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The impact of pyroclastic density
currents duration on humans:
the case of the AD 79 eruption
of Vesuvius
Pierfrancesco Dellino1*, Fabio Dioguardi2, Roberto Isaia3, Roberto Sulpizio1 & Daniela Mele1
Pyroclastic density currents are ground hugging gas-particle ows that originate from the collapse
of an eruption column or lava dome. They move away from the volcano at high speed, causing
devastation. The impact is generally associated with ow dynamic pressure and temperature. Little
emphasis has yet been given to ow duration, although it is emerging that the survival of people
engulfed in a current strongly depends on the exposure time. The AD 79 event of Somma-Vesuvius is
used here to demonstrate the impact of pyroclastic density currents on humans during an historical
eruption. At Herculaneum, at the foot of the volcano, the temperature and strength of the ow were
so high that survival was impossible. At Pompeii, in the distal area, we use a new model indicating
that the current had low strength and low temperature, which is conrmed by the absence of signs of
trauma on corpses. Under such conditions, survival should have been possible if the current lasted a
few minutes or less. Instead, our calculations demonstrate a ow duration of 17 min, long enough to
make lethal the breathing of ash suspended in the current. We conclude that in distal areas where the
mechanical and thermal eects of a pyroclastic density currents are diminished, ow duration is the
key for survival.
e impact of pyroclastic density currents (PDCs) is generally attributed to the combination of ow temperature
and dynamic pressure1–3. e latter is expressed by the dynamic pressure,
that represents the lateral force per unit area acting on buildings and living bodies, where
is the gas-particle mixture density, ρs and ρg are particle and gas density, C is particle volumetric concentration
and U is current velocity. A complete symbol list is found in Table1.
Engineering investigations1,4,5 show that dynamic pressures higher than 5kPa produce signicant damage,
while pressures under 1kPa have minimal to no consequence on structures or infrastructures. Particle volumetric
concentration represents an important parameter too because dynamic pressure is proportional to it. Currents
moving in the vicinity of a volcano can have a high concentration of hot magmatic particles that confer high
temperature and high dynamic pressure to the ow. is can cause burning of buildings, breaking of windows
and toppling of walls, which make survival impossible6.
Concerning eects on humans, it is emerging that even in areas far from a volcano, where particle concentra-
tion, temperature and dynamic pressure strongly decrease, people engulfed in the ow have “high probability
of receiving fatal skin burns and inhalation injury of the upper and lower respiratory tract, unless the duration
is very brief”7. e presence of ne-ash particles suspended in air for a long time, even in very small amounts,
can be very harmful to human health, and represents one major cause of injury2. Exposure to pure hot air at
200–250°C can be survived for 2–5 minutes8, but the presence of inhalable hot ne ash drastically reduces sur-
vival times. e exposure time therefore plays a major role in determining the impact of PDCs on human beings,
(1)
P
dyn =
1
2
ρmixU
2
(2)
ρmix =ρsC+ρg(1−C)
OPEN
Dipartimento Di Scienze Della Terra E Geoambientali, Università Di Bari, Bari, Italy. British Geological Survey, The
Lyell Centre, Edinburgh, UK.
Napoli, Napoli, Italy. *email: pierfrancesco.dellino@uniba.it
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but, until now, it has not been quantied2,7. We study here the famous AD 79 eruption of Somma-Vesuvius9,10
and we reconstruct, for the rst time, also the eect of ow duration on humans.
The 79 AD eruption of Vesuvius and associated deposits. e eruption started on October 24th,
with the deposition of a thin bed of ne ash to the east11. is short opening event heralded the main explosive
phase, which started around noon of October 24th with the formation of a 25km high eruptive column that,
favored by stratospheric winds, caused the propagation of a south-eastwardly dispersed volcanic plume. e
Roman towns and villages around Somma-Vesuvius and along the plume dispersal axis were covered by pumice
Table 1. List of symbols, with description and physical dimension.
Symbol Description Dimension
ArAggradation Rate m s−1
C0Reference particle concentration (0.7) –
CParticle volumetric concentration –
Ctot Total particle volumetric concentration –
CdParticle drag coecient –
Csf Depth-averaged concentration in the basal shear ow –
Cpa Air specic heat J kg−1°C−1
Cpg Gas specic heat J kg−1°C−1
Cps Solid specic heat J kg−1°C−1
dparticle size mm
gGravity acceleration (9.81) m s−2
g′Reduced gravity m s−2
HTotal ow thickness m
Hdep Deposit thickness m
Hsf Shear ow height m
kVon Karman constant (0.4) –
kssubstrate roughness m
Pdyn Dynamic pressure k Pa
PnParticle Rouse number –
Pn*Normalized Rouse number –
Pnavg Average Rouse number of the solid material –
Pni Rouse number of the ith particle-size class –
Pnsusp Rouse number at maximum suspension capacity –
Ri0Richardson number –
SrSedimentation rate kg m−2 s−1
tAggradation time s
Taair temperature °C
TgGas temperature °C
Tmix Temperature of mixture °C
Tssolid temperature °C
u*Flow shear velocity m s−1
UCurrent velocity m s−1
wtParticle terminal velocity m s−1
wti Terminal velocity of the ith particle-size class m s−1
yFlow vertical coordinate m
y0Basal lamina thickness m
αSlope angle Deg
ϕiWeight fraction of the ith size class Weight%
ρaAtmospheric density kg m−3
ρdep Deposit density kg m−3
ρgGas density kg m−3
ρmix Density of the gas–particle mixture kg m−3
ρsParticle density kg m−3
ρsf Shear ow density kg m−3
ρsi Density of the ith particle-size class kg m−3
τShear-driving stress of shear ow Pa
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lapilli and ash with thickness up to 3m at Pompeii9, which caused roof collapse of several houses. Aer a few
hours, the plume became unstable and partially collapsed, generating small volume PDCs that hit the slopes of
the volcano and buried the town of Herculaneum9,10 (Fig.1a,b). e main explosive phase ended in the morn-
ing of October 25th, with the eruption resuming aer a few hours with a high column that suddenly collapsed,
generating the most destructive PDC of the whole eruption (the EU4 unit), causing injuries up to 20km south
from the volcano10,11. e EU4 unit invaded Pompeii (about 10km from the vent), causing the death of people
not yet escaped from the town. Pompeii is a particularly important site for evaluating the impact of an eruption
on human beings, because during the eighteenth century excavations archaeologists found a way of producing
plaster casts of the victims, giving clues on the eect that the PDCs had on people12.
Our survey at the archaeological excavation of Pompeii allowed the visit of the site of Casa di Stabianus
(Regio I, insula 22), where in the perimeter of a house some corpses lay embedded by the sediment that formed
aer the passage of the ow that deposited the EU4 unit. e EU4 deposit rests on top of the fallout pumice bed
of the main explosive phase, meaning that the PDC entered the house through the openings and the collapsed
roof, and engulfed people that were resting in the house in the time interval between the two main phases of the
eruption12,13. e deposit consists of a 0.23m thick bed with internal stratication (Fig.1c), showing tractional
structures such as sand waves. ese are the typical features of deposits formed from a dilute current, where ash
particles are sustained by turbulence until they settle out of suspension and into a bed load14–16. e deposit was
formed by continuous aggradation, i.e. by the stacking up of one ash lamina over the other, during the time-
integrated passage of the current.
Some preliminary indication of the impact that the PDCs had on human beings comes plaster casts of the
bodies that lay embedded in the ash layer (Fig.1d). ey show intact bodies without evidence of any traumatic
sign12 and suggest that the current did not possess a high dynamic pressure (i.e. high dynamic pressure). Fur-
thermore, clothes are preserved and show that the original texture was not burnt by the passage of the PDC,
Figure1. e PDC deposits of the AD 79 Vesuvius eruption. (a)—Map showing Herculaneum and Pompeii
locations (courtesy of Osservatorio Vesuviano); (b)—Herculaneum: the white arrow shows the massive bed
formed by the concentrated current that caused charring of woods (yellow arrow) and toppling of walls
(red arrows); (c)—Pompeii: the stratied layer with tractional structures that was formed by the stacking up
of laminae during suspension sedimentation from the dilute PDC, is shown; (d)—Pompeii: some corpses,
embedded in the ash layer, which show intact bodies and preserved dressings (white arrow), are shown.
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indicating a temperature below the clothes decomposition, which ranges between 130 and 150°C for silk and
wool, respectively17.
The impact parameters of the PDC at Pompeii. e approach we used to reconstruct of the impact
parameters is described in the method section, which includes a description of the equations, from (3) to (14),
up on which the model is based. e main data used as input in the model are reported in Table2. Here the
results of ow dynamic pressure, temperature and duration, as representing the main impacts, are illustrated.
Flow dynamic pressure. In order to illustrate how ow strength varies as a function of current height at Pom-
peii, the proles of particle concentration, density, velocity and dynamic pressure are shown on Fig.2. Results are
presented by means of three curves representing the minimum (16th percentile), the average (50th percentile)
and the maximum (84th percentile) solution of the probability density functions that were calculated with the
method of Dioguardi and Dellino18 (see the method section). Velocity, U, while increasing upward in the ow
(Fig.2a), reaches values in the range of a few tens m/s. Concentration, C, strongly decreases with height (Fig.2b),
and already in the rst few meters is lower than 0.001. e density prole, ρmix (Fig.2c), mimics the trend of
the concentration prole, and already in the lower two meters decreases rapidly upward to a value lower than
atmosphere, making the upper part of the current buoyant. e dynamic pressure Pdyn, which represents the
combination of velocity and density, has a maximum in the rst few decimeters (Fig.2d). Higher in the current,
dynamic pressure is lower than 1kPa. With these values, no severe mechanical damages are expected to struc-
tures, infrastructure or human bodies.
Flow temperature. Flow temperature of the current was calculated by using as input in Eq.(11) (see the method
section) the values of density, concentration, temperature and specic heat of the three components of the gas-
particle mixture, namely: magmatic gas, air and volcanic particles. e temperature of magmatic gas and of vol-
canic particles was set to 850°C, which is compatible with the 79 AD eruption composition19. Air temperature
Table 2. Pompeii deposit data used as input in the model.
Hdep (m) ρdep (kg/m3)djuv (mm) ρjuv (kg/m3)Cd juv dxx (mm) ρxx (kg/m3)Cd xx
0.23 1900 0.40 2200 1.73 0.19 3280 1.39
Figure2. Proles of the impact parameters representing the ow dynamic pressure. e curves refer to
the minimum (16th percentile), the average (50th percentile) and the maximum (84th percentile) of the
probabilistic model solution. (a)—Velocity proles. (b)—Particle volumetric concentration proles. (c)—
Density proles. (d)—Dynamic pressure proles. British Geological Survey (UKRI) 2021.
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was set to 18°C, which is a reasonable value for the Somma-Vesuvius area at sea level in the autumn season20.
Average density was set to 1700kg/m3 for the volcanic particles, to 0.2kg/m3 for volcanic gas at 850°C and
to 1.2kg/m3 for air at 18°C, respectively. e specic heats were set to 2200J/kg°C for volcanic gas, 700J/
kg°C for the volcanic particles and 1005J/kg°C for air. As for particle concentration, an average value of
0.001 was set, obtained by integrating the concentration prole of the average solution over ow height (see
Fig.2b) by means of Eq.(4). e relative concentrations of magmatic gas and air were obtained by means of
ρg=ρmCm+ρa(1−Cm)
and by using as gas density the value calculated by the system of Eqs.(8) and (9). e
concentration values of air and volcanic gas resulted 0.941 and 0.058, respectively. By setting all parameters in
(11), a temperature of 115°C was obtained. Zanella etal.21 and Cioni etal.19 made measurements on the PDC
deposit at Pompeii, which indicated temperatures, at the time of deposition, ranging between 140 and 300°C,
which is consistent with the values obtained in this paper when considering that the temperature in the com-
pacted deposit can be a little higher than that of the dilute gas-particle mixture.
e low temperature that we calculated at Pompeii is due to the much higher content of cold atmosphere air
in the current, with respect to the hot magmatic gas. is is attributed to the air entrainment process that char-
acterizes PDCs along runout. It is the sum of the air entrainment that occurs at the turbulent interface between
the ow head and atmosphere, which is regulated by the Richardson number of the current
Ri
0=g
′Hcosa
U
2 where
g
′
=
ρmix−ρa
ρa
g is the reduced gravity22, and of the entrainment due to the ingestion of air occurring upon the
impact of the eruptive column with the ground. e latter eect is particularly ecient in diluting magmatic
gas with atmosphere air in the vicinity of the volcano, as it has been reported both by experiments22,23 and by
observation of recent eruptions24.
Flow duration. Flow duration was calculated by using as input in Eqs.(12) and (13) (Method section) data
obtained both directly on the PDC deposit at Pompeii, and by means of laboratory analyses carried out on
ash samples. Among input, particle concentration, Rouse number and settling velocity are all functions of the
shear ow density, which was calculated in terms of a probability density function with PYFLOW v2.025. As a
consequence, the results of ow duration are also expressed in terms of probabilities. e average value of ow
duration was about 17min. is duration is quite long when compared to the couple of minutes considered as a
survivable time for people engulfed in a PDC, even at low temperature2,7.
Our ow duration represents the time during which the layer thickness was formed by continuous settling of
particles out of suspension. It does not take into consideration the waning phase of the current, where sedimenta-
tion could have been minimal and not completely recorded in the deposit layer, or any periods of nondeposition
through bypassing, or pulses of erosion.
Indeed, the time here calculated is to be considered as a minimum estimation. is ow duration represents,
therefore, the phase when the current had a signicant load of life-threatening ash.
Discussion and conclusion
e PDCs of the AD 79 eruption of Somma–Vesuvius show a major dierence between proximal and distal
areas in terms of impact. In the vicinity of the volcano the main eect was related to dynamic pressure and
temperature19,26. is conclusion is corroborated by our observations at Herculaneum (Fig.1a), where the cur-
rent le a massive layer formed by a highly concentrated and hot ow that was capable of breaking and toppling
thick walls and of charring wood (see Fig.1b). ese characteristics are indicative of a highly destructive event
that did not permit survival, as discussed by previous authors27,28.
e situation in distal locations, such as in Pompeii, 10km from the volcano, is quite dierent (Fig.1a).
Here, the thermal and mechanical aects. e thermal and mechanical eects of the dilute PDC drastically
diminished there. If we integrate the prole of the average solution of the dynamic pressure over the rst 10m
(a typical building height in the Vesuvian area) a value lower than 1kPa results. According to engineering
investigations2,3, no damage to walls should be expected with such a ow strength, which is consistent with the
fact that at Pompeii the walls of Roman buildings do not show evidence of damage12,29 related to the passage of
the PDC. Furthermore, the bodies embedded in the ash bed do not show any evidence of bone dislocations or
fracture, and the bodies look intact, which is consistent with the low ow strength. Even the clothing, whose
textures remain visible throughout the plaster casts, look intact. is is in agreement with the low temperature
(115°C) of the gas-particle mixture calculated in this study.
e average value of ow duration that we calculated is about 17min, which combined with the concentra-
tion of ash particles (about 0.001), was a long enough time to cause death by asphyxia at Pompeii. e recent
literature on the subject suggests, in fact, that the exposure to ne ash, even at a low particle concentration, can
be survived only for a couple of minutes7. e ow duration of PDCs can be shorter or longer than this, depend-
ing on the scale of the eruption. ere are reports of recent eruptions showing that in the marginal reaches of
the current, where the ow duration was only a few minutes, people were able to survive7. In other cases, longer
ow durations did not permit survival and death was caused by ne-ash inhalation7,30. Flow duration is a key
factor for assessing the impact of PDCs on human beings, especially in distal areas, where the primary risk to life
is asphyxiation, as at Pompeii. We agree with Baxter etal.7 that the emergency planning for explosive eruptions
should concentrate on the distal parts of PDCs where survival could be likely, and where the primary risk to life
is asphyxiation from ash inhalation, rather than thermal or mechanical injury.
For Pompeii, we were able to reconstruct ow duration using a novel method that was applied for the rst
time in this paper. Our method should be used to infer the probable duration of pyroclastic density currents in
future events, with this contributing to hazard assessment of active volcanoes.
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Method
e reconstruction of the impact parameters of PDCs is based on a ow mechanical model that starts with the
assumption that the current is velocity and density stratied15,31,32. In the stratied multiphase gas-particle cur-
rent, the basal part is a shear ow that moves attached to the ground and has a density higher than atmosphere.
e upper part is buoyant, because particle concentration decreases with height down to a value that, combined
with the eect of gas temperature, makes the mixture density lower than the surrounding atmosphere.
e inputs needed, in our model, for the calculation of the impact parameters at Pompeii are reported in
Table2. Some of the input data are obtained directly in the eld, such as deposit and lamina thickness. Deposit
density is obtained by weighing a known volume of deposit. Other data come from laboratory analyses on
samples extracted from the deposit. In the laboratory, rst, the grain-size distribution is determined, then from
each size class a sample of particles per each component (crystal, glass, lithics) is extracted, and density data are
obtained on such particle samples by means of pycnometers33. Particle shape parameters, which are needed for
the calculation of settling velocity, are obtained by image analysis methods34.
In a PDC, particles are mainly transported by turbulent suspension and sedimentation is controlled by a bal-
ance between ow shear velocity u*, which is controlled by uid turbulence and favors suspension, and particle
settling velocity, wt = (4gd(ρs −ρmix)/3Cdρmix)0.5, which favors sedimentation, where g is gravity acceleration, d is
particle size and Cd is drag coecient. e median of the grain-size distribution was used for particle size. e
capacity of a current to transport particles in suspension is quantied by the Rouse number35
P
n=
wt
ku∗
, where
k is the Von Karman constant (0.4). During sedimentation, it is assumed that the particles of dierent com-
position that form a lamina settle at the same aerodynamic conditions, e.g., with the same terminal velocity15.
erefore, by equating the settling velocity of the glass and crystal components in the deposit, and assuming
that sedimentation starts when Pn = 2.5, hence when wt = u*, ow shear velocity and density ρsf of the shear ow
can be calculated aer d, ρs and Cd are measured in the laboratory36. ese results are then input in a numerical
code18,25 and the current parameters are reconstructed. e velocity prole follows the equation of a turbulent
boundary layer shear ow moving over a rough surface37
where ks is the substrate roughness (measured in the eld as 0.1m at Pompeii) and y is ow height.
where C0 is the particle volumetric concentration at the reference height y0 and H is the total current thickness.
In this work, y0 is taken as the basal lamina thickness, hence C0 is the particle concentration in the lamina (0.7
in this paper). Assuming steady sedimentation, H is obtained by the ratio Hdep/Csf where Hdep is deposit thickness
and Csf is the depth-averaged concentration in the basal shear ow, which can be calculated by ρsf = ρs Csf + ρg(1-
Csf), when ρsf and ρg are known.
e shear ow height and density are obtained by solving the system of (5) and (6), which is valid for a
turbulent current
where
τ
is the shear-driving stress of the ow moving down an inclined slope of angle
α
, in our case 3.2°, meas-
ured in the eld.
e density prole, which is a function of concentration, particle density and gas density, is:
Gas density and Rouse number are obtained by solving numerically the following system:
Equation(8) states that atmospheric density,
ρa
, is reached at the top of the shear ow, Hsf, and Eq.(9) states
that the average density of the shear ow,
ρsf
refers to the part of the ow that goes from the reference level, y0,
to the shear ow top height, Hsf.
By combining the velocity and density proles, the dynamic pressure prole is nally obtained
(3)
U
y
=u∗
1
k
ln
y
ks
+8.5
(4)
C
y
=C0
y0
H−y0
H−y
yPn
(5)
τ
=
ρ
sf
−ρ
a
gsinαH
sf
(6)
τ
=ρ
sf
u
2
∗
(7)
ρ
mix
y
=ρg+C0
y0
H
−
y0
H−y
yP
n
ρs−ρg
(8)
ρ
a
y
=ρg+C0
y0
H−y0
H−Hsf
H
sf P
n
ρs−ρg
(9)
ρ
sf =
1
Hsf −y0
Hsf
∫
y0
ρg+C0
y0
H−y0
H−y
y
P
n
ρs−ρg
dy
(10)
Pdyn
y
=0.5U
2
y
ρ
mix
y
.
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e proles of the ow parameters are expressed in terms of a probability density function that depends on
the variance of particle characteristics. e model has been validated by experiments3 and already applied to
other eruptions15,33.
e temperature of a PDC is quantied as the weighted average between the relative proportions of the three
components that make up the gas-particle mixture, namely the volcanic gas and solid particles that issue from
the crater, plus the atmospheric air that is entrained by the current during its spreading. e temperature of the
mixture can be approximated by
where T and Cp are the temperature and specic heat (at constant pressure), respectively. e subscripts g, s and
a stand for gas, solid particle and air, respectively.
Concerning ow duration, in a PDC, sedimentation occurs at a rate
Sr
that represents the mass of particles
settling over a unit area in the unit time. Deposit thickness grows by aggradation of ash laminae during the time-
integrated passage of the current. e aggradation rate
Ar
, which is the rate at which deposit thickness grows, is
equal to the sedimentation rate divided by deposit density,
ρdep
.
e total time of aggradation, t, which is a proxy of ow duration, is equal to deposit thickness divided by the
aggradation rate, Ar, which is represented by the ratio of deposit density and sedimentation rate:
Deposit density and thickness are measured in the eld, consequently the only missing quantity for the cal-
culation of ow duration is the sedimentation rate.
Dellino etal. 38, recently proposed a model for the calculation of the sedimentation rate
with the subscript i referring to the ith particle-size class and n being the number of size classes of the grain-size
distribution of the sediment, with
φi
,
ρsi
and
Pni
being the weight percent, the density and the Rouse number of
the ith grain-size fraction, respectively. Pn* = Pnavg/Pnsusp is the normalized Rouse number of the current, i.e. the
ratio between the average Rouse number of the solid material in the current and the Rouse number at maximum
suspension capacity. e model considers the contribution of each size class of particles to the sedimentation,
and not the average grain size, because the solid load constituting a suspension current, especially in the case
of PDCs, is made up of a mixture of dierent components (lithics, glassy fragments and crystals) with dierent
size, density and shape, thus dierent terminal velocity. e average Rouse number of the solid material in the
current is calculated as the average of the particulate mixture,
When Pn* is higher than 1, a current has a particle volumetric concentration in excess of its maximum
capacity, e.g. it is over-saturated of particles, which favours sedimentation. When it is lower than 1, a current
has a particle volumetric concentration lower than its maximum capacity, e.g. it is under-saturated, and could
potentially include additional sediment in suspension by erosion from the substrate. For a specic discussion
see Dellino etal.38.
Received: 11 January 2021; Accepted: 16 February 2021
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(11)
T
mix =
ρ
g
T
g
C
g
Cp
g
+ρ
s
T
s
C
s
Cp
s
+ρ
a
T
a
C
a
Cp
a
ρ
gCgCpg
+ρ
sCsCps
+ρ
aCaCpa
(12)
t
=
H
dep
Ar
(13)
S
r=
n
i
ρsiwti
φ
i
/ρ
si
n
i=1φi/ρsi
∗Ctot
10.065 ∗Pni
P∗
n
+0.1579
∗0, 7 +
φ
i+1
/ρ
si+1
n
i=1φi+1/ρsi+1
∗Ctot
10.065 ∗Pni
P∗
n
+0.1579
∗0.3
−
0.01.
(14)
P
navg =
n
i=1
PniCi/
C
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Vol:.(1234567890)
Scientic Reports | (2021) 11:4959 |
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Acknowledgements
e associate editor (Marco Viccaro), Greg Valentine and an anonymous reviewer greatly helped in improving
the manuscript. Soprintendenza Speciale per i Beni Archeologici di Pompei, Ercolano e Stabia is acknowledged
for the hospitality at the excavations. Part of the instrumentation was obtained by the grant PON 3a SISTEMA
of MIUR. is work is published with permission of the Executive Director of British Geological Survey (UKRI).
Author contributions
P.D. wrote the manuscript adn coordinated the reseach F.D. perfromed calculation R.S. and R.I. contributed in
the eld work DM helped in the laboratory analyses.
Competing interests
e authors declare no competing interests.
Additional information
Correspondence and requests for materials should be addressed to P.D.
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