Biological Modeling

Starting from a philosophical perspective, which states that the living structures are actually a combination between matter and information, this article presents the results on an analysis of the bipolar information-matter structure of the human organism, distinguishing three fundamental circuits for its survival, which demonstrates and supports this statement, as a base for further development of the informational model of consciousness to a general informational model of the human organism. For this, it was examined the Informational System of the Human (...) Body and its components from the perspective of the physics/information/neurosciences concepts, showing specific functions of each of them, highlighting the correspondence of these centers with brain support areas and with their projections in consciousness, which are: Center of Acquisition and Storing of Information (CASI) reflected in consciousness as memory, Center of Decision and Command (CDC) (decision), Info-Emotional Center (IES) (emotions), Maintenance Informational System (MIS) (personal status), Genetic Transmission System (GTS) (associativity/genetic transmission) and Info Genetic Generator (IGG) related by the body development and inherited behaviors. The Info Connection (IC), detected in consciousness as trust and confidence can explain the Near-Death Experiences (NDEs) and associated phenomena. This connection is antientropic and informational, because from the multitude of uncertain possibilities is selected a certain one, helping/supporting the survival and life. The human body appears therefore as a bipolar structure, connected to two poles: information and matter. It is argued that the survival, which is the main objective of the organism, is complied in three main ways, by means of: (i) the reactive operation for adaptation by attitude; (ii) the info-genetic integration of information by epigenetic processes and genetic transmission of information for species survival, both circuits (i) and (ii) being associated to the information pole; (iii) maintenance of the material body (defined as informed matter) and its functions, associated to the matter pole of the organism. It results therefore that the informational system of the human body is supported by seven informational circuits formed by the neuro-connections between the specific zones of the brain corresponding to the informational subsystems, the cognitive centers, the sensors, transducers and execution (motor/mobile) elements. The fundamental informational circuits assuring the survival are the reactive circuit, expressible by attitude, the epigenetic/genetic circuit, absorbing and codifying information to be transmitted to the next generations, and the metabolic circuit, connected to matter (matter pole). The presented analysis allows to extend the informational modeling of consciousness to an Informational Model of Consciousness and Organism, fully describing the composition/functions of the organism in terms of information/matter and neurosciences concept. (shrink)

Following the development of the selectionist theory of the immune system, there was an attempt to characterize many biological mechanisms as being "selectionist" as juxtaposed to "instructionist." But this broad definition would group Darwinian evolution, the immune system, embryonic development, and Chomsky's language-acquisition mechanism as all being "selectionist." Yet Chomsky's mechanism (and embryonic development) are significantly different from the selectionist mechanisms of biological evolution or the immune system. Surprisingly, there is a very abstract way using two dual mathematical logics to (...) make the distinction between genuinely selectionist mechanisms and what are better called "generative" mechanisms. This note outlines that distinction. (shrink)

Endocrinologists apply the idea of feedback loops to explain how hormones regulate certain bodily functions such as glucose metabolism. In particular, feedback loops focus on the maintenance of the plasma concentrations of glucose within a narrow range. Here, we put forward a different, organicist perspective on the endocrine regulation of glycaemia, by relying on the pivotal concept of closure of constraints. From this perspective, biological systems are understood as organized ones, which means that they are constituted of a set of (...) mutually dependent functional structures acting as constraints, whose maintenance depends on their reciprocal interactions. Closure refers specifically to the mutual dependence among functional constraints in an organism. We show that, when compared to feedback loops, organizational closure can generate much richer descriptions of the processes and constraints at play in the metabolism and regulation of glycaemia, by making explicit the different hierarchical orders involved. We expect that the proposed theoretical framework will open the way to the construction of original mathematical models, which would provide a better understanding of endocrine regulation from an organicist perspective. (shrink)

Philosophers have committed sins while studying science, it is said – philosophy of science focused on physics to the detriment of biology, reconstructed idealizations of scientific episodes rather than attending to historical details, and focused on theories and concepts to the detriment of experiments. Recent generations of philosophers of science have tried to atone for these sins, and by the 1980s the exculpation was in full swing. Marcel Weber’s Philosophy of Experimental Biology is a zenith mea culpa for philosophy of (...) science: it carefully describes several historical examples from twentieth century biology to address both ‘old’ philosophical topics, like reductionism, inference, and realism, and ‘new’ topics, like discovery, models, and norms. Biology, experiments, history – at last, philosophy of science, free of sin. (shrink)

Cancer is a paradigmatic case of a complex causal process; causes of cancer operate at a variety of temporal and spatial scales, and the respects in which these causes act and interact are diverse. There are, for instance, temporal order effects, organizational effects, structural effects, and dynamic relationships between causes operating at different temporal and spatial scales. Because of this complexity, models of cancer initiation and progression often involve deliberate choices to focus on one time scale, one causal pathway, or (...) one aspect of cancer’s dynamics. As in most of biology, modeling cancer involves simplification and idealization. At the same time, theoretical perspectives inform the construction of these models. Such perspectives might involve viewing cancer ‘as’ a genetic disease, metabolic disease, stem cell disease, an infectious disease, or a disease of tissue disorganization. This paper will argue that purportedly competing theoretical views of cancer are not at odds, but can be viewed as mutually informative. Models are most often developed in the service of asking very specific questions, and this requires limiting our view of the phenomena to a specific temporal or spatial scale, a particular cause, or a particular outcome, dynamic, or pattern. Thus, while some models may seem at odds, often they are simply concerned with different questions, or, they are complementary and mutually informative. I hope to bring this case to bear on debates among philosophers of science over perspectivism and realism, as well pluralism about the aims and scope of scientific theory. (shrink)

Optimality models are widely used in different parts of biology. Two important questions that have been asked about such models are: are they explanatory and, if so, what type of explanations do they offer? My concern in this paper is with the approach of Rice (2012, 2015) and Irvine (2015), who claim that these models provide non-causal explanations. I argue that there are serious problems with this approach and with the accounts of explanation it is intended to justify. The idea (...) behind this undertaking is to draw attention to an important issue associated with the recent pluralist stance on explanation: the rampant proliferation of theories of explanation. This proliferation supports a pluralist perspective on explanation, and pluralism encourages such a proliferation. But, if we are not careful about how we arrive at and how we justify new accounts of explanation — i.e., if we do not try to avoid the sort of problems discussed in this paper — we may end up trivializing the concept of explanation. (shrink)

Among those speaking in the name of materialism, whether speculative, dialectical, or "new," it is commonplace to dismiss with a single gesture a vast field of theoretical and philosophical endeavor, indicated as the last 50 or 250 years of theory and philosophy. Self-styled "speculative" writers who would surpass all philosophy since Kant, and various New Materialists who sequester decades of thought under the heading of "constructivism," manufacture the avant-garde status of their own work by claiming to delineate a simple break (...) with the past. We would be at a loss, and perhaps at risk of missing the point, if we sought to uncover the common essence underlying this "new" work, either by looking for an agreement... (shrink)

The mantra that "the best way to predict the future is to invent it" (attributed to the computer scientist Alan Kay) exemplifies some of the expectations from the technical and innovative sides of biomedical research at present. However, for technical advancements to make real impacts both on patient health and genuine scientific understanding, quite a number of lingering challenges facing the entire spectrum from protein biology all the way to randomized controlled trials should start to be overcome. The proposal in (...) this chapter is that philosophy is essential in this process. By reviewing select examples from the history of science and philosophy, disciplines which were indistinguishable until the mid-nineteenth century, I argue that progress toward the many impasses in biomedicine can be achieved by emphasizing theoretical work (in the true sense of the word 'theory') as a vital foundation for experimental biology. Furthermore, a philosophical biology program that could provide a framework for theoretical investigations is outlined. (shrink)

The fracture in the emerging discipline of biosemiotics when the code biologist Marcello Barbieri claimed that Peircian biosemiotics is not genuine science raises anew the question: What is science? When it comes to radically new approaches in science, there is no simple answer to this question, because if successful, these new approaches change what is understood to be science. This is what Galileo, Darwin and Einstein did to science, and with quantum theory, opposing interpretations are not merely about what theory (...) is right, but what is real science. Peirce's work, as he acknowledged, is really a continuation of efforts of Schelling to challenge the heritage of Newtonian science for the very good reason that the deep assumptions of Newtonian science had made sentient life, human consciousness and free will unintelligible, the condition for there being science. Pointing out the need for such a revolution in science has not succeeded as a defence of Peircian biosemiotics, however. In this paper, I will defend the scientific credentials of Peircian biosemiotics by relating it to the theoretical biology of the bio-mathematician, Robert Rosen. Rosen's relational biology, focusing on anticipatory systems and giving a place to final causes, should also be seen as a rigorous development of the Schellingian project to conceive nature in such a way that the emergence of sentient life, mind and science are intelligible. Rosen has made a very strong case for the characterization of his ideas as a real advance not only in science, but in how science should be understood, and I will argue that it is possible to provide a strong defence of Peircian biosemiotics as science through Rosen's defence of relational biology. In the process, I will show how biosemiotics can and should become a crucial component of anticipatory systems theory. (shrink)

The role of genetic relatedness in social evolution has recently come under critical attention. These arguments are here critically analyzed, both theoretically and empirically. It is argued that when the conceptual structure of the theory of natural selection is carefully taken into account, genetic relatedness can be seen to play an indispensable role in the evolution of both facultative and advanced eusociality. Although reviewing the empirical evidence concerning the evolution of eusociality reveals that relatedness does not play a role in (...) the initial appearance of helper phenotypes, this follows simply from the fact that natural selection – of which relatedness is a necessary component – does not play a causal role in the origin of any traits. Further, separating two logically distinct elements of causal explanation – necessity and sufficiency – explains why the debate lingers on: although relatedness plays a necessary role in the evolution of helping and advanced eusociality, relatedness alone is not sufficient for their appearance. Therefore, if the relatedness variable in a given data set is held at a uniformly high value, then it indeed may turn out that other factors occupy a more prominent role. However, this does not change the fact that high relatedness functions as a necessary background condition for the evolution of advanced eusociality. (shrink)

We provide a new perspective on the relation between the space of description of an object and the appearance of novelties. One of the aims of this perspective is to facilitate the interaction between mathematics and historical sciences. The definition of novelties is paradoxical: if one can define in advance the possibles, then they are not genuinely new. By analyzing the situation in set theory, we show that defining generic (i.e., shared) and specific (i.e., individual) properties of elements of a (...) set are radically different notions. As a result, generic and specific definitions of possibilities cannot be conflated. We argue that genuinely stating possibilities requires that their meaning has to be made explicit. For example, in physics, properties playing theoretical roles are generic; then, generic reasoning is sufficient to define possibilities. By contrast, in music, we argue that specific properties matter, and generic definitions become insufficient. Then, the notion of new possibilities becomes relevant and irreducible. In biology, among other examples, the generic definition of the space of DNA sequences is insufficient to state phenotypic possibilities even if we assume complete genetic determinism. The generic properties of this space are relevant for sequencing or DNA duplication, but they are inadequate to understand phenotypes. We develop a strong concept of biological novelties which justifies the notion of new possibilities and is more robust than the notion of changing description spaces. These biological novelties are not generic outcomes from an initial situation. They are specific and this specificity is associated with biological functions, that is to say, with a specific causal structure. Thus, we think that in contrast with physics, the concept of new possibilities is necessary for biology. (shrink)

This authored monograph introduces a genuinely theoretical approach to biology. Starting point is the investigation of empirical biological scaling including their variability, which is found in the literature, e.g. allometric relationships, fractals, etc. The book then analyzes two different aspects of biological time: first, a supplementary temporal dimension to accommodate proper biological rhythms; secondly, the concepts of protension and retention as a means of local organization of time in living organisms. Moreover, the book investigates the role of symmetry in biology, (...) in view of its ubiquitous importance in physics. In relation with the notion of extended critical transitions, the book proposes that organisms and their evolution can be characterized by continued symmetry changes, which accounts for the irreducibility of their historicity and variability. The authors also introduce the concept of anti-entropy as a measure for the potential of variability, being equally understood as alterations in symmetry. By this, the book provides a mathematical account of Gould's analysis of phenotypic complexity with respect to biological evolution. The target audience primarily comprises researchers interested in new theoretical approaches to biology, from physical, biological or philosophical backgrounds, but the book may also be beneficial for graduate students who want to enter this field. (shrink)

The importation of computational methods into biology is generating novel methodological strategies for managing complexity which philosophers are only just starting to explore and elaborate. This paper aims to enrich our understanding of methodology in integrative systems biology, which is developing novel epistemic and cognitive strategies for managing complex problem-solving tasks. We illustrate this through developing a case study of a bimodal researcher from our ethnographic investigation of two systems biology research labs. The researcher constructed models of metabolic and cell-signaling (...) pathways by conducting her own wet-lab experimentation while building simulation models. We show how this coupling of experiment and simulation enabled her to build and validate her models and also triangulate and localize errors and uncertainties in them. This method can be contrasted with the unimodal modeling strategy in systems biology which relies more on mathematical or algorithmic methods to reduce complexity. We discuss the relative affordances and limitations of these strategies, which represent distinct opinions in the field about how to handle the investigation of complex biological systems. (shrink)

In recent years, the philosophical focus of the modeling literature has shifted from descriptions of general properties of models to an interest in different model functions. It has been argued that the diversity of models and their correspondingly different epistemic goals are important for developing intelligible scientific theories. However, more knowledge is needed on how a combination of different epistemic means can generate and stabilize new entities in science. This paper will draw on Rheinberger’s practice-oriented account of knowledge production. The (...) conceptual repertoire of Rheinberger’s historical epistemology offers important insights for an analysis of the modelling practice. I illustrate this with a case study on network modeling in systems biology where engineering approaches are applied to the study of biological systems. I shall argue that the use of multiple means of representations is an essential part of the dynamic of knowledge generation. It is because of – rather than in spite of – the diversity of constraints of different models that the interlocking use of different epistemic means creates a potential for knowledge production. (shrink)

This paper examines the very disparate positions that various actors have taken towards the argument of subversion from within in a set of related debates on group selection, altruism and the handicap principle. Using this set of debates as a case study, this paper argues that different applications of epistemic values were one of the factors behind the disagreements between John Maynard Smith and Amotz Zahavi over a number of important evolutionary issues. The paper also argues that these different applications (...) were connected to important epistemological differences related in part to their disciplinary background. Apart from conflicting evolutionary views concerning the theoretical feasibility of the handicap effect, these antagonists both differed in the confidence they ascribed to mathematical modeling and over the hereditary basis for altruistic behavior. (shrink)

I examine to what extent accounts of mechanisms based on formal interventionist theories of causality can adequately represent biological mechanisms with complex dynamics. Using a differential equation model for a circadian clock mechanism as an example, I first show that there exists an iterative solution that can be interpreted as a structural causal model. Thus, in principle it is possible to integrate causal difference-making information with dynamical information. However, the differential equation model itself lacks the right modularity properties for a (...) full integration. A formal mechanistic model will therefore either have to leave out non-causal or causal explanatory relations. (shrink)

Although there is increasing recognition that theory and practice in science are often inseparably intertwined, discussions of scientific controversies often continue to focus on theory, and not practice or methodologies. As a contribution to constructing a framework towards understanding controversies linked to scientific practices, we introduce the notion of borrowed epistemic credibility, to describe the situation in which scientists exploit fallacious similarities between accepted tenets in other fields to garner support for a given position in their own field. Our proposal (...) is based on the analysis of a recent controversy in phylogeography, a biological subdiscipline concerned with the study of the historical causes of variation in genetic diversity within species in concrete biogeographical locations. Through a review of the arguments that support the two conflicting phylogeographic schools, we show that ‘theory’ plays essentially no role as a foundation of the controversy, whereas both sides borrow epistemic credibility from sources such as formal logic, similarity of results to those in other scientific areas, the authority of prominent scientists, or the presumed superiority of quantitative vs. verbal reasoning. Our case study underscores the indivisibility of theory and practice and provide a means to re-examine important philosophical issues such as the meaning of inference, rationality, justification, and objectivity in scientific practice. (shrink)

_This paper deals with the interrelationship between causal explanation and methodology in a relatively young discipline in biology: epigenetics. Based on cases from molecular and ecological epigenetics, I show that James Woodward’s interventionist account of causation captures essential features about how epigeneticists using highly diverse methods, i.e. laboratory experiments and purely observational studies, think about causal explanation. I argue that interventionism thus qualifies as a useful unifying explanatory approach when it comes to cross-methodological research efforts: It can act as a (...) guiding rationale to link causal models in molecular biology with statistical models derived from observational data analysis and to identify test-criteria for reciprocal transparent studies in different fields of research, which is a shared issue across the sciences.___. (shrink)

Building a meaningful model of biological regulatory network is usually done by specifying the components and their interactions, by guessing the values of parameters, by comparing the predicted behaviors to the observed ones, and by modifying in a trial-error process both architecture and parameters in order to reach an optimal fitness. We propose here a different approach to construct and analyze biological models avoiding the trial-error part, where structure and dynamics are represented as formal constraints. We apply the method to (...) Hopfield-like networks, a formalism often used in both neural and regulatory networks modeling. The aim is to characterize automatically the set of all models consistent with all the available knowledge . The available knowledge is formalized into formal constraints. The latter are compiled into Boolean formula in conjunctive normal form and then submitted to a Boolean satisfiability solver. This approach allows to formulate a wide range of queries, expressed in a high level language, and possibly integrating formalized intuitions. In order to explore its potential, we use it to find cycles for 3-nodes networks and to determine the flower morphogenesis regulatory network of Arabidopsis thaliana. Applications of this technique are numerous and concern the building of models from data as well as the design of biological networks possessing specified behaviors. (shrink)

This article revisits a reduced model of cardiac electro-physiology which was proposed to understand the genesis of unidirectional block pathology and of ectopic foci. We underline some specificities of the model from the viewpoint of dynamical systems and bifurcation theory. We point out that essentially the same properties are shared by a simpler system more accessible to analysis. With this simpler system, it becomes possible to give a new presentation of the phenomenon in a phase plane with time moving slow (...) manifolds. This presentation can be of interest both for cardiac electro-physiologists and for mathematicians. (shrink)

The aim of this study is to provide a feedback control, called the Chemotherapy Protocol Law, with the purpose to keep the density of tumor cells that are treated by chemotherapy below a “tolerance level” L_c, while retaining the density of normal cells above a “healthy level” N_c. The mathematical model is a controlled dynamical system involving three nonlinear differential equations, based on a Gompertzian law of cell growth. By evoking viability and set-valued theories, we derive sufficient conditions for the (...) existence of a Chemotherapy Protocol Law. Thereafter, on a suitable viability domain, we build a multifunction whose selections are the required Chemotherapy Protocol Laws. Finally, we propose a design of selection that generates a Chemotherapy Protocol Law. (shrink)

The aim of this article is to show how a tumor can modify energy substrates fluxes in the brain to support its own growth. To address this question we use a modeling approach to explain brain nutrient kinetics. In particular we set up a system of 17 equations for oxygen, lactate, glucose concentrations and cells number in the brain. We prove the existence and uniqueness of nonnegative solutions and give bounds on the solutions. We also provide numerical simulations.

This paper proposes an outline for a typology of the different forms that scientific objects can take in the life sciences. The first section discusses preparations (or specimens)—a form of scientific object that accompanied the development of modern biology in different guises from the seventeenth century to the present: as anatomical–morphological specimens, as microscopic cuts, and as biochemical preparations. In the second section, the characteristics of models in biology are discussed. They became prominent from the end of the nineteenth century (...) onwards. Some remarks on the role of simulations—characterising the life sciences of the turn from the twentieth to the twenty-first century—conclude the paper. -/- . (shrink)

The seventh section of Gregor Mendel’s famous 1866 paper contained a peculiar mathematical model, which predicted the expected ratios between the number of constant and hybrid types, assuming self-pollination continued throughout further generations. This model was significant for Mendel’s argumentation and was perceived as inseparable from his entire theory at the time. A close examination of this model reveals that it has several perplexing aspects which have not yet been systematically scrutinized. The paper analyzes those aspects, dispels some common misconceptions (...) regarding the interpretation of the model, and re-evaluates the role of this model for Mendel himself. In light of the resulting analysis, Mendel’s position between nineteenth-century hybridist tradition and twentieth-century population genetics is reassessed, and his sophisticated use of mathematics to legitimize his innovative theory is uncovered. (shrink)

Dusky groupers (Epinephelus marginatus) are characterized by a complex sex allocation strategies and overexploitation of bigger individuals. We developed an individual based model to investigate the long-term effects of density dependence on grouper population dynamics and to analyze the variabilities of extinction probabilities as a result of interacting mortalities at different life stages. We conduct several simulations with different forms of sex allocation functions and different combinations of mortality rates. The model was parametrized using data on dusky grouper populations from (...) the literature. The most important insights produced by this simulation study are that density dependence of sex allocation is an evolutionarily stable strategy, increases the population biomass, mitigates the effect of the removal of large male and indicates a need for protection of females and flexible stages. (shrink)

Scientific models are used to predict and understand the target phenomena in the reality. The kind of epistemic relationship between the model and the reality is always regarded by most of the philosophers as a representational one. I argue that, complementary to this representational role, some of the scientific models have a constructive role to play in altering and reconstructing the reality in a physical way. I hold that the idealized model assumptions and elements bestow the constructive force of a (...) model on the reality. By recognizing the physical constructive force of some scientific models, the merit of these models could be judged by how successful they are in the reality construction, rather than by the traditional criterion of model-world representation. (shrink)

Holobionts, consisting of a host and diverse microbial symbionts, function as distinct biological entities anatomically, metabolically, immunologically, and developmentally. Symbionts can be transmitted from parent to offspring by a variety of vertical and horizontal methods. Holobionts can be considered levels of selection in evolution because they are well-defined interactors, replicators/reproducers, and manifestors of adaptation. An initial mathematical model is presented to help understand how holobionts evolve. The model offered combines the processes of horizontal symbiont transfer, within-host symbiont proliferation, vertical symbiont (...) transmission, and holobiont selection. The model offers equations for the population dynamics and evolution of holobionts whose hologenomes differ in gene copy number, not in allelic or loci identity. The model may readily be extended to include variation among holobionts in the gene identities of both symbionts and host. (shrink)

A model representing isotope separation during water evaporation in plants was constructed. The model accounts for substance diffusion, convective transfer and evaporation from the surface of the leaves. The dependence of the system’s separation and enrichment coefficients on various parameters was determined. A comparison was made between the enrichment coefficients calculated from experimental data from different plants and those based on the model. Qualitative agreement between the experimental and theoretical values was obtained for the case of $$\frac{uh}{D} {\gg} 1$$ uh (...) D ≫ 1, where u is the average velocity of water in the plant, h is the height of the plant, and D is the diffusion coefficient of the substance. (shrink)

Conventional methods of genetic engineering and more recent genome editing techniques focus on identifying genetic target sequences for manipulation. This is a result of historical concept of the gene which was also the main assumption of the ENCODE project designed to identify all functional elements in the human genome sequence. However, the theoretical core concept changed dramatically. The old concept of genetic sequences which can be assembled and manipulated like molecular bricks has problems in explaining the natural genome-editing competences of (...) viruses and RNA consortia that are able to insert or delete, combine and recombine genetic sequences more precisely than random-like into cellular host organisms according to adaptational needs or even generate sequences de novo. Increasing knowledge about natural genome editing questions the traditional narrative of mutations (error replications) as essential for generating genetic diversity and genetic content arrangements in biological systems. This may have far-reaching consequences for our understanding of artificial genome editing. (shrink)

In this paper, we propose two four-base related 2D curves of DNA primary sequences and their corresponding single-base related 2D curves. The constructions of these graphical curves are based on the assignments of individual base to four different sinusoidal functions; then by connecting all these points on these four sinusoidal functions, we can get the F-B curves; similarly, by connecting the points on each of the four sinusoidal functions, we get the single-base related 2D curves. The proposed 2D curves are (...) all strictly non degenerate. Then, a 8-component characteristic vector is constructed to compare similarity among DNA sequences from different species based on a normalized geometrical centers of the proposed curves. As examples, we examine similarity among the coding sequences of the first exon of beta-globin gene from eleven species, similarity of cDNA sequences of beta-globin gene from eight species, and similarity of the whole mitochondrial genomes of 18 eutherian mammals. The experimental results well demonstrate the effectiveness of the proposed method. (shrink)

In this work, we study a several species aerobic chemostat model with constant recycle sludge concentration in continuous culture. We reduce the number of parameters by considering a dimensionless model. First, the existence of a global positive uniform attractor for the model with different removal rates is proved using the theory of dissipative dynamical systems. Hence, we investigate the asymptotic behavior of the model under small perturbations using methods of singular perturbation theory and we prove that, in the case of (...) two species in competition, the unique equilibrium which is positive is globally asymptotically stable. Finally, we establish the link between the open problem of the chemostat with different removal rates and monotone functional responses, and our model when two species compete on the same nutrient. We give some numerical simulations to illustrate the results. (shrink)

This article is devoted to the characterization of the basin of attraction of pattern solutions for some slow–fast reaction–diffusion systems with a symmetric property and an underlying oscillatory reaction part. We characterize some subsets of initial conditions that prevent the dynamical system to evolve asymptotically toward solutions which are homogeneous in space. We also perform numerical simulations that illustrate theoretical results and give rise to symmetric and non-symmetric pattern solutions. We obtain these last solutions by choosing particular random initial conditions.

To date, our knowledge of Rift Valley fever disease spread and maintenance is still limited, as flooding, humid weather and presence of biting insects such as mosquitoes, have not completely explained RVF outbreaks. We propose a model that includes livestock, mosquitoes and ticks compartments structured according to their questing and feeding behaviour in order to study the possible role of ticks on the dynamics of RVF. To quantify disease transmission at the initial stage of the epidemic, we derive an explicit (...) formula of the basic reproductive number, $$R_0$$ R 0. Using the concept of Metzler matrix, we state necessary conditions for global asymptotic stability of the disease-free equilibrium. Results suggest that although host-ticks interactions may serve as disease reservoirs or disease amplifiers, the Aedes reproductive number should be kept under unity if disease post-epizootics activities are to be controlled. Results of both local and global sensitivity analysis of selected model parameters indicate that $$R_0$$ R 0 is more sensitive to the ticks attachment and detachment rates, probability of transmission from ticks to host and from host to ticks, length of infection in livestock and ticks death rate. Furthermore, when comparing the mean value of $$R_0$$ R 0 with that from previous studies which did not include ticks we found that our $$R_0$$ R 0 is very much larger resulting in an increase in the exponential phase of an outbreak. These findings suggest that if ticks are capable of transmitting the virus, they may be contributing to disease outbreaks and endemicity. (shrink)

This paper addresses the existence of Hopf bifurcations in a directed acyclic network of neurons, each of them being modeled by a Hindmarsh–Rose neuronal model. The bifurcation parameter is the small parameter corresponding to the ratio of time scales between the fast and the slow dynamics. We first prove that, under certain hypotheses, the single uncoupled neuron can undergo a Hopf bifurcation. Hopf bifurcation occurrences in a directed acyclic network of HR neurons are then discussed. Numerical simulations are carried out (...) to observe these bifurcations and to illustrate the theoretical results. (shrink)

This work presents a mathematical model describing the interactions between the cross-shore structure of small pelagic fish population an their exploitation by coastal and offshore fisheries. The complete model is a system of seven ODE’s governing three stocks of small pelagic fish population moving and growing between three zones. Two types of fishing fleets are inter-acting with the fish population, industrial boats, constrained to offshore area, and artisanal boats, operating from the shore. Two time scales were considered and we use (...) aggregation methods that allow us to reduce the dimension of the model and to obtain an aggregated model, which is a four dimension one. The analysis of the aggregated model is performed. We discuss the possible equilibriums and their meaning in terms of fishery management. An interesting equilibrium state can be obtained for which we can expect coexistence and a stable equilibrium state between fish stocks and fishing efforts. Some identification parameters are also given in the discussion part of the model. (shrink)

In the present paper, we propose and analyze a harvested predator–prey model that incorporates the dynamics of tourists in the Djoudj National Park of Birds, Senegal. The model describes the impact of migration of waterbirds and seasonal fishing on the global coexistence of species in the site of the Djoudj. By the Mahwin continuation theorem of coincidence degree theory, we investigate the existence of a positive periodic solution. The global asymptotic stability is discussed by constructing a suitable Lyapunov functional. Some (...) computational results are also addressed. (shrink)

The present work is a contribution to the understanding of the sempiternal problem of the “burden of factor two” implied by sexual reproduction versus asexual one, as males are energy consumers not contributing to the production of offspring. We construct a deterministic mathematical model in population dynamics where a species enjoys both sexual and parthenogenetic capabilities of reproduction and lives on a limited resource. We then show how polygamy implies instability of a parthenogenetic population with a small number of sexually (...) born males. This instability implies evolution of the system towards an attractor involving both populations. We also exhibit the analogy with a parasite/host system. (shrink)

We present a mathematical model of two competing marine species that are harvested. We consider three models according to different levels of complexity, without and with species refuge and density-independent and density-dependent species movement between fishing area and refuge. We particularly study the effects of the fishing pressure on the outcome of the competition. We focus on conditions that allow an inferior competitor to invade as a result of fishing pressure. The model is discussed in relationship to the case of (...) the thiof and the octopus along the Atlantic West African coast. At the origin, the thiof was abundant and the octopus scarce in that region. Since, the fishing pressure has strongly increased in some fishing areas leading to the depletion of the thiof and the invasion of its competitor, the octopus. (shrink)

Blood coagulation is regulated through a complex network of biochemical reactions of blood factors. The main acting enzyme is thrombin whose propagation in blood plasma leads to fibrin clot formation. Spontaneous clot formation is normally controlled through the action of different plasma inhibitors, in particular, through the thrombin binding by antithrombin. In the current study we develop a mathematical model of clot formation both in quiescent plasma and in blood flow and determine the analytical conditions on the antithrombin concentration corresponding (...) to different regimes of blood coagulation. (shrink)

A method for the recursive identification of physiological models of the cardiovascular baroreflex is proposed and applied to the time-varying analysis of vagal and sympathetic activities. The proposed method was evaluated with data from five newborn lambs, which were acquired during injection of vasodilator and vasoconstrictors and the results show a close match between experimental and simulated signals. The model-based estimation of vagal and sympathetic contributions were consistent with physiological knowledge and the obtained estimators of vagal and sympathetic activities were (...) compared to traditional markers associated with baroreflex sensitivity. High correlations were observed between traditional markers and model-based indices. (shrink)

Cognition in living entities -- and their social groupings or institutional artifacts -- is necessarily as complicated as their embedding environments, which, for humans, includes a particularly rich cultural milieu. The asymptotic limit theorems of information and control theories permit construction of a new class of empirical 'regression-like' statistical models for cognitive developmental processes, their dynamics, and modes of dysfunction. Such models may, as have their simpler analogs, prove useful in the study and remediation of cognitive failure at and across (...) the scales and levels of organization that constitute and drive the phenomena of life. These new models particularly focus on the roles of sociocultural environment and stress, in a large sense, as both trigger for the failure of the regulation of biocognition and as 'riverbanks' determining the channels of pathology, with implications across life-course developmental trajectories. We examine the effects of an embedding cultural milieu and its socioeconomic implementations using the 'lenses' of metabolic optimization, control system theory, and an extension of symmetry-breaking appropriate to information systems. A central implication is that most, if not all, human developmental disorders are fundamentally culture-bound syndromes. This has deep implications for both individual treatment and public health policy. (shrink)

There is considerable correspondence between theories and models used in biology and the social sciences. One type of model that is in use in both biology and the social sciences is the fitness landscape model. The properties of the fitness landscape model have been applied rather freely in the social domain. This is partly due to the versatility of the model, but it is also due to the difficulties of transferring a model to another domain. We will demonstrate that in (...) order to transfer the biological fitness landscape model to the social science it needs to be substantially modified. We argue that the syntactic structure of the model can remain unaltered, whilst the semantic dimension requires considerable modification in order to fit the specific phenomena in the social sciences. We will first discuss the origin as well as the basic properties of the model. Subsequently, we will demonstrate the considerations and modifications pertaining to such a transfer by showing how and why we altered the model to analyse collective decision-making processes. We will demonstrate that the properties of the target domain allow for a transfer of the syntactic structure but don’t tolerate the semantic transfer. (shrink)

This computational study generates a hypothesis for the coagulation protein whose initial concentration greatly influences the course of coagulation. Many clinical malignancies of blood coagulation arise due to abnormal initial concentrations of coagulation factors. Sensitivity analysis of mechanistic models of blood coagulation is a convenient method to assess the effect of such abnormalities. Accordingly, the study presents sensitivity analysis, with respect to initial concentrations, of a recently developed mechanistic model of blood coagulation. Both the model and parameters to which model (...) sensitivity is being analyzed provide newer insights into blood coagulation: the model incorporates distinct equations for plasma-phase and platelet membrane-bound species, and sensitivity to initial concentrations is a new dimension in sensitivity analysis. The results show that model predictions are most uncertain with respect to changes in initial concentration of factor VIII, and this hypothesis is supported by results from other models developed independently. (shrink)

In a broad brush, biological models are often constructed in two general types: as a concrete model; as an abstract model. A concrete model is a material model such as model organisms, while an abstract model is a mathematical or computational model consists of equations or algorithms. Though there are types of biological models that cannot be strictly categorized as either concrete or abstract, they are falling somewhere in between this spectrum. In view of the fact that biological phenomena are (...) sui generis and distinct from physical phenomena in many respects, using the concepts in standard modeling fails to account for the differences between biological sciences and physical sciences. Drawing from the resources of a credible-world account of models in economic modeling, I propose to reinterpret abstract models and concrete models in the light of the credible world account of models. (shrink)