MARINE ECOLOGY PROGRESS SERIES Vol. 269: 153–162, 2004 Published March 25 Mar Ecol Prog Ser
Zooplankton use of chemodetection to find and eat particles
George A. Jackson1,*, Thomas Kiørboe2
1Department of Oceanography, Texas A&M University, College Station, Texas 77843-3146, USA 2Danish Institute for Fisheries Research, Kavalergården 6, 2920 Charlottenlund, Denmark
ABSTRACT: The ability of raptorial zooplankton to find large particles such as marine aggregates is crucial to their use of the particles as food and to the fate of the particles. Kiørboe & Thygesen (2001) developed a numerical approach to describe particle detection by chemosensory zooplankton. In this paper, we develop and test a simplified mathematical description of the process and explore the ecological implications of chemosensory particle detection. Our results suggest that chemosensory particle detection can be more efficient than hydrodynamic detection. The exact extent depends greatly on the sensitivity of chemodetection in zooplankton, a process that has not been well studied experimentally.
KEY WORDS: Marine snow · Zooplankton feeding · Plumes · Hydromechanical signals · Chemical signals
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INTRODUCTION regime around a falling aggregate with a Reynolds number Re < 20, that is leaking organic material as it Once believed to consist of simple sieving of water to falls. Kiørboe & Thygesen (2001) applied the technique remove food particles, zooplankton feeding is now to show that the chemical plume around the particle known to involve sophisticated sensing of the environ- could enhance the ability of animals to find and con- ment as the organism looks for environmental pertur- sume the aggregate, but they did not systematically bations induced by the food. The traces left by a falling explore its implications. The high computational cost particle range from disruptions of the fluid flow to makes such an exploration difficult. chemical trails. The ability of an organism to sense its Here we develop a simplified analytical model of the environment determines its ability to eat and to avoid formation of the plume behind a moving and leaking being eaten, and determines where it lives. particle, and we use the result to calculate the ability of Understanding the detection of environmental cues a chemosensory animal to find the particle. Note that requires a description of the physical and chemical such search strategies do not apply to all zooplankton, effects of a particle (including the organism itself) as pure filter feeders such as salps and flux feeders and its movement as well as observations of organism such as pteropods are not known to actively search for sensory responses. The nature of fluid-mechanical particles. We compare our analytical results to those interactions have been best described for moving ani- from the more rigorous numerical simulations and use mals (e.g. Kiørboe & Visser 1999, Titelman 2001) and these to render the analytical result more accurate. We for animals in turbulent environments. Chemical cues then compare the efficiency of animals with different have been better studied for microorganisms looking search behaviors in finding falling particles by differ- for favorable environments, including falling aggre- ent sensory mechanisms. gates (Jackson 1989, Blackburn et al. 1998). Because the ability of zooplankton to find and con- Thygesen & Kiørboe (2002) developed a numerical sume falling aggregates depends on the sizes of the technique to calculate the hydrodynamic and chemical animals as well as on the particles, we initially focus on
*Email: [email protected] © Inter-Research 2004 · www.int-res.com 154 Mar Ecol Prog Ser 269: 153–162, 2004
describing the factors associated with the detection of the velocity field around the falling particle has no a single particle by a single animal. We then extend effect in moving the material once it is released, so the analysis to include the distribution of particles over that the description of the solute distribution is a pure a range of sizes. A list of the symbols used is given in diffusion problem. Table 1. The concentration enhancement C associated with leakage from the particle is then described by: ∂C ∂2C ∂2C CROSS-SECTION OF THE PLUME v = D + (1) ∂z ∂x 2 ∂y 2 Perspective of a point-sized copepod where the fall velocity v is in the vertical (z) direction and D is the diffusion coefficient. If the aggregate We start by calculating the cross-sectional area that releases material at a rate L, then the release rate per a particle falling vertically presents to an animal unit distance is related to the sinking velocity: L/v. swimming horizontally. While the particle has a finite (Notice that the coordinate system has been trans- size and spreads out water passing near it, this water formed so that the particle is fixed and z is actually the comes together again on the upstream side. We will distance to the particle.) The resulting equation has the assume that the particle acts as a point source (infini- solution: tesimally small spatial extension). Because the largest L vx()22+ y L vρ 2 concentration gradients are perpendicular to the di- C =−exp=− exp (2) 4444ππDz Dz Dz Dz rection of movement, diffusion in the direction of motion is less important than in the perpendicular where C is the concentration enhancement above any directions. For simplicity, we will ignore the former background concentration and ρ is the distance away unless otherwise noted. We will further assume that from the plume centerline (e.g. Okubo 1980, but modi- fied by the absence of a reflecting boundary: Fischer et Table 1. Notation al. 1979). The enhancement at which the concentration is too small for an animal to detect, C , determines the Symbol Description Dimensions 0 bounds of the plume. We can estimate the effective –4+b a,b Constants for n(r) cm length of the plume Z, at which C = C0 on the z-axis 1–d –1 c,d Constants for v(r) cm s (ρ = 0; Fig. 1), as: C(z) Concentration at boundary of plume mol cm–3 –3 C0 Threshold detection concentration for mol cm L Z = (3) plume π D Diffusion coefficient cm2 s–1 4 DC0 –f –1 e,f Constants for L(r) mol cm s ρ F(r) Food consumption rate by zooplankter mol s–1 The plume radius * at any distance z can be calcu- g(r) Food consumption per contact mol lated as the horizontal distance from the particle path g Fixed food consumption per contact mol 0 to the location at which C = C0 using Eq. (2): l Specific leakage rate s–1 L(r) Leakage rate mol s–1 4Dz 05.. L 05 m(r) Particle mass mol ρ*ln= –4 n(r) Particle size spectrum cm v 4πDC0 z r Particle radius cm 4Dz 05. (4) rZ Zooplankter radius cm ()05. = − lnzZ / S Sensory distance from center of cm v zooplankter u Threshold signal strength cm s–1 * The cross-sectional area of the plume is σ0; the value v(r) Aggregate fall velocity cm s–1 –1 estimated with this point source approximation, σ0,pt, vZ Zooplankton swimming speed cm s –1 vZH Horizontal component of vZ cm s is then given by: z Vertical distance from aggregate cm Z 05. Z Length of plume, where C(Z,0) = C0 cm 4Dz 05. β 3 –1 σ = 2 ()− lnZz / d z Encounter rate kernel cm s 0,pt ∫ v ρ(z) Plume radius cm 0 σ 2 0 Plume cross-section cm 4DZ 05. 1 σ σ 2 = 05. ()− 05. (5) 0,fit Plume cross-section fit to 0,num cm 2 Zz∫ ’ln’’ zd z 2 v 0 σ0,num Plume cross-section calculated cm numerically 15. σ 024. L 0,pt Plume cross-section calculated from = 2 05. analytical approximation cm Dv πC0 2 σs Additional sensory cross-section cm σ Total cross-section cm2 1 =−05. ()05. ==2π where zzZ’’ln’’.. and ∫ z z d z 27 0 481 0 Jackson & Kiørboe: Particle finding by chemosensing zooplankton 155
S length of the detectable plume for a 0.25 cm radius particle is as long as 99 cm and the cross-section for the 2 point animal is 20 cm . This value of σ0,pt is consider- ably larger than that of the particle by itself, here 0.19 cm2. The plume length is well predicted by Eq. (3) over the whole particle size range (Fig. 2A) but the
value of σ0 underestimates the results from the Z numerical simulations for large r (Fig. 2B). A more detailed comparison requires the normaliza- tion of the above equations (length using r, time using 2 r/v and mass using Lr/v, C’ = C0vr /L, Pe = vr/D = Peclet number). The resulting equations are: Fig. 1. Diagram of plume = ()π –1 behind a falling particle. ZPeC’’pt 4 (7) The effective cross-section σπ= ()–.15 of the plume can be in- ’.0,pt 024Pe C ’ (8) creased by the width of the where the subscript indicates that these are for the sensory apparatus point model and the primes that these are normalized. The simplified model again works well to predict the Perspective of a finite size animal normalized plume length (Fig. 3A). The predictions of σ0 for the simplified equations become inaccurate for If the animal has its antennae out a distance S from Pe > 103, equivalent to Re > 1 (Fig. 3B). Particles with its center and can sense anything within S, the effect Re > 1 include large marine snow particles. The point is to increase the width of the plume by S on either approximation also diverges from the numerical solu- side, for a total of 2S. Hence, the total detection cross- tion for high values of C’, equivalent to large leakage section for an animal becomes: rates. That is, the values of σ0,pt are too small for high Z Re and too large for high C’. σρ=+() ∫ 2 * Szd We adjusted the analytical results for σ’ by fitting a 0 0 curve to the anomalies for high values of Re (Fig. 4): =+σ 2SZ 0 (6) L σ’ = 0.24Pe(πC’)–1.5(1 + 1.98×10–7Pe1.97C’–1.33) =+σ 2S 0,fit 0 πDC for 10 > Re ≥ 1 0 (9) =+σσ 0 s = 0.24Pe(πC’)–1.5 for Re < 1 σ where s = 2SZ is the extra cross-sectional area associated with the animal’s size. 3 3 10 10 σ 0,pt Comparison with numerical solutions 2 σ 10 0,num 2 The above solutions are for a point 10 1 particle that does not disturb water flow; 10 )
real aggregates are not points and they 2 1 0 do perturb the water flow. The added 10 10 (cm complexity of flow around particles has σ -1 been addressed using numerical solu- 10 tions of the relevant advective-diffusive Plume length (cm) 0 10 equations. We make a more systematic -2 10 comparison with the results of such A B numerical calculations using the pro- -1 -3 10 10 gram of Thygesen & Kiørboe (2002). -3 -2 -1 0 -3 -2 -1 0 10 10 10 10 10 10 10 10 Results are shown for particles with Particle radius (cm) Particle radius (cm) the properties of typical marine snow particles (e.g. Kiørboe & Jackson 2001) Fig. 2. Effect of particle size on length of plume Z and plume cross-section σ 0.26 × –12 1.5 × –9 –3 : v = 0.13rp , L = 1 10 rp , and C0 = 1 10 mol cm . (A) plume length and chemosensory capability of zoo- calculated from numerical simulations (+), and Eq. 3 (solid line); (B) plume cross –9 –3 plankters (here with C0 = 10 mol cm ) sections: σ0,pt (solid line), and σ0,num calculated using the method of Kiørboe & (Fig. 2). For this set of properties, the Thygesen (2001; +) 156 Mar Ecol Prog Ser 269: 153–162, 2004
In dimensional form, these become: lyzed the sensory efficiency for ambush feeding (in 15. 064.. 133 which a motionless animal waits for a hydromechan- 024. L –7 vL σ0,fit = 1198+×. 10 05. π 069. 133. 197. ical cue) and cruising (in which an animal searches Dv C0 rC0 D while swimming). Both involve the detection of the for 10 > Re ≥ 1 hydrodynamic disturbance associated with particle 024. L 15. (10) = passage. The efficiencies of the different particle 05. π Dv C0 for Re < 1 encounter mechanisms are best compared by con- Eq. (10) was used in subsequent calculations. sidering the respective encounter rate kernels. For plume-finding, this is: Comparison with other feeding mechanisms β σ σ plume = vZH( 0 + s) (11)
In addition to plume-finding, animals have other where vZH is the horizontal component of the swim- ways of sensing falling particles. Visser (2001) has ana- ming velocity (= 0.82vZ, assuming isotropic swimming speeds and vZ is the zooplankton swim- σ ’ Z’ 0 ming speed). For the ambush feeder, it is: 5 5 10 10 C’=1E-4 β = πS 2 v (12) 1E-3 ambush am 1E-2 4 4 0.1 10 where Sam is the sum of the physical radius 10 1 10 of the particle and sensory radius of the 3 10 animal. For the cruising animal, the en- 3 10 counter rate kernel is: ’ ’ 2
0 2 2 2 0.5 Z 10 β = π + ) (13) σ cruise Scr (vZ v 2 10 1 where S is the appropriate sensory radius, 10 cr the distance from the center of mass of the 1 10 0 animal to the center of the particle. Since 10 both cruisers and ambushers are utilizing A B hydromechanical signals, assume for con- 0 -1 10 10 -1 0 1 2 3 4 -1 0 1 2 3 4 venience that they are equal: Sam = Scr. 10 10 10 10 10 10 10 10 10 10 10 10 Pe Pe Flux feeding, in which the animal pas-
Fig. 3. Normalized and numerical values of (A) Z’ and (B) σ0’ as a function of sively collects the particles that fall on a Pe. Lines represent the values of Z’pt and σ’0,pt for a given value of C’and sym- feeding structure, is an additional particle bols represent the results from numerical computations. Differences arise for feeding mechanism (Jackson 1993). For 3 Pe > 10 , equivalent to the Reynolds number Re > 1, and for high values of C’ the flux feeder: β π 2 0.6 flux = Sfluxv (14) Because the form of β is identical 0.4 flux to that of the ambush feeder, we will not 0.2 consider it further here. 0,pt
σ If the particle is very small relative to the / ) 0 animal, then it is the fluid velocity gener- 0,fit
σ C’=1E-4 ated by the particle which provides the rel- - -0.2 1E-3 evant cue; if the particle is much larger 1E-2 0,num than the animal, it is the fluid deformation σ ( -0.4 3E-2 0.1 that matters (Kiørboe & Visser 1999). 0.3 Visser (2001) developed an expression that -0.6 1 considers both of these extremes as well as 10 the transition: -0.8 -4 -3 -2 -1 0 1 2 10 10 10 10 10 10 10 05. rv Re Sr=+05. r 1 + 3− 1 cr ZZ (15) Fig. 4. Errors after fitting procedure. For the 17 data points with Re ≥ 1, the ruZ * mean error for the uncorrected fit was (–1 ∑(σ’ – σ’ )2 σ’2 )0.5 = 14.8; 17 0,num 0,pt 0,pt where r is the animal radius and u is 1 ∑ σ σ 2 σ 2 0.5 Z * the mean error calculated using Eq. (9) was (17– ( ’0,num – ’0,fit) ’ 0,pt) = 1.29. The legend provides the values of C’ represented by each plotting the threshold signal strength required to symbol. The fitting procedure reduced the error for the points with Re ≥ 1 to elicit an attack response (estimated as values similar to those for points with Re < 1 100 µm s–1; Titleman 2001, Lenz & Hartline Jackson & Kiørboe: Particle finding by chemosensing zooplankton 157
1999). (Note that this predicts a larger sensory distance gate, fill their guts, and move off the particle, a strategy than the simpler but less accurate formula used by called mining; other animals eat the entire particle, Kiørboe & Thygesen 2001). We have assumed that the engulfing it. Small animals tend to mine. For mining, length of a sensory appendage away from the center of g = g0, where g0 is a constant; for engulfing, g = m(r), the animal is the same as the animal radius rZ. where m is the mass of the particle. In the case of Note that βcruise > βambush because the swimming pro- mining, Eq. (16) simplifies to: vides an additional velocity component. In order to rU F = ∫ βn dr focus on the differences between the hydrodynamic rL (17) and chemical sensing rates, we will focus on com- while for engulfing: paring β and β . rU cruise plume F = ∫ βnm dr (18) rL
FEEDING RATE OVER A RANGE OF PARTICLE SIZES Numerical results
Particle size distributions Because particle properties and size distributions vary, it is impossible to reach definitive conclusions Animals feed on a range of particle sizes whose rela- about the rates at which zooplankton and particles tive contributions to the animal diet depends on the par- interact. We can, however, choose representative ticle size distributions as well as the relative efficiencies sets of properties. For example, particle abundance, for feeding on the particles. Falling particles occur with sinking speed, mass, and leakage rate are frequently a range of sizes which can be represented with particle described by power-law expressions: size distribution n(r) (e.g. Jackson et al. 1997). n = ar –b (19) Expressed mathematically, the rate at which an ani- d mal encounters particles with sizes between r and r +dr v = cr (20) is βn dr, where β can be the encounter rate kernel for m = er f (21) any search mechanism. If the amount eaten at each L = lm = ler f (22) contact is g, then the total rate of food consumption F is given by: where l is the specific leakage rate (e.g. Kiørboe & r ∫ U β Jackson 2001). We assume that the animal swims at F = r ng dr (16) L a rate proportional to its length: vZ = 2.9 body lengths –1 –1 where rL and rU are the lower and upper size ranges s = 5.8rZ (body lengths s ) (n = 51; data from Mauch- × –10 –3 for particle feeding. line 1998), S = rZ, and that C0 = 0.5 10 mol cm There are different strategies that animals use when (Kiørboe & Thygesen 2001 and references therein). For feeding on the particles. Some animals find an aggre- the size spectra of both marine snow and fecal pellets,
1 A: marine snow B: fecal pellet 10 101
0 0 plume 10 plume 10 β β / /
-1 -1 cruise 10 cruise 10 β β -1 10-1 10
rz (cm) rz (cm) -2 0 -2 -1 10 -1 10 10 -2 10 10-2 10 10-3 10 r (cm) r (cm)
Fig. 5. Comparison of the βs for plume seekers relative to cruisers as functions of zooplankton and particle radii. (A) Parameters typical of marine snow particles: v = 0.13r 0.26 cm s–1, L = 1 × 10–12r 1.5 mol s–1 (Kiørboe & Jackson 2001); : plume length > 1 m. (B) Parameters typical of fecal pellets, with v calculated assuming Stokes sinking with an excess density of 0.125 g cm–3 (consistent with Komar et al. 1981), carbon density = 0.1 µg µm–3, C:N = 6.7 mol/mol, l = 0.2 d–1, and resulting v = 2656r 2 cm s–1, = 1.21 × 10–8 3 –1 × –10 –3 –1 L r mol s . In both cases, C0 = 0.5 10 mol cm , u* = 0.01 cm s (Titelman 2001, Lenz & Hartline 1999), and r is in cm. Light areas indicate conditions where the βcruise is greater than βplume; dark areas indicate the reverse 158 Mar Ecol Prog Ser 269: 153–162, 2004 ) A: marine snow ) B: fecal pellet 1 1 -1 10 -1 10 s 10 0 s 100 -1 -1 10 -1 10-1 -2 -2 (cm 10 (cm 10 n n
⋅ ⋅ 10 -3 10-3 10 -4 10-4 plume -1 plume -1 β 10 β 10
rz (cm) rz (cm) -2 -2 10 -1 10 -1 0 -2 -2 10 -3 10 10 10 10 10 r (cm) r (cm)
Fig. 6. Number feeding rate spectrum for zooplankton consuming a fixed amount of a particle per visit (βplume n). This can be converted into the mass feeding rate spectrum similar to that shown in Fig. 7 by multiplying with the mass eaten per visit (g0). (A) Particle distribution and types typical of marine snow; (B) particle typical of fecal pellets. Values as in Fig. 5 we use values observed in Monterey Bay, California, but larger particles are more efficiently found by the (a = 2.5 × 10–5 and b = 3; Jackson et al. 1997). These plume finders (Fig. 5B). More interesting than the certainly greatly overstate the concentration of fecal differences between different-sized fecal pellets is the pellets but provide a starting point for discussion. fact that the 2 particle finding modes are so similar. For typical particle characteristics of marine snow and The feeding rate spectrum for plume finding fecal pellets, the comparison shows that plume-finding (= βplumen) suggests that it is easier to find a small is more effective than cruising but that the differences marine snow-type particle than a large one, but that between the 2 strategies are relatively slight (Fig. 5). fecal pellet-type particles are easiest to find and that While there is a small effect of animal size, there is a large and small pellets are encountered at similar rates much greater effect of particle size and settling rate. For (Fig. 6). The relative spectral shape shifts to favoring a particle characteristic of marine snow, the relative larger particles if the greater mass of the larger parti- efficiency of plume-finding exceeds that of cruising for cles is included (βplumenm; Fig. 7). For the marine snow all but the smallest particles, in part because of the ever particles, the mass feeding rate spectrum is essen- lengthening plume (Fig. 5A). For the largest particles, tially flat, whereas for fecal pellets the larger ones are the plume can exceed 1 m. It is unknown how long such favored. The greater swimming rates and sensory a plume can become before other processes such as ranges favor the larger animals. turbulence disrupt it. A small particle characteristic of a The feeding rate spectra describe the relative impor- fecal pellet is also more efficiently found by the cruiser, tance of each size class in the potential diet of an ani- ) ) -1
-1 -5 A: marine snow -5 B: fecal pellet s 10
s 10 -1 -1 -7 10-7 10
-9 10-9 10 m (g cm ⋅ m (g cm ⋅ n ⋅
n -11 ⋅ 10-11 10 -1 -1
10 plume 10 plume β β
rz (cm) rz (cm) -2 -2 10 0 10 -1 -2 -1 10 -3 -2 10 10 10 10 10 r (cm) r (cm) Fig. 7. Mass feeding rate spectrum for zooplankton consuming the entire particle. (A) Particle distribution and types typical of marine snow; (B) particle typical of fecal pellets. Values as in Fig. 5 Jackson & Kiørboe: Particle finding by chemosensing zooplankton 159
A: marine snow B: fecal pellet -2 10-2 10 ) ) -3 10-3
-1 10 -1
(s -4 (s -4 0 10 0 10 g g / /
F F -5 10-5 10 -1 10-1 10
r (cm) z rz (cm)
-2 0 -2 -1 10 -2 -1 10 10 -3 -2 10 10 10 10 10 r (cm) r (cm) Fig. 8. Integrated feeding rate divided by the food ration for a zooplankter consuming a fixed amount per visit to the particle r (∫ β ndr= F/g ). When multiplied by the food ration, it represents the total rate of food concentration when eating from rL plume 0 particles between rL = 30 µm and r in size. (A) Particle distribution and types typical of marine snow; (B) particle typical of fecal pellets. Values as in Fig. 6. The maximum amount that an animal can eat is 3× the fecal pellet volume. The relationship between 3 fecal pellet volume and prosome length is logVF = 2.474 logLP +5.226 where VF is fecal pellet volume (µm ) and LP is prosome length (mm), using data for copepods from Mauchline (1998). We estimate the prosome as 3× the zooplankton radius
mal. Integrating the feeding rate spectra provides a approximately 50% body carbon d–1. This is a very measure of the total food available for an animal reasonable number for the marine snow, but too high
(Figs. 8 & 9). The quantity F/g0 provides a contact rate for the fecal pellets, probably reflecting the greatly for the mining zooplankter, with the inverse providing overstated fecal pellet concentrations assumed in the an estimate for the time between contacts. For the calculations. larger animals, the contact time between aggregates could be less than 220 s for the marine snow particles and 10 s for the fecal pellets (Fig. 8). DISCUSSION The integrated feeding rate for the animals that con- sume the entire particle is heavily weighted toward the We emphasized 2 sets of particle properties and dis- larger particles (Fig. 9). For the largest animals, the tributions as a way of exploring a range of possibilities. consumption levels can be as high as 63 ngC s–1 for However, marine snow particles have a range of mass, fecal pellets and 2.4 ngC s–1 for marine snow, corre- fall velocities, and size distributions. These differences sponding to, respectively, more than 10 times and will affect the actual rates of zooplankton feeding. The
A: marine snow B: fecal pellet 10-8 10-8 -9 -9
) 10 ) 10 -10 -10 -1 10 -1 10 10-11 10-11 10-12 10-12 (g-C s -13 (g-C s -13 F 10 F 10 -1 10 10-1
r (cm) z rz (cm)
-2 -2 10 0 10 -1 -1 -2 -2 10 10 -3 10 10 10 10 r (cm) r (cm)
Fig. 9. Feeding rate for a zooplankter consuming the entire particle upon contact. This represents the rate if it consumes particles between rL = 30 µm and r. (A) Particle distribution and types typical of marine snow; (B) particle typical of fecal pellets. Values as in Figs. 5 & 7 160 Mar Ecol Prog Ser 269: 153–162, 2004
-3 -3 A: C0 = 2.5e-010 mol cm B: C0 = 1e-011 mol cm 1 101 10 plume plume β
0 β 0 / 10 / 10 cruise cruise β
β -1 10-1 10 -1 10 10-1
rz (cm) rz (cm)
-2 -2 10 -1 0 10 0 -2 10 -2 -1 10 10 10 10 10 r (cm) r (cm)
Fig. 10. Effect of threshold concentration on the comparison of the βs for plume seekers relative to cruisers as functions of zoo- plankton and particle radii. Parameters are the same as those for Fig. 5A, with the exception of the threshold concentrations. × –10 –3 × –11 –3 × 1 (A) C0 = 2.5 10 mol cm ; (B) C0 = 1 10 mol cm . These are 5 and ⁄5 of the C0 used elsewhere focus of this paper has been on demonstrating that Plume size plume feeding can be described relatively simply and that it appears to be a very efficient way for animals to Experimental observations allow the estimation of find falling food. the parameters describing particle detection by hydro- This analysis has focussed only on the effect of feed- mechanical mechanisms. There are few corresponding ing strategy on feeding rate, showing the importance observations for plume finding in animals, although of animal size in determining feeding rate. The analy- there are more such measurements of particle detec- sis did not include the costs of the different strategies. tion by microorganisms (e.g. Blackburn et al. 1998,
These include the metabolic costs of being large and of Mitchell et al. 1996). For example, the value of C0 used moving to find particles. The costs also do not include here could be high. A reasonable first estimate would any enhanced mortality rate associated with swim- be that the minimum increment in concentration of an ming, which increases the detectability of an animal, amino acid that is detectable equals its background as well as increasing the rate at which it collides with concentration. A typical value for the sum of all dis- an ambush predator. These costs are similar for cruis- solved free amino acids in the ocean is 25 nM = 2.5 × ers and plume finders, but different for sedentary 10–11 mol cm–3 (e.g. Lee & Bada 1977). Because the ambush and flux feeders. The final analysis of the concentration of any single amino acid is less, a value –11 –3 value of a feeding strategy for any animal must include of C0 = 10 mol cm is reasonable and one-fifth of the these costs as well as the gains. value used in the above simulations. Using this smaller
value of C0 increases the plume length by a factor of 1.5 5 and the σ0 by 5 = 11 (Eqs. 3 & 5). Higher sensitivi- Comparison of predictions with observations ties to specific amino acids have been observed in copepods (10–12 mol cm–3; Yen et al. 1998) and even While the prediction is that plume finding should be a greater sensitivities have been reported for marine common strategy, we know very little about the poten- crustaceans (e.g. Fuzessery & Childress 1975, Olla tial for zooplankton to employ this strategy. It has been 1977, Pearson et al. 1980). The resulting increases in demonstrated qualitatively for only 2 species, a plank- contact rates for plume feeders further enhance the tonic shrimp (Hamner & Hamner 1977) and a plank- advantage of this mode of particle feeding. Con- tonic copepod (Kiørboe 2001), and it is known that versely, an increase in the threshold concentration several copepods can follow pheromone trails to find would decrease the contact rates. mates (Tsuda & Miller 1998, Yen et al. 1998). Such As an example, the results for the conditions used observations are difficult to make. Many more obser- here suggest that plume-sensing and cruising are gen- vations have demonstrated that zooplankton can use erally similar in the rates of zooplankton contact with hydromechanical cues (Haury et al. 1980, Fields & Yen marine snow, although cruising is more effective for 1997, Kiørboe et al. 1999). This does not necessarily re- smaller particles and plume sensing more effective for flect the relative occurrence of the different strategies. larger ones (Fig. 5). Increasing the threshold concen- Jackson & Kiørboe: Particle finding by chemosensing zooplankton 161
tration by a factor of 5 makes the cruising mode more finders should be more effective with the other effective (Fig. 10A); decreasing the threshold concen- particles. tration by a factor of 5 makes plume-sensing more The importance of both particle mass and diameter effective (Fig. 10B). There is enough variability in the for animal feeding suggests that they are important properties and distributions of natural particles to make properties to measure. Among the possible approaches a simple generalization impossible, but the comparison are the determination of the rate of fecal pellet produc- is interesting. tion and the pellet properties (e.g. Feinberg & Dam The other important factor that we have simplified is 1998). the rate of particle solubilization. It can be expected to vary with the state of decay of the particle, as well as anything that changes bacterial metabolic rates, such Effect of depth as temperature. Turbulence is an important process that has not been Depth provides a dramatic range of environments included in this analysis. It could be expected to over relatively short distances for planktonic animals. decrease the plume length by disrupting the integrity This range has implications for different particle feed- of the plume, thereby decreasing the rate of particle ing types. Aside from the decrease in particle flux and feeding. The intermittent nature of turbulence affects concentration with depth, there are changes in the both the time interval that a plume exists as well as physical environment and in the nature of the par- its total length. As a result, a rapidly falling particle ticles. should have its plume less disrupted by turbulence Turbulence levels decrease with depth (e.g. Gargett than an equal length plume from a slowly settling & Osborn 1981). As a result, there should be less dis- particle. ruption of the plume structure, allowing longer plumes and more effective plume finding. Less turbulence also implies less hydrodynamic noise and, hence, more Particle distributions and properties efficient detection of hydrodynamic signals. In addition, the rate of aggregation should de- The properties of the sinking particles are crucial to crease with depth as a result of the lower particle the encounter rates. While there are numerous obser- concentrations and lower turbulent shear conditions. vations on particle size distributions as a function of This should change the slope of the particle size dis- diameter, there are substantially fewer on the simulta- tributions. The relative contribution of fecal pellets to neous variations in particle mass. Simultaneous in situ the fluxing particulate material also decreases with measurements of particle settling speed and diameter depth, since fecal pellets are remineralized rapidly in have shown considerable variability in the average the upper water column (e.g. Smetacek 1980, Riser et properties at different locations as well as in the prop- al. 2001). erties at any one time and place. Examples where this Because the background concentrations of organic has been done include the settling measurements of matter decrease with depth (e.g. Lee & Bada 1977), Alldredge & Gotschalk (1988) and Asper (1987) as well there may be a decrease in the concentration enhance- as settling spectra determined from sediment traps ment needed for plume detection. These changes (Kiørboe et al. 1996, Waite & Nodder 2001). Previous would lead to an increase with depth of the relative theoretical studies of aggregate generation suggest advantage of the plume-finding strategy over the that the multiple particle sources in the environment cruising strategy. This might be partially compensated can affect the mass and settling properties of particles, by a change with depth of the composition of the so that they need to be characterized by multiple mea- falling particles, which includes a decrease in the rela- surements on the same particles (Jackson 1998, 2001). tive concentration of labile organic matter (e.g. Arm- Because particle settling speed depends on both mass strong et al. 2001) and a consequent weakening of the and diameter, the implication is that there is consider- resulting chemical signal. able variation in particle composition. Lastly, the decrease in zooplankton abundance with Our use of a hypothetical distribution for fecal pellets depth should reduce the predation pressure and in this analysis was an attempt to broaden the ex- increase the value of active vs passive strategies. pected range of particle behaviors. It shows that parti- The conclusion from these considerations is that the cle type can be important in determining the relative efficiency of particle feeding should have a strong success of different feeding behaviors. In particular, depth component. Overall, the prediction is that the hydrodynamic sensing should be most efficient at relative advantage of plume finders is expected to sensing the most massive particles, such as large fecal increase with depth, while cruisers are at a relative pellets (Svensen & Kiørboe 2000). In contrast, plume advantage near the surface. 162 Mar Ecol Prog Ser 269: 153–162, 2004
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Editorial responsibility: Otto Kinne (Editor), Submitted: November 19, 2002; Accepted: October 11, 2003 Oldendorf/Luhe, Germany Proofs received from author(s): March 4, 2004