In order to understand the dynamics of emergence and spreading of socio-technical innovations and population moves it is important to determine the place of origin of these populations. Here we focus on the role of geographical factors, such as land fertility and mountains in the context of human population evolution and distribution dynamics. We use a constrained diffusion-based computational model, computer simulations and the analysis of geographical and land-quality data. Our analysis shows that successful human populations, i.e. those which become dominant in their socio - geographical environment, originate from lands of many valleys with relatively low land fertility, which are close to areas of high land fertility. Many of the homelands predicted by our analysis match the assumed homelands of known successful populations (e.g. Bantus, Turkic, Maya). We also predict other likely homelands as well, where further archaeological, linguistic or genetic exploration may confirm the place of origin for populations with no currently identified urheimat. Our work is significant because it advances the understanding of human population dynamics by guiding the identification of the origin locations of successful populations.

We report complete analysis of a deterministic model of deleterious mutations and negative selection against them at two haploid loci without recombination. As long as mutation is a weaker force than selection, mutant alleles remain rare at the only stable equilibrium, and otherwise, a variety of dynamics are possible. If the mutation-free genotype is absent, generally the only stable equilibrium is the one that corresponds to fixation of the mutant allele at the locus where it is less deleterious. This suggests that fixation of a deleterious allele that follows a click of the Muller's ratchet is governed by natural selection, instead of random drift.

The life cycle of parasitic organisms that are the cause of much morbidity in humans often depend on reservoirs of infection for transmission into their hosts. Understanding the daily, monthly and yearly movement patterns of individuals between reservoirs is therefore of great importance to implementers of control policies seeking to eliminate various parasitic diseases as a public health problem. This is due to the fact that the underlying spatial extent of the reservoir of infection, which drives transmission, can be strongly affected by inputs from external sources, i.e., individuals who are not spatially attributed to the region defined by the reservoir itself can still migrate and contribute to it. In order to study the importance of these effects, we build and examine a novel theoretical model of human movement between spatially-distributed focal points for infection clustered into regions defined as 'reservoirs of infection'. Using our model, we vary the spatial scale of human moment defined around focal points and explicitly calculate how varying this definition can influence the temporal stability of the effective transmission dynamics - an effect which should strongly influence how control measures, e.g., mass drug administration (MDA), define evaluation units (EUs). Considering the helminth parasites as our main example, by varying the spatial scale of human movement, we demonstrate that a critical scale exists around infectious focal points at which the migration rate into their associated reservoir can be neglected for practical purposes. This scale varies by species and geographic region, but is generalisable as a concept to infectious reservoirs of varying spatial extents and shapes. Our model is designed to be applicable to a very general pattern of infectious disease transmission modified by the migration of infected individuals between clustered communities. In particular, it may be readily used to study the spatial structure of hosts for macroparasites with temporally stationary distributions of infectious focal point locations over the timescales of interest, which is viable for the soil-transmitted helminths and schistosomes. Additional developments will be necessary to consider diseases with moving reservoirs, such as vector-born filarial worm diseases.

The question of which mechanical variables are responsible for inducing osteogenic activity is unresolved despite extensive experimental and theoretical investigation. Candidate variables include strain magnitude, loading frequency, the interaction of magnitude and frequency (strain rate), and strain gradients. An additional challenge is discerning the coordination of periosteal and endosteal expansion during growth, and whether this coordination (or lack thereof) is fully dependent or partially independent of the local mechanical environment. In this study, under the assumption that calculated stresses correspond to relative strain magnitudes, we specify alternative growth algorithms of bone cross-sectional size and geometry to explore skeletal growth under alternative scenarios of osteogenic activity that are tracking 1) an attractor stress, 2) local stress magnitude or 3) steepness of stress gradients. These developmental simulations are initiated from two initial geometries (symmetrical and asymmetrical ellipses) under a time-varying torsional load whose magnitude is proportional to body size growth in a model primate. In addition, we model endosteal expansion under three conditions hypothesized in the literature, in which endosteal expansion is 1) independent of the mechanical milieu, 2) completely dependent on the mechanical milieu, and 3) a "hybrid" model in which intrinsic biological (independent) growth is operative early but gives way to mechanically-sensitive (dependent) growth at later ages. Three variables were recorded over each growth simulation: the safety factor (ratio of yield stress to actual stress), an efficiency ratio (invested bone area per unit of stress), and proximity to an isostress condition (an optimal design criterion in which stress is invariant throughout the structure). The attractor stress algorithm produces the most "adapted" bones in terms of mechanical competence and economy of material. Localized osteogenic activity that is guided in direct proportion to stress magnitude produces competent bones but with variable adult geometries depending on conditions of endosteal expansion. Stress gradients also produce functional but relatively inefficient bones, with widely variable safety factors during growth and heterogeneous stress fields. If, in fact, the osteocyte network monitors strain gradients to generate osteogenic signals, the resulting morphology is competent but falls well short of an optimal mechanical solution.

Finding ways to overcome the temptation to exploit one another is still a challenge in behavioural sciences. In the framework of evolutionary game theory, punishing strategies are frequently used to promote cooperation in competitive environments. Here, we introduce altruistic punishers in the spatial public goods game. This strategy acts as a cooperator in the absence of defectors, otherwise it will punish all defectors in their vicinity while bearing a cost to do so. We observe three distinct behaviours in our model: i) in the absence of punishers, cooperators (who don't punish defectors) are driven to extinction by defectors for most parameter values; ii) clusters of punishers thrive by sharing the punishment costs when these are low; iii) for higher punishment costs, punishers, when alone, are subject to exploitation but in the presence of cooperators can form a symbiotic spatial structure that benefits both. This last observation is our main finding since neither cooperation nor punishment alone can survive the defector strategy in this parameter region and the specificity of the symbiotic spatial configuration shows that lattice topology plays a central role in sustaining cooperation. Results were obtained by means of Monte Carlo simulations on a square lattice and subsequently confirmed by a pairwise comparison of different strategies' payoffs in diverse group compositions, leading to a phase diagram of the possible states.

In this paper we consider the time evolution of a population of size N with overlapping generations, in the vicinity of m genes. We assume that this population is subject to point mutations, genetic drift, and selection. More specifically, we analyze the statistical distribution of the waiting time Tm until the expression of these genes have changed for all individuals, when transcription factors recognize and attach to short DNA-sequences (binding sites) within regulatory sequences in the neighborhoods of the m genes. The evolutionary dynamics is described by a multitype Moran process, where each individual is assigned a m×L regulatory array that consists of regulatory sequences with L nucleotides for all m genes. We study how the waiting time distribution depends on the number of genes, the mutation rate, the length of the binding sites, the length of the regulatory sequences, and the way in which the targeted binding sites are coordinated for different genes in terms of selection coefficients. These selection coefficients depend on how many binding sites have appeared so far, and possibly on their order of appearance. We also allow for back mutations, whereby some acquired binding sites may be lost over time. It is further assumed that the mutation rate is small enough to warrant a fixed state population, so that all individuals have the same regulatory array, at any given time point, until the next successful mutation arrives in some individual and spreads to the rest of the population. We further incorporate stochastic tunneling, whereby successful mutations get mutated before their fixation. A crucial part of our approach is to divide the huge state space of regulatory arrays into a small number of components, assuming that the array component varies as a Markov process over time. This implies that Tm is the time until this Markov process hits an absorbing state, with a phase-type distribution. A number of interesting results can be derived from our general setup, for instance that the expected waiting time increases exponentially with m, for a selectively neutral model, when back-mutations are possible.

The metastasis of malignant epithelial tumors begins with the egress of transformed cells from the confines of their basement membrane (BM) to their surrounding collagen-rich stroma. Invasion can be morphologically diverse: when breast cancer cells are separately cultured within BM-like matrix, collagen I (Coll I), or a combination of both, they exhibit collective-, dispersed mesenchymal-, and a mixed collective-dispersed (multimodal)- invasion, respectively. In this paper, we asked how distinct these invasive modes are with respect to the cellular and microenvironmental cues that drive them. A rigorous computational exploration of invasion was performed within an experimentally motivated Cellular Potts-based modeling environment. The model comprised of adhesive interactions between cancer cells, BM- and Coll I-like extracellular matrix (ECM), and reaction-diffusion-based remodeling of ECM. The model outputs were parameters cognate to dispersed- and collective- invasion. A clustering analysis of the output distribution curated through a careful examination of subsumed phenotypes suggested at least four distinct invasive states: dispersed, papillary-collective, bulk-collective, and multimodal, in addition to an indolent/non-invasive state. Mapping input values to specific output clusters suggested that each of these invasive states are specified by distinct input signatures of proliferation, adhesion and ECM remodeling. In addition, specific input perturbations allowed transitions between the clusters and revealed the variation in the robustness between the invasive states. Our systems-level approach proffers quantitative insights into how the diversity in ECM microenvironments may steer invasion into diverse phenotypic modes during early dissemination of breast cancer and contributes to tumor heterogeneity.

Macrophages' role in the evolution of solid tumours is a well accepted fact, with the M1-like macrophages having an anti-tumour role and the M2-like macrophages having a pro-tumour role. Despite the fact that some clinical studies on lung tumours have emphasised also the presence of macrophages with mixed M1 and M2 phenotypes in addition to macrophages with distinct phenotypes, the majority of studies still use the distinct M1-M2 classification to predict the evolution of tumours and patient survival. In this theoretical study we use a mathematical modelling and computational approach to investigate the role of macrophages with mixed phenotype on growth/control/elimination of lung tumours. We show that tumour control in the presence of M2→M1 re-polarising treatments is mainly the result of macrophages with mixed phenotypes (due to the assumption of short half-life of M1-like macrophages). We also show that the half-life of various macrophage phenotypes (distinct M1 or mixed M1/M2 phenotypes) impacts the outcome of various therapeutic strategies targeting tumour-associated macrophages. All these results suggest the need for a better experimental understanding of the kinetics of macrophages inside solid tumours.

BACKGROUND: Random walks (RWs) have proved to be a powerful modelling tool in ecology, particularly in the study of animal movement. An application of RW concerns trapping which is the predominant sampling method to date in insect ecology and agricultural pest management. A lot of research effort has been directed towards modelling ground-dwelling insects by simulating their movement in 2D, and computing pitfall trap counts, but comparatively very little for flying insects with 3D elevated traps. METHODS: We introduce the mathematics behind 3D RWs and present key metrics such as the mean squared displacement (MSD) and path sinuosity, which are already well known in 2D. We develop the mathematical theory behind the 3D correlated random walk (CRW) which involves short-term directional persistence and the 3D Biased random walk (BRW) which introduces a long-term directional bias in the movement so that there is an overall preferred movement direction. In this study, we focus on the geometrical aspects of the 3D trap and thus consider three types of shape; a spheroidal trap, a cylindrical trap and a rectangular cuboidal trap. By simulating movement in 3D space, we investigated the effect of 3D trap shapes and sizes and of movement diffusion on trapping efficiency. RESULTS: We found that there is a non-linear dependence of trap counts on the trap surface area or volume, but the effect of volume appeared to be a simple consequence of changes in area. Nevertheless, there is a slight but clear hierarchy of trap shapes in terms of capture efficiency, with the spheroidal trap retaining more counts than a cylinder, followed by the cuboidal type for a given area. We also showed that there is no effect of short-term persistence when diffusion is kept constant, but trap counts significantly decrease with increasing diffusion. CONCLUSION: Our results provide a better understanding of the interplay between the movement pattern, trap geometry and impacts on trapping efficiency, which leads to improved trap count interpretations, and more broadly, has implications for spatial ecology and population dynamics.

Ever since Nirenberg's discovery in 1961 in which codons code individual amino acids, numerous scientists searched for symmetries within the genetic code. The standard genetic code (SGC) table is an alphabetic artificial construct based on the U-C-A-G ordering of nucleotides without natural symmetries. Up to the present, complete symmetry in the genetic code has not been found, leaving doubt as to whether the symmetrical nature as the protector of order even exists. Our novel Ideal Symmetry Genetic Code (ISyGC) table reflects a unique fundamental physicochemical purine-pyrimidine symmetry net for all more than thirty known variations of nuclear and mitochondrial genetic codes. The nuclear genetic code for RNA and DNA viruses also contains the same purine-pyrimidine symmetry net. We show that the ISyGC table leads to automatic transformation into a DNA sequence akin to the 5'3 codon and 3'5 anticodon patterns. As a result of purine-pyrimidine symmetries between codons in the ISyGC table, algorithms of the first two bases as well of the third base of codons show how tRNA cognate anticodons can recognize synonymous codons during mRNA decoding. We show that the ISyGC purine-pyrimidine net with its physicochemical properties represents an evolutionary common "frozen accident" at the onset of each genetic code creation and RNA to DNA evolution. As such, during all of evolution the unique fundamental purine-pyrimidine symmetry net of all genetic codes remains unchangeable. In this way, evolution is a road paved with symmetries.

A plant can sire more seeds by increasing the number of pollen recipient flowers or the amount of pollen deposited on recipient flowers. We theoretically analyzed how pollen stickiness contributes to paternal fitness through changing the pattern of pollen dispersal including both the number of recipient flowers and overall pollen deposition (the overall amount of pollen deposited on recipient flowers) in animal-pollinated plants. We developed a numerical model in which pollen stickiness to pollinators increases with production of expensive materials on pollen surfaces, and a high level of stickiness diminishes the proportions of pollen lost from a pollinator body during a flight and pollen deposited on a stigma during a visit. We found that the number of recipient flowers monotonically increased with increasing pollen stickiness allocation while overall pollen deposition was maximized at a certain amount of stickiness allocation. We demonstrated that evolutionarily stable pollen stickiness attained many recipient flowers at the expense of overall pollen deposition in most cases while it merely favored maximization of overall pollen deposition in all other cases. Sticky pollen evolved if pollinators were highly likely to drop pollen during flights and did not diffuse well. In this situation, the evolutionarily stable pattern of pollen dispersal was acquisition of many pollen recipient flowers rather than maximization of overall pollen deposition. Sticky pollen also evolved if additional sticking elements were moderately effective in increasing the force of adhesion to pollinators. Pollen stickiness has a significant effect on the pattern of pollen dispersal via the extent of pollen carryover, and our results suggest that plants maximize paternal fitness by giving pollen the optimal stickiness, which varies with pollinating partners.

Erratum for J Theor Biol. 2011 Nov 21;289:1-11.

Respiratory syncytial virus (RSV) is a common, contagious infection of the lungs and the respiratory tract. RSV is characterized by syncytia, which are multinuclear cells created by cells that have fused together. We use a mathematical model to study how different assumptions about the viral production and lifespan of syncytia change the resulting infection time course. We find that the effect of syncytia on viral titer is only apparent when the basic reproduction number for infection via syncytia formation is similar to the reproduction number for cell free viral transmission. When syncytia fusion rate is high, we find the presence of syncytia can lead to slowly growing infections if viral production is suppressed in syncytia. Our model provides insight into how the presence of syncytia can affect the time course of a viral infection.

Many sea slugs of Sacoglossa (Mollusca: Heterobranchia) are sometimes called "solar-powered sea slugs" because they keep chloroplasts obtained from their food algae and receive photosynthetic products (termed kleptoplasty). Some species show life cycle dimorphism, in which a single species has some individuals with a complex life cycle (the mother produces planktotrophic larvae, which later settle in the adult habitat) and others with a simple life cycle (mothers produce benthic offspring by direct development or short-term nonfeeding larvae in which feeding planktonic stages are skipped). Life cycle dimorphism is not common among marine species. In this paper, we ask whether some aspects of the ecology of solar-powered sea slugs have promoted the evolution of life cycle dimorphism in them. We study the population dynamics of the two life-cycle types that differ in summer (one with planktonic life and the other with benthic life), but both have benthic life in other seasons. We obtain the conditions in which two types with different life cycles coexist stably or a single type generating offspring with different life cycles evolves. We conclude that the stable coexistence of two life cycles can evolve if benthic individuals in summer experience strongly density-dependent processes or if the between-year fluctuation of biomass growth in summer is very large. We discuss whether these results match the life cycles of solar-powered sea slugs with life cycle dimorphism.

Organisms continuously modify their living conditions via extended genetic effects on their environment, microbiome, and in some species culture. These effects can impact the fitness of current but also future conspecifics due to non-genetic transmission via ecological or cultural inheritance. In this case, selection on a gene with extended effects depends on the degree to which current and future genetic relatives are exposed to modified conditions. Here, we detail the selection gradient on a quantitative trait with extended effects in a patch-structured population, when gene flow between patches is limited and ecological inheritance within patches can be biased towards offspring. Such a situation is relevant to understand evolutionary driven changes in individual condition that can be preferentially transmitted from parent to offspring, such as cellular state, micro-environments (e.g., nests), pathogens, microbiome, or culture. Our analysis quantifies how the interaction between limited gene flow and biased ecological inheritance influences the joint evolutionary dynamics of traits together with the conditions they modify, helping understand adaptation via non-genetic modifications. As an illustration, we apply our analysis to a gene-culture coevolution scenario in which genetically-determined learning strategies coevolve with adaptive knowledge. In particular, we show that when social learning is synergistic, selection can favour strategies that generate remarkable levels of knowledge under intermediate levels of both vertical cultural transmission and limited dispersal. More broadly, our theory yields insights into the interplay between genetic and non-genetic inheritance, with implications for how organisms evolve to transform their environments.

Plant morphology emerges from cellular growth and structure. The turgor-driven diffuse growth of a cell can be highly anisotropic: significant longitudinally and negligible radially. Such anisotropy is ensured by cellulose microfibrils (CMF) reinforcing the cell wall in the hoop direction. To maintain the cell's integrity during growth, new wall material including CMF must be continually deposited. We develop a mathematical model representing the cell as a cylindrical pressure vessel and the cell wall as a fibre-reinforced viscous sheet, explicitly including the mechano-sensitive angle of CMF deposition. The model incorporates interactions between turgor, external forces, CMF reorientation during wall extension, and matrix stiffening. Using the model, we reinterpret some recent experimental findings, and reexamine the popular hypothesis of CMF/microtubule alignment. We explore how the handedness of twisting cell growth depends on external torque and intrinsic wall properties, and find that cells twist left-handedly 'by default' in some suitable sense. Overall, this study provides a unified mechanical framework for understanding left- and right-handed twist-growth as seen in many plants.

The retina is a part of the central nervous system that is accessible, well documented, and studied by researchers spanning the clinical, experimental, and theoretical sciences. Here, we mathematically model the subcircuits of the outer plexiform layer of the retina on two spatial scales: that of an individual synapse and that of the scale of the receptive field (hundreds to thousands of synapses). To this end we formulate a continuum spine model (a partial differential equation system) that incorporates the horizontal cell syncytium and its numerous processes (spines) within cone pedicles. With this multiscale modeling approach, detailed biophysical mechanisms at the synaptic level are retained while scaling up to the receptive field level. As an example of its utility, the model is applied to study background-induced flicker enhancement in which the onset of a dim background enhances the center flicker response of horizontal cells. Simulation results, in comparison with flicker enhancement data for square, slit, and disk test regions, suggest that feedback mechanisms that are voltage-axis modulators of cone calcium channels (for example, ephaptic and/or pH feedback) are robust in capturing the temporal dynamics of background-induced flicker enhancement. The value and potential of this continuum spine approach is that it provides a framework for mathematically modeling the input-output properties of the entire receptive field of the outer retina while implementing the latest models for transmission mechanisms at the synaptic level.

Traditional predictive microbiology is not suited for cell growth predictions for low-level contamination, where individual cell heterogeneity becomes apparent. Accordingly, we simulated a stochastic birth process of bacteria population using kinetic parameters. We predicted the variation in behavior of Salmonella enterica serovar Typhimurium cells at low inoculum density. The modeled cells were grown in tryptic soy broth at 25 °C. Kinetic growth parameters were first determined empirically for an initial cell number of 104 cells. Monte Carlo simulation based on the growth kinetics and Poisson distribution for different initial cell numbers predicted the results of 50 replicate growth experiments with the initial cell number of 1, 10, and 64 cells. Indeed, measured behavior of 85% cells fell within the 95% prediction area of the simulation. The calculations link the kinetic and stochastic birth process with Poisson distribution. The developed model can be used to calculate the probability distribution of population size for exposure assessment and for the evaluation of a probability that a pathogen would exceed critical contamination level during food storage.

Apoptosis has been extensively characterized by both experimental approaches and model simulations. However, it is still not fully understood how the regulation occurs, especially in the intrinsic pathway, which can be activated by a great variety of signals. In addition, the conditions in which a point of no return could be reached remain elusive. In this work, we use differential equations models to approach these issues. Our starting point was the model for caspase activation of Legewie et al. (Legewie S, et al., PLoS Computational Biology 2006, 2(9): e120), which exhibits irreversible bistability. We added an activation module to this model, with the main events related to mitochondrial outer membrane permeabilization, which includes cytochrome C release by the mitochondria and its effects on caspase activation and respiratory chain disruption. This "Extended Legewie Model" (ELM) uses BAK as the apoptotic stimulus and active caspase 3 as a measure of apoptosis activation. Unexpectedly, in the extended model, BAK cannot trigger apoptosis activation using physiologically sound initial values of the variables, due to limitations in apoptosome concentration increase. Therefore, the next step was to find a regulatory mechanism, allowing apoptosis activation in the ELM, starting from physiological initial concentrations. For this aim, we performed a sensitivity analysis on the 61 parameters of the system, finding that those producing the most relevant changes in the qualitative behaviour were the rates of synthesis of caspase 3, caspase 9 and XIAP. Based on these results, the transcription factor E2F was included in the ELM because it directly regulates the rate of synthesis of caspase 3 and 9. Depending on the concentration of E2F, the ELM shows different qualitative behaviours. On one hand, for low E2F apoptosis is impossible and for high E2F apoptosis is inevitable. Therefore, if E2F is sufficiently increased, the point of no return is crossed. On the other hand, for intermediate values of E2F there is a bistable region where the fate of the system also depends on the concentration of BAK and other signalling species.