Planktonic contact rates in homogeneous isotropic turbulence: theoretical predictions and kinematic simulations

The key role played by turbulence in the environment of plankton and larval fish populations has become appreciated in recent years. In particular, the turbulent enhancement of encounter rates between different species of microorganisms, either swimming or passively advected by the flow, is well established. However, most of the current modelling approaches are rather ad hoc, giving rise to ambiguities in the specification of certain key parameters. In this paper, the encounter problem in a turbulent flow of large Reynolds number is re-examined from first principles and a number of new formulae will be established for different swimming strategies. The key innovation is the proposal of a model form for the conditional joint probability density function of predator and prey velocities when the organisms are separated by their given contact radius, R. Particular attention will be paid to the case when a microorganism follows a random trajectory, due to a combination of its own swimming and the action of the flow. The theoretical predictions are subsequently tested against corresponding quantities derived from a series of kinematic simulations of a turbulent-like flow field. Good agreement is demonstrated between the predictions and simulations.     

The influence of turbulence on plankton predation strategies

The importance of predation in regulating the size of competing plankton and larval fish populations has long been appreciated. However, it has only recently been recognized that turbulence must have a significant influence on predator-prey interactions because most rival species of microorganisms co-exist in oceanic or fast moving fresh water flows. Turbulence is likely to influence predation strategies in two ways. The extra energy imparted to a micro-organism from the flow field will enhance the number of encounters or "contacts" between predators and prey. At the same time, because the velocity of a predator relative to its potential prey will be increased, the time-scale over which a capture must be completed is reduced. Balancing the benefits of extra encounters with the drawbacks of more difficult captures, will dictate an optimal predation strategy, either foraging behaviour or ambush feeding, on the predator. This will depend on its own and the prey's swimming capabilities, as well as the characteristics of the turbulent environment. In this paper some previous work, examining the increased encounter rate in turbulence, will be extended to look at the capture problem. The main proposal is that the capture event should be encapsulated in a capture probability function, from which the optimal predation strategy can be derived. As an illustration, plausible capture probability functions will be postulated and the resulting predictions tested against numerical simulations carried out in a turbulent-like flow field. Good agreement between the predictions and the simulations is demonstrated.     

Small-scale turbulence affects the division rate and morphology of two red-tide dinoflagellates

The effects of small-scale turbulence on two species of dinoflagellates were examined in cultures where the turbulent forces came randomly from all directions and were intermittent both spatially and temporally; much like small-scale turbulence in the ocean. With Lingulodinium polyedrum (Stein) Dodge (syn. Gonyaulax polyedra), division rate increased linearly (from 0.35 to 0.5 per day) and the mean cross-sectional area (CSA) decreased linearly (from 1100 to 750 μm²) as a function of the logarithmic increase in turbulence energy dissipation rate (). These effects were noted when values increased between 10⁻⁸ and 10⁻⁴ m² s⁻³. However, when increased to 10⁻³ m² s⁻³, division rate sharply decreased and mean CSA increased. Over the same range of , Alexandrium catenella (Wheedon and Kofoid) Balech had its division rate decrease linearly (from 0.6 to 0.45 per day) and its CSA increase linearly (from 560 to 650 μm²) as a function of the logarithmic increase in . Even at the highest examined (10⁻³ m² s⁻³), which may be unrealistically high for their ambits, both L. polyedra and A. catenella still had fairly high division rates, 0.2 and 0.45 per day, respectively. Turbulence strongly affected chain formation in A. catenella. In non-turbulent cultures, the mode was single cells (80–90% of the population), but at of 10⁻⁵ to 10⁻⁴ m² s⁻³, the mode was 8 cells per chain. At the highest (10⁻³ m² s⁻³), the mode decreased to 4 cells per chain. The vertical distributions of A. catenella populations in relation to hydrographic flow fields were studied in the summers of 1997 and 1998 in East Sound, Washington, USA (latitude 48°39′N, 122°53′W). In both summers, high concentrations of A. catenella were found as a subsurface bloom in a narrow depth interval (2 m), where both current shear and turbulence intensity were at a minimum. Other researchers have shown that A. catenella orients its swimming in shear flows, and that swimming speed increases with chain length. These responses, when combined with our observations, support a hypothesis that A. catenella actively concentrates at depths with low turbulence and shear.     

Small-scale experimental habitat fragmentation reduces colonization rates in species-rich grasslands

Habitat fragmentation is one of the most important threats to biodiversity. Decreasing patch size may lead to a reduction in the size of populations and to an increased extinction risk of remnant populations. Furthermore, colonization rates may be reduced in isolated patches. To investigate the effects of isolation and patch size on extinction and colonization rates of plant species, calcareous grasslands at three sites in the Swiss Jura Mountains were experimentally fragmented into patches of 0.25, 2.25, and 20.25 m² by frequent mowing of the surrounding area from 1993 to 1999. Species richness in the fragment plots and adjacent control plots of the same sizes was recorded during these 7 years. In agreement with the theory of island biogeography, colonization rate was reduced by 30% in fragments versus non-isolated controls, and extinction increased in small versus large plots. Habitat specialists, in contrast to generalists, were less likely to invade fragments. In the last 4 years of the experiment, extinction rates tended to be higher in fragment than in control plots at two of the three sites. Despite reduced colonization rates and a tendency of increased extinction rates in fragments, fragmented plots had only marginally fewer species than control plots after 7 years. Hence, rates were a more sensitive measure for community change than changes in species richness per se. From a conservation point of view, the detected reduced colonization rates are particularly problematic in small fragments, which are more likely to suffer from high extinction rates in the long run.Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

Reduced contact order and RNA folding rates

We investigated the relationship between RNA structure and folding rates accounting for hierarchical structural formation. Folding rates of two-state folding proteins correlate well with relative contact order, a quantitative measure of the number and sequence distance between tertiary contacts. These proteins do not form stable structures prior to the rate-limiting step. In contrast, most secondary structures are stably formed prior to the rate-limiting step in RNA folding. Accordingly, we introduce "reduced contact order", a metric that reflects only the number of residues available to participate in the conformational search after the formation of secondary structure. Plotting the folding rates and the reduced contact order from ten different RNAs suggests that RNA folding can be divided into two classes. To examine this division, folding rates of circularly permutated isomers are compared for two RNAs, one from each class. Folding rates vary by tenfold for circularly permuted Bacillus subtilis RNase P RNA isomers, whereas folding rates vary by only 1.2-fold for circularly permuted catalytic domains. This difference is likely related to the dissimilar natures of their rate-limiting steps.     

Computer simulation of error rates of Poisson-based interval estimates of plankton abundance

The routine assignment of error rates (confidence intervals) to Poisson distribution estimates of plankton abundance should be rejected. In addition to the interval estimation procedure being pseudoreplicative, it is not robust to common violations of its assumptions. Because the spatial dispersion of organisms in sampling units from the counting chamber to the field is rarely random and because counting protocols are usually terminated by a count threshold having been equalled or exceeded, Poisson based estimates are usually derived from sampling non-Poisson distributions. Computer simulation was used to investigate the quantitative consequences of such estimates. The expected mean error rate of 95% confidence intervals is inflated from 5% to 15% as contagion increases, as the parametric variance-mean ratio increases from 1 to 2. Also, count threshold termination of the counting protocol effects both a biased estimate of the parametric mean (or total) and alters expected mean error rates, especially if the total count is low (< 100 organisms) and the mean density in the sampling unit is low.     

Protein folding rates estimated from contact predictions

Folding rates of small single-domain proteins that fold through simple two-state kinetics can be estimated from details of the three-dimensional protein structure. Previously, predictions of secondary structure had been exploited to predict folding rates from sequence. Here, we estimate two-state folding rates from predictions of internal residue-residue contacts in proteins of unknown structure. Our estimate is based on the correlation between the folding rate and the number of predicted long-range contacts normalized by the square of the protein length. It is well known that long-range order derived from known structures correlates with folding rates. The surprise was that estimates based on very noisy contact predictions were almost as accurate as the estimates based on known contacts. On average, our estimates were similar to those previously published from secondary structure predictions. The combination of these methods that exploit different sources of information improved performance. It appeared that the combined method reliably distinguished fast from slow two-state folders.     

Simulations of the effect of advective-diffusive processes on observations of plankton abundance and population rates

The transport of plankters by water currents is acknowledgedto have an important influence on observations of organism abundanceand population processes, but assessment of this effect hasbeen difficult to achieve. This paper presents simulations usingthe theory of A.Okubo and co-workers. The transport of multiplecurrent drogues over time in a physically realistic advectiveand diffusive current field was simulated. The impact of transportprocesses on the plankton abundance associated with each currentdrogue was then evaluated, and the results are presented graphically.Although plankton numbers were held constant in the simulation,the inferred, but incorrect, population rate parameters thatwould be obtained using successive observations of planktonabundance in the simulated flow field are also presented.     

Small-scale spatial patterns determine ecological relationships: an experimental example using nectar production rates

The structuring of populations at small scales has important consequences for ecological relationships and may contribute to the maintenance of genetic diversity within populations. As an example we tested the effects of variation in nectar production rates (NPR) on pollinator visitation in experimental populations of Echium vulgare with different spatial arrangements. Bumblebees discriminate between groups of plants with different NPRs only when these groups are separated by distances larger than 6 m. Within groups, plants with high and low NPR receive similar numbers of approaches. Plants with high NPR increase the average number of approaches to all plants in the group; therefore, plants with low NPR benefit from nectar-rich plants nearby. These results demonstrate that the effects of NPR on pollinator service depend on the spatial structuring of the population. We suggest that this may help to explain the large genetic differences in NPR that we find for E. vulgare at our study site.     

Infections with varying contact rates: application to varicella

We develop methods for the analysis of infectious disease data when age-specific contact rates vary over time. Our methods are valid when contact rates vary slowly on the time scale of the infection process, and are applicable to a variety of data types including serial seroprevalence surveys and case reports. The methods exploit approximate endemic equilibria, and require numerical solution of an associated integral equation in age and time. We also estimate summary statistics such as time-dependent analogs of the basic reproduction number and critical immunization threshold. We illustrate the methods with data on varicella (chickenpox) in the United Kingdom.     

Transition state contact orders correlate with protein folding rates

We have used molecular dynamics simulations restrained by experimental phi values derived from protein engineering experiments to determine the structures of the transition state ensembles of ten proteins that fold with two-state kinetics. For each of these proteins we then calculated the average contact order in the transition state ensemble and compared it with the corresponding experimental folding rate. The resulting correlation coefficient is similar to that computed for the contact orders of the native structures, supporting the use of native state contact orders for predicting folding rates. The native contacts in the transition state also correlate with those of the native state but are found to be about 30% lower. These results show that, despite the high levels of heterogeneity in the transition state ensemble, the large majority of contributing structures have native-like topologies and that the native state contact order captures this phenomenon.     

Nest Mosquito Trap quantifies contact rates between nesting birds and mosquitoes

Accurate estimates of host-vector contact rates are required for precise determination of arbovirus transmission intensity. We designed and tested a novel mosquito collection device, the Nest Mosquito Trap (NMT), to collect mosquitoes as they attempt to feed on unrestrained nesting birds in artificial nest boxes. In the laboratory, the NMT collected nearly one-third of the mosquitoes introduced to the nest boxes. We then used these laboratory data to estimate our capture efficiency of field-collected bird-seeking mosquitoes collected over 66 trap nights. We estimated that 7.5 mosquitoes per trap night attempted to feed on nesting birds in artificial nest boxes. Presence of the NMT did not have a negative effect on avian nest success when compared to occupied nest boxes that were not sampled with the trap. Future studies using the NMT may elucidate the role of nestlings in arbovirus transmission and further refine estimates of nesting bird and vector contact rates.     

Predicting protein folding rates from geometric contact and amino acid sequence

Protein folding speeds are known to vary over more than eight orders of magnitude. Plaxco, Simons, and Baker (see References) first showed a correlation of folding speed with the topology of the native protein. That and subsequent studies showed, if the native structure of a protein is known, its folding speed can be predicted reasonably well through a correlation with the "localness" of the contacts in the protein. In the present work, we develop a related measure, the geometric contact number, N (alpha), which is the number of nonlocal contacts that are well-packed, by a Voronoi criterion. We find, first, that in 80 proteins, the largest such database of proteins yet studied, N (alpha) is a consistently excellent predictor of folding speeds of both two-state fast folders and more complex multistate folders. Second, we show that folding rates can also be predicted from amino acid sequences directly, without the need to know the native topology or other structural properties.     

Specific growth rates of heterotrophic plankton organisms in a eutrophic lake during a spring bloom

The in situ growth of the dominating pelagic organisms at severaltrophic levels was investigated during a spring bloom characterizedby well-mixed cold water. The study includes primary productionand the carbon flow through the nano-, micro- and mesozooplanktonpopulations based on population dynamics and specific growthrates. The phytoplankton biomass and production were totallydominated by small algae <20 µm. of which {small tilde}5%were <3µm. potentially a food source for the nano-and microzooplankton. The mean carbon-specific primary productionwas 0.15 day^–1 and was regulated solely by light. Themean volume-based specific growth rate of bacterioplankton wasmodest. 0.1 day^–1. and probably controlled by the lowtemperature. The volume-based specific growth rates of heterotrophicnanoflagellates. ciliates. rotifers and copepods were 0.35.0.13. 0.16 and 0.03 day^–1, respectively. The observedgrowth of the heterotrophic plankton was generally not foodlimited, but was controlled by temperature. The stable temperatureduring the experiment therefore allows a cross-taxonomic comparisonof specific growth rates. The b exponent in the allometric relationship(G = aV^th) between volume-specific growth rate (G) and individualbody size (V) was –0.15 ± 0.03 for all filtratingzooplankton. indicating an in situ scaling not far from thephysiological principles onginally demonstrated for laboratorypopulations.     

Measurement of in situ growth rates of phytoplankton under conditions of simulated turbulence

In situ measurement of the growth rates of planktonic populationscan be improved by using dialysis chambers (‘cage cultures’)to avoid shifts in the chemical environment during incubation.Vertical mixing and small-scale turbulence affect the growthof planktonic populations, there fore natural mixing conditionsshould be simulated as closely as possible during the incubation.A new device is described here which combines the advantagesof a dialysis chamber with a programmable vertical mixing regime.Realistic phytoplankton growth rates can thus be measured insitu under con ditions of vertical mixing and small-scale turbulence.The chamber made of transparent, UV-transmitting acrylic glasswas fitted at both ends with permeable polycarbonate membranes.It was moved vertically through the water column by a pocket-sizedlift and rotated simultaneously on its central axis. The methodwas applied to two typos of experiments on growth and lossesof phytoplankton in the River Severn, UK. The first one comparedchanges in biovolume of phytoplankton in a water parcel flowingdownstream (6% h^–1 decline) with those in a simultaneouslyincubated dialysis chamber moved between water surface and riverbottom (7% h^–1 increase). The difference equates to algallosses prevented in the chamber but suffered along the river(mainly sedimentation and grazing of benthic filter feeders).Loss rate of diatoms was three times higher than those of chlorophytes.In another experiment growth of phytoplankton from the mainstream and lateral dead zone was compared under different mixingconditions. Algae from the main stream grew faster than fromthe dead zone. Only cryptophytes preferred calm conditions,all the other algal groups grew faster in chambers moved throughthe water column than in stationary ones. Further possible applicationsin both standing and flowing waters are discussed.     

Climate,plankton and cod

While a few North Atlantic cod stocks are stable, none have increased and many have declined in recent years. Although overfishing is the main cause of most observed declines, this study shows that in some regions, climate by its influence on plankton may exert a strong control on cod stocks, complicating the management of this species that often assumes a constant carrying capacity. First, we investigate the likely drivers of changes in the cod stock in the North Sea by evaluating the potential relationships between climate, plankton and cod. We do this by deriving a Plankton Index that reflects the quality and quantity of plankton food available for larval cod. We show that this Plankton Index explains 46.24% of the total variance in cod recruitment and 68.89% of the variance in total cod biomass. Because the effects of climate act predominantly through plankton during the larval stage of cod development, our results indicate a pronounced sensitivity of cod stocks to climate at the warmer, southern edge of their distribution, for example in the North Sea. Our analyses also reveal for the first time, that at a large basin scale, the abundance of Calanus finmarchicus is associated with a high probability of cod occurrence, whereas the genus Pseudocalanus appears less important. Ecosystem‐based fisheries management (EBFM) generally considers the effect of fishing on the ecosystem and not the effect of climate‐induced changes in the ecosystem state for the living resources. These results suggest that EBFM must consider the position of a stock within its ecological niche, the direct effects of climate and the influence of climate on the trophodynamics of the ecosystem.     

Enhanced excretion rates induced by small-scale turbulence in Acartia (Copepoda: Calanoida)

Several experiments have been performed on three congenericspecies of the calanoid copepod Acartia to determine the effectsof small-scale turbulence on metabolic rates. Both inorganicnitrogen and phosphorus excretion rates significantly increased     

Climate change and marine plankton

Understanding how climate change will affect the planet is a key issue worldwide. Questions concerning the pace and impacts of climate change are thus central to many ecological and biogeochemical studies, and addressing the consequences of climate change is now high on the list of priorities for funding agencies. Here, we review the interactions between climate change and plankton communities, focusing on systematic changes in plankton community structure, abundance, distribution and phenology over recent decades. We examine the potential socioeconomic impacts of these plankton changes, such as the effects of bottom-up forcing on commercially exploited fish stocks (i.e. plankton as food for fish). We also consider the crucial roles that plankton might have in dictating the future pace of climate change via feedback mechanisms responding to elevated atmospheric CO(2) levels. An important message emerges from this review: ongoing plankton monitoring programmes worldwide will act as sentinels to identify future changes in marine ecosystems.     

Sequence determinants of protein folding rates: positive correlation between contact energy and contact range indicates selection for fast folding

In comparison with intense investigation of the structural determinants of protein folding rates, the sequence features favoring fast folding have received little attention. Here, we investigate this subject using simple models of protein folding and a statistical analysis of the Protein Data Bank (PDB). The mean-field model by Plotkin and coworkers predicts that the folding rate is accelerated by stronger-than-average interactions at short distance along the sequence. We confirmed this prediction using the Finkelstein model of protein folding, which accounts for realistic features of polymer entropy. We then tested this prediction on the PDB. We found that native interactions are strongest at contact range l = 8. However, since short range contacts tend to be exposed and they are frequently formed in misfolded structures, selection for folding stability tends to make them less attractive, that is, stability and kinetics may have contrasting requirements. Using a recently proposed model, we predicted the relationship between contact range and contact energy based on buriedness and contact frequency. Deviations from this prediction induce a positive correlation between contact range and contact energy, that is, short range contacts are stronger than expected, for 2/3 of the proteins. This correlation increases with the absolute contact order (ACO), as expected if proteins that tend to fold slowly due to large ACO are subject to stronger selection for sequence features favoring fast folding. Our results suggest that the selective pressure for fast folding is detectable only for one third of the proteins in the PDB, in particular those with large contact order.