Fractal characterization of three-dimensional zooplankton swimming trajectories

Several natural processes, such as swimming and flying, occur in a three-dimensional reference frame and thus describe three-dimensional trajectories. Analysing such tracks is no easy task. To this aim, here we propose a new technique, based on the box-counting approach, by which to estimate the three-dimensional fractal dimension (D_3D) of spatially-evolving routes. This technique has been preliminary tested on two sets of random walks (pure and correlated). Then, our approach has been utilised to characterise the swimming trajectories performed by the freshwater cladoceran Daphnia pulex under two light conditions.Morphologically different tracks attain statistically different D_3D values, smoother paths having lower values than more tortuous ones; therefore, our proposed methodology proves to be fruitful in direct comparisons. Moreover D_3D can highlight bizarre situations, in which differently convoluted tracks are characterised by the same degree of contortion.     

Relationship of oxygen consumption to swimming speed in Euphausia pacifica

Oxygen consumption rate was measured as a function of swimming velocity for the vertically migrating euphausiid Euphausia pacifica at two temperatures (8° and 12°C) and pressures (1 and 40 atm) typical of its bathymetric distribution. Increased swimming speed (x; mh^-1) required increased oxygen consumption (y; μl O₂ mg dry weight^-1 h^-1), described by the equation y = 0.012x + 0.64 at 8°C, and by y = 0.020x + 0.85 at 12° C. The current concept of low swimming costs of zooplankton, based on determinations of dead drag in copepods, is contradicted by our measurements. Temperature had a more profound effect on metabolism at higher swimming speeds (112 m h^-1; Q₁₀=2.8) than on standard metabolism (O m h^-1; Q₁₀=2.0), indicating that activity is more costly at higher temperatures. Pressure caused a small but significant (P>0.05) rise in the relationship of respiratory rate to swimming speed at both temperatures. The energy cost of vertical migration for E. pacifica was estimated by applying our data on oxygen consumption vs swimming speed to published observations on sonic scattering layer movement and the day-night distribution pattern of this species. Results indicate that the cost of a diel migration of 254 m, through a temperature change of 4 °C (8° to 12° C), would cancel any energetic benefit gained by time spent at the lower temperature typical of daytime depth. The act of vertical migration is energetically expensive; its cost should be thoroughly considered in attempts to describe the energetics of vertically migrating species.     

Selection of unicellular algae by the littoral amphipods Gammarus oceanicus and Calliopius laeviusculus (Crustacea)

The effect of microalgal strength of adhesion to surfaces was examined with regard to their susceptibility to grazing by Gammarus oceanicus Segerstråle and Calliopius laeviusculus (Krøyer). Observations of the feeding behaviour and two feeding experiments were carried out under laboratory conditions. Naturally attached periphyton (strongly attached cells), homogenized periphyton (loosely attached cells), filtered phytoplankton (unattached cells) and bare surfaces (controls) were randomly located in a grid and offered for grazing to a fixed number of amphipods of each species separately. The number of individuals visiting each type of food presented in the grid was recorded for 24-h periods. The feeding habit of each species, their effect on food distribution and their efficiency at collecting small particles were also recorded. G. oceanicus has a low efficiency at collecting particles and does not select a particular type of food, owing to its feeding habit of indiscriminately resuspending loosely attached particles. C. laeviusculus is a highly efficient and selective grazer, preferring homogenized periphyton and phytoplankton to naturally attached periphyton. For epibenthic diatoms, strong adhesion to surfaces is advantageous to avoid grazers.     

Swimming pattern as an indicator of the roles of copepod sensory systems in the recognition of food

The roles of copepod sensory systems in the recognition of food were investigated using the Bugwatcher, a video-computer system designed to track and describe quantitatively the swimming patterns of aquatic organisms. The swimming behavior of the copepodPseudocalanus minutus in the presence of phytoplankton is characterized by a decrease in average swimming speed and an increase in pause behaviors compared to its swimming behavior in filtered seawater. Copepods exposed to chemosensory stimulation alone (filtered phytoplankton exudate) exhibited an increase in average swimming speed and an increase in the number of burst swimming behaviors. When exposed to a novel, non-food chemosensory stimulus (morpholine), no change in swimming behavior was observed unless the copepods had been conditioned to this odor in the presence of phytoplankton. Copepods exposed to mechanosensory stimulation alone (plastic spheres) exhibited a decrease in swimming speed and an increase in pause behaviors. When exposed to both forms of stimulation simultaneously (phytoplankton exudate and plastic spheres), a further decrease in swimming speed and increase in pause behaviors occurs, yielding a swimming pattern similar to that found in the presence of phytoplankton. This analysis of swimming pattern indicates that both chemoreception and mechanoreception contribute to the recognition of food inP. minutus.Contribution No. 406 of the US EPA Environmental Research Laboratory; Narragansett, Rhode Island 02882, USA     

Incorporating behaviour into simple models of dispersal using the biological control agent Dicyphus hesperus

We explored the utility of incorporating easily measured, biologically realistic movement rules into simple models of dispersal. We depart from traditional random walk models by designing an individual-based simulation model where we decompose animal movement into three separate processes: emigration, between-patch movement, and immigration behaviour. These processes were quantified using experiments on the omnivorous insect Dicyphus hesperus moving through a tomato greenhouse. We compare the predictions of the individual-based model, along with a series of biased random walk models, against an independent experimental release of D. hesperus. We find that in this system, the short-term dispersal of these insects is described well by our individual-based model, but can also be described by a 2D grid-based biased random walk model when mortality is accounted for.     

Stochastic theory of ecological interactions

It is possible, using the distribution of random numbers of random variables, to derive bimodal vertical distributions of phytoplankton biomass similar to those observed in nature. On the basis of the distribution of pseudorandom events, equations for the probability of individual mortality from one of several reasons, and for the capture of one of several preys by the predators were obtained. From these theoretical formulations the empirical equations of Beverton and Holt, Ricker and Ivlev were derived. An equation for the average feed intake of one individual interacting in a swarm, feeding on aggregated food, is derived from an estimate of the average interval between the random encounters of aggregates, in the nodes of an α-dimensional net.     

Langmuir circulations and plankton patchiness

A computer simulation model of oceanic Langmuir circulations illustrates the role of these vortical water movements as physical forcing mechanisms affecting the horizontal and vertical distributions of planktonic organisms. The diel migration of omnivorous and herbivorous zooplankton (approximately by literature values for the swimming speeds of Meganyctiphanes norvegica and Calanus finmarchicus, respectively) and the sinking of phytoplankton interact with the Langmuir cells, resulting in a spatially heterogeneous community. The patchy distributions, in turn, affect the prey—predator interactions in this simple food web. Situations involving threshold and non-threshold feeding strategies as well as constant and changing circulations are investigated. The simulations are restricted to twilight and nocturnal events.     

Spatial memory, habitat auto-facilitation and the emergence of fractal home range patterns

Animals interact with their habitat in a manner which involves both negative and positive feedback mechanisms. We apply a specific modeling approach, “multi-scaled random walk”, for the scenario where a spatially explicit positive feedback process emerges from a combination of a spatial memory-dependent tendency to return to familiar patches and a consequently objective or subjective improvement of the quality of these patches (habitat auto-facilitation). In addition to the potential for local resource improvement from physically altering a patch, primarily known from the ecology of grazing ungulates, auto-facilitation from site fidelity may also embed more subtle subjective, individual-specific advantages from patch familiarity. Under the condition of resource superabundance, fitness gain from intra-home range patch fidelity creates a self-reinforcing use of the preferred patches on expense of a broader foraging in a priori equally favorable patches. Through this process, our simulations show that a spatially fractal dispersion of accumulated locations of the individual will emerge under the given model assumptions. Based on a conjecture that intra-home range patch fidelity depends on spatial memory we apply the multi-scaled random walk model to construct a spatially explicit habitat suitability parameter H_ij, which quantifies the dispersion of the generally most constraining resource from the individual's perspective. An intra-home range set of observed H-scores, H_obs, can then be estimated from a simple 2-scale calculation that is derived from the local dispersion of fixes. We show how the spatially explicit habitat utilization index H_obs not necessarily correlates positively with the local density fluctuations of fixes. The H-index solves some well-known problems from using the pattern of local densities of telemetry fixes - the classic utilization distribution - as a proxy variable for relative intra-home range habitat quality and resource selection. A pilot study on a set of telemetry fixes collected from a herd of free-ranging domestic sheep with overlapping summer home ranges illustrates how the H-index may be estimated and interpreted as a first-level approach towards a more extensive analysis of intra-home range habitat resource availability and patch preferences. Spatial memory in combination with site fidelity requires a modeling framework that explicitly describes the property of positive feedback mechanism under auto-facilitation in a spatio-temporally explicit manner.     

Lévy walk patterns in the foraging movements of spider monkeys (<Emphasis Type="Italic">Ateles geoffroyi</Emphasis>)

Scale invariant patterns have been found in different biological systems, in many cases resembling what physicists have found in other, nonbiological systems. Here we describe the foraging patterns of free-ranging spider monkeys (Ateles geoffroyi) in the forest of the Yucatan Peninsula, Mexico and find that these patterns closely resemble what physicists know as Lévy walks. First, the length of a trajectorys constituent steps, or continuous moves in the same direction, is best described by a power-law distribution in which the frequency of ever larger steps decreases as a negative power function of their length. The rate of this decrease is very close to that predicted by a previous analytical Lévy walk model to be an optimal strategy to search for scarce resources distributed at random. Second, the frequency distribution of the duration of stops or waiting times also approximates to a power-law function. Finally, the mean square displacement during the monkeys first foraging trip increases more rapidly than would be expected from a random walk with constant step length, but within the range predicted for Lévy walks. In view of these results, we analyze the different exponents characterizing the trajectories described by females and males, and by monkeys on their own and when part of a subgroup. We discuss the origin of these patterns and their implications for the foraging ecology of spider monkeys.Communicated by D. Watts     

Change in a bacterial population during the process of degradation of a phytoplankton bloom in a brackish lake

Change in a bacterial population during the process of degradation of a phytoplankton bloom was investigated at Lake Hamana, Japan in June 1981. The predominant phytoplankton were Prorocentrum micans Ehrenberg and P. triestinum Schiller. While most phytoplankton cells were living and moving actively, most bacteria were those in a free-living state (free-living bacteria) and the number of bacteria associated with particulate materials (attached bacteria) was less than a few percent of the total bacterial number. As the decline process proceeded, the number of free-living bacteria remained almost constant or decreased slightly; on the other hand, the number of attached bacteria increased gradually and reached about 40% of the total bacterial number. These results indicate that some of the free-living bacteria become attached to particulate organic matter and grow on the surface of the particles.     

The effect on dispersal from complex correlations in small-scale movement

Calculations of large-scale displacement distances were made to evaluate the combined effect of small-scale movement pattern of a Collembola, Protaphorura armata. The effect of presence of food and conspecific density on turning angle, step length and activity/motility was investigated. Calculations of net square displacement were made both by assuming correlated random walk (CRW) and by resampling data to account for correlation structures in movement patterns that violate the assumptions of CRW.     

A general random walk model for the leptokurtic distribution of organism movement: Theory and application

The movement of organisms is usually leptokurtic in which some individuals move long distances while the majority remains at or near the area they are released. There has been extensive research into the origin of such leptokurtic movement, but one important aspect that has been overlooked is that the foraging behaviour of most organisms is not Brownian as assumed in most existing models. In this paper we show that such non-Brownian foraging indeed gives rise to leptokurtic distribution. We first present a general random walk model to describe the organism movement by breaking the foraging of each individual into events of active movement and inactive stationary period; its foraging behaviour is therefore fully characterized by a joint probability of how far the individual can move in each active movement and the duration it remains stationary between two consecutive movements. The spatio-temporal distribution of the organism can be described by a generalized partial differential equation, and the leptokurtic distribution is a special case when the stationary period is not exponentially distributed. Empirical observations of some organisms living in different habitats indicated that their rest time shows a power-law distribution, and we speculate that this is general for other organisms. This leads to a fractional diffusion equation with three parameters to characterize the distributions of stationary period and movement distance. A method to estimate the parameters from empirical data is given, and we apply the model to simulate the movement of two organisms living in different habitats: a stream fish (Cyprinidae: Nocomis leptocephalus) in water, and a root-feeding weevil, Sitona lepidus in the soil. Comparison of the simulations with the measured data shows close agreement. This has an important implication in ecology that the leptokurtic distribution observed at population level does not necessarily mean population heterogeneity as most existing models suggested, in which the population consists of different phenotypes; instead, a homogeneous population moving in homogeneous habitat can also lead to leptokurtic distribution.     

Données sur la respiration de différents organismes communs dans le plancton de Villefranche-sur-Mer

Respiratory rates of a number of planctonic organisms from coastal Mediterranean waters are well related to dry weight (PS) (log R=0.844+0.706 log PS); the correlation coefficient is r=0.929. A comparison with literature reveals great similarity between the relation we established and those of other authors, despite a difference between Mediterranean copepods and those of other origins, at the metabolic level. The slope of the relation log R — log PS, established for organisms other than copepods, was found to be steeper than that of the general equation; this difference is discussed in terms of metabolic rate, temperature variations in the sea, and experimental conditions; the metabolic advantage of vertically migrating plankton is considered. The incidence of a copepod population on phytoplankton has been calculated from our data; in various areas of Villefranche Bay, the minimal requirements of the copepods are not met.     

Effects of ocean acidification, temperature and nutrient regimes on the appendicularian Oikopleura dioica: a mesocosm study

Increasing pCO₂ is hypothesized to induce shifts in plankton communities toward smaller cells, reduced carbon export rates and increased roles of gelatinous zooplankton. Appendicularians, among the most numerous pan-global “gelatinous” zooplankton, continuously produce filter-feeding houses, shortcutting marine food webs by ingesting submicron particles, and their discarded houses contribute significantly to carbon fluxes. We present a first mesocosm-scale study on the effects of temperature, pCO₂ and bloom structures on the appendicularian, Oikopleura dioica. There were effects of temperature and nutrients on phytoplankton communities. No shifts in functional phytoplankton groups, nor changes in particle sizes/morphotypes, known to impact appendicularian feeding, were observed under manipulated pCO₂ conditions. However, appendicularian abundance was positively correlated with increased pCO₂, temperature and nutrient levels, consistent with hypotheses concerning gelatinous zooplankton in future oceans. This suggests appendicularians will play more important roles in marine pelagic communities and vertical carbon transport under projected ocean acidification and elevated temperature scenarios.     

Diffusion about the mean drift location in a biased random walk

Random walks are used to model movement in a wide variety of contexts: from the movement of cells undergoing chemotaxis to the migration of animals. In a two-dimensional biased random walk, the diffusion about the mean drift position is entirely dependent on the moments of the angular distribution used to determine the movement direction at each step. Here we consider biased random walks using several different angular distributions and derive expressions for the diffusion coefficients in each direction based on either a fixed or variable movement speed, and we use these to generate a probability density function for the long-time spatial distribution. We demonstrate how diffusion is typically anisotropic around the mean drift position and illustrate these theoretical results using computer simulations. We relate these results to earlier studies of swimming microorganisms and explain how the results can be generalized to other types of animal movement.     

Filtering rates of the juvenile Atlantic menhaden Brevoortia tyrannus (Pisces: Clupeidae), with consideration of the effects of detritus and swimming speed

From July to September 1982 feeding experiments were conducted with 138-mm fork length Atlantic menhaden Brevoortia tyrannus (Latrobe) (Pisces: Clupeidae) to determine their particle size-specific feeding abilities. Monoculture clearing-rate experiments showed that the minimum size of particles filtered, the minimum size threshold, for 138-mm fish is 7 to 9 m. Filtration efficiency for three species of phytoplankton below the minimum size threshold. Pseudoisochrysis paradoxa, Monochrysis lutheri, and Isochrysis galbana, averaged 1.0% (n=14). Tetraselmis suecica, Prorocentrum minimum, and 2-celled Skeleionema costatum, phytoplankton which are larger than the minimum size threshold and smaller than the 20-m upper limit for nanoplankton, were filtered at efficiencies averaging 21% (n=24). S. costatum chains of 3 to 6 cells, prey particles exceeding the size limits of nanoplankton, were filtered at average efficiencies ranging from 22 to 84%. The mean filtration efficiency for Artemia sp. nauplii (San Francisco Bay Brand) of 36% (n=7) was lower than for smaller phytoplankton prey. The presence of detritus at concentrations usually encountered in nature enhanced filtering efficiency and lowered minimum size thresholds at which phytoplankton were retained. For small food particles, filtering efficiency decreased as swimming speed of the menhaden increased. As menhaden grow, their feeding tepertoire shifts to larger planktonic organisms.Contribution No. 1201 Virginia Institute of Marine Science     

Ecological significance of salp fecal pellets collected by sediment traps in the eastern North Pacific

Five sediment traps were moored at depths of 740, 940, 1 440, 3 440 and 4 240 m for 7 d in December 1982 at Station 5 in the eastern North Pacific about 400 km from San Francisco. Dark green sinking particles enclosed in tough membrane consisted of mostly coccolithophores with some diatoms, dinoflagellates and chrysophytes. The average size of the particles was 10x5x2 mm. These characteristics indicate that the particles were fecal pellets of salp inhabiting the surface waters. Vertical fluxes of the organic carbon and nitrogen through sinking of the salp fecal pellets ranged from 6.7 to 23 mgC m^-2 d^-1 and from 0.88 to 3.2 mgN m^-2 d^-1, respectively. These values were several times higher than those determined in other oceanic areas by sediment trap experiments. Hydrocarbons consisting of short-chain n-alkanes (n-C₁₅-C₂₀) with n-C₁₇, the most predominant component, heneicosa-hexaene (n-C_21:6), br-C₂₅ alkenes and long-chain n-alkanes (n-C₂₁-C₃₀), without any odd or even carbon number predominance, were found from five depths. The presence of short-chain n-alkanes and n-C_21:6 indicated that phytoplankton in the surface waters was a primary source of organic matter in the sinking particles. Two isomers of br-C_25:3 and br-C_25:4 alkenes found in these particles also indicated that br-C₂₅ alkenes were the important biological marker of fecal pellet of zooplankton. The distribution pattern of the long-chain n-alkanes suggested that the sinking particles may be affected by bacteria to some extent. Fatty acids of the sinking particles were separated into free, triglyceride and wax ester fractions consisting of mono- and poly-unsaturated, and saturated fatty acids, with a range from C₁₄ to C₃₀. Concentrations of mono- and poly-unsaturated fatty acids decreased more rapidly toward the deep than those of saturated fatty acids, which cause low ratios of mono- and poly-unsaturated fatty acids/saturated fatty acids. This indicates that unsaturated fatty acids were more rapidly decayed by marine microbes than saturated fatty acids in the deep water, despite the fact that a significant amount of unsaturated fatty acids still remained in the sinking particles collected from the deep waters. Our results revealed that the salp fecal pellet plays an important role in supplying foods to organisms in intermediate and deep seas.     

Matching species traits to environmental variables: a new three-table ordination method

This paper addresses the question of studying the joint structure of three data tablesR,L andQ. In our motivating ecological example, the central tableL is a sites-by-species table that contains the number of organisms of a set of species that occurs at a set of sites. At the margins ofL are the sites-by-environment data tableR and the species-by-trait data table Q. For relating the biological traits of organisms to the characteristics of the environment in which they live, we propose a statistical technique calledRLQ analysis (R-mode linked toQ-mode), which consists in the general singular value decomposition of the triplet (R ^t D _I LD _J Q,D _q ,D _p ) whereD _I ,D _J ,D _q ,D _p are diagonal weight matrices, which are chosen in relation to the type of data that is being analyzed (quantitative, qualitative, etc.). In the special case where the central table is analysed by correspondence analysis,RLQ maximizes the covariance between linear combinations of columns ofR andQ. An example in bird ecology illustrates the potential of this method for community ecologists.     

Impact of ocean acidification in the metabolism and swimming behavior of the dolphinfish (Coryphaena hippurus) early larvae

Since the industrial revolution, [CO₂]_atm has increased from 280 μatm to levels now exceeding 380 μatm and is expected to rise to 730–1,020 μatm by the end of this century. The consequent changes in the ocean’s chemistry (e.g., lower pH and availability of the carbonate ions) are expected to pose particular problems for marine organisms, especially in the more vulnerable early life stages. The aim of this study was to investigate how the future predictions of ocean acidification may compromise the metabolism and swimming capabilities of the recently hatched larvae of the tropical dolphinfish (Coryphaena hippurus). Here, we show that the future environmental hypercapnia (ΔpH 0.5; 0.16 % CO₂, ~1,600 μatm) significantly (p < 0.05) reduced oxygen consumption rate up to 17 %. Moreover, the swimming duration and orientation frequency also decreased with increasing pCO₂ (50 and 62.5 %, respectively). We argue that these hypercapnia-driven metabolic and locomotory challenges may potentially influence recruitment, dispersal success, and the population dynamics of this circumtropical oceanic top predator.     

Shadow cinematography of fish larvae

A simple system of shadow cinematography, consisting of a small tungsten halogen lamp, 2 large biconvex lenses and a 16 mm camera, is described for recording the swimming and feeding behaviour of larval fish. The system can be used either with infra-red film to record swimming behaviour independently of ambient light intensity, or with high-resolution film to record food organisms and feeding behaviour. Small plankton organisms of 0.2 mm width can be resolved using high-resolution film. The technique has been used to record the behaviour of plaice larvae (Pleuronectes platessa L.) feeding on the nauplii of Artemia salina L. The perceptive field of the larvae extends to approximately ±60° in azimuth, ±40° in elevation and 1.5 body lengths in range.