Theory in Biosciences

In this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results.

We consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of neurons, which Green's function does not...

The multilevel model of behavioral selection (MLBS) by Borgstede and Eggert (Behav Process 186:104370. 10.1016/j.beproc.2021.104370 , 2021) provides a formal framework that integrates reinforcement learning with natural selection using an extended Price equation. However, the MLBS is so far only formulated for homogeneous populations, thereby excluding all sources of variation between individuals. This limitation is of primary theoretical concern because any application of the MLBS to real data requires to account for variation between individuals...

A two-patch logistic metapopulation model is investigated both analytically and numerically focusing on the impact of dispersal on population dynamics. First, the dependence of the global dynamics on the stability type of the full extinction equilibrium point is tackled. Then, the behaviour of the total population with respect to the dispersal is studied analytically. Our findings demonstrate that diffusion plays a crucial role in the preservation of both subpopulations and the full metapopulation under the presence of stochastic perturbations...

Mathematical models of cancer and bacterial evolution have generally stemmed from a gene-centric framework, assuming clonal evolution via acquisition of resistance-conferring mutations and selection of their corresponding subpopulations. More recently, the role of phenotypic plasticity has been recognized and models accounting for phenotypic switching between discrete cell states (e.g., epithelial and mesenchymal) have been developed. However, seldom do models incorporate both plasticity and mutationally driven resistance, particularly when the state space is continuous and resistance evolves in a continuous fashion...

In 1913, the geneticist William Bateson called for a halt in studies of genetic phenomena until evolutionary fundamentals had been sufficiently addressed at the molecular level. Nevertheless, in the 1960s, the theoretical population geneticists celebrated a "modern synthesis" of the teachings of Mendel and Darwin, with an exclusive role for natural selection in speciation. This was supported, albeit with minor reservations, by historians Mark Adams and William Provine, who taught it to generations of students...

In recent years, some scholars have explicitly questioned the desirability or utility of applying the classical and "old-fashioned" theories of scientific change by the likes of Karl Popper and Thomas S. Kuhn to the question of the precise nature and significance of the extended evolutionary synthesis (EES). Supposedly, these twentieth-century philosophers are completely irrelevant for a better understanding of this new theoretical framework for the study of evolution. Here, it will be argued that the EES can be fruitfully interpreted in terms of, as yet, insufficiently considered or even overlooked elements from Kuhn's theory...

Counting transcripts of mRNA are a key method of observation in modern biology. With advances in counting transcripts in single cells (single-cell RNA sequencing or scRNA-seq), these data are routinely used to identify cells by their transcriptional profile, and to identify genes with differential cellular expression. Because the total number of transcripts counted per cell can vary for technical reasons, the first step of many commonly used scRNA-seq workflows is to normalize by sequencing depth, transforming counts into proportional abundances...

We study the dynamics of a discrete model with two different stages of the population, the pre-adult stage governed by a Beverton-Holt-type map and the adult stage by a [Formula: see text]-Ricker map. The composition of both maps gives the dynamics. The existence of the Allee effect is easily observed. We check that the model can evolve from a sure extinction to complicated dynamics. The presence of an almost sure extinction is proved to exist when the dynamical complexity is the highest possible.

In this paper, we develop a network-based methodology to investigate the problems related to matrix stability and bifurcations in nonlinear dynamical systems. By matching a matrix with a network, i.e., interaction graph, we propose a new network-based matrix analysis method by proving a theorem about matrix determinant under which matrix stability can be considered in terms of feedback loops. Especially, the approach can tell us how a node, a path, or a feedback loop in the interaction graph affects matrix stability...

In our paper, we analyse the relationship of the evolutionary philosophy of Charles Sanders Peirce to Lamarckian natural philosophy and link it to concepts of teleology, focusing especially on Aristotelian and Peircean conceptions of the final cause. Peirce commented on evolution in many of his writings, especially in 1891-1893 in essays such as 'Evolutionary Love' (1893) or 'Man's Glassy Essence' (1892). After introducing the three types of evolution distinguished by Peirce, we compare Peirce's and Lamarck's views on evolution, habit, and teleology...

Two ideas are popular among biologists. The first idea is concerned with the biased nature of biology, especially the idea that biologists have overemphasized the importance of competition in the past. The second idea is concerned with progress in correcting for biases, namely, that the biased nature of biology decreases with time. To test these ideas, data on the popularity of interaction topics, such as competition, predation, and mutualism, was collected from articles published in biology journals. Research biases should be visible in publication data as systematic over- and underemphases regarding the popularity of alternative, viable research topics...

A biosemiotic approach to the interpretation of morphological data is apt to highlight morphological traits that have hitherto gone unnoticed for their crucial roles in intraspecific sign interpretation and communication processes. Examples of such traits include specific genital structures found in the haplogyne spiders Dysdera erythrina (Walckenaer 1802) and Dysdera crocata (Koch 1838). In both D. erythrina and D. crocata, the distal sclerite of the male bulb and the anterior diverticulum of the female endogyne exhibit a striking, previously unreported correspondence in size and shape, allowing for a precise match between these structures during copulation...

Methylation is an important epigenetic regulation of methylation genes that plays a crucial role in regulating biological processes. While traditional methods for detecting methylation in biological experiments are constantly improving, the development of artificial intelligence has led to the emergence of deep learning and machine learning methods as a new trend. However, traditional machine learning-based methods rely heavily on manual feature extraction, and most deep learning methods for studying methylation extract fewer features due to their simple network structures...

Rooted acyclic graphs appear naturally when the phylogenetic relationship of a set X of taxa involves not only speciations but also recombination, horizontal transfer, or hybridization that cannot be captured by trees. A variety of classes of such networks have been discussed in the literature, including phylogenetic, level-1, tree-child, tree-based, galled tree, regular, or normal networks as models of different types of evolutionary processes. Clusters arise in models of phylogeny as the sets [Formula: see text] of descendant taxa of a vertex v...

This work concerns a many-body deterministic model that displays life-like properties such as emergence, complexity, self-organization, self-regulation, excitability and spontaneous compartmentalization. The model portraits the dynamics of an ensemble of locally coupled polar phase oscillators, moving in a two-dimensional space, that under certain conditions exhibit emergent superstructures. Those superstructures are self-organized dynamic networks, resulting from a synchronization process of many units, over length scales much greater than the interaction range...

Advancement of new technologies such as laser, focused ultrasound, microwave and radio frequency for thermal therapy of skin tissue has increased numerous challenging situations in medical treatment. In this article, a new meticulous bio-heat transfer model based on memory-dependent derivative with dual-phase-lag has been developed under different thermal conditions such as thermal shock and harmonic-type heating. Laplace transform method is acquired to perceive the analytical consequences. Quantitative results are evaluated for displacement, strain and temperature along with stress distributions in time domain by adopting the technique of inverse Laplace transform...

We consider a modified SIR model with a four-dimensional system of ordinary differential equations to consider the influence of a limited isolation capacity on the final epidemic size defined as the total number of individuals who experienced the disease at the end of an epidemic season. We derive the necessary and sufficient condition that the isolation reaches the capacity in a finite time on the way of the epidemic process, and show that the final epidemic size is monotonically decreasing in terms of the isolation capacity...

In this work, we analyse the dynamics of a five-dimensional hepatitis C virus infection mathematical model including the spatial mobility of hepatitis C virus particles, the transmission of hepatitis C virus infection by mitosis process of infected hepatocytes with logistic growth, time delays, antibody response and cytotoxic T lymphocyte (CTL) immune response with general incidence functions for both modes of infection transmission, namely virus-to-cell as well as cell-to-cell. Firstly, we prove rigorously the existence, the uniqueness, the positivity and the boundedness of the solution of the initial value and boundary problem associated with the new constructed model...

For this research, the properties of the logistic growth model for independent and coexisting species were used to set definitions for the possible regulation of one or two growth variables through their coupling parameters. The present analysis is done for the single-species Verhulst model without coupling, the single-species Verhulst model coupled with an exogenous signal, and the two-species Verhulst coexistence growth model which represents six different ecological regimes of interaction. The models' parameters, such as the intrinsic growth rate and the coupling, are defined...