,42,43. These models describe expression as a continuous trait and
incorporate the sampling process using a Poisson or other distribution,
avoiding normalization and transformation, and returning fitted estimates of
relative expression. These estimates can be compared using models that
describe continuous trait evolution. One feature of generalized linear models
models is they can report uncertainty values for our estimates of relative
expression, which can then be passed along to phylogenetic methods to assess
confidence in the evolutionary conclusions drawn.

###  6.3 Cell diversity

In a standard scRNA-seq approach cells are analyzed in a reduced dimensional
space and clustered by patterns of gene expression37. There are several types
of cellular data that can be compared. The evolution of the presence or
absence of cell types can be modeled as a binary trait. When cell type labels
are unambiguously assigned, this approach can answer questions about when cell
types evolved and are lost. Such a comparison is hampered, however, when cells
do not fall into discrete categories14, or when equivalent cell types cannot
be identified across species due to substantial divergence in gene expression
patterns. An alternative is to model the evolution of cell differentiation
pathways as a binary trait on a tree, to ask when pathways, rather than types,
evolved and have been lost.

Similarly, the abundance of cells of a given type might be compared across
species, for example to ask how how dynamics of cell proliferation have
evolved. The number of cells within a cluster, however, can be influenced by
technical features of the experiment, such as the total number of clusters
identified (often influenced by user-supplied parameters), as well as where
cluster boundaries are defined. An alternative is to compare relative cell
abundance values, which may account for experimental factors but will still be
susceptible to variation in how clusters are determined.

###  6.4 Cellular manifolds

One area for further development are methods that can model the evolution of
the entire manifold of cellular gene expression on an evolutionary tree.
Practically, this might be accomplished by parameterizing the manifold, for
example by calculating measures of manifold shape and structure such as
distances between cells in a reduced dimensional space. The evolution of such
parameters could be studied by analyzing them as characters on a phylogenetic
tree.

Alternatively, we can envision a method in which we reconstruct entire
ancestral landscapes of cellular gene expression, and then describe how this
landscape has been reshaped over evolutionary time. Such an approach would
require an expansion of existing phylogenetic comparative models to ones that
can incorporate many thousands of dimensions. It would also likely require
dense taxonomic sampling to build robust reconstructions.

##  7 Discussion

Comparative single-cell RNA sequencing spans the fields of evolutionary,
developmental, and cellular biology. Phylogenetic trees–branching structures
depicting relationships across time–are the common denominator of these
fields. Taking a step back reveals that many of the trees we typically
encounter, such as species phylogenies, gene phylogenies, cell phylogenies,
and cell fate maps, can be reconciled as part of a larger whole (Figure 4).
Because all cellular life is related via an unbroken chain of cellular
divisions, species phylogenies and cell fate maps are two representations of
the same larger phenomenon, visualized at vastly different scales. Gene trees
and cell trees (i.e. cell phylogenies) depict the evolution of specific
characters (genes and cells) across populations within a species tree. These
characters may have discordant evolutionary histories due to patterns of gene
and cell duplication, loss, and incomplete sorting across populations.

Figure 4: All cellular life is related by an unbroken chain of cell divisions.
Species phylogenies describe the relationship between populations. Populations
are themselves a description of the genealogical relationships between
individuals. Peering even closer reveals that each individual consists of a
lineage of cells, connected to other individuals via reproductive cells.
Therefore, species trees, genealogies, and cell lineages are all descriptions
of the same concept–the tree of life–but at different scales. Gene trees and
cell trees (i.e. cellular phylogenies) describe the evolutionary histories of
specific characters within the tree of life. These trees may be discordant
with species trees due to duplication, loss, and incomplete sorting in
populations.

The synthesis of species, gene, and cell trees makes several key points clear.
First, phylogenetic trees are essential for testing hypotheses about cellular
gene expression evolution. Mapping single-cell data to trees, whether gene
trees, cell trees, or species trees, allows us to build statistical tests of
co-evolution, diversification, and convergence. The choice of which trees to
use for mapping data will be determined by the questions we hope to answer.
For example, mapping cellular expression data to gene trees would allow us to
test whether expression evolves differently following gene duplication events
(i.e. to test the ortholog conjecture44).

Second, because the fields of evolutionary, developmental, and cellular
biology study the same phenomena at different scales, there is a potential
benefit from sharing methods. In the case of single-cell sequencing, building
evolutionary context around data can prove essential for understanding the
fundamental biology, including how to interpret cell types and cellular
differentiation trajectories, and how to reconcile gene relationships. An
evolutionary perspective is also critical for building robust null
expectations of how much variation we might expect to observe across
species16, which will allow us to interpret the significance of results as new
species atlases come to light.

Methods that infer and incorporate trees are essential not only for
evolutionary biology, but for developmental and cellular biology as well. As
single-cell data become increasingly available, rather than reinvent methods
for building cell trees or comparing across cellular network diagrams, we can
draw approaches from the extensive and robust fields of phylogenetic inference
and phylogenetic comparative methods. These approaches include Bayesian and
Maximum Likelihood inference of trees, evolutionary models, ancestral state
reconstruction, character state matrices, phylogenetic hypothesis testing,
among many others45–47.

Biology has benefited in the past from syntheses of disparate fields of study,
including the modern synthesis of Darwinian evolution and Mendelian
genetics48, and the synthesis of evolution and development in the field of
evo-devo49. With the advent and commercialization of technologies like single-
cell sequencing, there is broadened opportunity for new syntheses50. Rich and
complex datasets are increasingly available from understudied branches on the
tree of life, and comparisons between species will invariably invoke
evolutionary questions. By integrating phylogenetic thinking across fields, we
can start to answer these questions and raise new ones.

##  8 Acknowledgments

We thank Daniel Stadtmauer, Namrata Ahuja, Seth Donoughe and other members of
the Dunn lab for helpful conversation and comments on an initial version of
the manuscript.

##  9 Declaration of interests

The authors declare no competing interests.

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