JPR Advance Access originally published online on November 16, 2008
Journal of Plankton Research 2009 31(2):121-133; doi:10.1093/plankt/fbn109
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Swimming in turbulence: zooplankton fitness in terms of foraging efficiency and predation risk
1 Danish Institute for Fisheries Research, Department of Marine Ecology and Aquaculture, Technical University of Denmark, Kavalergaarden 6, DK-2920 Charlottenlund, Denmark 2 Niels Bohr Institute, Niels Bohr International Academy, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
* CORRESPONDING AUTHOR: awv{at}dfu.min.dk
Received on September 17, 2008; accepted on October 23, 2008
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODRESULTSDISCUSSIONFUNDINGREFERENCES |
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Turbulence impacts zooplankton fitness in opposing manners, by increasing contacts with prey but at the same time increasing contacts with predators. We investigate the fitness of individual zooplankton in terms of a trade-off between energetic gains and costs, and risk of predation. Through idealized descriptions of foraging and predation in a turbulent water column, we determine how fast a zooplankter should swim, if at all, and where should it position itself in the vertical to maximize its fitness given certain environmental conditions. Suspension feeding has an advantage over ambush feeding at high turbulence levels, whereas cruise feeding becomes optimal at low turbulence levels. In general, behaviours that seek out low levels of turbulence increase an individual's fitness, a prediction that runs counter to turbulent encounter rate arguments, and exposes the fallacy of examining only the foraging aspects of the fitness trade-off.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODRESULTSDISCUSSIONFUNDINGREFERENCES |
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Nearly all the important life processes of plankton (e.g. growth, reproduction and mortality) are mediated by encounter rates; the rate at which individual plankters contact other organisms, particles or patches of resource. These contacts are brought about by the relative motion of the organisms involved, either through swimming or stirring by turbulence (or both). In this work, we investigate the fitness of individual zooplankton with a view to establishing their optimal behaviour in a turbulent environment. In particular, zooplankton are sandwiched between opposing pressures; to find prey so as to grow and reproduce, while at the same time, to minimize their risk of predation (Lima and Dill, 1990
; Tiselius et al., 1997). These pressures are in part due to environmental conditions (e.g. predator and prey concentration, temperature, light and turbulence) and in part due to their own behaviour (e.g. swimming speed and vertical migration). Often, a behavioural strategy that increases a potential feeding benefit also increases risk. Increasing swimming speed, for instance, increases the rate an organism finds prey, but also increases the probability of encountering a predator (Visser, 2007). Likewise, feeding in sunlit surface waters where autotrophic prey are abundant can increase a zooplankter's feeding opportunity but also expose it to the attentions of visual predators (Fiksen and Carlotti, 1998). By whatever means behavioural changes are initiated, the rules by which they are governed have been shaped by evolutionary processes. Indeed, one might expect that the behavioural rules expressed in nature should reflect the evolutionary processes that shaped them in the past. Specifically, behaviour is an adaptive trait that seeks to maximize the fitness of individuals under ever-changing conditions. One specific aspect of this is the trade-off between beneficial and detrimental encounters, encounters with prey on the one hand and encounters with predators on the other.
Twenty years ago, Rothschild and Osborn (Rothschild and Osborn, 1988) introduced the seminal concept to plankton ecology, that increasing turbulence increases the rate of contacts between planktonic organisms and their prey. In the intervening years, a large number of studies have delved deeper into different aspects of this concept as it relates to zooplankton ecology. Although differing in detail and focus, some broad lines of consensus can be drawn from these studies.
Turbulence increases contact rates (Costello et al., 1990; Marrasé et al., 1990; Mann et al., 2005) but this does not necessarily translate into increased ingestion rates. Ingestion rates only increase when prey concentrations are less than saturating (Saiz et al., 1992). When prey concentrations are greater than this, ingestion rates are governed by handling time rather than contact rates. Furthermore, turbulence can interfere with an organism's ability to remotely detect (Saiz et al., 1992; Saiz and Kiørboe, 1995) and/or capture prey (MacKenzie et al., 1994). In general, at low levels of turbulence, ingestion rate increases with turbulent intensity, but flattens off and eventually decreases as turbulence levels increase further, giving a dome-shaped relationship (MacKenzie and Kiørboe, 2000), as seen both in the laboratory (Saiz et al., 2003) and field (Irigoien et al., 2000), and confirmed in individual-based numerical simulations (Lewis and Pedley, 2000; Mariani et al., 2007).
Zooplankton also exhibit changes in behaviour in response to turbulence. Their metabolic rates increase as turbulence increases (Alcaraz et al., 1988). Swimming behaviour, both in speed and path geometry, vary with different levels of turbulence (Saiz and Alcaraz, 1992; Seuront et al., 2004) as does feeding mode and subsequent prey selectivity (Kiørboe et al., 1996; Caparroy et al., 1998). Lastly, turbulence is a highly variable environmental parameter; changing in both time and space over many orders of magnitude. In particular, vertical variations may be many orders of magnitude in the space of a few metres. Many pelagic species of copepod appear to migrate deeper into the water column to avoid high levels of turbulence in the surface (Incze et al., 2001; Visser et al., 2001), a behaviour that is often accompanied by a decreased ingestion rate (Irigoien et al., 2000; Visser et al., 2001).
We will address the questions, how fast a zooplankter should swim, if at all, and where should it position itself in the vertical to maximize its fitness given certain environmental conditions. Our primary focus is on the effects of turbulence in that it is highly variable in both time and space, and it directly impacts fitness both positively and negatively through a number of mechanisms. In particular, turbulence enhances an organism's contacts with prey, but also its contacts with predators. The basic method is to examine the net rate of energy gain (energy ingested minus energy expended) and mortality rate of a test organism following a fixed behavioural option in a given environment. The test organism can be thought of as either a member of a single species with plastic behaviour, or a generic member of a range of species that face similar opportunities, hazards and constraints. As a measure of fitness, we take the ratio of net rate of energy gain to mortality rate, essentially a measure of potential reproduction. We investigate the general principals as well as a specific example of pelagic adult copepods (e.g. Acrtia tonsa, Temora longicornis, Oithona similis and Centropages typicus) commonly found in temperate shelf seas. Since feeding mode is intimately connected to motility, we consider three feeding modes exhibited by pelagic copepods: suspension feeding (i.e. generating a feeding current), ambush feeding (i.e. remaining motionless while relying on prey motility to bring about contacts) and cruise feeding (i.e. actively searching for prey). Thus, deducing how optimal swimming behaviour varies as a function of depth, also says something about how feeding modes, and the species that practice them, should be arranged in space.
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METHOD |
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TOPABSTRACTINTRODUCTIONMETHODRESULTSDISCUSSIONFUNDINGREFERENCES |
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Foraging: benefit and cost
The growth rate and (in part) reproduction rate of planktonic organisms depend ultimately on the net rate at which they acquire energy while foraging. This can be written in a relatively general form as:
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; Morris et al., 1985; Buskey, 1998). For the purposes of this work, we choose β = 1%.
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The ingestion rate can be related to encounter rate Zp as
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). The equations are closed with respect to turbulence by applying Richardson's law. That is
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is turbulent dissipation rate and CR is Richardson's constant and is of order 1. The turbulent velocity scale, wp, is the turbulence-induced relative velocity of two particles separated by the distance Rp as is appropriate for turbulence-enhanced contacts (Visser and MacKenzie, 1998), making equation (3) consistent with the experimental findings (e.g. Mann et al., 2006) and numerical models (Yamazaki et al., 1991; Lewis and Pedley, 2000). The above formulation covers both ambush and cruise feeding modes, the former being for v = 0, and the latter for v > 0.
The cruise–ambush formulation proceeds under the tacit assumption that the organism is neutrally buoyant, and that all the swimming energy expended is converted into forward movement through the water. Many marine organisms, however, are not neutrally buoyant, and have excess densities, 
, with respect to seawater of 30–50 kg m–3 (Mauchline, 1998), resulting in a sinking speed (assuming Stokes flow) of
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Thus, in order to remain at a given depth, the organisms must constantly expend energy at the average rate cv02. There is, however, an advantage to be gained from being negatively buoyant. For the same effort, a gravitationally tethered organism (i.e. one that swims upwards to compensate for its sinking) has a clearance rate approximately 1.5 times higher than that of a cruising, neutrally buoyant organism of the same size (Tiselius and Jonsson, 1990, Jiang et al., 2002). In this case, we write the encounter rate with prey Zp = 1.5
R2v0. Furthermore, a gravitationally tethered suspension feeder reduces its marginal predation risk as it contributes no relative motion to its encounter rate with predators. Effort in excess of that required to hold the organism suspended will result in its forward motion, switching from suspension feeding to cruise feeding. Combining these effects, we can write, in a simplified fashion, the net encounter rate as
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The cost of swimming and maintaining a feeding current can be written as c (v0+v)2. Here, v is the speed of the organism relative to the fluid.
This formulation equation (6) merges with the ambush–cruise formulation given above [equation (3)], as a function of the density contrast between the organism and the fluid. Specifically, when =0, v0=0, and both the encounter rate and energetic cost become the same as for an ambush–cruise feeding organism.
The mortality rate of a zooplankter is in part due to background attrition from unavoidable risks, parasites, disease and old-age, and in part due to direct predation through risky behaviour tempered by environmental conditions. Combining these, and assuming a 100% capture efficiency, we can write the overall mortality rate as
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We note here that the detection distance Rq may be a function of environmental conditions. Specifically, for a visual predator, Rq depends on light and thus on time of day and depth below the surface. When we come to examine the vertical distribution of optimal behaviour, we will simulate this as a simple linear relationship
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Darwinian fitness, the central concept of evolutionary theory, describes the capability of an individual to increase its representation (specifically of its genotype) in future generations. Elements of fitness thus include growth, reproduction and survival. Precisely how these elements combine together to define fitness though is not that clear, and a variety of parameterizations have been promoted in the literature (Giske et al., 1993; Kozlowski, 1996). Nonetheless, a parameter that has a relatively simple interpretation and captures the gross aspects of fitness is g the ratio of instantaneous rate of energy intake to mortality rate:
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This can be related as a proxy formulation to Fisher's reproductive value, the expected contribution to future reproduction given current conditions (Clark, 1994). This formulation is essentially the same as the optimal fitness criterion proposed by Gilliam and Fraser (Gilliam and Fraser, 1987) and explored subsequently in theoretical studies (Gilliam, 1990; Houston et al., 1993), experiments (Gilliam and Fraser, 1987; Skalski and Gilliam, 2002) and models (Giske et al., 1997). While it has been criticized in certain applications (see Discussion), it has a well-founded ecological significance in an idealized sense (Clark, 1994).
Formally, we will explore the fitness parameter
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It has units of energy and, in a very simple interpretation, is the net future energy acquired by an organism over its expected life-span following a given behaviour.
Vertical variation of forcing parameters
Turbulence, prey and predation risk are, in general, functions of depth. Turbulence, for instance, is high at the surface where wind-induced shear stresses are high, and falls off in some exponential manner with depth (MacKenzie and Leggett, 1993). Prey concentrations likewise tend to be higher at the surface, and while predators may be anywhere in the water column, the risk posed by visual predators is light-dependent, and thus also depth-dependent. To illustrate the impact of this on swimming speed, feeding mode and vertical position, we present an idealized diagnostic model of water column properties.
Specifically, we introduce three profile functions, 
(z), 
(z) and 
(z), that determine the vertical distribution of prey, the attenuation of light with depth and the vertical profile of turbulent dissipation rate, respectively. That is
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), with e-folding scale z1 = 15 m (MacKenzie and Leggett, 1991). At any given depth z, prey concentration, light intensity [and thus predator perception distance via equation (10)] and turbulent dissipation rate can be specified. The optimal swimming speed and maximum attainable fitness can thus be estimated via equation (12) as functions of depth. The depth at which maximum attainable fitness peaks is the optimal depth where, ceteris paribus, an organism should try to position itself.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODRESULTSDISCUSSIONFUNDINGREFERENCES |
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The fitness landscape
The general mechanisms are illustrated in Fig. 1, which show the fitness (in terms of energy acquired in an expected lifetime) as a function of swimming speed and turbulence. This example is for cruise–ambush feeding ( = 0) for a prey concentration of P = 108 m–3 and a predator density Q = 10 m–3. This illustrative example is for a generic adult copepod (prosome length 700 µm) with detection distance Rp = 600 µm, feeding on a typical prey such as Thalassiosira weissflogii or Oxyrrhis marina (size=20 µm, energy content e = 6 x 10–6 J cell–1) while being preyed upon by a typical predator such as larval herring (MacKenzie and Kiørboe, 2000) or chaetognaths (Saito and Kiørboe, 2001): detection distance Rq = 6 mm.
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There are three regions where the fitness goes to zero. When both swimming speed and turbulence are low, encounter rates with prey are too low to meet base metabolic costs. When swimming speeds are high, the cost of swimming exceeds any energy income from foraging. Finally, when turbulence is high, ingestion of prey becomes saturated while predation risk increases so that the fitness decreases. Bracketed by these zones, fitness exhibits a dome-shaped relationship, both with respect to swimming speed and turbulence.
Figure 2A plots the optimal swimming speed (i.e. where g is a maximum) for the same configuration as in Fig. 1. At low turbulence levels, these have a well-defined optimum at 
2 mm/s, a realistic swimming speed for adult copepods (Mauchline, 1998). As turbulence levels increases, the optimum swimming speed increases slightly until it suddenly drops to zero. That is, optimal behaviour switches from cruise to ambush feeding at about = 10–4 m2/s.
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At high turbulence levels, optimal swimming speed has a broad, shallow peak. To quantify this, the 95% of optimal is also plotted. Anywhere within this range, swimming speed will have a marginal impact on fitness. Specifically, at high levels of turbulence, swimming speeds in the range 0–2 mm/s will have similar fitness consequences to within 5%.
For the case where the prey swims (Fig. 2B; up=1 mm/s), switching between feeding modes becomes more pronounced. Ambush feeding become optimal at low levels of turbulence as well, below = 10–7 m2/s, where energy intake is facilitated by prey swimming: g > 0 at low turbulence and low swimming speed as distinct for the case where the prey is non-motile (Fig. 2A). This low-turbulence ambush-feeding optimum disappears when the predator swims (Fig. 2D; up = 0, uq = 10 mm/s). Somewhat surprisingly, optimum swimming speed increases over a broad range of turbulence levels, from 2 mm/s for ambush predator (Figs 2A and B) to 8 mm/s for motile predator (Fig. 2D). For a negatively buoyant organism (Fig. 2C; = 50 kg m–3), optimal swimming speed drops to zero at a somewhat lower turbulence level than the equivalent case for a neutrally buoyant organism (Fig. 2A).
Optimal swimming speed in turbulence
The fitness landscape is a function of a suite of parameters; not only swimming speed and turbulence but a great many more. In particular, we present here in Fig. 3, the optimal swimming speed as a function of (Fig. 3A) prey concentration P (Fig. 3B), prey swimming speed up (Fig. 3C), predator concentration Q and (Fig. 3D) predator swimming speed uq. The example here is for a neutrally buoyant organism ( = 0), while other parameters not specifically varying, are set to default values (Table I).
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As prey concentration decreases, there comes a level below which fitness becomes negative even at its optimal value (Fig. 3A). That is, some prey concentrations are simply too low to sustain the organism. This is indicated as the non-viable region in Fig. 3A. As prey concentration increases from this level, optimal swimming speed decreases; the organism can afford to move slower, reducing its intake of prey but also reducing its predation risk. Eventually, at high enough prey concentrations, optimal behaviour is to not swim at all; the region indicated as ambush feeding in Fig. 3A. Not surprisingly, fitness is maximal at low turbulence levels, and high prey concentrations.
Optimal swimming speeds approach zero (i.e. switch to ambush feeding) as prey swimming speeds increase (Fig. 3B), and at high levels of turbulence (>10–3 m2/s3). Here, energy income is sufficiently high without the organism having to expose itself to predation risk by swimming. High prey swimming speeds also correspond to high fitness. Somewhat surprisingly, for moderate and low levels of turbulence (<10–3 m2/s3), the range of prey swimming speeds for which ambush feeding is optimal decreases as turbulence increases.
Optimal swimming speeds and fitness are high for low predator concentrations (Fig. 3C), with ambush feeding becoming optimal at high turbulence levels. The transition to ambush feeding occurs at lower turbulence levels as predator concentration increases. Ambush feeding also becomes optimal at extremely low turbulence and high predator numbers.
More surprisingly, however, optimal swimming speed increases with increasing predator swimming speed (Fig. 3D). When a slow swimming organism is exposed to a fast swimming predator, its own swimming speed has a relatively small impact on its predation risk. The organism should, therefore, increase its swimming speed to optimize its energy income. Fitness, however, decreases with predator swimming speed.
For negatively buoyant organisms, the pattern is similar, albeit that the overall fitness of a negatively buoyant organism is greater than that for neutrally buoyant, and the region of parameter space for which suspension feeding is optimal is greater than that for ambush feeding.
Vertical positioning in a turbulent water column
The shape functions for vertical profiles (Fig. 4) of prey abundance, light intensity and turbulent dissipation rate [equation (13)] are chosen so as to be consistent with conditions typically found in temperate shelf seas (e.g. Visser et al., 2001). Specific parameters are listed in Table I. In the following, when referring to turbulent dissipation rate, we refer to 0, that found at the surface (z = 0) with the understanding that it falls off rapidly with depth as governed by (z) [equation (13)].
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For a spatially uniform predation risk (e.g. with hydromechanically sensitive uniformly distributed chaetognaths), optimal swimming speed at the depth of maximum fitness for a neutrally buoyant copepod is relatively constant at 2 mm/s over a wide range of surface turbulent intensities (Fig. 5B). The depth of maximum fitness, however, increases from
10 m for low turbulence, to 40 m at high turbulence (Fig. 5A). To give a measure of the sensitivity, we also plot the depth range over which fitness varies by 95% of its maximum attainable value. This depth range is relatively constant at ±7 m.
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When predation risk becomes attenuated with depth (e.g. for a visual predator), the depth of maximum fitness for low turbulence levels increases to about 30 ± 10 m (Fig. 5C) for 95% of maximum attainable fitness. Optimal swimming speeds within this depth range are relatively constant at 2 mm/s (Fig. 5D). Overall fitness in this case (Fig. 5C), as may be expected, is somewhat higher than for a uniform but higher predation risk (Fig. 5A).
For both visual and hydromechanical predation risk, ambush feeding becomes optimal close to the surface at high turbulence intensities (Figs 5B and D). For the same situation as in (Fig. 5B) but for a negatively buoyant copepod, = 50 kg/m3, ambush feeding becomes the optimal strategy down to 40 m (Fig. 5F). The overall fitness for a negatively buoyant copepod is higher than that for one that is neutrally buoyant (Figs 5C and E). The depth of maximum fitness for a negatively buoyant copepod decreases at low turbulence levels (Fig. 5E) compared to that for a neutrally buoyant copepod (Fig. 5C).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODRESULTSDISCUSSIONFUNDINGREFERENCES |
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Turbulence, along with light and temperature, strongly structure the marine pelagic environment along its vertical dimension. Organisms that live in this realm have to contend with these factors at the most fundamental level; specifically how these factors influence their individual growth and reproduction and survival probability. Within this context, behavioural strategies such as foraging effort, feeding mode and vertical migration are options that an organism can select from to maximize its fitness.
While these effects are fundamentally driven at the level of individuals, their cumulative impact can propagate throughout populations, communities and ecosystems through behaviourally mediated indirect interactions (Dill et al., 2003). Indeed, adaptive foraging behaviour has been identified as a key factor that dynamically shapes the structure and function of ecosystems (Schmitz et al., 2008). One aspect of this seen here is that adaptive (plastic) behaviour has a cascading effect through trophic levels. For example, higher predator abundance reduces an organism's optimal swimming speed which in turn reduces the organism's clearance rate on its prey. For instance, Fig. 6A shows a 5-fold decrease in clearance rate from low to high predator abundance, an effect most pronounced at low turbulence levels. Top–down control by a predator can be mediated not only in terms of prey density, but also in shaping the prey's foraging behaviour. Likewise, higher prey abundance also reduces an organism's optimal swimming speed which in turn reduces its predator's clearance rate. This is shown in Fig. 6B, where clearance rate decreases over many orders of magnitude as prey concentration increases. The results in Fig. 6B should not be taken too literally as the organism's viability is in question over part of this range, and density-dependent effects in predation may limit clearance rates at high contact rates. While these adaptive responses in inter-trophic level links are in the same sense as cascading effects through density-mediated interactions (e.g. more predators, fewer organisms and increased prey growth), they have a moderating effect on population dynamics (Abrams, 1992), damping out chaotic oscillations and giving the system greater resilience against stochastic extinctions.
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With respect to foraging, it has long been considered that turbulence has a dome-shaped effect. At low turbulence levels, increasing turbulence increases ingestion, while at high levels, increasing turbulence impairs the ability of organisms to either detect, or capture prey. This does not appear to be the full story. In considering predation risk, we see that nearly universally, fitness at optimal foraging effort is a decreasing function of turbulence, and this is true even in the absence of any negative effects of turbulence on ingestion rate. This is counter to the general paradigm that turbulence enhances encounter (and thus ingestion) rates. The reason for this is straight forward: since in general the detection distance of the organism to its prey is less than the detection distance of its predator to the organism (Rp < Rq) turbulence increases an organism's encounter with its predator faster than it increases its contacts with its prey. That is, as turbulence increases, predation risk increases faster than foraging benefit.
This has consequences on the optimal vertical distribution of organisms. In general, organisms should seek out low levels of turbulence, and position themselves at a depth where the marginal decrease in ingestion with respect to depth due to decreasing prey concentration exactly balances the marginal decrease in predation risk (e.g. due to decreasing turbulence with depth, decreasing light or both). In general, organisms that can, should migrate down with increasing surface turbulence, a process governed in this case by fitness considerations rather than impaired foraging ability as is usually argued (Visser et al., 2001). There is a fairly good agreement with observed turbulence-related downward migration of O. similis (Visser et al., 2001), a cruise–ambush feeder, which, at night appears to migrate downwards 2.5 m per decade of surface turbulent dissipation rate, consistent with results (Fig. 5A).
Whether this optimal depth-seeking behaviour applies in nature, depends of course on the ability of organisms to hold their position in the face of turbulent stirring. Large organisms such as adult copepods appear to have this ability, while this is less so for nauplii and even less for ciliates (Maar et al., 2003).
It appears that suspension feeding (i.e. gravitationally tethered feeding current) is always superior to a cruise–ambush feeding mode in terms of fitness. This arises through the twinned effects of increased clearance rate, and decreased predation risk per unit effort. However, to be effective, a suspension feeding organism must have excess density with respect to sea water. Such excess density does not come for free, and there are probably energetic costs involved (e.g. in maintaining an ion pump, or synthesizing high density materials such as chitin). A density deficit in collecting and storing lipids, for example, would have a similar effect (Jiang and Strickler, 2005), but would also incur costs. Factoring in these costs will in all likelihood limit the efficiency of maintaining a density contrast, and hence the ensuing fitness trade-off.
Within the context of our idealized analytic frame work, we can make some relatively general conclusions regarding optimal behaviour by noting that the essential details of the fitness trade-off are captured by
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Under different conditions, behavioural shifts should be controlled by the following criteria:
- A neutrally buoyant organism (v0=0, P, Q and L constant), should switch to ambush feeding when its prey swimming speed
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- A negatively buoyant organism (v0
0, P, Q and L constant), should switch to suspension feeding when its own sinking speed
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- At optimum swimming speed (i.e. maximizing g, P and L constant), all organisms should seek out the lowest turbulence levels.
- For the general case where L, P and vary with depth, an organism should migrate to a depth where
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While we can make these general remarks on the behavioural adaptation of zooplankton to turbulence, there are still a number of issues that remain unexplored. For instance, how well does Richardson's law, an abstraction for the relative motion of ideal point particles, actually describe the relative motion of inertial finite-sized bodies such as planktonic predators and their prey? How does the "down-side" effect of turbulence in detection and capture ability impact these conclusions? Other issues that are far from clear include the cost and benefit of gravitationally tethered suspension feeding, how effective feeding currents are in a turbulent flow and the power expenditure of maintaining them.
Perhaps most critical to these studies is the formulation of fitness. The fitness landscape is not static and changes not only with environmental factors, such as predator and prey densities, turbulence and light, but also with the abundance and behaviour of conspecifics, as well as the state (e.g. age) of the individuals involved. The maximization of fitness is achieved by continually changing behavioural rules reflecting trade-offs at many levels.
Furthermore, our parameterization of fitness, g = E/µ, may be less than ideal in several cases. It originally appeared in the literature as µi/
i (Gilliam and Fraser, 1987), where µi and i are the mortality rate and growth (or reproduction or net energy intake) rate associated with a particular behavioural option i. It was devised in a somewhat ad hoc manner to derive habitat selection rules, i.e. the best choice of habitat is that for which µi/i is a minimum. Some of the criticism of Gilliam's parameter stems from the odd behaviour it exhibits as i
0 (Railsback et al., 1999), behaviour that can be averted by inverting the parameter as we have done. It has also been criticized in that it assumes a constant environment (Clark, 1994). This is not actually correct in the context here. It is fully capable of giving behavioural rules that adapt according to prevailing conditions. What is does assume, is that future environmental conditions (both biotic and abiotic) are unpredictable, and the organism should proceed on the assumption that "this is as good as it gets". Further, in insisting that mortality rate is composed of two components, one independent and the other dependent on behaviour, we incorporate the concept of asset-protection (Clark, 1994), an important factor in evaluating reproductive value. Where the parameterization fails is when future environmental conditions are predictable, as in diel or seasonal cycles. A case, of some relevance for this study, is diel vertical migration. If, for instance it takes a finite time for an organism to migrate vertically, it may be beneficial in the long term to initiate downward migration before increased predation risk becomes manifest (Fiksen, 1997), effecting a trade off between lost feeding opportunity and projected risk.
Finally, an absolute maximization of fitness may be sub-optimal in that it locks organisms into a local, rather than a perhaps more global fitness maximum. There is also the problem of cognition in that behaviour can only be attuned to environmental factors that can be sensed. In the context here, mortality rate is perhaps most important; an organism may have a good sense of how many prey are available through its recent feeding success, but a direct measure of predation pressure is a rather dead-end pursuit. Proxy signals such as light, chemical smells or hydrodynamic regime may be of some use, and it is perhaps with regard to the more poorly known fitness elements that behavioural personalities are expressed, risk-aversion for instance (Fiksen et al., 2007).
In this work, we have chosen a simple expression for fitness, electing transparency over rigour. While there are any number of complicating issues regarding the estimation of fitness, what it is, how it is maximized and the behavioural rules that optimize various aspects of the trade-offs involved, it can be expected to play a central role not only in providing a mechanistic rationale for the behaviour of organisms, but in integrating evolutionary and ecosystem ecology.
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FUNDING |
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This study was supported by grants from the Danish Research Agency (272-07-0485, 21-03-0299, 3304-FFVFP-060683-01), and EurOceans.
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ACKNOWLEDGEMENTS |
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We thank Thomas Kiørboe, Ken Andersen, George Jackson and Uffe Tyggesen for discussion and advice.
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Notes |
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Corresponding editor: Roger Harris
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMETHODRESULTSDISCUSSIONFUNDINGREFERENCES |
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Abrams P. A. Predators that benefit prey and prey that harm predators: unusual effects of interacting foraging adaptations. Am. Nat. (1992) 140:573–600.[CrossRef][Web of Science]
Alcaraz M., Saiz E., Marrasé C., et al. Effects of turbulence on the development of phytoplankton biomass and copepod populations in marine microcosms. Mar. Ecol. Prog. Ser. (1988) 49:117–125.
Buskey E. J. Energetic costs of swarming behavior for the copepod Dioithona oculata. Mar. Biol. (1998) 130:425–431.[CrossRef]
Caparroy P., Pérez M. T., Carlotti F. Feeding behaviour of Centropages typicus in calm and turbulent conditions. Mar. Ecol. Prog. Ser. (1998) 168:109–118.
Clark C. W. Antipredator behavior and the asset-protection principle. Behavior. Ecol. (1994) 5:159–161.
Costello J. H., Strickler J. R., Marrasé C., et al. Grazing in a turbulent environment: behavioural response of the calanoid copepod Centropages hamatus. Proc. Natl Acad. Sci. USA (1990) 87:1648–1652.
Dill L. M., Heithaus M. R., Walters C. L. Behaviorally mediated indirect interactions in marine communities and their conservation implications. Ecology (2003) 84:1151–1157.[CrossRef][Web of Science]
Evans G. T. The encounter speed of moving predator and prey. J. Plankton Res. (1989) 11:415–417.
Fiksen Ø. Allocation patterns and diel vertical migration: modeling the optimal Daphnia. Ecology (1997) 78:1446–1456.[Web of Science]
Fiksen Ø., Carlotti F. A model of optimal life history and Diel vertical migration in Calanus finmarchicus. Sarsia (1998) 83:129–147.
Fiksen Ø., Jørgensen C., Kristiansen T., et al. Linking behavioural ecology and oceanography: larval behaviour determines growth, mortality and dispersal. Mar. Ecol. Prog. Ser. (2007) 347:195–205.[CrossRef]
Gilliam J. F. Hunting by the hunted: optimal prey selection by foragers under predation hazard. In: Behavioural Mechanisms of Food Selection—Huges R. N., ed. (1990) Berlin: Springer-Verlag. 797–818.
Gilliam J. F., Fraser D. F. Habitat selection under predation hazard: test of a model with stream-dwelling minnows. Ecology (1987) 68:1856–1862.[CrossRef][Web of Science]
Giske J., Aksnes D. L., Førland B. Variable generation times and Darwinian fitness measures. Evol. Ecol. (1993) 7:233–239.
Giske J., Rosland R., Berntsen J., et al. Ideal free distribution of copepods under predation risk. Ecol. Model. (1997) 95:45–59.
Houston A. I., McNamara J. M., Hutchinson J. M. C. General results concerning the trade-off between gaining energy and avoiding predation. Phil. Trans. R. Soc. Lond. B (1993) 341:375–397.
Incze L. S., Herbert D., Wolff N., et al. Changes in copepod distributions associated with increased turbulence from wind stress. Mar. Ecol. Prog. Ser. (2001) 213:215–227.[CrossRef]
Irigoien X., Harris R. P., Head R. N. Does turbulence play a role in feeding and reproduction of Calanus finmarchicus. J. Plankton Res. (2000) 22:399–407.
Jiang H., Strickler J. R. Mass density contrast in relation to the feeding currents in calanoid copepods. J. Plankton Res. (2005) 27:1003–1012.
Jiang H., Meneveau C., Osborn T. R. The flow field around a freely swimming copepod in steady motion: Part II numerical simulation. J. Plankton Res. (2002) 24:191–213.
Kiørboe T., Saiz E., Viitasalo M. Prey switching behaviour in the planktonic copepod Acartia tonsa. Mar. Ecol. Prog. Ser. (1996) 143:65–75.[CrossRef]
Kozlowski J. Energetic definition of fitness? Yes, but not that one. Am. Nat. (1996) 147:1087–1091.[CrossRef]
Lewis D. M., Pedley T. J. Planktonic contact rates in homogeneous isotropic turbulence: theoretical predictions and kinematic simulations. J. Theor. Biol. (2000) 205:377–408.[Medline]
Lima S., Dill L. M. Behavioral decisions made under the risk of predation: a review and prospectus. Can. J. Zool. (1990) 68:619–640.[CrossRef]
Maar M., Nielsen T. G., Stips A., et al. Microscale distribution of zooplankton in relation to turbulent diffusion. Limnol. Oceanogr. (2003) 48:1312–1325.
MacKenzie B. R., Kiørboe T. Larval fish feeding and turbulence: a case for the downside. Limnol. Oceanogr. (2000) 45:1–10.
MacKenzie B. R., Leggett W. C. Quantifying the contribution of small-scale turbulence to the encounter rates between larval fish and their zooplankton prey: effects of wind and tide. Mar. Ecol. Prog. Ser. (1991) 73:149–160.
MacKenzie B. R., Leggett W. C. Wind-based models for estimating the dissipation rates of turbulent energy in aquatic environments: empirical comparisons. Mar. Ecol. Prog. Ser. (1993) 94:207–216.[CrossRef]
MacKenzie B. R., Miller T. J., Cyr S., et al. Evidence for a dome-shaped relationship between turbulence and larval fish ingestion rates. Limnol. Oceanogr. (1994) 39:1790–1799.
Mann J., Ott S., Pécseli H. L., et al. Turbulent particle flux to a perfectly absorbing surface. J. Fluid Mech. (2005) 534:1–21.[CrossRef]
Mann J., Ott S., Pecseli H. L., et al. Laboratory studies of predator-prey encounters in turbulent environments: effects of changes in orientation and field of view. J. Plankton Res. (2006) 28:509–522.
Mariani P., MacKenzie B. R., Visser A. W., et al. Individual based simulations of larval fish feeding in turbulent environments. Mar. Ecol. Prog. Ser. (2007) 347:155–169.
Marrasé C., Costello J. H., Granata T. C., et al. Grazing in a turbulent environment: energy dissipation, encounter rates and efficacy of feeding currents in Centropages hamatus. Proc. Natl Acad. Sci. USA (1990) 87:1653–1657.
Mauchline J. The Biology of Calanoid Copepods (1998) San Diego: Academic Press.
Minkina N. I. Estimation by hydrodynamic method of energy expenditure of copepods (Copepoda, Crustacea) on swimming. Dokl. Akad. Nauk SSSR (CTC Translation) (1981) 257:141–144.
Morris M. J., Gust G., Torres J. J. Propulsion efficiency and cost of transport for copepods: a hydromechanical model of crustacean swimming. Mar. Biol. (1985) 86:283–295.[CrossRef]
Railsback S. F., Lamberson R. H., Harvey B. C., et al. Movement rules for individual-based models of stream fish. Ecol. Model. (1999) 123:73–89.
Rothschild B. J., Osborn T. R. Small-scale turbulence and plankton contact rates. J. Plankton Res. (1988) 10:465–474.
Saito H., Kiørboe T. Feeding rates in the chaetognath Sagitta elegans: effects of prey size, prey swimming behaviour and small-scale turbulence. J. Plankton Res. (2001) 23:1385–1398.
Saiz E., Alcaraz M. Free-swimming behaviour of Acartia clausi (Copepoda: Calanoida) under turbulent water movement. Mar. Ecol. Prog. Ser. (1992) 80:229–236.
Saiz E., Kiørboe T. Predatory and suspension feeding of the copepod Acartia tonsa in turbulent environments. Mar. Ecol. Prog. Ser. (1995) 122:147–158.[CrossRef]
Saiz E., Alcaraz M., Paffenhöfer A. Effects of small-scale turbulence on feeding rate and gross-growth efficiency of three Acartia species (Copepoda: Calanoida). J. Plankton Res. (1992) 14:1085–1097.
Saiz E., Calbet A., Broglio E. Effects of small scale turbulence on copepods: the case of Oithona davisae. Limnol. Oceanogr. (2003) 48:1304–1331.
Schmitz O. J., Grabowski J. H., Peckarsky B. L., et al. From individuals to ecosystem function: towards an integration of evolutionary and ecosystem ecology. Ecology (2008) 89:2436–2445.[CrossRef][Web of Science][Medline]
Seuront L., Yamazaki H., Souissi S. Hydrodynamic disturbance and zooplankton swimming behaviour. Zool. Stud. (2004) 43:376–387.
Skalski G. T., Gilliam J. F. Feeding under predation hazard: testing models of adaptive behavior with stream fish. Am. Nat. (2002) 160:158–172.[Medline]
Tiselius P., Jonsson P. R. Foraging behaviour of six calanoid copepods: observations and hydrodynamic analysis. Mar. Ecol. Prog. Ser. (1990) 66:23–33.[CrossRef]
Tiselius P., Jonsson P. R., Kaartveldt S., et al. Effects of copepod foraging behavior on predation risk: an experimental study of the predatory copepod Parechaeta norvegica feeding on Acartia clausi and A.tonsa (Copepoda). Limnol. Oceanogr. (1997) 42:164–170.
Visser A. W. Motility of zooplankton: fitness, foraging and predation. J. Plankton Res. (2007) 29:447–461.
Visser A. W., MacKenzie B. R. Turbulence induced contact rates of plankton: the question of scale. Mar. Ecol. Prog. Ser. (1998) 166:307–310.
Visser A. W., Saito H., Saiz E., et al. Observations of copepod feeding and vertical distribution under natural turbulent conditions in the North Sea. Mar. Biol. (2001) 138:1011–1019.[CrossRef]
Yamazaki H., Osborn T. R., Squires K. D. Direct numerical simulation of planktonic contact in turbulent flow. J. Plankton Res. (1991) 13:629–643.
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