Sensing ability Find food Find mates Avoid predators Encounter rate is everything to plankton How to Relative motion Turbulence

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?

Microscopic Mechanistic Individual Macroscopic Empirical Population

Individual based models How individuals move interact with environment interact with each other

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

Viscosity is all important How important is determined by the Reynolds number a is the size (radius say) of the particle u is the speed at which it is moving relative to the fluid is the kinematic viscosity of the fluid Physics of small organisms in a fluid: hydrodynamics

Note: kinematic viscosity, dynamic viscosity  dimensions L 2 T  1 dimensions M L  1 T  1 ≈ cm 2 s -1 for water Re < 1: vicosity dominates, Stokes' regime Re > 1: inertia becomes important Re > 2000: flow becomes turbulent Typical values swimming bacterium swimming flagellate copepod feeding current 1 Physics of small organisms in a fluid: hydrodynamics

particle acceleration local fluid acceleration (pressure gradient) buoyancydragself induced force ff pp Settling velocity (Stokes' law) radius a marine snow (1 mm) 6 m/day v u Physics of small organisms in a fluid: hydrodynamics

U r  Stokes' flow around a sphere Effected volume >> then particle

Diffusion of solutes: nutrients waste products (oxygen) Diffusivity (D) of many solutes (salt, sugar, O 2, nitrate) D ≈ cm 2 /s Osmotroph Inward flux Volume Specific flux Becomes less efficient for larger organism Steady state Physics of small organisms in a fluid: diffusion

time dependent flux to a sphere Q t Physics of small organisms in a fluid: diffusion So why not just jump form place to place ?

advectiondiffusion Physics of small organisms in a fluid: advection - diffusion Pe < 1: diffusion dominates Pe > 1: advection dominates Heuristic says nothing about flux

Physics of small organisms in a fluid: advection - diffusion Calculate using model: solve Sherwood number Step 1: calculate the flow

Step 2: solve for a solute. Physics of small organisms in a fluid: advection - diffusion

Agar sphere filled with oxygen consuming yeast cells Suspended in flow (= sinking) Physics of small organisms in a fluid: advection - diffusion

Re Sherwood number Numerical result Empirical Physics of small organisms in a fluid: advection - diffusion Thoretical

0.5 µ bacteria, u = 2  cm/s, Re = 10 -7, Pe = 10 -4, Sh = µ flagellate, u = 3  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  cm/s, Re = 0.4, Pe = 400, Sh = 5 1 mm marine snow, u = 7  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

Acartia tonsa nauplii Jumps 3 times per second. Why? a few 100 µ in size

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.

Ciliates entrained into the feeding current of Temora

Sensory ability of copepods

40  m 200  m Labidocera madurae 5  m Mechano-receptive setae are velocity detectors Neurological sensitivity  20  m / s

Sensory ability of copepods: Acatia tonsa

Siphon flow  longitudinal deformation  acceleration Oscillating chamber  acceleration Couette device  shear deformation  acceleration  vorticity Rotating cylinder  acceleration  vorticity Acartia tonsa 150  m / s Velocity difference rate of strain (deformation)

Translating sphere Spherical pump sinking particlefeeding current 2 models for the price of one Small prey entrained into a copepod feeding current

TranslationDeformation Translation Rotation Deformation (b) Across flow velocity gradient: Simple shear flow (a) Along flow velocity gradient Small prey entrained into a copepod feeding current

Peak: Because typically swimming velcity (U) scales with size (a) maximum deformation rate is approximately constant and size independent Deformation rate Distance, units ofa Deformation rate (units U/a)  = 0 o Small prey entrained into a copepod feeding current

Reaction distance To find R, solve for r = R at ∆(r) = ∆* Reaction distance function of size and velocity Distance (units ofa) Deformation rate (units U/a)   R Small prey entrained into a copepod feeding current

Data taken from Tiselus & Jonsson 1991 Distance, cm Deformation rate, s Deformation Distance, cm Feeding current velocity, cm s Observed Modelled Centropages feeding current: observed and modelled

Observed reaction distance, cm Predicted reaction distance, cm : Stickleback-Temora; 2: Centropages-Acartia nauplii; 3: Temora-Acartia nauplii; 4: Stickleback-Eurytemora; 5: Larval cod - Acartia nauplii

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

Large predator detecting a particle There is a fundamental difference between the a body force (gravity and sinking) and a self-prpoelled body (swimming) drag buoyancy drag thrust STRESSLETSTOKESLET

Large predator detecting a particle

Find R at u r = S * Reaction distance function of size and velocity R S*S* Large predator detecting a particle: reaction distance For sinking particle Similar for swimming organism

Does it work like this?

Acartia percieving sinking fecal pellets

Ambush feeding: remotely perceived prey are attacked Oithona feeding on motile Gymnodinium

Detection distance = 0.14 mm => S* = 40 µm/s Oithona percieves small swimming flagellates

Oithona: Predicted and observed clearance rates (S* = 40  m/s) Flagellates Sinking faecal pellets Data from Turner

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