Mean Field Games for Diel Vertical Migration with Diffusion.

We present a theoretical framework, based on differential mean field games, for expressing diel vertical migration in the ocean as a game with a continuum of players. In such a game, each agent partially controls its own state by adjusting its vertical velocity but the vertical position in a water column is also subject to random fluctuations. A representative player has to make decisions based on aggregated information about the states of the other players. For this vertical differential game, we derive a mean field system of partial differential equations for finding a Nash equilibrium for the whole population. It turns out that finding Nash equilibria in the game is equivalent to solving a PDE-constrained optimization problem. We detail this equivalence when the expected fitness of the representative player can be approximated with a constant and solve both formulations numerically. We illustrate the results on simple numerical examples and construct several test cases to compare the two analytical approaches.

Evolution of toxins as a public good in phytoplankton.

Toxic phytoplankton blooms have increased in many waterbodies worldwide with well-known negative impacts on human health, fisheries and ecosystems. However, why and how phytoplankton evolved toxin production is still a puzzling question, given that the producer that pays the costs often shares the benefit with other competing algae and thus provides toxins as a 'public good' (e.g. damaging a common competitor or predator). Furthermore, blooming phytoplankton species often show a high intraspecific variation in toxicity and we lack an understanding of what drives the dynamics of coexisting toxic and non-toxic genotypes. Here, by using an individual-based two-dimensional model, we show that small-scale patchiness of phytoplankton strains caused by demography can explain toxin evolution in phytoplankton with low motility and the maintenance of genetic diversity within their blooms. This patchiness vanishes for phytoplankton with high diffusive motility, suggesting different evolutionary pathways for different phytoplankton groups. In conclusion, our study reveals that small-scale spatial heterogeneity, generated by cell division and counteracted by diffusive cell motility and turbulence, can crucially affect toxin evolution and eco-evolutionary dynamics in toxic phytoplankton species. This contributes to a better understanding of conditions favouring toxin production and the evolution of public goods in asexually reproducing organisms in general.

A Diffusion Approximation Based on Renewal Processes with Applications to Strongly Biased Run-Tumble Motion.

We consider organisms which use a renewal strategy such as run-tumble when moving in space, for example to perform chemotaxis in chemical gradients. We derive a diffusion approximation for the motion, applying a central limit theorem due to Anscombe for renewal-reward processes; this theorem has not previously been applied in this context. Our results extend previous work, which has established the mean drift but not the diffusivity. For a classical model of tumble rates applied to chemotaxis, we find that the resulting chemotactic drift saturates to the swimming velocity of the organism when the chemical gradients grow increasingly steep. The dispersal becomes anisotropic in steep gradients, with larger dispersal across the gradient than along the gradient. In contrast to one-dimensional settings, strong bias increases dispersal. We next include Brownian rotation in the model and find that, in limit of high chemotactic sensitivity, the chemotactic drift is 64% of the swimming velocity, independent of the magnitude of the Brownian rotation. We finally derive characteristic timescales of the motion that can be used to assess whether the diffusion limit is justified in a given situation. The proposed technique for obtaining diffusion approximations is conceptually and computationally simple, and applicable also when statistics of the motion is obtained empirically or through Monte Carlo simulation of the motion.

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.

Electronic reporting of diagnostic laboratory test results from all healthcare sectors is a cornerstone of national preparedness and control of COVID-19 in Denmark.

The COVID-19 pandemic has led to an unprecedented demand for real-time surveillance data in order to inform critical decision makers regarding the management of the pandemic. The aim of this review was to describe how the Danish national microbiology database, MiBa, served as a cornerstone for providing data to the real-time surveillance system by linkage to other nationwide health registries. The surveillance system was established on an existing IT health infrastructure and a close network between clinical microbiologists, information technology experts, and public health officials. In 2020, testing capacity for SARS-CoV-2 was ramped up from none to over 10,000 weekly PCR tests per 100,000 population. The crude incidence data mirrored this increase in testing. Real-time access to denominator data and patient registries enabled adjustments for fluctuations testing activity, providing robust data on crude SARS-CoV-2 incidence during the changing diagnostic and management strategies. The use of the same data for different purposes, for example, final laboratory reports, information to the public, contact tracing, public health, and science, has been a critical asset for the pandemic response. It has also raised issues concerning data protection and critical capacity of the underlying technical systems and key resources. However, even with these limitations, the setup has enabled decision makers to adopt timely interventions. The experiences from COVID-19 may motivate a transformation from traditional indicator-based public health surveillance to an all-encompassing information system based on access to a comprehensive set of data sources, including diagnostic and reference microbiology.

Positioning of aquatic animals based on time-of-arrival and random walk models using YAPS (Yet Another Positioning Solver).

Aquatic positional telemetry offers vast opportunities to study in vivo behaviour of wild animals, but there is room for improvement in the data quality provided by current procedures for estimating positions. Here we present a novel positioning method called YAPS (Yet Another Positioning Solver), involving Maximum Likelihood analysis of a state-space model applied directly to time of arrival (TOA) data in combination with a movement model. YAPS avoids the sequential positioning-filtering-approach applied in alternative tools by using all available data in a single model, and offers better accuracy and error control. Feasibility and performance of YAPS was rigorously tested in a simulation study and by applying YAPS to data from an acoustic transmitter towed in a receiver array. Performance was compared to an alternative positioning model and proprietary software. The simulation study and field test revealed that YAPS performance was better and more consistent than alternatives. We conclude that YAPS outperformed the compared alternative methods, and that YAPS constitute a vast improvement to currently available positioning software in acoustic telemetry. Additionally, in contrast to vendor-supplied solutions, YAPS is transparent, flexible and can easily be adapted and extended for further improvements or to meet study specific requirements such as three-dimensional positioning.

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.

Size-dependent diffusion promotes the emergence of spatiotemporal patterns.

Spatiotemporal patterns, indicating the spatiotemporal variability of individual abundance, are a pronounced scenario in ecological interactions. Most of the existing models for spatiotemporal patterns treat species as homogeneous groups of individuals with average characteristics by ignoring intraspecific physiological variations at the individual level. Here we explore the impacts of size variation within species resulting from individual ontogeny, on the emergence of spatiotemporal patterns in a fully size-structured population model. We found that size dependency of animal's diffusivity greatly promotes the formation of spatiotemporal patterns, by creating regular spatiotemporal patterns out of temporal chaos. We also found that size-dependent diffusion can substitute large-amplitude base harmonics with spatiotemporal patterns with lower amplitude oscillations but with enriched harmonics. Finally, we found that the single-generation cycle is more likely to drive spatiotemporal patterns compared to predator-prey cycles, meaning that the mechanism of Hopf bifurcation might be more common than hitherto appreciated since the former cycle is more widespread than the latter in case of interacting populations. Due to the ubiquity of individual ontogeny in natural ecosystems we conclude that diffusion variability within populations is a significant driving force for the emergence of spatiotemporal patterns. Our results offer a perspective on self-organized phenomena, and pave a way to understand such phenomena in systems organized as complex ecological networks.

Diffusive transport in Stokeslet flow and its application to plankton ecology.

In this paper we consider the advective/diffusive transport of a solute near a hovering zooplankter. We approximate the fluid flow with that of a Stokeslet, corresponding to the plankter exerting a point force on the water, and assume that the plankter acts as a point source for the transported solute, located at the same point as the force. We find an analytical expression in closed form for the steady-state concentration of the solute. We also discuss the situation where the plankter performs Brownian motion. Finally we apply the results to the courtship of the marine copepod Pseudocalanus elongatus, where the male performs a mating dance below the hovering female. For this situation, our model supports the hypothesis that the mating dance is guided by the plume of a signalling pheromone.