Uffe Høgsbro Thygesen

Vertical migration and dispersion of sprat (Sprattus sprattus) and herring (Clupea harengus) schools at dusk in the Baltic Sea

In populations of herring (Clupea harengus) or sprat (Sprattus sprattus), one typically observes a pattern of schools forming at dawn and dispersing at dusk, usually combined with vertical migration. This behaviour influences interactions with other species; hence a better understanding of the processes could contribute to deeper insight into ecosystem dynamics. This paper reports field measurements of the dispersal at dusk and examines two hypotheses through statistical modelling: that the vertical migration and the dissolution of schools is determined by decrease in light intensity, and that the dissolution of schools can be modelled by diffusion, i.e. active repulsion is not required. The field measurements were obtained during 3 days in March at one location in the Baltic Sea and included continuous hydroacoustical monitoring, trawl samples, and hydrographical CTD data. Echogram patterns were analysed using the school detection module in Echoview ® and local light intensities were calculated using a model for surface illuminance. The data and the analysis support that schools migrate upwards during dusk, possibly trying to remain aggregated by keeping the local light intensities above a critical threshold, that schools initiate their dissolution when ambient light intensity drops below this critical threshold, and that fish subsequently swim in an uncorrelated random walk pattern.

How optimal life history changes with the community size-spectrum

This paper derives optimal life histories for fishes or other animals in relation to the size spectrum of the ecological community in which they are both predators and prey. Assuming log-linear size-spectra and well known scaling laws for feeding and mortality, we first construct the energetics of the individual. From these we find, using dynamic programming, the optimal allocation of energy between growth and reproduction as well as the trade-off between offspring size and numbers. Optimal strategies were found to be strongly dependent on size spectrum slope. For steep size spectra (numbers declining rapidly with size), determinate growth was optimal and allocation to somatic growth increased rapidly with increasing slope. However, restricting reproduction to a fixed mating season changed optimal allocations to give indeterminate growth approximating a von Bertalanffy trajectory. The optimal offspring size was as small as possible given other restrictions such as newborn starvation mortality. For shallow size spectra, finite optimal maturity size required a decline in fitness for large size or age. All the results are compared with observed size spectra of fish communities to show their consistency and relevance.

Geolocating Fish Using Hidden Markov Models and Data Storage Tags

Geolocation of fish based on data from archival tags typically requires a statistical analysis to reduce the effect of measurement errors. In this paper we present a novel technique for this analysis, one based on Hidden Markov Models (HMM’s). We assume that the actual path of the fish is generated by a biased random walk. The HMM methodology produces, for each time step, the probability that the fish resides in each grid cell. Because there is no Monte Carlo step in our technique, we are able to estimate parameters within the likelihood framework. The method does not require the distribution to be Gaussian or belong to any other of the usual families of distributions and can thus address constraints from shorelines and other nonlinear effects; the method can and does produce bimodal distributions. We discuss merits and limitations of the method, and perspectives for the more general problem of inference in state-space models of animals. The technique can be applied to geolocation based on light, on tidal patterns, or measurement of other variables that vary with space. We illustrate the method through application to a simulated data set where geolocation relies on depth data exclusively.

Trait diversity promotes stability of community dynamics

The theoretical exploration of how diversity influences stability has traditionally been approached by species-centric methods. Here we offer an alternative approach to the diversity–stability problem by examining the stability and dynamics of size and trait distributions of individuals. The analysis is performed by comparing the properties of two size spectrum models. The first model considers all individuals as belonging to the same “average” species, i.e., without a description of diversity. The second model introduces diversity by further considering individuals by a trait, here asymptotic body size. The dynamic properties of the models are described by a stability analysis of equilibrium solutions and by the non-equilibrium dynamics. We find that the introduction of trait diversity expands the set of parameters for which the equilibrium is stable and, if the community is unstable, makes the oscillations smaller, slower, and more regular. The stabilizing mechanism is the variation in growth rate between individuals with the same body size but different trait values.

Interrelations between senescence, life-history traits, and behavior in planktonic copepods

The optimal allocation of resources to repair vs. reproduction in an organism may depend on the magnitude and pattern of the external mortality it is experiencing, which, in turn, may depend on its feeding and mate-finding behavior. Thus, the fundamental activities of an organism, i.e., to feed, to survive, and to reproduce, are interrelated through trade-offs. Here, we use small planktonic copepods to examine how adult longevity and ageing patterns in a protected laboratory environment relate to the feeding mode (active searching vs. passive ambush feeding), mate-finding behavior, and spawning mode of the species. We show that average adult longevity varies between species by an order of magnitude and is independent of body size. Ambush feeders that carry their eggs have longer average life spans and experience higher mortality later in life relative to active feeders that broadcast their eggs. Males generally have shorter life spans and experience higher mortality earlier in life than females, and this difference may be accentuated in species where dangerous mate-finding is male biased. We finally show a trade-off between longevity and fecundity, with ambush feeders producing eggs at a rate five to 10 times lower than the active feeders, consistent with predictions from optimal resource allocation theory.

Diel vertical migration arising in a habitat selection game

Predator and prey react to each other, adjusting their behavior to maximize their fitness and optimizing their food intake while keeping their predation risk as low as possible. In a pelagic environment, prey reduce their predation mortality by adopting a diel vertical migration (DVM) strategy, avoiding their predator during their peak performance by finding refuge in deep layers during daylight hours and feeding at the surface during the night. Due to the duality of the interaction between prey and predator, we used a game theory approach to investigate whether DVM can be a suitable strategy for the predator as well as the prey. We formulated three scenarios in plankton ecology in order to address this question. A novel finding is that mixed strategies emerge as optimal over a range of the parameter space, where part of the predator or prey population adopts a DVM while the rest adopt one or other “sit and wait” strategies.

Ctenophore population recruits entirely through larval reproduction in the central Baltic Sea

The comb jelly Mertensia ovum, widely distributed in Arctic regions, has recently been discovered in the northern Baltic Sea. We show that M. ovum also exists in the central Baltic but that the population consists solely of small-sized larvae (less than 1.6 mm). Despite the absence of adults, eggs were abundant. Experiments revealed that the larvae were reproductively active. Egg production and anticipated mortality rates suggest a self-sustaining population. This is the first account of a ctenophore population entirely recruiting through larval reproduction (paedogenesis). We hypothesize that early reproduction is favoured over growth to compensate for high predation pressure.

A Model of Extracellular Enzymes in Free-Living Microbes: Which Strategy Pays Off?

ABSTRACT An initial modeling approach was applied to analyze how a single, nonmotile, free-living, heterotrophic bacterial cell may optimize the deployment of its extracellular enzymes. Free-living cells live in a dilute and complex substrate field, and to gain enough substrate, their extracellular enzymes must be utilized efficiently. The model revealed that surface-attached and free enzymes generate unique enzyme and substrate fields, and each deployment strategy has distinctive advantages. For a solitary cell, surface-attached enzymes are suggested to be the most cost-efficient strategy. This strategy entails potential substrates being reduced to very low concentrations. Free enzymes, on the other hand, generate a radically different substrate field, which suggests significant benefits for the strategy if free cells engage in social foraging or experience high substrate concentrations. Swimming has a slight positive effect for the attached-enzyme strategy, while the effect is negative for the free-enzyme strategy. The results of this study suggest that specific dissolved organic compounds in the ocean likely persist below a threshold concentration impervious to biological utilization. This could help explain the persistence and apparent refractory state of oceanic dissolved organic matter (DOM). Microbial extracellular enzyme strategies, therefore, have important implications for larger-scale processes, such as shaping the role of DOM in ocean carbon sequestration.

Lessons from a Prototype Geolocation Problem

This paper establishes simple and general expressions for the accuracy of geolocation, which may be obtained by optimal filtering of measurements from archival tags. We investigate an idealized geolocation problem where the animal performs a random walk. We derive simple closed-form expressions for the steady-state variance and for the characteristic time scale of the filter, i.e. the smoothing horizon. This leads to temporal and spatial scales defining the limit of resolution and explains the difference between what can be obtained for fast-moving and slow-moving animals. Using frequency-domain methods, we consider the effect of adding additional sensors, and examine the substitution of the random walk model with anomalous diffusion, e.g. a Levy flight. We also discuss time variations in the accuracy near start and end of the time series, and due to holes in the data stream which e.g. arise in the tidal method for geolocation when the animal is pelagic. Our results are particularly useful to the planning of a tagging study, because our estimates of accuracy can be computed using only three parameters: the swimming speed of the animal, the sample interval, and the variance on the measurement error.

Higher Order Moments and Conditional Asymptotics of the Batch Markovian Arrival Process

We consider the number of arrivals in a Batch Markovian Arrival Process (BMAP) and derive matrix analytic expressions for its moments of arbitrary order. These expressions consist of decomposition formulas connected to the semigroup structure of the moments, forward and backward differential equations, and recursive as well as direct integral formulas. This extends earlier work by Narayana and Neuts on the first two factorial moment matrices. We next turn to the terminating BMAP, i.e., a BMAP with an absorbing state in which no arrivals occur. We consider the asymptotic behavior of the moments conditional on the process not yet having terminated. We show that the conditional mean and variance possess affine asymptotics and derive the coefficients explicitly. Finally, we discuss how parts of our work also apply to the more general class of Rational Arrival Processes (RAPs).