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The lodging of cereal crops due to high wind and rain is of considerable significance in many parts of the world, leading to major economic losses and yield reductions. In earlier papers the authors have developed a model of the lodging of winter wheat that identified the major parameters of the problem and enabled the relationship between root and stem lodging to be examined. It has formed the basis of a methodology used in the UK for guidance to farmers and agronomists on ways of reducing lodging risk. However the authors would be the first to acknowledge that there are limitations to the model that make it difficult to apply for a wide range of crops--particularly in the specification of the wind field and the root/soil interaction, and in allowing for stem lodging elsewhere than at the base of the stem. This paper thus describes the development of a generalised model that overcomes these shortcomings. After a discussion of the lodging phenomenon in general and a description of the earlier work, the basis of the new model is set out, based upon a mechanical model of the wind/plant/soil interactions that capture most of the important physical processes. The manner in which this model can be applied to clarify the nature of the lodging process and calculate lodging risk through a simple graphical formulation is discussed. In particular simple formulae are defined for lodging risk that are functions of a small number of dimensionless variables with identified physical meanings. The model is then applied to the lodging of wheat, oat and oilseed rape crops and considers the sensitivity of the risk calculations to uncertainties in the model parameters. In general it is suggested that the risk of lodging can be determined from very simple functions of dimensionless stem and root lodging velocities.

Understanding design principles of molecular interaction networks is an important goal of molecular systems biology. Some insights have been gained into features of their network topology through the discovery of graph theoretic patterns that constrain network dynamics. This paper contributes to the identification of patterns in the mechanisms that govern network dynamics. The control of nodes in gene regulatory, signaling, and metabolic networks is governed by a variety of biochemical mechanisms, with inputs from other network nodes that act additively or synergistically. This paper focuses on a certain type of logical rule that appears frequently as a regulatory pattern. Within the context of the multistate discrete model paradigm, a rule type is introduced that reduces to the concept of nested canalyzing function in the Boolean network case. It is shown that networks that employ this type of multivalued logic exhibit more robust dynamics than random networks, with few attractors and short limit cycles. It is also shown that the majority of regulatory functions in many published models of gene regulatory and signaling networks are nested canalyzing., Comment: gene regulation; signaling; mathematical model; nested canalyzing function; robustness

A pedigree is a directed graph that describes how individuals are related through ancestry in a sexually-reproducing population. In this paper we explore the question of whether one can reconstruct a pedigree by just observing sequence data for present day individuals. This is motivated by the increasing availability of genomic sequences, but in this paper we take a more theoretical approach and consider what models of sequence evolution might allow pedigree reconstruction (given sufficiently long sequences). Our results complement recent work that showed that pedigree reconstruction may be fundamentally impossible if one uses just the degrees of relatedness between different extant individuals. We find that for certain stochastic processes, pedigrees can be recovered up to isomorphism from sufficiently long sequences., 20 pages, 3 figures

Game dynamics in which three or more strategies are cyclically competitive, as represented by the rock-scissors-paper game, have attracted practical and theoretical interests. In evolutionary dynamics, cyclic competition results in oscillatory dynamics of densities of individual strategists. In finite-size populations, it is known that oscillations blow up until all but one strategies are eradicated if without mutation. In the present paper, we formalize replicator dynamics with players that have different adaptation rates. We show analytically and numerically that the heterogeneous adaptation rate suppresses the oscillation amplitude. In social dilemma games with cyclically competing strategies and homogeneous adaptation rates, altruistic strategies are often relatively weak and cannot survive in finite-size populations. In such situations, heterogeneous adaptation rates save coexistence of different strategies and hence promote altruism. When one strategy dominates the others without cyclic competition, fast adaptors earn more than slow adaptors. When not, mixture of fast and slow adaptors stabilizes population dynamics, and slow adaptation does not imply inefficiency for a player., Comment: 4 figures

Optimal control theory has been extensively used to determine the optimal harvesting policy for renewable resources such as fish stocks. In such optimisations, it is common to maximise the discounted utility of harvesting over time, employing a constant time discount rate. However, evidence from human and animal behaviour suggests that we have evolved to employ discount rates which fall over time, often referred to as “hyperbolic discounting”. This increases the weight on benefits in the distant future, which may appear to provide greater protection of resources for future generations, but also creates challenges of time-inconsistent plans. This paper examines harvesting plans when the discount rate declines over time. With a declining discount rate, the planner reduces stock levels in the early stages (when the discount rate is high) and intends to compensate by allowing the stock level to recover later (when the discount rate will be lower). Such a plan may be feasible and optimal, provided that the planner remains committed throughout. However, in practice there is a danger that such plans will be re-optimized and adjusted in the future. It is shown that repeatedly restarting the optimization can drive the stock level down to the point where the optimal policy is to harvest the stock to extinction. In short, a key contribution of this paper is to identify the surprising severity of the consequences flowing from incorporating a rather trivial, and widely prevalent, “non-rational” aspect of human behaviour into renewable resource management models. These ideas are related to the collapse of the Peruvian anchovy fishery in the 1970's.

Animals that deploy chemical defences against predators often signal their unprofitability using bright colouration. This pairing of toxicity and conspicuous patterning is known as aposematism. Explaining the evolution and spread of aposematic traits in previously cryptic species has been the focus of much empirical and theoretical work over the last two decades. Existing research concerning the initial evolution of aposematism does not however properly consider that many aposematic species (such as members of the hymenoptera, the lepidoptera, and amphibia) are highly mobile. We argue in this paper that the evolution of aposematic displays is therefore often best understood within a metapopulation framework; hence in this paper we present the first explicit metapopulation model of the evolution of aposematism. Our most general finding is that migration tends to reduce the probability that an aposematic prey can increase from rarity and spread across a large population. Hence, the best case scenarios for the spread of aposematism required fixation of the aposematic form in one or more isolated sub-habitats prior to some event which subsequently enabled migration. We observed that changes in frequency of new aposematic forms within source habitats are likely to be nonmonotonic. First, aposematic prey tend to decline in frequency as they migrate outwards from the source habitat to neighbouring sink habitats, but subsequently they increase in relative abundance in the source, as the descendents of earlier migrants migrate back from newly converted sub-populations. This pattern of initial loss and subsequent gain between new source and neighbouring sink habitats is then repeated as the aposematic form spreads via a moving cline.

This is the first paper in a two-part series in which we develop, analyze, and simulate a diffuse interface continuum model of multispecies tumor growth and tumor-induced angiogenesis in two and three dimensions. Three-dimensional simulations of nonlinear tumor growth and neovascularization using this diffuse interface model were recently presented in Frieboes et al. [2007. Computer simulation of glioma growth and morphology. NeuroImage S59-S70], but that paper did not describe the details of the model or the numerical algorithm. This is done here. In this diffuse interface approach, sharp interfaces are replaced by narrow transition layers that arise due to differential adhesive forces among the cell species. Accordingly, a continuum model of adhesion is introduced. The model is thermodynamically consistent, is related to recently developed mixture models, and thus is capable of providing a detailed description of tumor progression. The model is well-posed and consists of fourth-order nonlinear advection-reaction-diffusion equations (of Cahn-Hilliard-type) for the cell species coupled with reaction-diffusion equations for the substrate components. We demonstrate analytically and numerically that when the diffuse interface thickness tends to zero, the system reduces to a classical sharp interface model. Using a new fully adaptive and nonlinear multigrid/finite difference method, the system is simulated efficiently. In this first paper, we present simulations of unstable avascular tumor growth in two and three dimensions and demonstrate that our techniques now make large-scale three-dimensional simulations of tumors with complex morphologies computationally feasible. In part II of this study, we will investigate multispecies tumor invasion, tumor-induced angiogenesis, and focus on the morphological instabilities that may underlie invasive phenotypes.

Cyclical thrombocytopenia (CT) is a rare hematological disease characterized by periodic oscillations in the platelet count. Although first reported in 1936, the pathogenesis and an effective therapy remain to be identified. Since besides fluctuations in platelet levels the patients hematological profile have been consistently normal, a destabilization of a peripheral control mechanism might play an important role in the genesis of this disorder. In this paper, we investigate through computer simulations the mechanisms underlying the platelet oscillations observed in CT. First, we collected the data published in the last 40 years and quantified the significance of the platelet fluctuations using Lomb-Scargle periodograms. Our analysis reveals that the incidence of the statistically significant periodic data is equally distributed in men and women. The mathematical model proposed in this paper captures the essential features of hematopoiesis and successfully duplicates the characteristics of CT. With the same parameter changes, the model is able to fit the platelet counts and to qualitatively reproduce the TPO oscillations (when data is available). Our results indicate that a variation in the megakaryocyte maturity, a slower relative growth rate of megakaryocytes, as well as an increased random destruction of platelets are the critical elements generating the platelet oscillations in CT.

This paper develops a set of simplified dynamical models with which to explore the conditions under which division of labor leads to optimized system output, as measured by the rate of production of a given product. We consider two models: In the first model, we consider the flow of some resource into a compartment, and the conversion of this resource into some product. In the second model, we consider the resource-limited growth of autoreplicating systems. In this case, we divide the replication and metabolic tasks among different agents. The general features that emerge from our models is that division of labor is favored when the resource to agent ratio is at intermediate values, and when the time cost associated with transporting intermediate products is small compared to characteristic process times. We discuss the results of this paper in the context of simulations with digital life. We also argue that division of labor in the context of our replication model suggests an evolutionary basis for the emergence of the stem-cell-based tissue architecture in complex organisms., Comment: 10 pages, submitted to the Journal of Theoretical Biology (figures are included with the journal version)

In this paper, we propose an easy to implement generalized linear models (GLM) methodology for estimating the basic reproduction number, R

Funding: EPSRC Grant No. EP/N014642/1 (EPSRC Centre for Multiscale Soft Tissue Mechanics - With Application to Heart & Cancer) (MAJC,CKM). Transcription factors are important molecules which control the levels of mRNA and proteins within cells by modulating the process of transcription (the mechanism by which mRNA is produced within cells) and hence translation (the mechanism by which proteins are produced within cells). Transcription factors are part of a wider family of molecular interaction networks known as gene regulatory networks (GRNs) which play an important role in key cellular processes such as cell division and apoptosis (e.g. the p53-Mdm2, NFκB pathways). Transcription factors exert control over molecular levels through feedback mechanisms, with proteins binding to gene sites in the nucleus and either up-regulating or down-regulating production of mRNA. In many GRNs, there is a negative feedback in the network and the transcription rate is reduced. Typically, this leads to the mRNA and protein levels oscillating over time and also spatially between the nucleus and cytoplasm. When experimental data for such systems is analysed, it is observed to be noisy and in many cases the actual numbers of molecules involved are quite low. In order to model such systems accurately and connect with the data in a quantitative way, it is therefore necessary to adopt a stochastic approach as well as take into account the spatial aspect of the problem. In this paper, we extend previous work in the area by formulating and analysing stochastic spatio-temporal models of synthetic GRNs e.g. repressilators and activator-repressor systems. Postprint

Individual animal movement has been a focus of intense research and considerable controversy over the last two decades, however the understanding of wider ecological implications of various movement behaviours is lacking. In this paper, we consider this issue in the context of pattern formation. Using an individual-based modelling approach and computer simulations, we first show that density dependence (“auto-taxis”) of the individual movement in a population of random walkers typically results in the formation of a strongly heterogeneous population distribution consisting of clearly defined animal clusters or patches. We then show that, when the movement takes place in a large spatial domain, the properties of the clusters are significantly different in the populations of Brownian and non-Brownian walkers. Whilst clusters tend to be stable in the case of Brownian motion, in the population of Levy walkers clusters are dynamical so that the number of clusters fluctuates in the course of time. We also show that the population dynamics of non-Brownian walkers exhibits two different time scales: a short time scale of the relaxation of the initial condition and a long time scale when one type of dynamics is replaced by another. Finally, we show that the distribution of sample values in the populations of Brownian and non-Brownian walkers is significantly different.

In this paper, we apply the diffuse domain framework developed in Chen and Lowengrub (Tumor growth in complex, evolving microenvironmental geometries: A diffuse domain approach, J. Theor. Biol. 361 (2014) 14–30) to study the effects of a deformable basement membrane (BM) on the growth of a tumor in a confined, ductal geometry, such as ductal carcinoma in situ (DCIS). We use a continuum model of tumor microcalcification and investigate the tumor extent beyond the microcalcification. In order to solve the governing equations efficiently, we develop a stable nonlinear multigrid finite difference method. Two dimensional simulations are performed where the adhesion between tumor cells and the basement membrane is varied. Additional simulations considering the variation of duct radius and membrane stiffness are also conducted. The results demonstrate that enhanced membrane deformability promotes tumor growth and tumor calcification. When the duct radius is small, the cell-BM adhesion is weak or when the membrane is slightly deformed, the mammographic and pathologic tumor extents are linearly correlated, as predicted by Macklin et al. (J. Theor. Biol. 301 (2012) 122–140) using an agent-based model that does not account for the deformability of the basement membrane and the active forces that the membrane imparts on the tumor cells. Interestingly, we predict that when the duct radius is large, there is strong cell-BM adhesion or the membrane is highly deformed, the extents of the mammographic and pathologic tumors are instead quadratically correlated. The simulations can help surgeons to measure DCIS surgical margins while removing less non-cancerous tissue, and can improve targeting of intra- and post-operative radiotherapy.

Network models of disease spread play an important role in elucidating the impact of long-lasting infectious contacts on the dynamics of epidemics. Moment-closure approximation is a common method of generating low-dimensional deterministic models of epidemics on networks, which has found particular success for diseases with susceptible-infected-recovered (SIR) dynamics. However, the effect of network structure is arguably more important for sexually transmitted infections, where epidemiologically relevant contacts are comparatively rare and longstanding, and which are in general modelled via the susceptible-infected-susceptible (SIS)-paradigm. In this paper, we introduce an improvement to the standard pairwise approximation for network models with SIS-dynamics for two different network structures: the isolated open triple (three connected individuals in a line) and the k -regular network. This improvement is achieved by tracking the rate of change of errors between triple values and their standard pairwise approximation. For the isolated open triple, this improved pairwise model is exact, while for k -regular networks a closure is made at the level of triples to obtain a closed set of equations. This improved pairwise approximation provides an insight into the errors introduced by the standard pairwise approximation, and more closely matches both higher-order moment-closure approximations and explicit stochastic simulations with only a modest increase in dimensionality to the standard pairwise approximation.

The human brain is a small organ which uses a disproportional amount of the total metabolic energy pro- duction in the body. While it is well understood that the most significant energy sink is the maintenance of the neuronal membrane potential during the brain signaling activity, the role of astrocytes in the energy balance continues to be the topic of a lot of research. A key function of astrocytes, besides clearing glutamate from the synaptic clefts, is the potassium clearing after neuronal activation. Extracellular potassium plays a significant role in triggering neuronal firing, and elevated concentration of potassium may lead to abnormal firing pattern, e.g., seizures, thus emphasizing the importance of the glial K+ buffering role. The predictive mathematical model proposed in this paper elucidates the role of glial potassium clearing in brain energy metabolism, integrating a detailed model of the ion dynamics which regulates neuronal firing with a three compartment metabolic model. Because of the very different characteristic time scales of electrophysiology and metabolism, care must be taken when coupling the two models to ensure that the predictions, e.g., neuronal firing frequencies and the oxygen- glucose index (OGI) of the brain during activation and rest, are in agreement with empirical observations. The temporal multi-scale nature of the problem requires the design of new computational tools to ensure a stable and accurate numerical treatment of the problem. The model predictions for different protocols, including combinations of elevated activation and ischemic episodes, are in good agreement with experimental observations reported in the literature., This work was supported by the Bizkaia Talent and European Commission through CO- FUND under the grant CIPAS: Computational Inverse Problems Across Scales (AYD-000-278, 2015), by the Basque Government through the BERC 2014-2017 program, and by the Spanish Ministry of Economics and Competitive- ness MINECO through the BCAM Severo Ochoa excellence accreditation SEV-2013-0323 and the Spanish ”Plan Estatal de Investigacio ́n, Desarrollo e Innovacio ́n Orientada a los Retos de la Sociedad” under Grant BELEMET - Brain ELEctro-METabolic modeling and numerical approximation (MTM2015-69992-R). The work of Daniela Cal- vetti was partly supported by Grant Number 246665 from the Simons Foundation, and the work of Erkki Somersalo was partly supported by NSF Grant DMS 1016183. Daniela Calvetti and Erkki Somersalo were partly supported by NIH, grant 1U01GM111251-01.

Highlights • By fitting the SIQ model, which employs a squashing-type function for β(t), to the real data on the confirmed cases and the quarantined cases, we obtained reasonable performance. Also, it turned out that the resultant estimated parameters belonged to plausible ranges. By comparison, the conventional SIQ model utilizing a constant transmission probability could not explain the observed data well. • As a practical guideline to avoid another similar unexpected outbreak, we draw the conclusion that combined efforts in the early stage are critically important, and sharing information including the names of affected hospitals or countries, clinical situations, and prevention methods might be important for global public health control. • We applied optimal control theory to the controlled SIQ model with the goal of minimizing the infectious compartment population and the cost of implementing the quarantine and isolation strategies. Simulation results show that the number of the MERS cases can be controlled reasonably well via the optimal control approach., Much concern has arisen regarding serious epidemics due to the Middle East Respiratory Syndrome (MERS) coronavirus. The first MERS case of Korea was reported on 20 May 2015, and since then, the MERS outbreak in Korea has resulted in hundreds of confirmed cases and tens of deaths. Deadly infectious diseases such as MERS have significant direct and indirect social impacts, which include disease-induced mortality and economic losses. Also, a delayed response to the outbreak and underestimating its danger can further aggravate the situation. Hence, an analysis and establishing efficient strategies for preventing the propagation of MERS is a very important and urgent issue. In this paper, we propose a class of nonlinear susceptible-infectious-quarantined (SIQ) models for analyzing and controlling the MERS outbreak in Korea. For the SIQ based ordinary differential equation (ODE) model, we perform the task of parameter estimation, and apply optimal control theory to the controlled SIQ model, with the goal of minimizing the infectious compartment population and the cost of implementing the quarantine and isolation strategies. Simulation results show that the proposed SIQ model can explain the observed data for the confirmed cases and the quarantined cases in the MERS outbreak very well, and the number of the MERS cases can be controlled reasonably well via the optimal control approach.

Neuromyelitis Optica (NMO) is a severe neuro-inflammatory disease of the central nervous system characterized by predominant damage to the optic nerve and of the spinal cord. The pathogenic antibody found in the majority of patients targets the AQP4 channels on astrocytic endfeet and causes the cells to swell. Although, the pathophysiology of the disease is broadly known, there are no specific targeted treatments for this process clinically available nor accurate prognostic markers both during attacks and for predicting long term neuronal damage. This lack is, in part, due to the rarity of the disease and its relatively recent pathogenic clarity. Hence, the ability to mathematically model the progress of the condition to test prospective therapies in silico would be a step forward. This paper combines state of the art models of cellular metabolism and cytotoxic oedema in neurons and astrocytes and augments it with a detailed characterization of water transport across the cellular membrane. In particular, we capture the process of perforation of the cell through the human complement cascade and resulting water and ionic fluxes. Simulating NMO by injecting its antibody and human complement into the extracellular space showed a 25% increase of the astrocytic volume after 12 h from onset. Most of the volume change occurred during the first 30 min of simulation with a peak volume change of 38%. The model was further adapted to simulate the therapeutic potential of CD59. It was found that there is a threshold of CD59 concentration that can prevent the swelling of astrocytes. Since the astrocyte volume changes mostly during the first hour, further experimental work should focus on this time scale to provide data for further model refinement and validation.

COVID-19 testing has become a standard approach for estimating prevalence which then assist in public health decision making to contain and mitigate the spread of the disease. The sampling designs used are often biased in that they do not reflect the true underlying populations. For instance, individuals with strong symptoms are more likely to be tested than those with no symptoms. This results in biased estimates of prevalence (too high). Typical post-sampling corrections are not always possible. Here we present a simple bias correction methodology derived and adapted from a correction for publication bias in meta analysis studies. The methodology is general enough to allow a wide variety of customization making it more useful in practice. Implementation is easily done using already collected information. Via a simulation and two real datasets, we show that the bias corrections can provide dramatic reductions in estimation error., Comment: 14 pages. Title changed. The whole Section 7 with information from Lombardy, Italy, was added (another real dataset). Some typos were corrected. In spite of several lengthy additions, no substantial changes were done to the paper. The goal of the additions was more to clarify than to correct

The role of punishment in the maintenance of cooperation has been emphasized recently. However, the maintenance of punishment is not an obvious consequence because punishment itself is also a public good; it is costly to perform and hence vulnerable to exploitation. For example, cooperative punishers, who help others and punish free riders, are disadvantageous in competition against pure cooperators, who cooperate but do not punish free riders. In addition, pure punishers, who do not help others but punish free riders, have been considered to be selfish in conventional models, because they do not perform cooperation. Instead, here we assume that performing either cooperation or punishment is sufficient to avoid accusation from others because not only cooperators but also pure punishers contribute to their society by reducing a threat of free riders. Under such an assumption, we analyzed the evolutionary dynamics of pure cooperators, pure punishers and free riders. We first showed that cooperation is never maintained in a well-mixed population. When the population is spatially structured, however, oscillatory rock-paper-scissors dynamics among those strategies appear. We further find that a stable polymorphism of the three strategies is attained when mutation is introduced. Our results indicate that cooperation and punishment can be stably maintained even when one cannot perform cooperation and punishment at the same time, and provide insights about the coexistence of cooperation and punishment in real societies.

How to select and combine good traits of rice to get high-production individuals is one of the key points in developing crop ideotype cultivation technologies. Existing cultivation methods for producing ideal plants, such as field trials and crop modeling, have some limits. In this paper, we propose a method based on a genetic algorithm (GA) and a functional-structural plant model (FSPM) to optimize plant types of virtual rice by dynamically adjusting phenotypical traits. In this algorithm, phenotypical traits such as leaf angles, plant heights, the maximum number of tiller, and the angle of tiller are considered as input parameters of our virtual rice model. We evaluate the photosynthetic output as a function of these parameters, and optimized them using a GA. This method has been implemented on GroIMP using the modeling language XL (eXtended L-System) and RGG (Relational Growth Grammar). A double haploid population of rice is adopted as test material in a case study. Our experimental results show that our method can not only optimize the parameters of rice plant type and increase the amount of light absorption, but can also significantly increase crop yield.

Graphical abstract, Highlights • Homo-oligomerisation may offer an unexpected variety of signal processing functions. • These include: dynamic signal encoding via oligomeric complex size. • Homeostatic regulation of monomer concentration. • Bistability via pseudo-multisite modification and multi-enzyme regulation. • The findings partly explain why homo-oligomerisation is so commonly found in evolution., Homo-oligomerisation of proteins is a ubiquitous phenomenon whose exact role remains unclear in many cases. To identify novel functions, this paper provides an exploration of general dynamical mathematical models of homo-oligomerisation. Simulation and analysis of these models show that homo-oligomerisation on its own allows for a remarkable variety of complex dynamic and steady state regulatory behaviour such as transient overshoots or homeostatic control of monomer concentration. If post-translational modifications are considered, however, conventional mass action kinetics lead to thermodynamic inconsistencies due to asymmetric combinatorial expansion of reaction routes. Introducing a conservation principle to balance rate equations re-establishes thermodynamic consistency. Using such balanced models it is shown that oligomerisation can lead to bistability by enabling pseudo-multisite modification and kinetic pseudo-cooperativity via multi-enzyme regulation, thereby constituting a novel motif for bistable modification reactions. Due to these potential signal processing capabilities, homo-oligomerisation could play far more versatile roles in signal transduction than previously appreciated.

Gene regulatory networks are a popular tool for modelling important biological phenomena, such as cell differentiation or oncogenesis. Efficient identification of the causal connections between genes, their products and regulating transcription factors, is key to understanding how defects in their function may trigger diseases. Modelling approaches should keep up with the ever more detailed descriptions of the biological phenomena at play, as provided by new experimental findings and technical improvements. In recent years, we have seen great improvements in mapping of specific binding sites of many transcription factors to distinct regulatory regions. Recent gene regulatory network models use binding measurements; but usually only to define gene-to-gene interactions, ignoring regulatory module structure. Moreover, current huge amount of transcriptomic data, and exploration of all possible cis-regulatory arrangements which can lead to the same transcriptomic response, makes manual model building both tedious and time-consuming. In our paper, we propose a method to specify possible regulatory connections in a given Boolean network, based on transcription factor binding evidence. This is implemented by an algorithm which expands a regular Boolean network model into a “cis-regulatory” Boolean network model. This expanded model explicitly defines regulatory regions as additional nodes in the network, and adds new, valuable biological insights to the system dynamics. The expanded model can automatically be compared with expression data. And, for each node, a regulatory function, consistent with the experimental data, can be found. The resulting models are usually more constrained (by biologically-motivated metadata), and can then be inspected in in silico simulations. The fully automated method for model identification has been implemented in Python, and the expansion algorithm in R. The method resorts to the Z3 Satisfiability Modulo Theories (SMT) solver, and is similar to the RE:IN application (Yordanov et al., 2016). It is available on https://github.com/regulomics/expansion-network .

While deterministic metapopulation models for the spread of epidemics between populations have been well-studied in the literature, variability in disease transmission rates and interaction rates between individual agents or populations suggests the need to consider stochastic fluctuations in model parameters in order to more fully represent realistic epidemics. In the present paper, we have extended a stochastic SIS epidemic model - which introduces stochastic perturbations in the form of white noise to the force of infection (the rate of disease transmission from classes of infected to susceptible populations) - to spatial networks, thereby obtaining a stochastic epidemic metapopulation model. We solved the stochastic model numerically and found that white noise terms do not drastically change the overall long-term dynamics of the system (for sufficiently small variance of the noise) relative to the dynamics of a corresponding deterministic system. The primary difference between the stochastic and deterministic metapopulation models is that for large time, solutions tend to quasi-stationary distributions in the stochastic setting, rather than to constant steady states in the deterministic setting. We then considered different approaches to controlling the spread of a stochastic SIS epidemic over spatial networks, comparing results for a spectrum of controls utilizing local to global information about the state of the epidemic. Variation in white noise was shown to be able to counteract the treatment rate (treated curing rate) of the epidemic, requiring greater treatment rates on the part of the control and suggesting that in real-life epidemics one should be mindful of such random variations in order for a treatment to be effective. Additionally, we point out some problems using white noise perturbations as a model, but show that a truncated noise process gives qualitatively comparable behaviors without these issues.

In genome-wide prediction, independence of marker allele substitution effects is typically assumed; however, since early stages in the evolution of this technology it has been known that nature points to correlated effects. In statistics, graphical models have been identified as a useful and powerful tool for covariance estimation in high dimensional problems and it is an area that has recently experienced a great expansion. In particular, Gaussian concentration graph models (GCGM) have been widely studied. These are models in which the distribution of a set of random variables, the marker effects in this case, is assumed to be Markov with respect to an undirected graph G. In this paper, Bayesian (Bayes G and Bayes G-D) and frequentist (GML-BLUP) methods adapting the theory of GCGM to genome-wide prediction were developed. Different approaches to define the graph G based on domain-specific knowledge were proposed, and two propositions and a corollary establishing conditions to find decomposable graphs were proven. These methods were implemented in small simulated and real datasets. In our simulations, scenarios where correlations among allelic substitution effects were expected to arise due to various causes were considered, and graphs were defined on the basis of physical marker positions. Results showed improvements in correlation between phenotypes and predicted additive genetic values and accuracies of predicted additive genetic values when accounting for partially correlated allele substitution effects. Extensions to the multiallelic loci case were described and some possible refinements incorporating more flexible priors in the Bayesian setting were discussed. Our models are promising because they allow incorporation of biological information in the prediction process, and because they are more flexible and general than other models accounting for correlated marker effects that have been proposed previously.

In this paper, we build a framework for the analysis and classification of collective behavior using methods from generative modeling and nonlinear manifold learning. We represent an animal group with a set of finite-sized particles and vary known features of the group structure and motion via a class of generative models to position each particle on a two-dimensional plane. Particle positions are then mapped onto training images that are processed to emphasize the features of interest and match attainable far-field videos of real animal groups. The training images serve as templates of recognizable patterns of collective behavior and are compactly represented in a low-dimensional space called embedding manifold. Two mappings from the manifold are derived: the manifold-to-image mapping serves to reconstruct new and unseen images of the group and the manifold-to-feature mapping allows frame-by-frame classification of raw video. We validate the combined framework on datasets of growing level of complexity. Specifically, we classify artificial images from the generative model, interacting self-propelled particle model, and raw overhead videos of schooling fish obtained from the literature.

Although the basic mechanics of evolution have been understood since Darwin, debate continues over whether macroevolutionary phenomena are driven by the fitness structure of genotype space or by ecological interaction. In this paper we propose a simple model capturing key features of fitness-landscape and ecological models of evolution. Our model describes evolutionary dynamics in a high-dimensional, structured genotype space with interspecies interaction. We find promising qualitative similarity with the empirical facts about macroevolution, including broadly distributed extinction sizes and realistic exploration of the genotype space. The abstraction of our model permits numerous applications beyond macroevolution, including protein and RNA evolution.

A simple way to model phenotypic evolution is to assume that after splitting, the trait values of the sister species diverge as independent Brownian motions. Relying only on a prior distribution for the underlying species tree (conditioned on the number, n, of extant species) we study the random vector (X_1,...,X_n) of the observed trait values. In this paper we derive compact formulae for the variance of the sample mean and the mean of the sample variance for the vector (X_1,...,X_n). The key ingredient of these formulae is the correlation coefficient between two trait values randomly chosen from (X_1,...,X_n). This interspecies correlation coefficient takes into account not only variation due to the random sampling of two species out of n and the stochastic nature of Brownian motion but also the uncertainty in the phylogenetic tree. The latter is modeled by a (supercritical or critical) conditioned branching process. In the critical case we modify the Aldous-Popovic model by assuming a proper prior for the time of origin., Comment: 19 pages, 5 figures

The strategies of structured treatment interruptions (STIs) of antiretroviral therapies have been proposed for clinical management of HIV infected patients, but clinical studies on STIs failed to achieve a consistent conclusion for this strategy. To evaluate the STI strategies, in particular, CD4(+) T cell count-guided STIs, and explain these controversial conclusions from different clinical studies, in this paper we propose to use piecewise HIV virus dynamic models to quantitatively explore the STI strategies and investigate their dynamic behaviors. Our analysis results indicate that CD4(+) T cell counts can be maintained above a safe level using the STI with a single threshold or a threshold window. Numerical simulations show that the CD4(+) T cell counts either fluctuate or approach a stable level for a patient, depending on the prescribed upper or lower threshold values. In particular, the CD4(+) T cell counts can be stabilized at a desired level if the threshold policy control is applied. The durations of drug-on and drug-off are very sensitive to the prescribed upper or lower threshold levels, which possibly explains why the on-off strategy with fixed schedule or an STI strategy with frequent switches are associated with the high rate of failure. Our findings suggest that it is critical to carefully choose the thresholds of CD4(+) T cell count and individualize the STIs for each individual patient based on initial CD4(+) T cell counts.

It has been known for some time that human autoimmune diseases can be triggered by viral infections. Several possible mechanisms of interactions between a virus and immune system have been analysed, with a prevailing opinion being that the onset of autoimmunity can in many cases be attributed to ‘‘molecular mimicry’’, where linear peptide epitopes, processed from viral proteins, mimic normal host self-proteins, thus leading to a cross-reaction of immune response against virus with host cells. In this paper we present a mathematical model for the dynamics of an immune response to a viral infection and autoimmunity, which takes into account T cells with different activation thresholds. We show how the infection can be cleared by the immune system, as well as how it can lead to a chronic infection or recurrent infection with relapses and remissions. Numerical simulations of the model are performed to illustrate various dynamical regimes, as well as to analyse the potential impact of treatment of autoimmune disease in the chronic and recurrent states. The results provide good qualitative agreement with available data on immune responses to viral infections and progression of autoimmune diseases.

Synechocystis sp., a common unicellular freshwater cyanobacterium, has been used as a model organism to study phototaxis, an ability to move in the direction of a light source. This microorganism displays a number of additional characteristics such as delayed motion, surface dependence, and a quasi-random motion, where cells move in a seemingly disordered fashion instead of in the direction of the light source, a global force on the system. These unexplained motions are thought to be modulated by local interactions between cells such as intercellular communication. In this paper, we consider only local interactions of these phototactic cells in order to mathematically model this quasi-random motion. We analyze an experimental data set to illustrate the presence of quasi-random motion and then derive a stochastic dynamic particle system modeling interacting phototactic cells. The simulations of our model are consistent with experimentally observed phototactic motion.

International audience; Identifying the right tools to express the stochastic aspects of neural activity has proven to be one of the biggest challenges in computational neuroscience. Even if there is no definitive answer to this issue, the most common procedure to express this randomness is the use of stochastic models. In accordance with the origin of variability, the sources of randomness are classified as intrinsic or extrinsic and give rise to distinct mathematical frameworks to track down the dynamics of the cell. While the external variability is generally treated by the use of a Wiener process in models such as the Integrate-and-Fire model, the internal variability is mostly expressed via a random firing process. In this paper, we investigate how those distinct expressions of variability can be related. To do so, we examine the probability density functions to the corresponding stochastic models and investigate in what way they can be mapped one to another via integral transforms. Our theoretical findings offer a new insight view into the particular categories of variability and it confirms that, despite their contrasting nature, the mathematical formalization of internal and external variability are strikingly similar.

Biological systems are typically modelled by nonlinear differential equations. In an effort to produce high fidelity representations of the underlying phenomena, these models are usually of high dimension and involve multiple temporal and spatial scales. However, this complexity and associated stiffness makes numerical simulation difficult and mathematical analysis impossible. In order to understand the functionality of these systems, these models are usually approximated by lower dimensional descriptions. These can be analysed and simulated more easily, and the reduced description also simplifies the parameter space of the model. This model reduction inevitably introduces error: the accuracy of the conclusions one makes about the system, based on reduced models, depends heavily on the error introduced in the reduction process. In this paper we propose a method to calculate the error associated with a model reduction algorithm, using ideas from dynamical systems. We first define an error system, whose output is the error between observables of the original and reduced systems. We then use convex optimisation techniques in order to find approximations to the error as a function of the initial conditions. In particular, we use the Sum of Squares decomposition of polynomials in order to compute an upper bound on the worst-case error between the original and reduced systems. We give biological examples to illustrate the theory, which leads us to a discussion about how these techniques can be used to model-reduce large, structured models typical of systems biology.

Gene regulatory networks (GRNs) play an important role in maintaining cellular function by correctly timing key processes such as cell division and apoptosis. GRNs are known to contain similar structural components, which describe how genes and proteins within a network interact - typically by feedback. In many GRNs, proteins bind to gene-sites in the nucleus thereby altering the transcription rate. If the binding reduces the transcription rate there is a negative feedback leading to oscillatory behaviour in mRNA and protein levels, both spatially (e.g. by observing fluorescently labelled molecules in single cells) and temporally (e.g. by observing protein/mRNA levels over time). Mathematical modelling of GRNs has focussed on such oscillatory behaviour. Recent computational modelling has demonstrated that spatial movement of the molecules is a vital component of GRNs, while it has been proved rigorously that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf-bifurcation. In this paper we consider the spatial aspect further by considering the specific location of gene and protein production, showing that there is an optimum range for the distance between an mRNA gene-site and a protein production site in order to achieve oscillations. We first present a model of a well-known GRN, the Hes1 system, and then extend the approach to examine spatio-temporal models of synthetic GRNs e.g. n-gene repressilator and activator-repressor systems. By incorporating the idea of production sites into such models we show that the spatial component is vital to fully understand GRN dynamics. Postprint

Cross-protection, which refers to a process whereby artificially inoculating a plant with a mild strain provides protection against a more aggressive isolate of the virus, is known to be an effective tool of disease control in plants. In this paper we derive and analyse a new mathematical model of the interactions between two competing viruses with particular account for RNA interference. Our results show that co-infection of the host can either increase or decrease the potency of individual infections depending on the levels of cross-protection or cross-enhancement between different viruses. Analytical and numerical bifurcation analyses are employed to investigate the stability of all steady states of the model in order to identify parameter regions where the system exhibits synergistic or antagonistic behaviour between viral strains, as well as different types of host recovery. We show that not only viral attributes but also the propagating component of RNA-interference in plants can play an important role in determining the dynamics., Comment: 28 pages, 7 figures

Human breath contains a myriad of endogenous volatile organic compounds (VOCs) which are reflective of ongoing metabolic or physiological processes. While research into the diagnostic potential and general medical relevance of these trace gases is conducted on a considerable scale, little focus has been given so far to a sound analysis of the quantitative relationships between breath levels and the underlying systemic concentrations. This paper is devoted to a thorough modeling study of the end-tidal breath dynamics associated with isoprene, which serves as a paradigmatic example for the class of low-soluble, blood-borne VOCs. Real-time measurements of exhaled breath under an ergometer challenge reveal characteristic changes of isoprene output in response to variations in ventilation and perfusion. Here, a valid compartmental description of these profiles is developed. By comparison with experimental data it is inferred that the major part of breath isoprene variability during exercise conditions can be attributed to an increased fractional perfusion of potential storage and production sites, leading to higher levels of mixed venous blood concentrations at the onset of physical activity. In this context, various lines of supportive evidence for an extrahepatic tissue source of isoprene are presented. Our model is a first step towards new guidelines for the breath gas analysis of isoprene and is expected to aid further investigations regarding the exhalation, storage, transport and biotransformation processes associated with this important compound., 14 pages

International audience; In this paper an advanced, clinically oriented multiscale cancer model of breast tumor response to chemotherapy is presented. The paradigm of early breast cancer treated by epirubicin according to a branch of an actual clinical trial (the Trial of Principle, TOP trial) has been addressed. The model, stemming from previous work of the Oncology Group, National Technical University of Athens, is characterized by several crucial new features, such as the explicit distinction of proliferating cells into stem cells of infinite mitotic potential and cells of limited proliferative capacity, an advanced generic cytokinetic model and an improved tumor constitution initialization technique. A sensitivity analysis regarding critical parameters of the model has revealed their effect on the behavior of the biological system. The favorable outcome of an initial step towards the clinical adaptation and validation of the simulation model, based on the use of anonymized data from the TOP clinical trial, is presented and discussed. Two real clinical cases from the TOP trial with variable molecular profile have been simulated. A realistic time course of the tumor diameter and a reduction in tumor size in agreement with the clinical data has been achieved for both cases by selection of reasonable model parameter values, thus demonstrating a possible adaptation process of the model to real clinical trial data. Available imaging, histological, molecular and treatment data are exploited by the model in order to strengthen patient individualization modeling. The expected use of the model following thorough clinical adaptation, optimization and validation is to simulate either several candidate treatment schemes for a particular patient and support the selection of the optimal one or to simulate the expected extent of tumor shrinkage for a given time instant and decide on the adequacy or not of the simulated scheme.

Food webs can be regarded as energy transporting networks in which the weight of each edge denotes the energy flux between two species. By investigating 21 empirical weighted food webs as energy flow networks, we found several ubiquitous scaling behaviors. Two random variables A i and C i defined for each vertex i , representing the total flux (also called vertex intensity) and total indirect effect or energy store of i , were found to follow power law distributions with the exponents α ≈ 1.32 and β ≈ 1.33 , respectively. Another scaling behavior is the power law relationship, C i ∼ A i η , where η ≈ 1.02 . This is known as the allometric scaling power law relationship because A i can be treated as metabolism and C i as the body mass of the sub-network rooted from the vertex i , according to the algorithm presented in this paper. Finally, a simple relationship among these power law exponents, η = ( α − 1 ) / ( β − 1 ) , was mathematically derived and tested by the empirical food webs.

The geometric complexity and variability of the human cerebral cortex has long intrigued the scientific community. As a result, quantitative description of cortical folding patterns and the understanding of underlying folding mechanisms have emerged as important research goals. This paper presents a computational 3-dimensional geometric model of cerebral cortex folding initialized by MRI data of a human fetal brain and deformed under the governance of a partial differential equation modeling cortical growth. By applying different simulation parameters, our model is able to generate folding convolutions and shape dynamics of the cerebral cortex. The simulations of this 3D geometric model provide computational experimental support to the following hypotheses: 1) Mechanical constraints of the skull regulate the cortical folding process. 2) The cortical folding pattern is dependent on the global cell growth rate of the whole cortex. 3) The cortical folding pattern is dependent on relative rates of cell growth in different cortical areas. 4) The cortical folding pattern is dependent on the initial geometry of the cortex.

Different physical features of an organism are often measured concurrently, because their correlations can be used as predictors of longevity, future health, or adaptability to an ecological niche. Since, in general, we do not know a priori if the temporal variations in the measured quantities are causally related, it may be useful to have a method that could help us to identify possible correlations and to obtain parameters that may vary from population to population. In this paper we develop a procedure that may detect underlying relationships. We do this by generalizing the recently introduced concept of phenomenological universalities to the complex field. In this generalization, allometric growth is described by a complex function, whose real and imaginary parts represent two phenotypic traits of the same organism. As particular solutions of the resulting problem, we obtain generalizations of the Gompertz and the von Bertalanffy-West growth equations. We then apply the procedure to two biological systems in order to show how to determine the existence of mutual interference between trait variations.

Evolutionary game theory studies frequency dependent selection. The fitness of a strategy is not constant, but depends on the relative frequencies of strategies in the population. This type of evolutionary dynamics occurs in many settings of ecology, infectious disease dynamics, animal behavior and social interactions of humans. Traditionally evolutionary game dynamics are studied in well-mixed populations, where the interaction between any two individuals is equally likely. There have also been several approaches to study evolutionary games in structured populations. In this paper we present a simple result that holds for a large variety of population structures. We consider the game between two strategies, A and B, described by the payoff matrix (abcd). We study a mutation and selection process. If the payoffs are linear in a, b, c, d, then for weak selection strategy A is favored over B if and only if σa + b > c + σd. This means the effect of population structure on strategy selection can be described by a single parameter, σ. We present the values of σ for various examples including the well-mixed population, games on graphs and games in phenotype space. We give a proof for the existence of such a σ, which holds for all population structures and update rules that have certain (natural) properties. We assume weak selection, but allow any mutation rate. We discuss the relationship between σ and the critical benefit to cost ratio for the evolution of cooperation. The single parameter, σ, allows us to quantify the ability of a population structure to promote the evolution of cooperation or to choose efficient equilibria in coordination games.

International audience; The model proposed here links together two approaches to describe tumours: a continuous medium to describe the movement and the mechanical properties of the tissue, and a population dynamics approach to represent internal genetic inhomogeneity and instability of the tumour. In this way one can build models which cover several stages of tumour progression. In this paper we focus on describing transition from aerobic to purely glycolytic metabolism (the Warburg effect) in tumour cords. From the mathematical point of view this model leads to a free boundary problem where domains in contact are characterized by different sets of equations. Accurate stitching of the solution was possible with a modified ghost fluid method. Growth and death of the cells and uptake of the nutrients are related through ATP production and energy costs of the cellular processes. In the framework of the bi-population model this allowed to keep the number of model parameters relatively small.

Maintenance of alternative chromatin states through cell divisions pose some fundamental constraints on the dynamics of histone modifications. In this paper, we study the systems biology of epigenetic inheritance by defining and analyzing general classes of mathematical models. We discuss how the number of modification states involved plays an essential role in the stability of epigenetic states. In addition, DNA duplication and the consequent dilution of marked histones act as a large perturbation for a stable state of histone modifications. The requirement that this large perturbation falls into the basin of attraction of the original state sometimes leads to additional constraints on effective models. Two such models, inspired by two different biological systems, are compared in their fulfilling the requirements of multistability and of recovery after DNA duplication. We conclude that in the presence of multiple histone modifications that characterize alternative epigenetic stable states, these requirements are more easily fulfilled.

Dans ce papier nous étudions des modèles abstraits de protocellules dans le but de comprendre le phénomène de la synchronisation de la production de matériel génétique et de l'enveloppe de la protocellule, qui résulte une condition nécessaire pour assurer une croissance soutenable et donner lieu à un évolution Darwinienne pour une population de protocellules. Nous avons démontré que la synchronisation est un phénomène émergeant dans plusieurs modèles de protocellules dans la classe de "Surface Reaction Models" (R. Serra, T. Carletti, I.Poli, Artificial Life 13, (2007), pp. 123), sous les hypothèses de dynamique linéaire ou non-linéaire pour les réactions chimiques. Nous allons ici élargir le domaine d'application de cette analyse en introduisant et étudiant une nouvelle classe de modèles où les réactions chimiques ont lieu à l'intérieur de la protocellule, in opposition avec les modèles précédents où ces réactions avaient lieu sur la surface de la protocellule. Dans des études précédentes les molécules génétiques étaient en compétition pour les ressources sans aucune interaction réciproque, par contre ici nous allons considérer une interaction linéaire entre elles: catalyse et/ou inhibition. En adaptant des techniques mises au point précédemment nous pouvons donner une réponse analytique sur la synchronisation dans ce contexte plus général. Nous présentons aussi quelques résultats de simulations numériques pour soutenir la théorie mais aussi pour nous guider dans des situations où la théorie analytique ne s'applique pas. In this paper we study general protocell models aiming to understand the synchronization phenomenon of genetic material and container productions, a necessary condition to ensure sustainable growth in protocells and eventually leading to Darwinian evolution when applied to a population of protocells. Synchronization has been proved to be an emergent property in many relevant protocell models in the class of the so-called Surface Reaction Models (R. Serra, T. Carletti, I.Poli, Artificial Life 13, (2007), pp. 123), assuming both linear and nonlinear dynamics for the involved chemical reactions. We here extend this analysis by introducing and studying a new class of models where the relevant chemical reactions are assumed to occur inside the protocell, in contrast with the former model where the reaction site was the external surface. While in our previous studies the replicators were assumed to compete for resources, without any direct interaction among them, we here improve the model by allowing linear interaction between replicators: catalysis and/or inhibition. Extending some techniques previously introduced, we are able to give a quite general analytical answer about the synchronization phenomenon in this more general context. We also report on the results of numerical simulations to support the theory, where applicable, and allow to investigate cases which are not amenable to analytical calculations.

The NK fitness landscape is a mathematical landscape model with a parameter k that governs the degree of ruggedness of the landscape. We presented a procedure to fit a given landscape to the NK fitness landscape by introducing the “apparent k -value” k app . In this paper, we defined the protein free energy ( Δ G ) landscape in amino acid sequence space, where Δ G is the folding free energy from a random coil to a “certain conformation”. Applying this landscape to our fitting procedure, we examined the statistical properties of the landscape. For calculation of a conformation energy, amino acid residues are represented by points, and interaction energies among amino acid residues are given as ( 1 + K ) -body interactions, that is, an unit of interacting ( 1 + K ) residues cooperatively contribute a single energy value to the conformational energy. Our results suggest that the apparent k -value of the free energy landscape is k app ≈ K , and that the number of possible interactions among residues is unrelated to the k app value. This leads to the inference that k app takes values about 1–3 in real landscapes, if nature adopts two-body ∼ four -body interaction energies.

Tissue engineered substitutes consisting of cells in biocompatible materials undergo remodeling with time as a result of cell growth and death processes. With inert matrices that do not directly influence cell growth, remodeling is driven mainly by the concentration of dissolved oxygen (DO). Insulin-secreting cell lines encapsulated in alginate-based beads and used as a pancreatic substitute represent such a case. Beads undergo remodeling with time so that an initially homogeneous distribution of cells is eventually replaced by a dense peripheral ring of primarily viable cells, whereas inner cells are mostly necrotic. This paper develops and analyzes a mathematical model of an encapsulated cell system of spherical geometry that tracks the viable and dead cell densities and the concentration of DO within the construct as functions of radial position and time. Model simulations are compared with experimental histology data on cell distribution. Correlations are then developed between the average intrabead DO concentration (AIDO) and the total viable cell number, as well as between AIDO and the radial cell and DO distributions in beads. As AIDO can be measured experimentally by incorporating a perfluorocarbon emulsion in the beads and acquiring (19)F nuclear magnetic resonance (NMR) spectroscopic data, these correlations can be used to track the remodeling that occurs in the construct in vitro and potentially in vivo. The usefulness of mathematical models in describing the dynamic changes that occur in tissue constructs with time, and the value of these models at obtaining additional information on the system when used interactively with experimental measurements, are discussed.

We propose a computational model of mating strategies for controlled animal breeding programs. A mating strategy in a controlled breeding program is a heuristic with some optimization criteria as a goal. Thus, it is appropriate to use the computational tools available for analysis of optimization heuristics. In this paper, we propose the first discrete model of the controlled animal breeding problem and analyse heuristics for two possible objectives: (1) breeding for maximum diversity and (2) breeding a target individual. These two goals are representative of conservation biology and agricultural livestock management, respectively. We evaluate several mating strategies and provide upper and lower bounds for the expected number of matings. While the population parameters may vary and can change the actual number of matings for a particular strategy, the order of magnitude of the number of expected matings and the relative competitiveness of the mating heuristics remains the same. Thus, our simple discrete model of the animal breeding problem provides a novel viable and robust approach to designing and comparing breeding strategies in captive populations.

In this paper I address the question — how large is a phylogenetic sample? I propose a definition of a phylogenetic effective sample size for Brownian motion and Ornstein–Uhlenbeck processes — the regression effective sample size. I discuss how mutual information can be used to define an effective sample size in the non-normal process case and compare these two definitions to an already present concept of effective sample size (the mean effective sample size). Through a simulation study I find that the AICc is robust if one corrects for the number of species or effective number of species. Lastly I discuss how the concept of the phylogenetic effective sample size can be useful for biodiversity quantification, identification of interesting clades and deciding on the importance of phylogenetic correlations.

For teleost fish fertilisation, sperm must proceed through a small opening on the egg surface, referred to as the micropyle. In this paper, we have used boundary element simulations to explore whether the hydrodynamic attraction between sperm and a fish egg can be a sperm guidance cue. Hydrodynamical egg-sperm interactions alone do not increase the chances of an egg encounter, nor do they induce surface swimming for virtual turbot fish sperm across smooth spheres with a diameter of 1mm, which is representative of a turbot fish egg. When a repulsive surface force between the virtual turbot sperm and the egg is introduced, as motivated by surface charge and van-der-Waals interactions for instance, we find that extended surface swimming of the virtual sperm across a model turbot egg occurs, but ultimately the sperm escapes from the egg. This is due to the small exit angle of the scattering associated with the initial sperm-egg interaction at the egg surface, leading to a weak drift away from the egg, in combination with a weak hydrodynamical attraction between both gametes, though the latter is not sufficient to prevent eventual escape. The resulting transience is not observed experimentally but is a detailed quantitative difference between theory and observation in that stable surface swimming is predicted for eggs with radii larger than about 1.8mm. Regardless, the extended sperm swimming trajectory across the egg constitutes a two-dimensional search for the micropyle and thus the egg is consistently predicted to provide a guidance cue for sperm once they are sufficiently close. In addition, the observation that the virtual turbot sperm swims stably next to a flat plane given repulsive surface interactions, but does not swim stably adjacent to a turbot-sized egg, which is extremely large by sperm-lengthscales, also highlights that the stability of sperm swimming near a boundary is very sensitive to geometry.

Understanding the mechanisms that control tissue morphogenesis and homeostasis is a central goal not only in developmental biology but also has great relevance for our understanding of various diseases, including cancer. A model organism that is widely used to study the control of tissue morphogenesis and proportioning is the Dictyostelium discoideum. While there are mathematical models describing the role of chemotactic cell motility in the Dictyostelium assembly and morphogenesis of multicellular tissues, as well as models addressing possible mechanisms of proportion regulation, there are no models incorporating both these key aspects of development. In this paper, we introduce a 1D hyperbolic model to investigate the role of two morphogens, DIF and cAMP, on cell movement, cell sorting, cell-type differentiation and proportioning in Dictysotelium discoideum. First, we use the non-spatial version of the model to study cell-type transdifferentiation. We perform a steady-state analysis of it and show that, depending on the shape of the differentiation rate functions, multiple steady-state solutions may occur. Then we incorporate spatial dynamics into the model, and investigate the transdifferentiation and spatial positioning of cells inside the newly formed structures, following the removal of prestalk or prespore regions of a Dictyostelium slug. We show that in isolated prespore fragments, a tipped mound-like aggregate can be formed after a transdifferentiation from prespore to prestalk cells and following the sorting of prestalk cells to the centre of the aggregate. For isolated prestalk fragments, we show the formation of a slug-like structure containing the usual anterior–posterior pattern of prestalk and prespore cells.

Traditionally the systematic study of animal behaviour using simulations requires the construction of a suitable mathematical model. The construction of such models in most cases requires advanced mathematical skills and exact knowledge of the studied animal's behaviour. Exact knowledge is rarely available. Usually it is available in the form of the observer's linguistic explanations and descriptions of the perceived behaviour. Mathematical models thus require a transition from the linguistic description to a mathematical formula that is seldom straightforward. The substantial increase of the processing power of personal computers has had as a result a notable progress in the field of fuzzy logic. In this paper we present a novel approach to the construction of artificial animals (animats) that is based on fuzzy logic. Our leading hypothesis is, that by omitting the transition from linguistic descriptions to mathematical formulas, ethologists would gain a tool for testing the existing or forming new hypotheses about 'why' and 'how' animals behave the way they do.