Key traits of unicellular species, such as cell size, often follow scale-free or self-similar distributions, hinting at the possibility of an underlying critical process. However, linking such empirical scaling laws to the critical regime of realistic individual-based model classes is difficult. Here, we reveal new empirical scaling evidence associated with a transition in the population and the chlorophyll dynamics of phytoplankton. We offer a possible explanation for these observations by deriving scaling laws in the vicinity of the critical point of a new universality class of non-local cell growth and division models. This “criticality hypothesis” can be tested through new scaling predictions derived for our model class, for the response of chlorophyll distributions to perturbations. The derived scaling laws may also be generalized to other cellular traits and environmental drivers relevant to phytoplankton ecology.

1.
J. R.
Banavar
,
J.
Damuth
,
A.
Maritan
, and
A.
Rinaldo
, “
Scaling in ecosystems and the linkage of macroecological laws
,”
Phys. Rev. Lett.
98
,
068104
(
2007
).
2.
D. R.
Chialvo
, “
Emergent complex neural dynamics
,”
Nat. Phys.
6
,
744
750
(
2010
).
3.
T.
Lux
and
M.
Marchesi
, “
Scaling and criticality in a stochastic multi-agent model of a financial market
,”
Nature
397
,
498
500
(
1999
).
4.
M.
Faloutsos
,
P.
Faloutsos
, and
C.
Faloutsos
, “On power-law relationships of the Internet topology,” in ACM SIGCOMM CCR (ACM, New York, 1999), Vol. 29, pp. 251–262.
5.
A.
Rinaldo
,
A.
Maritan
,
K. K.
Cavender-Bares
, and
S. W.
Chisholm
, “
Cross-scale ecological dynamics and microbial size spectra in marine ecosystems
,”
Proc. R. Soc. Lond. Biol.
269
,
2051
2059
(
2002
).
6.
E.
Marañón
, “
Cell size as a key determinant of phytoplankton metabolism and community structure
,”
Annu. Rev. Mar. Sci.
7
,
241
264
(
2015
).
7.
K. K.
Cavender-Bares
,
A.
Rinaldo
, and
S. W.
Chisholm
, “
Microbial size spectra from natural and nutrient enriched ecosystems
,”
Limnol. Oceanogr.
46
,
778
789
(
2001
).
8.
K.
Hosoda
,
T.
Matsuura
,
H.
Suzuki
, and
T.
Yomo
, “
Origin of lognormal-like distributions with a common width in a growth and division process
,”
Phys. Rev. E
83
(
3
),
031118
(
2011
).
9.
A.
Giometto
,
F.
Altermatt
,
F.
Carrara
,
A.
Maritan
, and
A.
Rinaldo
, “
Scaling body size fluctuations
,”
Proc. Natl. Acad. Sci. U.S.A.
110
,
4646
4650
(
2013
).
10.
H.
Salman
,
N.
Brenner
,
C.-K.
Tung
,
N.
Elyahu
,
E.
Stolovicki
,
L.
Moore
,
A.
Libchaber
, and
E.
Braun
, “
Universal protein fluctuations in populations of microorganisms
,”
Phys. Rev. Lett.
108
(
23
),
238105
(
2012
).
11.
S.
Iyer-Biswas
,
C. S.
Wright
,
J. T.
Henry
,
K.
Lo
,
S.
Burov
,
Y.
Lin
,
G. E.
Crooks
,
S.
Crosson
,
A. R.
Dinner
, and
N. F.
Scherer
, “
Scaling laws governing stochastic growth and division of single bacterial cells
,”
Proc. Natl. Acad. Sci. U.S.A.
111
(
45
),
15912
15917
(
2014
).
12.
P.
Bak
,
C.
Tang
, and
K.
Wiesenfeld
, “
Self-organized criticality: An explanation of the 1/f noise
,”
Phys. Rev. Lett.
59
,
381
384
(
1987
).
13.
G.
Grinstein
, “
Generic scale invariance in classical nonequilibrium systems
,”
J. Appl. Phys.
69
(
8
),
5441
5446
(
1991
).
14.
A.
Kern
and
R.
Stoop
, “
Essential role of couplings between hearing nonlinearities
,”
Phys. Rev. Lett.
91
,
128101
(
2003
).
15.
R.
Stoop
and
F.
Gomez
, “
Auditory power-law activation avalanches exhibit a fundamental computational ground state
,”
Phys. Rev. Lett.
117
,
038102
(
2016
).
16.
O.
Kinouchi
and
M.
Copelli
, “
Optimal dynamical range of excitable networks at criticality
,”
Nat. Phys.
2
,
348
351
(
2006
).
17.
C. B.
Field
,
M. J.
Behrenfeld
,
J. T.
Randerson
, and
P.
Falkowski
, “
Primary production of the biosphere: Integrating terrestrial and oceanic components
,”
Science
281
(
5374
),
237
240
(
1998
).
18.
S.
Fontana
,
M. K.
Thomas
,
M.
Reyes
, and
F.
Pomati
, “
Light limitation increases multidimensional trait evenness in phytoplankton populations
,”
ISME J.
13
,
1159
1167
(
2019
).
19.
M. K.
Thomas
,
S.
Fontana
,
M.
Reyes
, and
F.
Pomati
, “
Quantifying cell densities and biovolumes of phytoplankton communities and functional groups using scanning flow cytometry, machine learning and unsupervised clustering
,”
PLOS ONE
13
,
e0196225
(
2018
).
20.
E.
Álvarez
,
E.
Nogueira
, and
A.
López-Urrutia
, “
In vivo single-cell fluorescence and size scaling of phytoplankton chlorophyll content
,”
Appl. Environ. Microbiol.
83
,
e03317-16
(
2017
).
21.
A. G.
Fredrickson
,
D.
Ramkrishna
, and
H. M.
Tsuchiya
, “
Statistics and dynamics of procaryotic cell populations
,”
Math. Biosci.
1
(
3
),
327
374
(
1967
).
22.
J. W.
Sinko
and
W.
Streifer
, “
A new model for age-size structure of a population
,”
Ecology
48
(
6
),
910
918
(
1967
).
23.
J. W.
Sinko
and
W.
Streifer
, “
A model for population reproducing by fission
,”
Ecology
52
(
2
),
330
335
(
1971
).
24.
A.
Hall
and
G. C.
Wake
, “
A functional differential equation arising in modelling of cell growth
,”
ANZIAM J.
30
,
424
435
(
1989
).
25.
A.
Hall
and
G. C.
Wake
, “
Functional differential equations determining steady size distributions for populations of cells growing exponentially
,”
ANZIAM J.
31
,
434
453
(
1990
).
26.
T.
Friedlander
and
N.
Brenner
, “
Cellular properties and population asymptotics in the population balance equation
,”
Phys. Rev. Lett.
101
(
1
),
018104
(
2008
).
27.
M.
Osella
,
E.
Nugent
, and
M. C.
Lagomarsino
, “
Concerted control of Escherichia coli cell division
,”
Proc. Natl. Acad. Sci. U.S.A.
111
,
3431
3435
(
2014
).
28.
P.
Wang
,
L.
Robert
,
J.
Pelletier
,
W. L.
Dang
,
F.
Taddei
,
A.
Wright
, and
S.
Jun
, “
Robust growth of Escherichia coli
,”
Curr. Biol.
20
,
1099
1103
(
2010
).
29.
A. S.
Kennard
,
M.
Osella
,
A.
Javer
,
J.
Grilli
,
P.
Nghe
,
S. J.
Tans
,
P.
Cicuta
, and
M. C.
Lagomarsino
, “
Individuality and universality in the growth-division laws of single E. coli cells
,”
Phys. Rev. E
93
,
012408
(
2016
).
30.
A.
Merico
,
G.
Brandt
,
S. L.
Smith
, and
M.
Oliver
, “
Sustaining diversity in trait-based models of phytoplankton communities
,”
Front. Ecol. Evol.
2
,
59
(
2014
).
31.
E.
Litchman
and
C. A.
Klausmeier
, “
Trait-based community ecology of phytoplankton
,”
Annu. Rev. Ecol. Evol. Syst.
39
,
615
639
(
2008
).
32.
A. D.
Barton
,
A. J.
Pershing
,
E.
Litchman
,
N. R.
Record
,
K. F.
Edwards
,
Z. V.
Finkel
,
T.
Kiørboe
, and
B. A.
Ward
, “
The biogeography of marine plankton
,”
Ecol. Lett.
16
,
522
534
(
2013
).
33.
S. L.
Smith
,
M.
Pahlow
,
A.
Merico
, and
K. W.
Wirtz
, “
Optimality-based modeling of planktonic organisms
,”
Limnol. Oceanogr.
56
,
2080
2094
(
2011
).
34.
A.
Merico
,
J.
Bruggeman
, and
K.
Wirtz
, “
A trait-based approach for downscaling complexity in plankton ecosystem models
,”
Ecol. Modell.
220
,
3001
(
2009
).
35.
D. T.
Gillespie
, “
A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
,”
J. Comput. Phys.
22
,
403
434
(
1976
).
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