Lévy walks are a special class of random walks with step lengths that follow a power-law distribution. Lévy walks are observed in various biological movements and agents, ranging from cells and insects to mammals, including humans. The movement characteristic of Lévy walks leads to more efficient searching or foraging strategies than normal random walks, so-called Brownian walks, when the targets (e.g., food, mates, or habitats) are unpredictably and sparsely distributed in the environment. According to the Lévy walk foraging hypothesis, evolution through natural selection can explain why Lévy walks are widespread in biological movements. However, there has been a recent debate about the origin of Lévy walks. Some findings suggest that Lévy walks might also be epiphenomena arising from interactions with a complex environment. Thus, why Lévy walks are a common mode of biological movement and how they are generated remain controversial. In this talk, I will show that Lévy walks can emerge near a critical point between order and disorder and have the high flexibility of switching exploitation/exploration based on the nature of external cues [1]. These are one of the generative mechanisms and functional advantages derived from brain criticality. Moreover, I will discuss how these movement patterns affect macro-level phenomena such as ecosystems to understand biological Lévy walks comprehensively.

1. Masato S. Abe. Functional advantages of Lévy walks emerging near a critical point. PNAS 117 (39) 24336-24344 (2020).

It is often assumed that oceanic flows mix trophic levels of plankton and nutrients to the extent that spatially averaged ecological models can be used to describe the local population dynamics without the need to specify features of the flow. However, complex flows can drive segregation rather than mixing of planktonic species. Aside from active mechanisms, such as biased swimming, the physical and hydrodynamic properties of organisms may lead to species specific drift normal to the mean flow. The resulting physically-driven heterogeneity can have a qualitative impact on the population dynamics. Here, I will illustrate how the qualitative behaviour of a simple system describing excitable plankton bloom dynamics, for physically distinct phytoplankton and zooplankton, depends critically on the flow and induced interaction rates. Spatio-temporal dynamics and spatially averaged bifurcation diagrams reveal the wealth of solution behaviour. The main result is that fluid flows can lead to mean-field plankton population dynamics that are qualitatively different to that predicted for well-mixed systems.

Ocean nutrient cycling is driven by the concerted action of marine microbes, but the fine-scale interactions between these microbes and their physical and chemical environments remains elusive. I will present recent work which utilises a novel experimental platform for delivering sub-millimetre scale nutrient pulses, quantitatively mimicking those found in the ocean. Advanced video-microscopy is used to characterise microbial motion at the single cell level, and reveals the precise conditions under which bacteria can detect and climb dynamic nutrient gradients. New mathematical theory, based on the counting of individual molecules of dissolved organic matter, is in striking agreement with the experimental findings. From these quantitative foundations, we have developed a mechanistic framework for microbial motion, which directly unifies individual behaviour (cell motility, chemotaxis) with population-scale phenomena (collective nutrient uptake, symbiotic interactions).

REFERENCES

• Bacteria push the limits of chemotactic precision to navigate dynamic chemical gradients. D. R. Brumley, F. Carrara, A. M. Hein, Y. Yawata, S. A. Levin, R. Stocker. Proceedings of the National Academy of Sciences 116(22) 10792-10797 (2019)

• Cutting through the noise: bacterial chemotaxis in marine microenvironments. D. R. Brumley, F. Carrara, A. M. Hein, G. I. Hagstrom, S. A. Levin, R. Stocker. Frontiers in Marine Science 7:527 (2020)

Social insects such as ants, bees, wasps and termites are regarded as one of the most prosperous organisms on the earth. Their ecological and evolutionary success is often attributed to the group-living that is characterized by surprisingly well-organized division of labor among colony members. Their colonies have posed a conundrum of the evolution of biological cooperation (i.e., mutual enhancement of survival and reproduction), which has been an inspiration for evolutionary game theory. Moreover, how such complex and adaptive systems of division of labor are generated has long drawn much attention not only from biologists but also from physicists, leading to the establishment of the interdisciplinary study of “biological self-organization.” In this talk, I first introduce a basic biology of social insects focusing mainly on ants. I will then outline my research projects that correspond to the two questions mentioned above: genetically encoded public-goods dilemma in a Japanese ant [1] and evolutionary biology of ant-mimicking robot swarms [2].

1. Dobata S, Tsuji K (2013) Public goods dilemma in asexual ant societies. PNAS 110 (40): 16056-16060.

2. Fujisawa R, et al. (2019) Regulatory mechanism predates the evolution of self-organizing capacity in simulated ant-like robots. Commun. Biol. 2: 25.

Understanding of extinct animals in the ancient times allows us to understand living animals more deeply in the context of evolution. Especially, reconstruction of adaptive locomotion of extinct animals gives us significant insight into understand their lifestyle because locomotion capability is critical for animals to survive in the wildlife. However, there are few studies addressing how extinct animals have successfully adapted to their locomotion pattern to new situation (e.g., changes in locomotion speed, body shapes, and environment). To tackle the above problem, our research group introduces a control mechanism underlying adaptive extant animal locomotion to reconstruct adaptive extinct animal locomotion. Biological and robotics studies elucidate that extant animals generate adaptive locomotor patterns via decentralized control systems (e.g., central pattern generator CPG and local reflexes). It is very natural to assume that extinct animal exhibited adaptive locomotion via a similar flexible decentralized control system of extant animals. As a first step, We focus on plesiosaurs, an extinct aquatic reptile group which has two pairs of flipper-shaped limbs. As living analogues of plesiosaurs do not exist, their swimming style has been controversial for over a century. Our plesiosaur-like robot with a decentralized control scheme addresses how plesiosaurs coordinate their four flippers based on varying situations. In this presentation, we report the preliminary results of our reconstruction study of the plesiosaurs’ swimming style and discuss animal evolution from the viewpoint of decentralized control scheme and fluid in environments.

Evolutionary processes are commonly represented using phylogenetic trees, but more general models called phylogenetic networks are needed in order to accurately represent the complicated information in real data or complex evolutionary histories such as hybridisation of plants and horizontal gene transfer in bacterial evolution. However, because of the many computational difficulties involved in using phylogenetic networks, it is still a major challenge to recognise biologically meaningful problems that are solvable in polynomial time and to clarify how such networks can be actually useful in the analysis of evolutionary data. In this talk, I will first provide the necessary background in the field of combinatorial phylogenetics, and then present a 'structure theorem for rooted binary phylogenetic networks' and show how it yields a series of fast algorithms for solving various interesting problems in a unified manner.

[References]

M. Hayamizu, A structure theorem for rooted binary phylogenetic networks and its implications for tree-based networks, SIAM Journal on Discrete Mathematics, to appear. (Preprint arXiv:1811.05849 [math.CO], YouTube https://youtu.be/GLx18qLn1p8)

Ecosystems contain various biological phenomena in which fluid-mechanics viewpoints can be useful for understanding those dynamics. For example, spatial structures of population or individual levels are strongly related to ecological niches (thus biodiversity as well), and fluid mechanics would contribute to the understanding of the formation of such structures. Also, macroscopic description of the changes in the state of ecosystems may be possible by treating the ecosystem changes as viscous dynamics in a low-dimensional state space. However, it is challenging to try such approaches only by field and theoretical studies because there are too many factors in ecosystems. Here, we introduce our synthetic ecosystem as an experimental “model ecosystem” that enables high-throughput approaches. This synthetic ecosystem is composed of 12 cryopreservable microbial species with diverse interactions such as benefit-harm interactions and foraging interactions. In this synthetic ecosystem, we observed characteristic spatial patterns due to the interaction between organisms. We also found some phenomena that could be roughly described by the dynamics on a low-dimensional state space, e.g., stochastic bifurcation of ecosystem states, attraction in a state space by inter-ecosystem interactions, and constrained ecosystem responses to environmental temperature changes. In addition, we show a microfluidic device that was applied for observing movements of motile microbial individual that has another species endosymbiotically. Our results specifically suggest how fluid-mechanics perspectives can be useful for understanding ecosystems. The description of this experimental model ecosystem by mathematical models and their generalization may provide a basic strategy that can be applied to many ecosystems.

Sex ratio, males per females, is a target of natural selection, and has provided one of the most productive and successful areas of evolutionary biology. Düshing was the first to implicitly take a game-theoretical approach and demonstrated that, in well-mixed populations, the fifty-fifty sex ratios as in many animal species are the product of natural selection favouring producing the rarer sex. This story however came with some exceptions, especially in parasitoid wasps that exhibit female-biased sex ratios (e.g., 1 male per 5 females). Hamilton (1967) published a highly influential paper to address this puzzle, with the emphasis on limited spatial movement (population viscosity) and its effect on competition between brothers in favouring the female-biased sex ratios. With Hamilton’s “Local mate competition theory”, yet, some of the other wasps (genus Melittobia) show much more female-biased sex ratios (circa 1 male per 50 females), and this fact has been rendered a big puzzle in evolutionary biology. We took two approaches to address this puzzle. We first consider the effects of female-female cooperation on the evolution of sex ratios. Second we assess phenotypic plasticity in natural and experimental conditions, as well as mathematical models incorporating the phenotypic plasticity. In my talk at the workshop, I will outline the research history in this field and then show the model structure in some details thereby making it possible for the audience to get some ideas about the evolutionary dynamics of sex ratios in viscous populations.

In arthropods, several species have appendages performing ultrafast movements that far exceed muscle contraction speed. Mechanical morphologies of latch, spring, linkage mechanisms implemented in the appendages enable them to generate the ~2 msec movements in seawater. I will show you the movements of two arthropods: snapping shrimp and mantis shrimp. Their movements generate cavitation bubbles and the impacts when the bubbles collapse, is utilized in their behaviors: attacking, defending, signaling. The consequence of interaction with seawater with the appendages is important for their survival. By comparing the variations of the mechanisms between the two arthropods, those within and across individuals (Kagaya and Patek, 2016 J Exp Biol), I speculate how functionally modular morphology is integrated as an individual and how they evolved. Our recent preliminary attempt using robots to examine mechanisms is also introduced.

Organisms on Earth live under gravity. Even microorganisms in low Reynolds number conditions are known to swim against gravity: negative gravitaxis. In the model unicellular green alga Chlamydomonas, the mechanisms of negative gravitaxis have long been discussed in terms of both mechanics and physiology. Because Chlamydomonas is small and has rigid cell walls, we focused on mechanics, i.e. passive upward orientation due to cellular asymmetry. Chlamydomonas has a nearly spherical cell body and two anterior flagella. In the ‘density asymmetry model’, the cell is depicted as a bottom-heavy sphere. The ‘shape asymmetry model’ includes the shape of flagella. We quantified the contribution of these mechanisms by comparing rotation of flagellated, immobilized C. reinhardtii cells and deflagellated cells in falling.The flagellated cells rotated about 3 times faster than the deflagellated cells when medians were compared. From this result, we concluded that shape asymmetry is a dominant mechanism in passive gravitactic orientation of C. reinhardtii. Next, to clarify the contribution of density and shape asymmetries in swimming cells, we simulated swimming Chlamydomonas and calculated the angular velocity of the cell. The simulation results quantitatively agreed with the experimental results. Finally, we calculated that the simulated ‘Chlamydomonas’ cell with a constant flagellar waveform should take about 47 seconds to change its direction from downward to upward. This is in contrast to the experimental result of swimming with steep turning in typically less than 10 seconds, suggesting physiological regulation of gravitaxis in C. reinhardtii. (ref: Kage et al., 2020, JEB)

The rhinoceros auklet Cerorhinca monocerata, a seabird species, is capable of flying and swimming. Its name refers to the horn protruding from its beak. The horn appears on the upper side of the beak in both males and females only in the breeding season. Also, it has been reported that there are no differences in the size of the horn between the sexes. Hence, the horn may have a function besides affecting mating success. Regarding fluid dynamics, a protruding object like the horn of rhinoceros auklets would increase aerodynamic or hydrodynamic drag and hence the energetic cost of locomotion. Given this, there would be advantages to having the horn compensating for the potential costs. However, no plausible explanation has yet been suggested. To quantitatively measure the fluid dynamic cost and to explore potential fluid dynamic functions of the horn during flying and swimming, water-tunnel experiments were conducted using 3D-printed bird models. The horn slightly increases drag compared to the model without the horn. Meanwhile, with the prey fish in the beaks, the drag of the model with the horn was smaller than the no-horn model. Rhinoceros auklets carry prey from the sea to their chicks on land by holding fish in their beak. The results of the experiments suggest that the horn of the auklet have a fluid dynamic function for feeding their chick during the breeding season.

Fish decide their undulatory kinematics in a multi-dimensional parameter space, while energetic efficiency is a major factor to be considered. By utilizing both experimental and computational approaches, we examine the hypothesis that fish regulate undulatory kinematics to optimize speed-specific energetic efficiency during undulatory swimming, and investigate how the optimal kinematics evolve according to the swimming speed.

In cyclic swimming, tail-beat frequency and amplitude are two main parameters to control undulatory kinematics. By constructing simulation-based performance maps in the frequency-amplitude parameter space for a carangiform swimmer, an anguilliform swimmer, and larval fish, we obtained the speed-specific optimal strategy that minimizes the cost of transport (CoT) during cyclic swimming. The derived optimal strategies for various types of swimmers all suggest that fish should change tail-beat frequency to control speed with a nearly constant tail-beat amplitude.

In intermittent swimming, fish need to solve an even more complex parameter space, which at least involves tail-beat frequency, tail-beat amplitude, burst-coast bout time and the ratio of burst swimming in a burst-coast bout. Our results show that fish modulate a unique intrinsic cycle to sustain the demanded speed by modifying the bursting to coasting ratio while maintaining the duration of the cycle nearly constant, which basically consists with the requirement of energetic optimization according to our simulations.

Our results suggest that, while maintaining high energetic efficiency, some control parameters may be kept constant while others may be linearly correlated to swimming speed, as a result, fish can effectively reduce the complexity in kinematic optimisation.

Host–parasite interactions between phytoplankton and fungi (chytrids) are key processes in aquatic ecosystems. However, individual-level heterogeneity in these interactions remains unexplored, although its importance in predicting the spread of diseases has been demonstrated in epidemiology. In this study, we experimentally tested whether individual-level heterogeneity could be a good indicator of phytoplankton–chytrid interactions, using a freshwater green alga Staurastrum sp., the diatoms Ulnaria sp. and Fragilaria crotonensis, and chytrid fungi. The number of attached fungi per host cell showed a non-random clumped parasite distribution on Ulnaria sp. and F. crotonensis, but a random Poisson distribution on Staurastrum sp. To explore the potential mechanisms of these patterns, we developed a mathematical model describing sequential encounters between chytrid zoospores and host cells. As an equilibrium frequency distribution of the number of infections per host cell, we derived an exponentially-weighted Poisson distribution (EWPD) with a new weighting function. The statistical fits of the model explained the parasite distributions for Ulnaria sp. and F. crotonensis well, indicating that the clumped parasite distributions may result from an infection rate, increasing with the number of infections that already occurred on each host cell. In addition, chemical analysis revealed that, among 13 VOCs detected, 6 components characterized the differences in VOC compositions between species and infection status. The combination of mathematical and chemical analyses represents a promising approach to better understand the individual-level processes of phytoplankton–chytrid interactions.

Reference: https://doi.org/10.3354/ame01966

In the first part of my talk, I introduce the aims and method of our recent bioinformatics research [1] to identify proteins that may be important in biomineralisation in Silica cell walls of diatoms. Then I highlight a novel protein we have found, which contains characteristic repetitive sequences, that does not share homology with any known protein and is thought to be unique to diatoms.

In the second part of my talk, I discuss two types of the uncertainty in bioinformatics research that I as a researcher of fluid mechanics and a non-specialist of bioinformatics have found interesting, but difficult to deal with, while conducting the above-mentioned research. The first is related to the “tolerance” found in the ways in which bio-organisms can maintain their primary characteristics even if some minor errors have been made in the process of the transcription. The second type of uncertainty refers to the difficulty that originates from the process of data analysis depending on the method employed.

References:

1. M.Nemoto, S.Iwaki, H.Moriya, Y. Monden, T. Tamura, K.Inagaki, S. Mayama, and K.Obuse, “Comparative gene analysis focused on silica cell wall formation: Identification of diatom-specific SET domain protein methyltransferases”, Mar. Biotech. 22(4), 551-563, (2020)

Dispersal is one of the fundamental life-history strategies of organisms, so understanding the selective forces shaping the dispersal traits is important. In the Wright’s island model, dispersal evolves due to kin competition even when dispersal is costly, and it has traditionally been assumed that the living conditions are the same everywhere. To study the effect of spatial heterogeneity, we extend the model so that patches may receive different amounts of immigrants, foster different numbers of individuals, and give different reproduction efficiency to individuals therein. We obtain an analytical expression for the fitness gradient, which shows that directional selection consists of three components: As in the homogeneous case, the direct cost of dispersal selects against dispersal and kin competition promotes dispersal. The additional component, spatial heterogeneity, more precisely the variance of so-called relative reproductive potential, tends to select against dispersal. We also obtain an expression for the second derivative of fitness, which can be used to determine whether there is disruptive selection: Unlike the homogeneous case, we found that divergence of traits through evolutionary branching is possible in the heterogeneous case. Our numerical explorations suggest that evolutionary branching is promoted more by differences in patch size than by reproduction efficiency. Our results show the importance of the existing spatial heterogeneity in the real world as a key determinant in dispersal evolution.

Reference: Parvinen, Ohtsuki & Wakano (2020; PNAS 117:7290-7295)

Within the human respiratory tract (HRT), virus diffuses through the periciliary fluid (PCF) bathing the epithelium. But it also undergoes advection: as the mucus layer sitting atop the PCF is pushed along by the ciliated cell's beating cilia, the PCF and its virus contents are also pushed along, upwards towards the nose and mouth. Many mathematical models (MMs) describe the course of influenza virus infections in vivo, but none consider the impact of both diffusion and advection on the infection's kinetics and localization. Our MM represents the HRT as a one-dimensional track extending from the nose down to the lower HRT, wherein stationary cells interact with virus which moves within (diffusion) and along with (advection) the PCF. Diffusion was found to be negligible in the presence of advection which effectively sweeps away virus, preventing infection from disseminating below the depth of deposition. Higher virus production rates (10-fold) are required at higher advection speeds (40 micron/s) to maintain equivalent infection severity and timing. Because virus is entrained upwards, upper parts of the HRT located downstream of the advection flow see more virus than lower parts, and so infection grows, peaks, and resolves later in the lower HRT. This new MM offers a convenient and unique platform from which to study the localization and spread of respiratory viruses (flu, RSV, COVID-19) within the HRT during an infection.

In contrast to the modern “normality” in animals, fossil invertebrates exhibit bizarre appearances, suggesting unique biological performances. Because almost fossils have no information of soft tissues, functional morphology of fossilized, skeletal parts is crucial to understand ancient autecology.

Brachiopods are benthic marine invertebrates with two valves, encapsulated soft parts. It is noteworthy that they have the tentaculate feeding organ inside the shell to sieve small food particles from the seawater. In the Paleozoic, brachiopod diversity consists of the big two; wing-shaped spiriferids and concavo-convex productids. Hydrodynamic analyses revealed the functionality of extinct brachiopod Paraspirifer whose shell could generate spiral feeding flows to do nothing but “cast adrift” on the sea bottom. The productid shell also functions to generate passive gyrating flows as if an exhaust function of chimney. Surprisingly, spiriferids and productids have multi- and single-coiled feeding organs, respectively, both of which are advantageous for the filtration from the spiral, gyrating flows.

The hydrodynamic approaches to brachiopod shells tell us their “slow life” which was installed in each morphotype to generate passive feeding and respiratory flows. Such a concept of passivity may provide a better conclusion of how the brachiopod shells have evolved in terms of hydrodynamics.

Movement, i.e., a change in locations, is a fundamental behaviour in most animals. The ability to move to appropriate places at suitable times contributes to foraging, breeding, and risk avoidance and consequently to survival and fitness. The development of animal tracking technology (e.g., GPS devices, light-based geolocators, and satellite transmitters) has enabled us to investigate spatiotemporal patterns of movements beyond our observable field. In this presentation, I will talk about studies conducted on the movement patterns of a seabird genus (Calonectris) during homing from marine foraging areas. It was found that they adjust the onset time and route of homing depending on where they forage and the time left before sunset (Shiomi et al. 2012, 2019). Thereby, they appear to avoid offshore flights at night. To explore the cognitive basis of such movement patterns, their brain size was examined and compared with that of other avian groups. Although a causal relationship between movements and brain size remains unclear, Procellariiformes, including the genus Calonectris, have relatively larger brains. Based on insights from these movement analyses and brain size comparisons, a direction for future research will be discussed.

References:

• Shiomi, K., Yoda, K., Katsumata, N., & Sato, K. (2012). Temporal tuning of homeward flights in seabirds. Animal Behaviour, 83(2), 355-359.

• Shiomi, K., Sato, K., Katsumata, N., & Yoda, K. (2019). Temporal and spatial determinants of route selection in homing seabirds. Behaviour, 156(11), 1165-1183.

Understanding the processes regulating biodiversity patterns is central to ecology, conservation, and evolution. Ecological processes can occur at a large spatial scale, such as a continent and an ocean. Studying a large spatial scale is a challenge because it requires incorporating complex natural landscapes, including diverse environments and movements of organisms associated to the landscape.

To investigate how complex landscape structure regulates ecological processes and biodiversity patterns, I use theoretical and empirical networks representing dispersal trajectories (connectivity) of marine organisms. Our results suggest that (1) the spatial topology of connectivity affects biodiversity patterns and that (2) spatial distribution of dispersal determines the balance between different processes. I also show that advances in the estimation of ocean currents and dispersal connectivity promote studies in spatial ecology. This talk highlights that developing theories combined with data is critical to disentangle the complex nature of ecology and evolution.

Reference

• Suzuki, Y. and Economo, E.P. (2021), From species sorting to mass effects: spatial network structure mediates the shift between metacommunity archetypes. Ecography, 44: 715-726. https://doi.org/10.1111/ecog.05453