Online research in philosophy

We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical properties of species, shining some light onto the species problem. We prove a dualization of a law of T.A. Knight and C. Darwin, and sketch a decomposition result (...) involving the internodons of D. Kornet, J. Metz and H. Schellinx. A further goal of this paper is to respond to B. Sturmfels’ question, “Can biology lead to new theorems?”. (shrink)

Abstract Many apparently complex mechanisms in biology, especially in embryology and molecular biology, can be explained easily by reasoning at the level of the “efficient cause” of the observed phenomenology: the mechanism can then be explained by a simple geometrical argument or a variational principle, leading to the solution of an optimization problem, for example, via the co-existence of a minimization and a maximization problem (a min–max principle). Passing from a microscopic (or cellular) level (optimal min–max solution of the simple (...) mechanistic system) to the macroscopic level often involves an averaging effect (linked to the repetition of a large number of such microscopic systems with possible random choice of the parameters of each of them) that gives birth to a global functional feature (e.g. at the tissue level). We will illustrate these general principles by building in four different domains of application “a minima” models and showing the main properties of their solutions: (1) extraction of a minimal RNA structure functioning as the first “peptidic machine,” a kind of ancestral ribosome; (2) study of a genetic regulatory network of Drosophila centred on Engrailed gene and expressing successively two genes inside a limit cycle; (3) study of a genetic network regulating neural activity and proliferation in mammals; and (4) study of a simple geometric model of epiboly in zebrafish. Content Type Journal Article Category Regular Article Pages 1-17 DOI 10.1007/s10441-012-9146-4 Authors L. Almeida, AGIM, FRE CNRS 3405, Faculty of Medicine of Grenoble, University J. Fourier, 38 700 La Tronche, France J. Demongeot, AGIM, FRE CNRS 3405, Faculty of Medicine of Grenoble, University J. Fourier, 38 700 La Tronche, France Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342. (shrink)

Building a meaningful model of biological regulatory network is usually done by specifying the components (e.g. the genes) 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 (about structure and behavior). 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)

Abstract We present a dynamical model of a multi-site fishery. The fish stock is located on a discrete set of fish habitats where it is catched by the fishing fleet. We assume that fishes remain on fishing habitats while the fishing vessels can move at a fast time scale to visit the different fishing sites. We use the existence of two time scales to reduce the dimension of the model : we build an aggregated model considering the habitat fish densities (...) and the total fishing effort. We explore a regulation procedure, which imposes an average residence time in patches. Several equilibria exist, a Fishery Free Equilibria (FFEs) as well as a Sustainable Fishery Equilibria (SFEs). We show that the dynamics depends on a threshold which is similar to a basic reproduction ratio for the fishery. When the basic reproduction ratio is less or equal to 1, one of the FFEs is globally asymptotically stable (GAS), otherwise one of the SFEs is GAS. Content Type Journal Article Category Regular Article Pages 1-22 DOI 10.1007/s10441-012-9155-3 Authors Pierre Auger, UMI IRD 209, UMMISCO, & université Pierre et Marie Curie, Paris VI. IRD France Nord, 93143 Bondy, France Ali Moussaoui, Département de Mathématiques, Université Aboubekr Belkaid, Tlemcen, Algeria Gauthier Sallet, INRIA project team: MASAIE, INRIA-Nancy Grand Est, Nancy, France Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342. (shrink)

Several key areas in modeling the cardiovascular and respiratory control systems are reviewed and examples are given which reflect the research state of the art in these areas. Attention is given to the interrelated issues of data collection, experimental design, and model application including model development and analysis. Examples are given of current clinical problems which can be examined via modeling, and important issues related to model adaptation to the clinical setting.

Abstract Different concepts define species at the pattern-level grouping of organisms into discrete clusters, the level of the processes operating within and between populations leading to the formation and maintenance of these clusters, or the level of the inner-organismic genetic and molecular mechanisms that contribute to species cohesion or promote speciation. I argue that, unlike single-level approaches, a multi-level framework takes into account the complex sequences of cause-effect reinforcements leading to the formation and maintenance of various patterns, and allows for (...) revisions and refinements of pattern-based characterizations in light of the gradual elucidation of the causes and mechanisms contributing to pattern formation and maintenance. Content Type Journal Article Category Regular Article Pages 1-17 DOI 10.1007/s10441-011-9143-z Authors Tudor M. Baetu, Department of Philosophy, University of Maryland, 1125D Skinner Building, College Park, MD 20742, USA Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342. (shrink)

The excessive and unsustainable exploitation of our marine resources has led to the promotion of marine reserves as a fisheries management tool. Marine reserves, areas in which fishing is restricted or prohibited, can offer opportunities for the recovery of exploited stock and fishery enhancement. This study examines the impact of the creation of marine protected areas, from both economic and biological perspectives. The consequences of reserve establishment on the long-run equilibrium fish biomass and fishery catch levels are evaluated. We include (...) reserve size as control variable to maximize catch at equilibrium. A continuous time model is used to simulate the effects of reserve size on fishing catch. Fish movements between the sites is assumed to take place at a faster time scale than the variation of the stock and the change of the fleet size. We take advantage of these two time scales to derive a reduced model governing the dynamics of the total fish stock and the fishing effort. Simulation results suggest that the establishment of a protected marine reserve will always lead to an increase in total fish biomass, an optimal size of a marine reserve can achieve to maximize the catch at equilibrium. (shrink)

How can an incomplete and uncertain model of the environment be used to perceive, infer, decide and act efficiently? This is the challenge that both living and artificial cognitive systems have to face. Symbolic logic is, by its nature, unable to deal with this question. The subjectivist approach to probability is an extension to logic that is designed specifically to face this challenge. In this paper, we review a number of frequently encountered cognitive issues and cast them into a common (...) Bayesian formalism. The concepts we review are ambiguities, fusion, multimodality, conflicts, modularity, hierarchies and loops. First, each of these concepts is introduced briefly using some examples from the neuroscience, psychophysics or robotics literature. Then, the concept is formalized using a template Bayesian model. The assumptions and common features of these models, as well as their major differences, are outlined and discussed. (shrink)

Abstract Vision substitution by electro-stimulation has been studied since the 60s beginning with P. Bach-y-Rita. Camera pictures or movies encoded in gray levels are displayed using an electro-stimulation display device on the surface of a body part, such as the skin or the tongue. Medical-technical devices have been developed on this principle to compensate for sensory-motor disabilities such as blindness or loss of balance, or to guide specific actions, such as surgery. However, the electrical signals of stationary or moving slowly (...) moving objects, displayed on a Tongue display unit (TDU), are quickly lost due to saturation of receptors undergoing electrostimulation. We propose to add random saccades or sparkle to the displayed visual scene to increase the quality of pattern recognition by the subjects. In the present experimental trimodal study (normal vision, TDU vision substitution, or both), we show that the presence of a moderate sparkle level enhances the perception of the direction of lines drawn on a TDU and reduces the response time. Content Type Journal Article Category Regular Article Pages 1-13 DOI 10.1007/s10441-012-9148-2 Authors Abdessalem Chekhchoukh, AGIM Laboratory (Laboratory of AGeing Imaging and Modeling), University of Grenoble, CNRS FRE 3405, Domaine de la Merci, 38700 La Tronche, France Nicolas Glade, AGIM Laboratory (Laboratory of AGeing Imaging and Modeling), University of Grenoble, CNRS FRE 3405, Domaine de la Merci, 38700 La Tronche, France Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342. (shrink)

Abstract We provide a mathematical study of a model of energy metabolism and hemodynamics of glioma allowing a better understanding of metabolic modifications leading to anaplastic transformation from low grade glioma.This mathematical analysis allows ultimately to unveil the solution to a viability problem which seems quite pertinent for applications to medecine. Content Type Journal Article Category Regular Article Pages 1-9 DOI 10.1007/s10441-012-9157-1 Authors R. Costalat, UPMC, UMI 209, UMMISCO, University of Paris-6, 75005 Paris, France J.-P. Francoise, Laboratoire Jacques–Louis Lions, UMR (...) 7598 CNRS, Université P.-M. Curie, Paris 6, 4 Pl. Jussieu, 16-26, 75252 Paris, France C. Menuel, Inserm U678, Functional Imaging Laboratory, Department of Neuroradiology, Pitiè-Sapêtrière Hospital, Université P.-M. Curie, Paris 6, 4783, boulevard de l’Hôpital, 75651 Paris Cedex 13, France M. Lahutte, Hopital des Armées, Val-de-Grâce, Service de Radiologie, 74 Bd de Port-Royal, 75005 Paris, France J.-N. Vallée, Department of Neuroradiology, Amiens University Medical Center, University of Picardie-Jules Vernes, chemin du Thil, 80025 Amiens, France G. de Marco, Laboratoire contrôle moteur et mouvement, UFR STAPS, Paris X, 200, avenue de la République, 92001 Nanterre, France J. Chiras, Inserm U678, Functional Imaging Laboratory, Department of Neuroradiology, Pitiè-Sapêtrière Hospital, Université P.-M. Curie, Paris 6, 4783, boulevard de l’Hôpital, 75651 Paris Cedex 13, France R. Guillevin, Inserm U678, Functional Imaging Laboratory, Department of Neuroradiology, Pitiè-Sapêtrière Hospital, Université P.-M. Curie, Paris 6, 4783, boulevard de l’Hôpital, 75651 Paris Cedex 13, France Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342. (shrink)

Abstract Angiogenesis is a complex morphogenetic process regulated by growth factors, but also by the force balance between endothelial cells (EC) traction stresses and extracellular matrix (ECM) viscoelastic resistance. Studies conducted with in vitro angiogenesis assays demonstrated that decreasing ECM stiffness triggers an angiogenic switch that promotes organization of EC into tubular cords or pseudo-capillaries. Thus, mechano-sensitivity of EC with regard to proteases secretion, and notably matrix metalloproteinases (MMPs), should likely play a pivotal role in this switching mechanism. While most (...) studies analysing strain regulation of MMPs used cell cultured on stretched membranes, this work focuses on MMP expression during self-assembly of EC into capillary-like structures within fibrin gels, i.e. on conditions that mimics more closely the in vivo cellular mechanical microenvironment. The activity of MMP-2 and MMP-9, two MMPs that have a pivotal role in capillaries formation, has been monitored in pace with the progressive elongation of EAhy926 cells that takes place during the emergence of cellular cords. We found an increase of the zymogen proMMP-2 that correlates with the initial stages of EC cords formation. However, MMP-2 was not detected. ProMMP-9 secretion decreased, with levels of MMP-9 kept at a rather low value. In order to analyse more precisely the observed differences of EAhy926 response on fibrin and plastic substrates, we proposed a theoretical model of the mechano-regulation of proMMP-2 activation in the presence of type 2 tissue inhibitor of MMPs (TIMP-2). Using association/dissociation rates experimentally reported for this enzymatic network, the model adequately describes the synergism of proMMP-2 and TIMP-2 strain activation during pseudo-capillary morphogenesis. All together, these results provide a first step toward a systems biology approach of angiogenesis mechano-regulation by cell-generated extracellular stresses and strains. Content Type Journal Article Category Regular Article Pages 1-20 DOI 10.1007/s10441-012-9147-3 Authors Minh-Uyen Dao Thi, Faculté de Médecine de Grenoble, DyCTiM team, UJF-Grenoble 1, CNRS, Laboratoire TIMC-IMAG UMR 5525, 38041 Grenoble, France Candice Trocmé, BEP/DBTP, CHU Albert Michallon, BP 217, 38043 Grenoble Cedex 9, France Marie-Paule Montmasson, Faculté de Médecine de Grenoble, DyCTiM team, UJF-Grenoble 1, CNRS, Laboratoire TIMC-IMAG UMR 5525, 38041 Grenoble, France Eric Fanchon, Faculté de Médecine de Grenoble, BCM team, UJF-Grenoble 1, CNRS, Laboratoire TIMC-IMAG UMR 5525, 38041 Grenoble, France Bertrand Toussaint, BEP/DBTP, CHU Albert Michallon, BP 217, 38043 Grenoble Cedex 9, France Philippe Tracqui, Faculté de Médecine de Grenoble, DyCTiM team, UJF-Grenoble 1, CNRS, Laboratoire TIMC-IMAG UMR 5525, 38041 Grenoble, France Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342. (shrink)

We give in this paper indications about the dynamical impact (as phenotypic changes) coming from the main sources of perturbation in biological regulatory networks. First, we define the boundary of the interaction graph expressing the regulations between the main elements of the network (genes, proteins, metabolites, ...). Then, we search what changes in the state values on the boundary could cause some changes of states in the core of the system (robustness to boundary conditions). After, we analyse the role of (...) the mode of updating (sequential, block sequential or parallel) on the asymptotics of the network, essentially on the occurrence of limit cycles (robustness to updating methods). Finally, we show the influence of some topological changes (e.g. suppression or addition of interactions) on the dynamical behaviour of the system (robustness to topology perturbations). (shrink)

The genetic code has evolved from its initial non-degenerate wobble version until reaching its present state of degeneracy. By using the stereochemical hypothesis, we revisit the problem of codon assignations to the synonymy classes of amino-acids. We obtain these classes with a simple classifier based on physico-chemical properties of nucleic bases, like hydrophobicity and molecular weight. Then we propose simple RNA (or more generally XNA, with X for D, P or R) ring structures that present, overlap included, one and only (...) one codon by synonymy class as solutions of a combinatory variational problem. We compare these solutions to sequences of present RNAs considered as relics, with a high interspecific invariance, like invariant parts of tRNAs and micro-RNAs. We conclude by emphasizing some optimal properties of the genetic code. (shrink)

Abstract 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. Content Type Journal Article Category Regular Article Pages 1-7 DOI 10.1007/s10441-012-9158-0 Authors L. El Alaoui, Université Paris 13, C.N.R.S., U.M.R. 7539, L.A.G.A, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France J.-P. Francoise, Laboratoire Jacques-Louis Lions, UMR 7598 CNRS, Université P.-M. Curie, Paris 6, 4 Place Jussieu, 75252 Paris, France M. Landau, Laboratoire Jacques-Louis Lions, UMR 7598 CNRS, Université P.-M. Curie, Paris 6, 4 Place Jussieu, 75252 Paris, France Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342. (shrink)

We extend the concept that life is an informational phenomenon, at every level of organisation, from molecules to the global ecological system. According to this thesis: (a) living is information processing, in which memory is maintained by both molecular states and ecological states as well as the more obvious nucleic acid coding; (b) this information processing has one overall function—to perpetuate itself; and (c) the processing method is filtration (cognition) of, and synthesis of, information at lower levels to appear at (...) higher levels in complex systems (emergence). We show how information patterns, are united by the creation of mutual context, generating persistent consequences, to result in ‘functional information’. This constructive process forms arbitrarily large complexes of information, the combined effects of which include the functions of life. Molecules and simple organisms have already been measured in terms of functional information content; we show how quantification may be extended to each level of organisation up to the ecological. In terms of a computer analogy, life is both the data and the program and its biochemical structure is the way the information is embodied. This idea supports the seamless integration of life at all scales with the physical universe. The innovation reported here is essentially to integrate these ideas, basing information on the ‘general definition’ of information, rather than simply the statistics of information, thereby explaining how functional information operates throughout life. (shrink)

A simple numerical procedure is presented for the problem of estimating the parameters of models for the distribution of eggs oviposited in a host. The modelling is extended to incorporate both host density and time dependence to produce a remarkably parsimonious structure with only seven parameters to describe a data set of over 3,000 observations. This is further refined using a mixed model to accommodate several large outliers. Both models show that the level of superparasitism declines with increasing host density, (...) and the rate declines over time. It is proposed that the differing behaviours represented by the mixed model may reflect a balance between behavioural strategies of different selective benefit. (shrink)

The formal definition of species as explanatory hypotheses presented by Fitzhugh (Marine Biol 26:155–165, 2005a , b ) is emended. A species is an explanatory account of the occurrences of the same character(s) among gonochoristic or cross-fertilizing hermaphroditic individuals by way of character origin and subsequent fixation during tokogeny. In addition to species, biological systematics also employs hypotheses that are ontogenetic, tokogenetic, intraspecific, and phylogenetic, each of which provides explanatory hypotheses for distinctly different classes of causal questions. It is suggested (...) that species hypotheses can not be applied to organisms with obligate asexual, parthenogenetic, and self-fertilizing modes of reproduction. Hypotheses explaining shared characters among such organisms are, instead, strictly phylogenetic. Several implications of this emended definition are examined, especially the relations between species, intraspecific, and phylogenetic hypotheses, as well as the limitations of species names to be applied to temporally different characters within populations. (shrink)

Morphogenesis is a key process in developmental biology. An important issue is the understanding of the generation of shape and cellular organisation in tissues. Despite of their great diversity, morphogenetic processes share common features. This work is an attempt to describe this diversity using the same formalism based on a cellular description. Tissue is seen as a multi-cellular system whose behaviour is the result of all constitutive cells dynamics. Morphogenesis is then considered as a spatiotemporal organization of cells activities. We (...) show how this formalism relies on Reaction–Diffusion/Positional Information approach and how it permits to generalize its modelling possibilities. Three quite different applications for concrete morphogenetic processes are presented. The first one is a model for epithelial invagination, the second is a model of cellular differentiation by local cell–cell signalling. The last example is the secondary radial growth of conifer trees. From the mathematical point of view, different modelling tools are used according to the specificity of each process. (shrink)

Abstract Microtubules, major elements of the cell skeleton are, most of the time, well organized in vivo, but they can also show self-organizing behaviors in time and/or space in purified solutions in vitro. Theoretical studies and models based on the concepts of collective dynamics in complex systems, reaction–diffusion processes and emergent phenomena were proposed to explain some of these behaviors. In the particular case of microtubule spatial self-organization, it has been advanced that microtubules could behave like ants, self-organizing by ‘talking (...) to each other’ by way of hypothetic (because never observed) concentrated chemical trails of tubulin that are expected to be released by their disassembling ends. Deterministic models based on this idea yielded indeed like-looking spatio-temporal self-organizing behaviors. Nevertheless the question remains of whether microscopic tubulin trails produced by individual or bundles of several microtubules are intense enough to allow microtubule self-organization at a macroscopic level. In the present work, by simulating the diffusion of tubulin in microtubule solutions at the microscopic scale, we measure the shape and intensity of tubulin trails and discuss about the assumption of microtubule self-organization due to the production of chemical trails by disassembling microtubules. We show that the tubulin trails produced by individual microtubules or small microtubule arrays are very weak and not elongated even at very high reactive rates. Although the variations of concentration due to such trails are not significant compared to natural fluctuations of the concentration of tubuline in the chemical environment, the study shows that heterogeneities of biochemical composition can form due to microtubule disassembly. They could become significant when produced by numerous microtubule ends located in the same place. Their possible formation could play a role in certain conditions of reaction. In particular, it gives a mesoscopic basis to explain the collective dynamics observed in excitable microtubule solutions showing the propagation of concentration waves of microtubules at the millimeter scale, although we doubt that individual microtubules or bundles can behave like molecular ants. Content Type Journal Article Category Regular Article Pages 1-28 DOI 10.1007/s10441-012-9149-1 Authors Nicolas Glade, AGIM Laboratory, Laboratory of AGeing Imaging and Modeling, University of Grenoble, CNRS FRE 3405, Domaine de la Merci, 38700 La Tronche, France Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342. (shrink)

Dobzhansky argued that biology only makes sense if life on earth has a shared history. But his dictum is often reinterpreted to mean that biology only makes sense in the light of adaptation. Some philosophers of science have argued in this spirit that all work in ‘proximal’ biosciences such as anatomy, physiology and molecular biology must be framed, at least implicitly, by the selection histories of the organisms under study. Others have denied this and have proposed non-evolutionary ways in which (...) biologists can frame these investigations. This paper argues that an evolutionary perspective is indeed necessary, but that it must be a forward-looking perspective informed by a general understanding of the evolutionary process, not a backward-looking perspective informed by the specific evolutionary history of the species being studied. Interestingly, it turns out that there are aspects of proximal biology that even a creationist cannot study except in the light of a theory of their effect on future evolution. (shrink)

Hypoxia hampers ATP production and threatens cell survival. Since cellular energetics tightly controls cell responses and fate, ATP levels and dynamics are of utmost importance. An integrated mathematical model of ATP synthesis by the mitochondrial oxidative phosphorylation/electron transfer chain system has been recently published (Beard, PLoS Comput Biol 1(4):e36, 2005). This model was validated under static conditions. To evaluate its performance under dynamical situations, we implemented and simulated it (Simulink®, The Mathworks). Inner membrane potential (ΔΨ) and [NADH] (feeding the electron (...) transfer chain) were used as indicators of mitochondrial function. Root mean squared error (rmse) was used to compare simulations and experiments (isolated cardiac mitochondria, Bose et al. J Biol Chem 278(40):39155–39165, 2003). Steady-state experimental data were reproduced within 2–6%. Model dynamics were evaluated under: (i) baseline, (ii) activation of NADH production, (iii) addition of ADP, (iv) addition of inorganic phosphate, (v) oxygen exhaustion. In all phases, except the last one, ΔΨ and [NADH] as well as oxygen consumption, were reproduced (within 10, 7 and 12%, respectively). Under anoxia, simulated ΔΨ markedly depolarized (no change in experiments). In conclusion, the model reproduces dynamic data as long as oxygen is present. Anticipated improvement by the inclusion of ATP consumption and explicit Krebs cycle are under evaluation. (shrink)

Cancer is a complex disease, necessitating research on many different levels; at the subcellular level to identify genes, proteins and signaling pathways associated with the disease; at the cellular level to identify, for example, cell-cell adhesion and communication mechanisms; at the tissue level to investigate disruption of homeostasis and interaction with the tissue of origin or settlement of metastasis; and finally at the systems level to explore its global impact, e.g. through the mechanism of cachexia. Mathematical models have been proposed (...) to identify key mechanisms that underlie dynamics and events at every scale of interest, and increasing effort is now being paid to multi-scale models that bridge the different scales. With more biological data becoming available and with increased interdisciplinary efforts, theoretical models are rendering suitable tools to predict the origin and course of the disease. The ultimate aims of cancer models, however, are to enlighten our concept of the carcinogenesis process and to assist in the designing of treatment protocols that can reduce mortality and improve patient quality of life. Conventional treatment of cancer is surgery combined with radiotherapy or chemotherapy for localized tumors or systemic treatment of advanced cancers, respectively. Although radiation is widely used as treatment, most scheduling is based on empirical knowledge and less on the predictions of sophisticated growth dynamical models of treatment response. Part of the failure to translate modeling research to the clinic may stem from language barriers, exacerbated by often esoteric model renderings with inaccessible parameterization. Here we discuss some ideas for combining tractable dynamical tumor growth models with radiation response models using biologically accessible parameters to provide a more intuitive and exploitable framework for understanding the complexity of radiotherapy treatment and failure. (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)

Abstract In this paper we introduce a stochastic model for a population living and migrating between s sites without distinction in the states between residents and immigrants. The evolutionary stable strategies (ESS) is characterized by the maximization of a stochastic growth rate. We obtain that the expectation of reproductive values, normalized by some random quantity, are constant on all sites and that the expectation of the normalized vector population structure is proportional to eigenvector of the dispersion matrix associated to eigenvalue (...) one, which are, in some way, analogous to the results obtained in the deterministic case. Content Type Journal Article Category Regular Article Pages 1-11 DOI 10.1007/s10441-011-9142-0 Authors Mohamed Khaladi, Department of Mathematics, Faculty of Sciences, LMPDP and UMI UMMISCO, IRD-UPMC, 40001 Marrakesh, Morocco Jean-Dominique Lebreton, CEFE/CNRS, 1919 Route de Mende, 34293 Montpellier cedex 5, France Abdelaziz Khermjioui, Department of Mathematics, Faculty of Sciences, LMPDP and UMI UMMISCO, IRD-UPMC, 40001 Marrakesh, Morocco Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342. (shrink)

Deduction leads to causal explanation in phylogenetic inference when the evidence, the systematic character, is conceptualized as a transformation series. Also, the deductive entailment of modus tollens is satisfied when those kinds of events are operationalized as patristic difference. Arguments to the contrary are based largely on the premise that character-states are defined intensionally as objects, in terms of similarity relations. However, such relations leave biologists without epistemological access to the causal explanation and explanatory power of historical statements. Moreover, the (...) prediction-making to which those kinds of relations are limited in practice can lead to a category error—the mental conversion of an abstraction (the classes defined in terms of similarity relations) into a thing (such as an historical individual). The latter practices and problems characterize pattern cladistics, taxa being interpreted as homeostatic property cluster natural kinds, and other instrumentalist research programs. (shrink)

We consider a two-patch epidemiological system where individuals can move from one patch to another, and local interactions between the individuals within a patch are governed by the classical SIRS model. When the time-scale associated with migration is much smaller than the time-scale associated with infection, aggregation methods can be used to simplify the initial complete model formulated as a system of ordinary differential equations. Analysis of the aggregated model then shows that the two-patch basic reproduction rate is smaller than (...) the 1 patch one. We extend this result to a linear chain of P patches (P > 2). These results are illustrated by some examples for which numerical integration of the system of ordinary differential equations is performed. Simulations of an individual based model implemented with a multi-agent system are also carried out. (shrink)

WHO II low grade glioma evolves inevitably to anaplastic transformation. Magnetic resonance imaging is a good non-invasive way to watch it, by hemodynamic and metabolic modifications, thanks to multinuclear spectroscopy 1 H/ 31 P. In this work we study a multi-scale minimal model of hemodynamics and metabolism applied to the study of gliomas. This mathematical analysis leads us to a fast-slow system. The control of the position of the stationary point brings to the concept of domain of viability. Starting from (...) this system, the equations bring to light the parameters that push glioma cells out of their domain of viability. Four fundamental factors are highlighted. The first two are cerebral blood flow and the rate of lactate transport through monocarboxylate transporters, which must be reduced in order to push glioma out of its domain of viability. Another factor is the intra arterial lactate, which must be increased. The last factor is pH, indeed a decrease of intra cellular pH could interfere with glioma growth. These reflections suggest that these four parameters could lead to new therapeutic strategies for the management of low grade gliomas. (shrink)

In this paper, a mathematical model of the respiratory mechanics is used to reproduce experimental signal waveforms acquired from three newborn lambs. As the main challenge is to determine specific lamb parameters, a sensitivity analysis has been realized to find the most influent parameters, which are identified using an evolutionary algorithm. Results show a close match between experimental and simulated pressure and flow waveforms obtained during spontaneous ventilation and pleural pressure variations acquired during the application of positive pressure, since root (...) mean square errors equal to 0.0119, 0.0052 and 0.0094. The identified parameters were discussed in light of previous knowledge of respiratory mechanics in the newborn. (shrink)

In this work a mechanistic explanation of the classical algae growth model built by M. R. Droop in the late sixties is proposed. We first recall the history of the construction of the “predictive” variable yield Droop model as well as the meaning of the introduced cell quota. We then introduce some theoretical hypotheses on the biological phenomena involved in nutrient storage by the algae that lead us to a “conceptual” model. Though more complex than Droop’s one, our model remains (...) accessible to a complete mathematical study: its confrontation to the Droop model shows both have the same asymptotic behavior. However, while Droop’s cell quota comes from experimental bio-chemical measurements not related to intra-cellular biological phenomena, its analogous in our model directly follows our theoretical hypotheses. This new model should then be looked at as a re-interpretation of Droop’s work from a theoretical biologist’s point of view. (shrink)

It is argued that multiscale approaches are necessary for an explanatory modeling of biological systems. A first step, besides common to the multiscale modeling of physical and living systems, is a bottom-up integration based on the notions of effective parameters and minimal models. Top-down effects can be accounted for in terms of effective constraints and inputs. Biological systems are essentially characterized by an entanglement of bottom-up and top-down influences following from their evolutionary history. A self-consistent multiscale scheme is proposed to (...) capture the ensuing circular causality. Its differences with standard mean-field self-consistent equations and slow-fast decompositions are discussed. As such, this scheme offers a way to unravel the multilevel architecture of living systems and their regulation. Two examples, genome functions and biofilms, are detailed. (shrink)

We examine three critical aspects of Popper’s formulation of the ‘ Logic of Scientific Discovery ’—evidence, content and degree of corroboration—and place these concepts in the context of the Tree of Life (ToL) problem with particular reference to molecular systematics. Content, in the sense discussed by Popper, refers to the breadth and scope of existence that a hypothesis purports to explain. Content, in conjunction with the amount of available and relevant evidence, determines the testability, or potential degree of corroboration, of (...) a statement; content distinguishes scientific hypotheses from metaphysical assertions. Degree of corroboration refers to the relative and tentative confidence assigned to one hypothesis over another, based upon the performance of each under critical tests. Here we suggest that systematists attempt to maximize content and evidence to increase the potential degree of corroboration in all phylogenetic endeavors. Discussion of this “total evidence” approach leads to several interesting conclusions about generating ToL hypotheses. (shrink)

Apoptosis proteins play an essential role in regulating a balance between cell proliferation and death. The successful prediction of subcellular localization of apoptosis proteins directly from primary sequence is much benefited to understand programmed cell death and drug discovery. In this paper, by use of Chou’s pseudo amino acid composition (PseAAC), a total of 317 apoptosis proteins are predicted by support vector machine (SVM). The jackknife cross-validation is applied to test predictive capability of (...) proposed method. The predictive results show that overall prediction accuracy is 91.1% which is higher than previous methods. Furthermore, another dataset containing 98 apoptosis proteins is examined by proposed method. The overall predicted successful rate is 92.9%. (shrink)

The goal of this paper is to encourage a reconfiguration of the discussion about typology in biology away from the metaphysics of essentialism and toward the epistemology of classifying natural phenomena for the purposes of empirical inquiry. First, I briefly review arguments concerning ‘typological thinking’, essentialism, species, and natural kinds, highlighting their predominantly metaphysical nature. Second, I use a distinction between the aims, strategies, and tactics of science to suggest how a shift from metaphysics to epistemology might be accomplished. Typological (...) thinking can be understood as a scientific tactic that involves representing natural phenomena using idealizations and approximations, which facilitates explanation, investigation, and theorizing via abstraction and generalization. Third, a variety of typologies from different areas of biology are introduced to emphasize the diversity of this representational reasoning. One particular example is used to examine how there can be epistemological conflict between typology and evolutionary analysis. This demonstrates that alternative strategies of typological thinking arise due to the divergent explanatory goals of researchers working in different disciplines with disparate methodologies. I conclude with several research questions that emerge from an epistemological reconfiguration of typology. (shrink)

Abstract In this work we deal with a general class of spatially distributed periodic SIS epidemic models with two time scales. We let susceptible and infected individuals migrate between patches with periodic time dependent migration rates. The existence of two time scales in the system allows to describe certain features of the asymptotic behavior of its solutions with the help of a less dimensional, aggregated , system. We derive global reproduction numbers governing the general spatially distributed nonautonomous system through the (...) aggregated system. We apply this result when the mass action law and the frequency dependent transmission law are considered. Comparing these global reproductive numbers to their non spatially distributed counterparts yields the following: adequate periodic migration rates allow global persistence or eradication of epidemics where locally, in absence of migrations, the contrary is expected. Content Type Journal Article Category Regular Article Pages 1-16 DOI 10.1007/s10441-011-9141-1 Authors M. Marvá, Dpto Matemáticas, Universidad de Alcalá, 28871 Madrid, Spain R. Bravo de la Parra, Dpto Matemáticas, Universidad de Alcalá, 28871 Madrid, Spain P. Auger, UR UMMISCO, IRD France Nord, 93143 Bondy, France Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342. (shrink)

In an instant classic paper (Lazebnik, in Cancer Cell 2(3); 2002 : 179–182) biologist Yuri Lazebnik deplores the poor effectiveness of the approach adopted by biologists to understand and “fix” biological systems. Lazebnik suggests that to remedy this state of things biologist should take inspiration from the approach used by engineers to design, understand, and troubleshoot technological systems. In the present paper I substantiate Lazebnik’s analysis by concretely showing how to apply the engineering approach to biological problems. I use an (...) actual example of electronic circuit troubleshooting to ground the thesis that, in engineering, the crucial phases of any non-trivial troubleshooting process are aimed at generating a mechanistic explanation of the functioning of the system, which makes extensive recourse to problem-driven qualitative reasoning possibly based on cognitive artifacts applied to systems that are known to have been designed for function . To show how to translate these findings into biological practice I consider a concrete example of biological model building and “troubleshooting”, aimed at the identification of a “fix” for the human immune system in presence of progressing cancer, autoimmune disease, and transplant rejection. The result is a novel immune system model—the danger model with regulatory cells— and new, original hypotheses concerning the development, prophylaxis, and therapy of these unwanted biological processes. Based on the manifest efficacy of the proposed approach, I suggest a refocusing of the activity of theoretical biologists along the engineering-inspired lines illustrated in the paper. (shrink)

Sickle cell haemoglobin (HbS) polymerization reduces erythrocyte deformability, causing deleterous vaso-occlusions. The double-nucleation model states that polymers grow from HbS aggregates, the nuclei, (i) in solution (homogeneous nucleation), (ii) onto existing polymers (heterogeneous nucleation). When linearized at initial HbS concentration, this model predicts early polymerization and its characteristic delay-time (Ferrone et al. J Mol Biol 183(4):591–610, 611–631, 1985). Addressing its relevance for describing complete polymerization, we constructed the full, non-linearized model (Simulink®, The MathWorks). Here, we compare the simulated outputs to (...) experimental progress curves (n = 6–8 different [HbS], 3–6 mM range, from Ferrone’s group). Within 10% from start, average root mean square (rms) deviation between simulated and experimental curves is 0.04 ± 0.01 (25°C, n = 8; mean ± standard error). Conversely, for complete progress curves, averaged rms is 0.48 ± 0.04. This figure is improved to 0.13 ± 0.01 by adjusting heterogeneous pathway parameters (p 2 μ cc : + 40%), and the fraction of polymer surface available for nucleation (ϕ), from 5e−7, (3 mM) to 13 (6 mM). Similar results are obtained at 37°C. We conclude that the physico-chemical description of heterogeneous nucleation warrants refinements in order to capture the whole HbS polymerization process. (shrink)

Proceeding of the Third International Conference of the French-Speaking Society for Theoretical Biology Content Type Journal Article Category Editorial Pages 1-2 DOI 10.1007/s10441-012-9156-2 Authors Slimane Ben Miled, ENIT-LAMSIN, Tunis el Manar University, 13, place Pasteur, Belvédère, B.P. 74, 1002 Tunis, Tunisia Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342.

We consider metabolic networks with reversible enzymatic reactions. The model is written as a system of ordinary differential equations, possibly with inputs and outputs. We prove the global stability of the equilibrium (if it exists), using techniques of monotone systems and compartmental matrices. We show that the equilibrium does not always exist. Finally, we consider a metabolic system coupled with a genetic network, and we study the dependence of the metabolic equilibrium (if it exists) with respect to concentrations of enzymes. (...) We give some conclusions concerning the dynamical behavior of coupled genetic/metabolic systems. (shrink)

Optimal foraging theory has been criticized for underestimating patch exploitation time. However, proper modeling of costs not only answers these criticisms, but it also explains apparently irrational behaviors like the sunk-cost effect. When a forager is sure to experience high initial costs repeatedly, the forager should devote more time to exploitation than searching in order to minimize the accumulation of said costs. Thus, increased recognition or reconnaissance costs lead to increased exploitation times in order to reduce the frequency of future (...) costs, and this result can be used to explain paradoxical human preference for higher costs. In fact, this result also provides an explanation for how continuing a very costly task indefinitely provides the optimal long-term rate of gain; the entry cost of each new task is so great that the forager avoids ever returning to search. In general, apparently irrational decisions may be optimal when considering the lifetime of a forager within a larger system. (shrink)

Conservation Biologists have found that demographic stochasticity causes the mean time to extinction to increase exponentially with population size. This has proved helpful in analyses determining extinction times and characterizing the pathway to extinction. The aim of this investigation is to explore the possible interactions between environmental/demographic noises and the scaling effect of the mean population size with its variance, which is expected to follow Taylor’s power law relationship. We showed that the combined effects of environmental/demographic noises and the scaling (...) of population size variability interact with the population dynamics and affect the mean time to extinction. (shrink)

The influence of sediment oxygen heterogeneity, due to bioturbation, on diffusive oxygen flux was investigated. Laboratory experiments were carried out with 3 macrobenthic species presenting different bioturbation behaviour patterns: the polychaetes Nereis diversicolor and Nereis virens, both constructing ventilated galleries in the sediment column, and the gastropod Cyclope neritea, a burrowing species which does not build any structure. Oxygen two-dimensional distribution in sediments was quantified by means of the optical planar optode technique. Diffusive oxygen fluxes (mean and integrated) and a (...) variability index were calculated on the captured oxygen images. All species increased sediment oxygen heterogeneity compared to the controls without animals. This was particularly noticeable with the polychaetes because of the construction of more or less complex burrows. Integrated diffusive oxygen flux increased with oxygen heterogeneity due to the production of interface available for solute exchanges between overlying water and sediments. This work shows that sediment heterogeneity is an important feature of the control of oxygen exchanges at the sediment–water interface. (shrink)

In this paper we build a prey–predator model with discrete weight structure for the predator. This model will conserve the number of individuals and the biomass and both growth and reproduction of the predator will depend on the food ingested. Moreover the model allows cannibalism which means that the predator can eat the prey but also other predators. We will focus on a simple version with two weight classes or stage (larvae and adults) and present some general mathematical results. In (...) the last part, we will assume that the dynamics of the prey is fast compared to the predator’s one to go further in the results and eventually conclude that under some conditions, cannibalism can stabilize the system: more precisely, an unstable equilibrium without cannibalism will become almost globally stable with some cannibalism. Some numerical simulations are done to illustrate this result. (shrink)

Elliott Sober: Did Darwin Write the Origin Backwards? Philosophical Essays on Darwin’s Theory Content Type Journal Article Category Book Review Pages 1-6 DOI 10.1007/s10441-012-9151-7 Authors Raphael Scholl, History and Philosophy of Science, Institute of Philosophy, University of Bern, Länggassstr. 49a, 3012 Bern, Switzerland Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342.

I attempt to raise questions regarding elements of systematics—primarily in the realm of phylogenetic reconstruction—in order to provoke discussion on the current state of affairs in this discipline, and also evolutionary biology in general: e.g., conceptions of homology and homoplasy, hypothesis testing, the nature of and objections to Hennigian “phylogenetic systematics”, and the schism between (neo)Darwinian descendants of the “modern evolutionary synthesis” and their supposed antagonists, cladists and punctuationalists.

Previous studies have demonstrated that double phosphorylation of a protein can lead to bistability if some conditions are fulfilled. It was also shown that the signaling behavior of a covalent modification cycle can be quantitatively and, more importantly, qualitatively modified when this cycle is coupled to a signaling pathway as opposed to being isolated. This property was named retroactivity. These two results are studied together in this paper showing the existence of interesting phenomena—oscillations and bistability—in signaling cascades possessing at least (...) one stage with a double-phosphorylation cycle as in MAPK cascades. (shrink)

We study the SIS and SIRI epidemic models discussing different approaches to compute the thresholds that determine the appearance of an epidemic disease. The stochastic SIS model is a well known mathematical model, studied in several contexts. Here, we present recursively derivations of the dynamic equations for all the moments and we derive the stationary states of the state variables using the moment closure method. We observe that the steady states give a good approximation of the quasi-stationary states of the (...) SIS model. We present the relation between the SIS stochastic model and the contact process introducing creation and annihilation operators. For the spatial stochastic epidemic reinfection model SIRI, where susceptibles S can become infected I, then recover and remain only partial immune against reinfection R, we present the phase transition lines using the mean field and the pair approximation for the moments. We use a scaling argument that allow us to determine analytically an explicit formula for the phase transition lines in pair approximation. (shrink)

Abstract The presence of gene–environment statistical interaction ( G x E ) and correlation ( rGE ) in biological development has led both practitioners and philosophers of science to question the legitimacy of heritability estimates. The paper offers a novel approach to assess the impact of G x E and rGE on the way genetic and environmental causation can be partitioned. A probabilistic framework is developed, based on a quantitative genetic model that incorporates G x E and rGE , offering (...) a rigorous way of interpreting heritability estimates. Specifically, given an estimate of heritability and the variance components associated with estimates of G x E and rGE , I arrive at a probabilistic account of the relative effect of genes and environment. Content Type Journal Article Category Regular Article Pages 1-13 DOI 10.1007/s10441-011-9139-8 Authors Omri Tal, School of Philosophy and The Cohn Institute for the History and Philosophy of Science and Ideas, Tel Aviv University, Tel Aviv, 69978 Israel Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342. (shrink)

Toxic plants have been used for years in agriculture to control major crop pests. However, the continuous exposure of targeted pests to toxins dramatically increases the rate of resistance evolution (Gassman et al. in Annu Rev Entomol 54:147–163, 2009a ; Tabashnik et al. Nat Biotechnol 26:199–202, 2008 ). To prevent or delay resistance, non toxic host plants can be used as refuges. Our study considers spatial and temporal refuges that are respectively implemented concurrently or alternatively a toxic crop. A conceptual (...) model based on impulsive differential equations is proposed to describe the dynamics of the susceptible and resistant pest populations over time. The mathematical study enlightens threshold values of the proportion of the spatial refuge and key parameters that should help to understand evolution of pest resistance to toxic crop. (shrink)

Abstract Flax seedlings grown in the absence of environmental stimuli, stresses and injuries do not form epidermal meristems in their hypocotyls. Such meristems do form when the stimuli are combined with a transient depletion of calcium. These stimuli include the “manipulation stimulus” resulting from transferring the seedlings from germination to growth conditions. If, after a stimulus, calcium depletion is delayed, meristem production is also delayed; in other words, the meristem-production instruction can be memorised. Memorisation includes both storage and recall of (...) information. Here, we focus on information recall. We show that if the first transient calcium depletion is followed by a second transient depletion there is a new round of meristem production. We also show that if an excess of calcium follows calcium depletion, meristem production is blocked; but if the excess of calcium is in turn followed by another calcium depletion, again there is a new round of meristem production. The same stored information can thus be recalled repeatedly (at least twice). We describe a conceptual model that takes into account these findings. Content Type Journal Article Category Regular Article Pages 1-15 DOI 10.1007/s10441-012-9145-5 Authors Marie-Claire Verdus, Laboratoire AMMIS (Assemblages Moléculaires, Modélisation et Imagerie SIMS), CNRS (GDR DYCOEC), Faculté des Sciences et Techniques, Université de Rouen, 76821 Mont-Saint-Aignan Cedex, France Camille Ripoll, Laboratoire AMMIS (Assemblages Moléculaires, Modélisation et Imagerie SIMS), CNRS (GDR DYCOEC), Faculté des Sciences et Techniques, Université de Rouen, 76821 Mont-Saint-Aignan Cedex, France Vic Norris, Laboratoire AMMIS (Assemblages Moléculaires, Modélisation et Imagerie SIMS), CNRS (GDR DYCOEC), Faculté des Sciences et Techniques, Université de Rouen, 76821 Mont-Saint-Aignan Cedex, France Michel Thellier, Laboratoire AMMIS (Assemblages Moléculaires, Modélisation et Imagerie SIMS), CNRS (GDR DYCOEC), Faculté des Sciences et Techniques, Université de Rouen, 76821 Mont-Saint-Aignan Cedex, France Journal Acta Biotheoretica Online ISSN 1572-8358 Print ISSN 0001-5342. (shrink)

Despite the amount of work that has been produced on the subject over the years, the ‘transformation of cladistics’ is still a misunderstood episode in the history of comparative biology. Here, I analyze two outstanding, highly contrasting historiographic accounts on the matter, under the perspective of an influential dichotomy in the philosophy of science: the opposition between Scientific Realism and Empiricism. Placing special emphasis on the notion of ‘causal grounding’ of morphological characters ( sensu Olivier Rieppel) in modern developmental biology’s (...) (mechanistic) theories, I arrive at the conclusion that a ‘new transformation of cladistics’ is philosophically plausible. This ‘reformed’ understanding of ‘pattern cladistics’ entails retaining the interpretation of cladograms as ‘schemes of synapomorphies’, but in association to construing cladogram nodes as ‘developmental-genetic taxic homologies’, instead of ‘standard Darwinian ancestors’. The reinterpretation of pattern cladistics presented here additionally proposes to take Bas Van Fraassen’s ‘constructive empiricism’ as a philosophical stance that could properly support such analysis of developmental-genetic data for systematic purposes. The latter suggestion is justified through a reappraisal of previous ideas developed by prominent pattern cladists (mainly, Colin Patterson), which concerned a scientifically efficient ‘observable/non-observable distinction’ linked to the conceptual pair ‘ontogeny and phylogeny’. Finally, I argue that a robust articulation of Antirealist alternatives in systematics may provide a rational basis for its disciplinary separation from evolutionary biology, as well as for a critical reconsideration of the proper role of certain Scientific Realist positions, currently popular in comparative biology. (shrink)

In this work, we compare two global approaches which are usually considered as completely unconnected one with the other. The former is Thom’s topology and the latter is Jung’s psychology. More precisely, it seemed to us interesting to adapt some morphologies of Thom’s catastrophe theory to some Jung’s notions. Thus, we showed that the swallowtail, which is one of these morphologies, was able to describe geometrically the structural organisation of the psyche according to Jung, with its collective unconscious, personal unconscious (...) and conscious. Moreover, we have correlated this morphology with Jung’s evolutive processes like individualisation and individuation. These comparisons incited us to think that some morphologies of Thom’s catastrophe theory are the geometrical dealing of Jung’s archetypes. (shrink)

The development of comparative biology (systematics) has been of interest to philosophers and historians. Particular attention has been placed on the ‘war’ of the 1970s and 1980s, the apparent dispute among those who preferred this or that methodology. In this contribution we examine the history of comparative biology from the perspective of fundamentals rather than methodologies. Our examination is framed within the artificial—natural classification dichotomy, a viewpoint currently lost from view but (...) worth resurrecting. (shrink)

Matrix models are widely used in biology to predict the temporal evolution of stage-structured populations. One issue related to matrix models that is often disregarded is the sampling variability. As the sample used to estimate the vital rates of the models are of finite size, a sampling error is attached to parameter estimation, which has in turn repercussions on all the predictions of the model. In this study, we address the question of building confidence bounds around the predictions of matrix (...) models due to sampling variability. We focus on a density-dependent Usher model, the maximum likelihood estimator of parameters, and the predicted stationary stage vector. The asymptotic distribution of the stationary stage vector is specified, assuming that the parameters of the model remain in a set of the parameter space where the model admits one unique equilibrium point. Tests for density-dependence are also incidentally provided. The model is applied to a tropical rain forest in French Guiana. (shrink)