Hepatocyte insulin resistance is one of the early factors of developing type II diabetes. If insulin resistance is treated early, type II diabetes could be prevented. In recent years, scientists have been conducting extensive research on the underlying issues on a cellular and molecular level. It was found that the modulation of IP3-receptors, the mitochondrial ability to form the mitochondria-associated membranes (MAMs) and the endoplasmic reticulum stress during Ca2+ signaling play a key role in hepatocyte being able to maintain euglycemia and provide metabolic flexibility. However, researchers cannot agree on what factor is the key one in resulting in insulin resistance. In this work, we propose a mathematical model of Ca2+ signaling. We included in the model all the major contributors of a proper Ca2+ signaling during both the fasting and the postprandial state. Our modeling results are in good agreement with available experimental data. The analysis of modeling results suggests that MAMs dysfunction alone cannot result in abnormal Ca2+ signaling and the wrong modulation of IP3-receptors is a more definite reason. However, both the MAMs dysfunction and the IP3 signaling dysregulation combined can lead to a robust Ca2+ signal and improper glucose release. In addition, our model results suggest a strong dependence of Ca2+ oscillations pattern on morphological characteristics of the ER and the mitochondria.

Growing efforts to measure fitness landscapes in molecular and microbial systems are motivated by a longstanding goal to predict future evolutionary trajectories. Sometimes under-appreciated, however, is that the fitness landscape and its topography do not by themselves determine the direction of evolution: under sufficiently high mutation rates, populations can climb the closest fitness peak (survival of the fittest), settle in lower regions with higher mutational robustness (survival of the flattest), or even fail to adapt altogether (error catastrophes). I show that another measure of reproductive success, Fisher's reproductive value, resolves the trade-off between fitness and robustness in the quasi-species regime of evolution: to forecast the motion of a population in genotype space, one should look for peaks in the (mutation-rate dependent) landscape of genotypic reproductive values-whether or not these peaks correspond to local fitness maxima or flat fitness plateaus. This new landscape picture turns quasi-species dynamics into an instance of non-equilibrium dynamics, in the physical sense of Markovian processes, potential landscapes, entropy production, etc.

Haematopoiesis is the process of generation of blood cells. Lymphopoiesis generates lymphocytes, the cells in charge of the adaptive immune response. Disruptions of this process are associated with diseases like leukaemia, which is especially incident in children. The characteristics of self-regulation of this process make them suitable for a mathematical study. In this paper we develop mathematical models of lymphopoiesis using currently available data. We do this by drawing inspiration from existing structured models of cell lineage development and integrating them with paediatric bone marrow data, with special focus on regulatory mechanisms. A formal analysis of the models is carried out, giving steady states and their stability conditions. We use this analysis to obtain biologically relevant regions of the parameter space and to understand the dynamical behaviour of B-cell renovation. Finally, we use numerical simulations to obtain further insight into the influence of proliferation and maturation rates on the reconstitution of the cells in the B line. We conclude that a model including feedback regulation of cell proliferation represents a biologically plausible depiction for B-cell reconstitution in bone marrow. Research into haematological disorders could benefit from a precise dynamical description of B lymphopoiesis.

In this review, we focus on the antennal lobe (AL) of three insect species - the fruit fly, sphinx moth, and locust. We first review the experimentally elucidated anatomy and physiology of the early olfactory system of each species; empirical studies of AL activity, however, often focus on assessing firing rates (averaged over time scales of about 100 ms), and hence the AL odor code is often analyzed in terms of a temporally evolving vector of firing rates. However, such a perspective necessarily misses the possibility of higher order temporal correlations in spiking activity within a single cell and across multiple cells over shorter time scales (of about 10 ms). Hence, we then review our prior theoretical work, where we constructed biophysically detailed, species-specific AL models within the fly, moth, and locust, finding that in each case higher order temporal correlations in spiking naturally emerge from model dynamics (i.e., without a prioriincorporation of elements designed to produce correlated activity). We therefore use our theoretical work to argue the perspective that temporal correlations in spiking over short time scales, which have received little experimental attention to-date, may provide valuable coding dimensions (complementing the coding dimensions provided by the vector of firing rates) that nature has exploited in the encoding of odors within the AL. We further argue that, if the AL does indeed utilize temporally correlated activity to represent odor information, such an odor code could be naturally and easily deciphered within the Mushroom Body.

BACKGROUND AND OBJECTIVE: p53, an anti-tumour protein, is significantly inactivated in most tumours. A small molecule of nutlin-3a is used to activate its function by repressing (Mouse double minute 2 homolog) Mdm2 protein which inhibits its activity. In cancer patients, a high risk of drug-drug interactions (DDIs) is observed owing to their multi-dosing prescriptions, which may lead them to harmful effects. In the presented work, we have aimed to investigate the effect of pharmacodynamical interaction between two anti-cancer drugs, nutlin-3a and aspirin in the activation of p53 protein. METHODS: We have adapted control system techniques and designed a Proportional-Integral-Derivative (PID) controller. This controller is used to activate p53 protein. A drug interaction parameter is used to incorporate the effect of both drugs. Extensive simulation is performed using two different doses of aspirin, i.e. a low and a high dose of aspirin. RESULTS: The result shows no harmful effects of pharmacodynamical interaction when a low dose is administered along with nutlin-3a. When a high dose of aspirin is administered it acts as input disturbance and leads to undesirable over-expression of p53 protein. This can further harm other growth cells, thus inducing harmful effects. A comparative analysis is also tabulated with different dosing regimens which shows that a combination of nutlin-3a and a low dose of aspirin provides better results than a high dose of aspirin. CONCLUSION: Overall, the work provides an insight to the activation of p53 protein in cancer patients under the presence of pharmacodynamical interaction and might contribute to the effective management of cancer patients.

We develop a three-dimensional genuinely hybrid atomistic-continuum model that describes the invasive growth dynamics of individual cancer cells in tissue. The framework explicitly accounts for phenotypic variation by distinguishing between cancer cells of an epithelial-like and a mesenchymal-like phenotype. It also describes mutations between these cell phenotypes in the form of epithelial-mesenchymal transition (EMT) and its reverse process mesenchymal-epithelial transition (MET). The proposed model consists of a hybrid system of partial and stochastic differential equations that describe the evolution of epithelial-like and mesenchymal-like cancer cells, respectively, under the consideration of matrix-degrading enzyme concentrations and the extracellular matrix density. With the help of inverse parameter estimation and a sensitivity analysis, this three-dimensional model is then calibrated to an in vitro organotypic invasion assay experiment of oral squamous cell carcinoma cells.

Potato cyst nematodes (PCN) are responsible for large losses in potato yields in many of the world's potato-growing regions. As soil temperatures increase due to climate change, there is potential for faster growth rates of PCN, allowing development of multiple generations in a growing season. We develop a process-based temperature-dependent model representing the life cycle of Globodera pallida, comprising juvenile, adult and cyst/diapause stages. To incorporate variability in the amount of time spent in each stage caused by genetic/environmental variation, the model is based on a mix of ordinary differential equations (ODEs) with sub-stages, and delay differential equations (DDEs). The effect of climate change is incorporated through the influence of soil temperature on the rate of development and survival in the hatching and juvenile stages. The level of the plant resistance to PCN is incorporated via the proportion of juveniles which become adults. After comparing the model with field data we run simulations to explore the effects of temperature and resistance on PCN populations. We find that with higher temperatures and longer growing seasons multiple generations of PCN can develop within a season, provided any required diapause period is short. Despite this, we show that growing resistant potatoes is a very effective control strategy and planting potatoes with even moderate levels of resistance can counter the effects of climate change.

Tumors have developed multitude of ways to evade immune response and suppress cytotoxic T cells. Programed cell death protein 1 (PD-1) and programed cell death ligand 1 (PD-L1) are immune checkpoints that when activated, rapidly inactivate the cytolytic activity of T cells. Expression heterogeneity of PD-L1 and the surface receptor dynamics of both PD-1 and PD-L1 may be important parameters in modulating the immune response. PD-L1 is expressed on both tumor and non-tumor immune cells and this differential expression reflects different aspects of anti-tumor immunity. Here, we developed a mechanistic computational model to investigate the role of PD-1 and PD-L1 dynamics in modulating the efficacy of PD-1 and PD-L1 blocking antibodies. Our model incorporates immunological synapse restricted interaction of PD-1 and PD-L1, basal parameters for receptor dynamics, and T cell interaction with tumor and non-tumor immune cells. Simulations predict the existence of a threshold in PD-1 expression above which there is no efficacy for both anti-PD-1 and anti-PD-L1. Model also predicts that anti-tumor response is more sensitive to PD-L1 expression on non-tumor immune cells than tumor cells. New combination strategies are suggested that may enhance efficacy in resistant cases such as combining anti-PD-1 with a low dose of anti-PD-L1 or with inhibitors of PD-L1 recycling and synthesis. Another combination strategy suggested by the model is the combination of anti-PD-1 and anti-PD-L1 with enhancers of PD-L1 degradation rate. Virtual patients are then generated to test specific biomarkers of response. Intriguing predictions that emerge from the virtual patient simulations are that PD-1 blocking antibody results in higher response rate than PD-L1 blockade and that PD-L1 expression density on non-tumor immune cells rather than tumor cells is a predictor of response.

To better understand the environmental factors and ecological processes underlying the evolution of the irreversible transition from a free-swimming state to an immobile sessile state as seen in many aquatic invertebrates, we study the adaptive dynamics of the settling rate of a hypothetical microorganism onto the wall of a chemostat. The two states, floating or settled, differ in their nutrient ingestion, reproduction and death rate. We consider three different settling mechanisms involving competition for space on the wall: (i) purely exploitative competition where free-swimming individuals settle in vacant space only, (ii) mixed exploitative and interference competition where individuals attempt to settle in any place but fail and die if the space is already occupied, and (iii) mixed exploitative and interference competition, but now settling in occupied space is successful and the former occupant dies. In the simplified environment of the chemostat, the input concentration of nutrients and the dilution rate of the tank are the main environmental control variables. Using the theory of adaptive dynamics, we find that the settling mechanisms and environmental control variables have qualitatively different effects on the evolution of the settling rate in terms of the direction of evolution as well as on species diversity. In the case of purely exploitative competition a small change in the settings of the environmental control variables can lead to an abrupt reversal of the direction of evolution, while in the case of mixed exploitative and interference competition the effect is gradual. For all three settling mechanisms, periodic fluctuations in the nutrient input open the possibility of evolutionary branching leading to the long-term coexistence of an intermediate and an infinitely high settling rates (in the case of low-frequency fluctuations), and an intermediate and a zero settling rates (in the case of high-frequency fluctuations).

Spatial synchrony of population fluctuations is an important tool for predicting regional stability. Its application to natural systems is still limited by the complexity of ecological time series displaying great variation in the frequency and amplitude of their fluctuations, which are not fully resolved by current ecological theories of spatial synchrony. In particular, while environmental fluctuations and limited dispersal can each control the dynamics of frequency and amplitude of population fluctuations, ecological theories of spatial synchrony still need to resolve their role on synchrony and stability in heterogeneous metacommunities. Here, we adopt a heterogeneous predator-prey metacommunity model and study the response of dispersal-driven phase locking and frequency modulation to among-patch heterogeneity in carrying capacity. We find that frequency modulation occurs at intermediate values of dispersal and habitat heterogeneity. We also show how frequency modulation can emerge in metacommunities of autonomously oscillating populations as well as through the forcing of local communities at equilibrium. Frequency modulation was further found to produce temporal variation in population amplitudes, promoting local and regional stability through cyclic patterns of local and regional variability. Our results highlight the importance of approaching spatial synchrony as a non-stationary phenomenon, with implications for the assessment and interpretation of spatial synchrony observed in experimental and natural systems.

Attention Schema Theory (AST) is a recent proposal to provide a scientific explanation for the basis of subjective awareness. In AST, the brain constructs a representation of attention taking place in its own (and others') mind ('the attention schema'). Moreover, this representation is incomplete for efficiency reasons. This inherent incompleteness of the attention schema results in the inability of humans to understand how their own subjective awareness arises (related to the so-called 'hard problem' of consciousness). Given this theory, the present paper asks whether a mind (either human or machine-based) that incorporates attention, and that contains a representation of its own attention, can ever have a complete representation. Using a simple yet general model and a mathematical argument based on classical topology, we show that a complete representation of attention is not possible, since it cannot faithfully represent streams of attention. In this way, the study supports one of the core aspects of AST, that the brain's representation of its own attention is necessarily incomplete.

Protein synthesis is a crucial process in any cell. Translation, in which mRNA is translated into proteins, can lead to several errors, notably frame shifts where the ribosome accidentally skips or re-reads one or more nucleotides. So-called circular codes are capable of discovering frame shifts and their codons can be found disproportionately often in coding sequences. Here, we analyzed motifs of circular codes, i.e. sequences only containing codons of circular codes, in biological and artificial sequences. The lengths of these motifs were compared to a statistical model in order to elucidate if coding sequences contain significantly longer motifs than non-coding sequences. Our findings show that coding sequences indeed show on average greater motif lengths than expected by chance. On the other hand, the motifs are too short for a possible frame shift recognition to take place within an entire coding sequence. This suggests that as much as circular codes might have been used in ancient life forms in order to prevent frame shift errors, it remains to be seen whether they are still functional in current organisms.

Schistosomiasis is a parasite infection that affects millions of people around the world. It is endemic in 13 different states in Brazil and responsible for increasing morbidity in the population. One of its main characteristics is a heterogeneous distribution of worm burden in the human population, which makes the diagnosis difficult. We aimed to investigate how the sensitivity of the diagnostic method may contribute to successful control interventions against infections in a population. In order to do that, we present an ordinary differential equations model that considers three levels of worm burden in the human population, a snail population, and a miracidium reservoir. Through a steady-state analysis and its local stability, we show how this worm-burden heterogeneity can be responsible for the persistence of infection, especially due to reinfection in the highest level of worm burden. The analysis highlights sensitive diagnosis, besides treatment and sanitary improvements, as a key factor for schistosomiasis transmission control.

Protection of the healthcare workforce is of paramount importance for the care of patients in the setting of a pandemic such as coronavirus disease 2019 (COVID-19). Healthcare workers are at increased risk of becoming infected. The ideal organisational strategy to protect the workforce in a situation in which social distancing cannot be maintained remains to be determined. In this study, we have mathematically modelled strategies for the employment of the hospital workforce with the goal of simulating the health and productivity of the workers. The models were designed to determine if desynchronization of medical teams by dichotomizing the workers may protect the workforce. Our studies model workforce productivity and the efficiency of home office applied to the case of COVID-19. The results reveal that a desynchronization strategy in which two medical teams work alternating for 7 days increases the available workforce.

The canonical bacteriophage is obligately lytic: the virus infects a bacterium and hijacks cell functions to produce large numbers of new viruses which burst from the cell. These viruses are well-studied, but there exist a wide range of coexisting virus lifestyles that are less understood. Temperate viruses exhibit both a lytic cycle and a latent (lysogenic) cycle, in which viral genomes are integrated into the bacterial host. Meanwhile, chronic (persistent) viruses use cell functions to produce more viruses without killing the cell; chronic viruses may also exhibit a latent stage in addition to the productive stage. Here, we study the ecology of these competing viral strategies. We demonstrate the conditions under which each strategy is dominant, which aids in control of human bacterial infections using viruses. We find that low lysogen frequencies provide competitive advantages for both virus types; however, chronic viruses maximize steady state density by eliminating lysogeny entirely, while temperate viruses exhibit a non-zero 'sweet spot' lysogen frequency. Viral steady state density maximization leads to coexistence of temperate and chronic viruses, explaining the presence of multiple viral strategies in natural environments.

We studied the spatial pattern of two microbial strains along the intestinal duct. Probiotic bacteria acidify the environment and suppress their competitors, non-probiotic bacteria. Food resources are supplied from the proximal end, and there exists a flow from the proximal end to the distal end. In the steady state, we observed three major patterns. In the "standard" pattern (ST), the abundance of probiotic bacteria was high in the proximal end, and it decreased toward the distal end; in contrast, the abundance of non-probiotic bacteria was low in the proximal end, and it increased toward the distal end. In the "proximal reversion" pattern (PR), non-probiotic bacteria were dominant and probiotic bacteria were suppressed in the proximal portion of the duct. Subsequently, the abundance values of the two competitors switched, followed by a spatial pattern similar to ST. In the "distal suppression" pattern (DS), the pattern was similar to ST in the proximal portion; however, toward the distal end, the abundance of probiotic bacteria remained at an intermediate level and suppressed the abundance of non-probiotic bacteria, resulting in a peak abundance of non-probiotic bacteria in the middle portion of the duct. We additionally discuss the nonmonotonic increase in the abundance of non-probiotic bacteria in ST and the transition of the spatial pattern from one type to another due to changes in the resource abundance in the influx.

Cell signal transduction is an example of a nonequilibrium phenomenon. In this study, a nonequilibrium nonlinear thermodynamic model was formulated. First, we obtained a condition in which the Onsager's reciprocity theorem holds in the signal transduction. Second, it was found that the entropy production rate per signal molecule is conserved through signal transduction. Finally, it was determined that when Onsager's reciprocity theorem does not hold, fluctuation circulation is given by the phosphorylation rate of signal molecules. The simple relation implies that the fluctuation circulation can be an essential quantity of the signal transduction amount. These results expand the limit of nonequilibrium thermodynamics and can be used to provide ideas for signal transduction quantification.

The outbreak of coronavirus disease 2019 (COVID-19), caused by the virus severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has already created emergency situations in almost every country of the world. The disease spreads all over the world within a very short period of time after its first identification in Wuhan, China in December, 2019. In India, the outbreak, starts on 2nd March, 2020 and after that the cases are increasing exponentially. Very high population density, the unavailability of specific medicines or vaccines, insufficient evidences regarding the transmission mechanism of the disease also make it more difficult to fight against the disease properly in India. Mathematical models have been used to predict the disease dynamics and also to assess the efficiency of the intervention strategies in reducing the disease burden. In this work, we propose a mathematical model to describe the disease transmission mechanism between the individuals. Our proposed model is fitted to the daily new reported cases in India during the period 2nd March, 2020 to 12th November, 2020. We estimate the basic reproduction number, effective reproduction number and epidemic doubling time from the incidence data for the above-mentioned period. We further assess the effect of implementing preventive measures in reducing the new cases. Our model projects the daily new COVID-19 cases in India during 13th November, 2020 to 25th February, 2021 for a range of intervention strength. We also investigate that higher intervention effort is required to control the disease outbreak within a shorter period of time in India. Moreover, our analysis reveals that the strength of the intervention should be increased over the time to eradicate the disease effectively.

Biological experiments have shown that yeast can be restricted to grow in a uniaxial direction, vertically upwards from an agar plate to form a colony. The growth occurs as a consequence of cell proliferation driven by a nutrient supply at the base of the colony, and the height of the colony has been observed to increase linearly with time. Within the colony the nutrient concentration is non-constant and yeast cells throughout the colony will therefore not have equal access to nutrient, resulting in non-uniform growth. In this work, an agent based model is developed to predict the microscopic spatial distribution of labelled cells within the colony when the probability of cell proliferation can vary in space and time. We also describe a method for determining the average trajectories or pathlines of labelled cells within a colony growing in a uniaxial direction, enabling us to connect the microscopic and macroscopic behaviours of the system. We present results for six cases, which involve different assumptions for the presence or absence of a quiescent region (where no cell proliferation occurs), the size of the proliferative region, and the spatial variation of proliferation rates within the proliferative region. These six cases are designed to provide qualitative insight into likely growth scenarios whilst remaining amenable to analysis. We compare our macroscopic results to experimental observations of uniaxial colony growth for two cases where only a fixed number of cells at the base of the colony can proliferate. The model predicts that the height of the colony will increase linearly with time in both these cases, which is consistent with experimental observations. However, our model shows how different functional forms for the spatial dependence of the proliferation rate can be distinguished by tracking the pathlines of cells at different positions in the colony. More generally, our methodology can be applied to other biological systems exhibiting uniaxial growth, providing a framework for classifying or determining regions of uniform and non-uniform growth.

Individuals of different interacting populations often adjust to prevailing conditions by changing their behavior simultaneously, with consequences for trophic relationships throughout the system. While we now have a good theoretical understanding of how individuals adjust their behavior, the population dynamical consequences of co-adaptive behaviors are rarely described. Further, mechanistic descriptions of ecosystem functions are based on population models that seldom take behavior into account. Here, we present a model that combines the population dynamics and adaptive behavior of organisms of two populations simultaneously. We explore how the Nash equilibrium of a system - i.e. the optimal behavior of its constituent organisms - can shape population dynamics, and conversely how population dynamics impact the Nash equilibrium of the system. We illustrate this for the case of diel vertical migration (DVM), the daily movement of marine organisms between food-depleted but safe dark depths and more risky nutrition-rich surface waters. DVM represents the archetypal example of populations choosing between a foraging arena (the upper sunlit ocean) and a refuge (the dark depths). We show that population sizes at equilibrium are significantly different if organisms can adapt their behavior, and that optimal DVM behaviors within the community vary significantly if population dynamics are considered. As a consequence, ecosystem function estimates such as trophic transfer efficiency and vertical carbon export differ greatly when fitness seeking behavior is included. Ignoring the role of behavior in multi-trophic population modeling can potentially lead to inaccurate predictions of population biomasses and ecosystem functions.

Cerebrospinal fluid (CSF) flow in the perivascular space (PVS), which surrounds the arteries in the brain, is of paramount importance in the removal of metabolic waste. Despite a number of experimental and numerical studies regarding CSF flow, the underlying mechanics of CSF flow are still debated, especially regarding whether an arterial pulsation can indeed produce net CSF flow velocity. Furthermore, the relationship between CSF flow and arterial wall pulsation has not been fully defined. To clarify these questions, we numerically investigated the CSF flow in the PVS in an axisymmetric channel with a pulsating boundary, where CSF is modeled as an incompressible, Newtonian viscous fluid in non-porous space. Our numerical results show that the net CSF flow velocity driven by the arterial pulsation is consistent with that of previous animal experiments. However, the peak oscillatory velocity is two orders of magnitude larger than the net velocity. Interestingly, the net CSF flow velocity collapses on the analytical solution derived from the lubrication theory in analogy with Taylor's swimming sheet model.

A non-smooth SIR Filippov system is proposed to investigate the impacts of three control strategies (media coverage, vaccination and treatment) on the spread of an infectious disease. We synthetically consider both the number of infected population and its changing rate as the switching condition to implement the curing measures. By using the properties of the Lambert W function, we convert the proposed switching condition to a threshold value related to the susceptible population. The classical epidemic model involving media coverage, linear functions describing injecting vaccine and treatment strategies is examined when the susceptible population exceeds the threshold value. In addition, we consider another SIR model accompanied with the vaccination and treatment strategies represented by saturation functions when the susceptible population is smaller than the threshold value. The dynamics of these two subsystems and the sliding domain are discussed in detail. Four types of local sliding bifurcation are investigated, including boundary focus, boundary node, boundary saddle and boundary saddle-node bifurcations. In the meantime, the global bifurcation involving the appearance of limit cycles is examined, including touching bifurcation, homoclinic bifurcation to the pseudo-saddle and crossing bifurcation. Furthermore, the influence of some key parameters related to the three treatment strategies is explored. We also validate our model by the epidemic data sets of A/H1N1 and COVID-19, which can be employed to reveal the effects of media report and existing strategy related to the control of emerging infectious diseases on the variations of confirmed cases.

In strongly seasonal environments, many plants tend to divide the favorable season into an earlier part, where they allocate resources to vegetative growth, and a later part, where they allocate resources to reproduction. The onset of flowering typically indicates the shift from one to the other. We derive and analyze a model for the evolution of flowering onset on the phenotypic level. Our model tracks a continuous phenotype distribution through the various seasons from year to year. We analyze a special case of a monomorphic population with the tools of adaptive dynamics. We analyze the general case by a moment approximation. We find that (the mean of) flowering onset converges to some intermediate time within the favorable season. In the monomorphic case, we prove that this is an ESS. The moment approach reveals that there are different time scales involved on which the plant density, the mean flowering onset, and its variance converge.

The maximum running speed of legged animals is one evident factor for evolutionary selection-for predators and prey. Therefore, it has been studied across the entire size range of animals, from the smallest mites to the largest elephants, and even beyond to extinct dinosaurs. A recent analysis of the relation between animal mass (size) and maximum running speed showed that there seems to be an optimal range of body masses in which the highest terrestrial running speeds occur. However, the conclusion drawn from that analysis-namely, that maximum speed is limited by the fatigue of white muscle fibres in the acceleration of the body mass to some theoretically possible maximum speed-was based on coarse reasoning on metabolic grounds, which neglected important biomechanical factors and basic muscle-metabolic parameters. Here, we propose a generic biomechanical model to investigate the allometry of the maximum speed of legged running. The model incorporates biomechanically important concepts: the ground reaction force being counteracted by air drag, the leg with its gearing of both a muscle into a leg length change and the muscle into the ground reaction force, as well as the maximum muscle contraction velocity, which includes muscle-tendon dynamics, and the muscle inertia-with all of them scaling with body mass. Put together, these concepts' characteristics and their interactions provide a mechanistic explanation for the allometry of maximum legged running speed. This accompanies the offering of an explanation for the empirically found, overall maximum in speed: In animals bigger than a cheetah or pronghorn, the time that any leg-extending muscle needs to settle, starting from being isometric at about midstance, at the concentric contraction speed required for running at highest speeds becomes too long to be attainable within the time period of a leg moving from midstance to lift-off. Based on our biomechanical model, we, thus, suggest considering the overall speed maximum to indicate muscle inertia being functionally significant in animal locomotion. Furthermore, the model renders possible insights into biological design principles such as differences in the leg concept between cats and spiders, and the relevance of multi-leg (mammals: four, insects: six, spiders: eight) body designs and emerging gaits. Moreover, we expose a completely new consideration regarding the muscles' metabolic energy consumption, both during acceleration to maximum speed and in steady-state locomotion.

A substantial body of work has shown that local transmission selects for less acute, 'prudent' parasites that have lower virulence and transmission rates. This is because parasite strains with higher transmission rates 'self-shade' due to a combination of genetic correlations (self: clustered related parasite strains compete for susceptible individuals) and ecological correlations (shade: infected individuals clustering and blocking transmission). However, the interaction of ecological and genetic correlations alongside higher order ecological effects such as patch extinctions means that spatial evolutionary effects can be nuanced; theory has predicted that a relatively small proportion of local infection can select for highest virulence, such that there is a humped relationship between the degree of local infection and the harm that parasites are selected to cause. Here, we examine the separate roles of the interaction scales of reproduction and infection in the context of different degrees of pathogenic castration in determining virulence evolution outcomes. Our key result is that, as long as there is significant reproduction from infected individuals, local infection always selects for lower virulence, and that the prediction that a small proportion of local infection can select for higher virulence only occurs for highly castrating pathogens. The results emphasize the importance of demography for evolutionary outcomes in spatially structured populations, but also show that the core prediction that parasites are prudent in space is reasonable for the vast majority of host-parasite interactions and mixing patterns in nature.