sensing ability find food find mates avoid predators encounter rate is everything to plankton how to...
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Sensing ability
Find foodFind matesAvoid predators
Encounter rate is everything to plankton
How to
Relative motion
Turbulence
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Encounter rate is everything for plankton
understanding the mechanisms of individual organisms interacting
motion diffusion
challenging
gives a deeper understanding of macro-scale effects
why?
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Microscopic
Mechanistic
Individual
Macroscopic
Empirical
Population
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Individual based models
How individuals
move
interact with environment
interact with each other
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The particle nature of organisms
The physics of small particles in a fluid
Hydrodynamics: how small orgamisms move and the flow associated with them
Diffusion: how material is exchanged with small orgamisms.
At scales that do not lead to immediate intuition
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Viscosity is all important
How important is determined by the Reynolds number
uaRe
a is the size (radius say) of the particleu is the speed at which it is moving relative to the fluid is the kinematic viscosity of the fluid
forces viscous
forces inertialRe
Physics of small organisms in a fluid: hydrodynamics
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Note: kinematic viscosity , dynamic viscosity
dimensions L2 T1 dimensions M L1 T1
≈ 10-2 cm2 s-1 for water
Re < 1: vicosity dominates, Stokes' regimeRe > 1: inertia becomes importantRe > 2000: flow becomes turbulent
Typical valuesswimming bacterium 10-5
swimming flagellate 10-3
copepod feeding current 1
Physics of small organisms in a fluid: hydrodynamics
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fuvguv
22
9
aDt
D
dt
d ffpfp
particle acceleration
local fluidacceleration (pressure gradient)
buoyancy drag self induced force
f
p
Settling velocity (Stokes' law)
02
92
wa
g ffp
radius a
f
fpgaw
9
2 2
marine snow (1 mm) 6 m/day
vu
Physics of small organisms in a fluid: hydrodynamics
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Physics of small organisms in a fluid: hydrodynamics
-4 -3 -2 -1 0 1 2 3 4-4
-3
-2
-1
0
1
2
3
4
U
r
3
3
22
31cos
r
c
r
aUur
3
3
44
31sin
r
a
r
aUu
Stokes' flow around a sphere
Effected volume>> then particle
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Diffusion of solutes:nutrientswaste products (oxygen)
Diffusivity (D) of many solutes(salt, sugar, O2, nitrate)D ≈ 10-5 cm2/s
04 CCaDQ OsmotrophInward flux
02
3
* 3
34
CCDaa
VolumeSpecific flux
Becomes less efficient for larger organism
Steady state
Physics of small organisms in a fluid: diffusion
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Dt
aCCaDtQ
14)( 0
time dependent flux to a sphereQ
t
Physics of small organisms in a fluid: diffusion
So why not just jump form place to place ?
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02
CDCut
C
advection diffusion
D
uaPe
Physics of small organisms in a fluid: advection - diffusion
Pe < 1: diffusion dominates
Pe > 1: advection dominates
Heuristic
says nothing about flux
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0 4 CCShaDQ
Physics of small organisms in a fluid: advection - diffusion
diffusive
total
Q
QSh
Calculate using model: solve 02
CDCut
C
Sherwood number
-5 0 5-5
0
5Stokes' flow
Str
ea
mlin
es
-5 0 5-5
0
5
Ve
loci
tyR
ad
ial d
ista
nce
fro
m c
en
ter
( a)
0.9
-5 0 5-5
0
5
Vo
rtic
ity
0.1
-5 0 5-5
0
5 Re=1
-5 0 5-5
0
5
0.9
-5 0 5-5
0
5
Radial distance from center (a)
0.1
-5 0 5-5
0
5 Re=10
-5 0 5-5
0
5
-5 0 5-5
0
5
1.0
0.1
Step 1: calculate the flow
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Step 2: solve for a solute.
Physics of small organisms in a fluid: advection - diffusion
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Agar sphere filled with oxygen consuming yeast cellsSuspended in flow (= sinking)
Physics of small organisms in a fluid: advection - diffusion
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Re
0 5 10 15 20 25
Sh
erw
ood
num
ber
0
5
10
15
20
25
30
Numerical result
08.03/162.01 RePeSh
2/)21(1 3/1PeSh
Empirical
Physics of small organisms in a fluid: advection - diffusion
Thoretical
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0.5 µ bacteria, u = 2 10-5 cm/s, Re = 10-7, Pe = 10-4, Sh = 1.00
5 µ flagellate, u = 3 10-4 cm/s, Re = 10-5, Pe = 10-2, Sh = 1.01
Where advection (swimming, sinking etc) doesn't matter
500 µ algal colony, u = 7 10-2 cm/s, Re = 0.4, Pe = 400, Sh = 5
1 mm marine snow, u = 7 10-2 cm/s, Re = 1, Pe = 700, Sh = 6
1 cm marine snow, u = 0.13 cm/s, Re = 13, Pe = 1300, Sh = 19
and where it does
Physics of small particles in a fluid: advection - diffusion
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Acartia tonsa nauplii
Jumps 3 times per second.Why?
a few 100 µ in size
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Hydromechanical signals in the plankton
Many blind plankton organisms, from the smallest flagellates to crustaceans, are capable of perceiving and identifying moving objects - prey, predator, mate – and to react adequately.
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Ciliates entrained into the feeding current of Temora
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Sensory ability of copepods
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Sensory ability of copepods
40 m
200 m
Labidocera madurae
5 m
Mechano-receptive setae are velocity detectors
Neurological sensitivity 20 m / s
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Sensory ability of copepods: Acatia tonsa
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Siphon flow longitudinal deformation acceleration
Oscillating chamber acceleration
Couette device shear deformation acceleration vorticity
Rotating cylinder acceleration vorticity
Acartia tonsa150 m / s
Velocity difference
rate of strain(deformation)
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-4 -3 -2 -1 0 1 2 3 4-4
-3
-2
-1
0
1
2
3
4
-4 -3 -2 -1 0 1 2 3 4-4
-3
-2
-1
0
1
2
3
4
U
U
Translating sphere Spherical pump
sinking particle feeding current
2 models for the price of one
Small prey entrained into a copepod feeding current
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3
3
22
3cos
r
c
r
aUur
3
3
44
3sin
r
a
r
aUu
Small prey entrained into a copepod feeding current
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Translation Deformation
Translation
Rotation
Deformation
(b) Across flow velocity gradient: Simple shear flow
(a) Along flow velocity gradient
Small prey entrained into a copepod feeding current
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Small prey entrained into a copepod feeding current
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)2/()(3)( 422 rarUar
Peak: 0)(
r
r
a
Ur
ar
8
3*)(
2*
Because typically swimming velcity (U) scales with size (a)maximum deformation rate is approximately constant and size independent
Deformation rate
Distance, units of a
0 5 10 15 20 25
Def
orm
atio
n ra
te (
units
U/a
)
0.0
0.2
0.4 = 0o
Small prey entrained into a copepod feeding current
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Reaction distance
)2/()(3)( 422 rarUar
To find R, solve for r = R at ∆(r) = ∆*
U
a
a
UaR
3
*811
*4
3
Reaction distance function of size and velocity
Distance (units of a)
0 5 10 15 20 25
De
form
atio
n ra
te (
uni
ts U
/a)
0.0
0.2
0.4
R
Small prey entrained into a copepod feeding current
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Data taken from Tiselus & Jonsson 1991
Distance, cm
0.0 0.1 0.2 0.3 0.4D
efo
rma
tion
ra
te,
s-1
0
2
4
6
8
10
12
14
Deformation
Distance, cm
0.0 0.1 0.2 0.3 0.4
Fee
ding
cur
ren
t ve
loci
ty,
cm s
-1
0.2
0.4
0.6
0.8
1.0Observed
Modelled
Centropages feeding current: observed and modelled
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Observed reaction distance, cm
0.0 0.1 0.2 0.3 0.4 0.5Pre
dic
ted
rea
ctio
n d
ista
nce
, cm
0.0
0.1
0.2
0.3
0.4
0.5
1
2
3 4
5
1: Stickleback-Temora; 2: Centropages-Acartia nauplii;3: Temora-Acartia nauplii; 4: Stickleback-Eurytemora;5: Larval cod - Acartia nauplii
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A small prey is embedded in the flow generated by a large moving predator – hence responds to velocity gradients rather than velocity
Velocity or velocity gradients
A large predator is anchored in the fluid and not moved by the flow generated by a small swimming prey – hence respond to absolute flow velocity
what does he experience
what does he experience
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Large predator detecting a particleThere is a fundamental difference between the a body force (gravity and sinking) and a self-prpoelled body (swimming)
drag
buoyancy
drag
thrust
0
0
0 0
STRESSLETSTOKESLET
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Velocity
Distance, units a
0 5 10 15 20 25
Abs
olu
te fl
uid
ve
loci
ty (
un
its o
f U)
0
1 = 00
3
3
22
31
r
c
r
aUur
Large predator detecting a particle
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Velocity
Distance, units a
0 5 10 15 20 25
Abs
olu
te fl
uid
vel
ocity
(un
its o
f U)
0
1 = 00
3
3
22
31
r
c
r
aUur
Find R at ur = S*
))3/))/*(cos4cos((2/( 1 USaaR
Reaction distance function of size and velocity
R
S*
Large predator detecting a particle: reaction distance
For sinking particle
Similar for swimming organism
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Does it work like this?
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Acartia percieving sinking fecal pellets
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Ambush feeding:remotely perceived prey are attacked
Oithona feeding on motile Gymnodinium
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Detection distance = 0.14 mm => S* = 40 µm/s
Oithona percieves small swimming flagellates
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Oithona: Predicted and observed clearance rates (S* = 40 m/s)
Fecal pellet equivalent spherical radius, cm
0.001 0.01
Cle
aran
ce, m
l d-1
0.1
1.0
10.0
100.0
1000.0
10000.0
PredictedPredictedAcartia tonsa (lab)Large Calanoids (lab)Large Calanoids (field)
Prey volume, um^3
100 101 102 103 104 105
cle
ara
nce
, m
l /h
0.0
0.2
0.4
0.6Predicted, frontPredicted, sideobserved
Flagellates Sinking faecal pellets
Data from Turner
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• Simple, idealised models may provide insights in the basic mechanisms of hydrodynamic signalling in the plankton
• More realistic models are computationally heavy, but may be required to adress specific questions. Such models are now beginning to emerge
• Modelling is fine – but there is no substitute for direct observations
• Physics of small marine organisms are often not intuitive.
• Qualitative insights can be got from nondimensional numbers such as Re, Pe and Sh
Final remarks
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