Most mathematical modeling in biology relies either implicitly or explicitly on the epistemology of physics. The underlying conception is that the historicity of biological objects would not matter to understand a situation here and now, or, at least, historicity would not impact the method of modeling. We analyze that it is not the case with concrete examples. Historicity forces a conceptual reconfiguration

Microbial symbioses based on nutrient exchange and interdependence are ubiquitous in nature and biotechnologically promising; however, an in-depth mathematical description of their exact underlying dynamics from first principles is still missing. Hence, in this paper a novel mechanistic mathematical model of such a relationship in a continuous chemostat culture is derived. In contrast to preceding

Diversity in metacommunities is traditionally viewed to consist of the diversity within communities (\(\alpha\)) that is complemented by the differences between communities (\(\beta\)) so as to result in the total diversity (\(\gamma\)) of the metacommunity. This perception of the partitioning of diversity, where \(\beta\) is a function of \(\gamma\) and \(\alpha\) (usually \(\beta =\gamma /\alpha\)

Swimming of spermatozoa through couple stress fluid in an asymmetric human cervical canal is investigated in the present theoretical analysis. A couple of fourth-order partial differential equations arising from the mathematical modelling of the proposed model is solved analytically. Flow variables like pressure gradient, propulsive velocity, mucus velocity and time mean flow rate are analysed for

Embryonic development, which inspired the first theories of biological form, was eventually excluded from the conceptual framework of the Modern Synthesis as irrelevant. A major question during the last decades has centred on understanding whether new advances in developmental biology are compatible with the standard view or whether they compel a new theory. Here, I argue that the answer to this question

Extending the previous 2-gender dioecious diploid gene-mating evolution model, we attempt to answer "whether the Hardy-Weinberg global stability and the exact analytic dynamical solutions can be found in the generalized N-gender N-polyploid gene-mating system with arbitrary number of alleles?" For a 2-gender gene-mating evolution model, a pair of male and female determines the trait of their offspring

Unfortunately, part of the article title was updated as subtitle which in turn resulted with complete title not appearing on website and in the bibliographic data. The complete version of title is updated here.

Fundamental properties of macroscopic gene-mating dynamic evolutionary systems are investigated. A model is studied to describe a large class of systems within population genetics. We focus on a single locus, any number of alleles in a two-gender dioecious population. Our governing equations are time-dependent continuous differential equations labeled by a set of parameters, where each parameter stands

We determined the identity elements of each tRNA isoacceptor for the three domains of life: Eubacteria, Archaea, and Eukarya. Our analyses encompass the most updated and curated available databases using an information theory approach. We obtained a collection of identity clusters for each of the isoacceptors of the 20 canonical amino acids for the three major domains of life. The identity clusters

In this paper, a deterministic model for transmission of an epidemic has been proposed by dividing the total population into three subclasses, namely susceptible, infectious and recovered. The incidence rate of infection is taken as a nonlinear functional along with time delay, and treatment rate of infected is considered as Holling type III functional. We have structured a deterministic transmission

A non-smooth epidemic model with piecewise incidence rate dependent on the derivative of the case number is proposed for the transmission dynamics of an infectious disease with media coverage, enhanced vaccination and treatment policy. This is an implicitly defined system, which is converted into an explicit system with three thresholds by employing the properties of the Lambert W function. We first

The observed spatiotemporal ciliary beat patterns leading to proper mucociliary clearance on multiciliated epithelia are suspected to be the result of self-organizing processes on various levels. Here, we present a simplified pluricellular epithelium model, which intends to make the self-organization of ciliary beating patterns as well as of the associated fluid transport across the airway epithelium

In this paper, a delayed differential model based on the intravenous glucose tolerance test is considered. The conditions to determine stability or instability of the model's steady state are obtained. We obtain the necessary conditions for the appearance of a bifurcation, and we investigate the direction and stability of the local bifurcation. For this purpose, the normal form theory is used. In addition

The average fitness difference between adjacent sites in a fitness landscape is an important descriptor that impacts in particular the dynamics of selection/mutation processes on the landscape. Of particular interest is its connection to the error threshold phenomenon. We show here that this parameter is intimately tied to the ruggedness through the landscape's amplitude spectrum. For the NK model

Organisms must maintain proper regulation including defense and healing. Life-threatening problems may be caused by pathogens or by a multicellular organism's own cells through cancer or autoimmune disorders. Life evolved solutions to these problems that can be conceptualized through the lens of information security, which is a well-developed field in computer science. Here I argue that taking an information

With a few exceptions, the literature on evolutionary transitions in individuality (ETIs) has mostly focused on the relationships between lower-level (particle-level) and higher-level (collective-level) selection, leaving aside the question of the relationship between particle-level and collective-level inheritance. Yet, without an account of this relationship, our hope to fully understand the evolutionary

A stochastic differential game model for animal migration between two habitats under uncertain environment, a new population dynamics model, is formulated. Its novelty is the use of an impulse control formalism to naturally describe migrations with different timings and magnitudes that the conventional models could not handle. Uncertainty of the environment that the population faces with is formulated

Whether or not cooperation is favored in evolutionary games on graphs depends on the population structure and spatial properties of the interaction network. The population structure can be expressed as configurations. Such configurations extend scenarios with a single cooperator among defectors to any number of cooperators and any arrangement of cooperators and defectors on the network. For interaction

In this paper, a fractional-order predator-prey mathematical model has been developed considering Holling type II functional response. Here, we have investigated the interaction dynamics of prey, middle predator and top predator. We assume that the middle predator consumes only the prey, and the top predator consumes only the middle predator. Here, the logistic growth of prey has been considered. Then

The illustrations of the late nineteenth-/twentieth-century scientist/artist Ernst Haeckel, as depicted in his book Art Forms in Nature (originally in German as Kunstformen der Natur, 1898-1904), have been at the intersection of art, biology, and mathematics for over a century. Haeckel's images of radiolaria (microscopic protozoans described as amoeba in glass houses) have influenced various artists

Ernst Haeckel and Emil du Bois-Reymond were the most prominent champions of Darwin in Germany. This essay compares their contributions to popularizing the theory of evolution, drawing special attention to the neglected figure of du Bois-Reymond as a spokesman for a world devoid of natural purpose. It suggests that the historiography of the German reception of Darwin's theory needs to be reassessed

As Blackwell (Am Biol Teach 69:135-136, 2007) pointed out, multiple authors have attempted to discredit Haeckel, stating that modern embryological studies have shown that Haeckel's drawings are stylized or embellished. More importantly, though, it has been shown that the discussion within the scientific community concerning Haeckel's drawings and the question of whether embryonic similarities are convergent

The vast scientific heritage of Ernst Haeckel, evolutionist and thinker, comprises ecology as well. It is well known that it was he in 1866 introduced the term "ecology" for the science on interaction of the organisms and the environment. Haeckel built his system of the biological science (to be more precise, of the zoological science), including ecology, on the basis of Charles Darwin's evolutionary

The article aims to clarify the dynamics of the publication of E. Haeckel's works in Russia, and the evolution of their perception by the authorities, various social groups and scientists in a rapidly changing sociocultural context and in relation to the various stages of the evolutionary synthesis. It is shown that his works were reprinted nearly 50 times. Until the beginning of twentieth century

Nearly 150 years ago, Ernst Haeckel published a three volume monograph on the calcareous sponges. These volumes contained the results of his extensive investigation of the anatomy, reproduction, and development of these marine invertebrate organisms. This paper discusses how Haeckel's contribution to spongiology was so distinct from that of earlier writers on the natural history of sponges, by focusing

In the course of the second half of the nineteenth century, following the publication of Darwin's On the Origin of Species (1859) and Haeckel's Generelle Morphologie der Organismen (1866) (General Morphology of Organisms), the two men interacted like comrades in arms, leading the theory of evolution to victory in the international arena. This relationship broke up during the early decades of the twentieth

This paper offers the first ever published discussion of the ethical treatise Harmonie: Versuch einer monistischen Ethik [Harmony: an attempt at a monistic ethics] by Heinrich Schmidt (1874-1935), one of the leading figures in the circle of Ernst Haeckel. Published near the end of Schmidt's life (1931), it constituted a kind of summation of decades of intense involvement in the "project" of German

The "German Darwin" Ernst Haeckel was influential not only in Germany, but in non-German-speaking countries as well. Due to the widespread use of German as a language of science in the Russian Empire along with growing Russian-German links in various scientific fields, Haeckel directly and indirectly influenced Russian intellectual landscape. The objective of the present paper is to investigate Haeckel's

Biological individuality was a hotly debated concept in nineteenth-century German biology, both in botany and in zoology. Much discussion centered on a comparison of higher plants with colonial organisms that are subject to polymorphism and exhibit division of labor among their parts. Building on the work of Matthias Jakob Schleiden, Johannes Müller, Rudolf Leuckart, and especially the botanist Alexander

Detailed analyses into the life cycle of the soil-dwelling microbe Dictyostelium discoideum led to the conclusion that this "social amoeba" practices some form of "non-monoculture farming" via the transfer of bacteria to novel environments. Herein, we show that in myxomycetes (plasmodial slime molds or myxogastrids) a similar "farming symbiosis" has evolved. Based on laboratory studies of two representative

In our era of computers and computer models, the importance of physical or graphical models for both research and education in developmental biology (embryology) is often forgotten or at least underappreciated. Still, one important aspect of embryology is the (evolutionary) developmental anatomy of both human and animal embryos. Here, we present a short history of the visualization of Ernst Haeckel's

The Haeckel reception in different European countries has received some attention from historians of biology, but the reception in Scandinavia remains relatively unknown. We have found letters to and from Haeckel to Swedish scientists and students in the Ernst Haeckel House in Jena and in the archives of the Royal Swedish Academy of Sciences (RSAS) in Stockholm. Here we present correspondence with

The year 2019 marks the 100th anniversary of the death of Ernst Haeckel, a German zoologist, artist, and philosopher of science, who defended and supplemented Charles Darwin's system of theories regarding the mechanisms of biological evolution. We briefly recapitulate Haeckel's remarkable career and reproduce the Laudatio read by the President of the Linnean Society of London (1 July 1908), when Haeckel

Ageing is the leading risk factor for the emergence of cancer in humans. Accumulation of pro-carcinogenic events throughout life is believed to explain this observation; however, the lack of direct correlation between the number of cells in an organism and cancer incidence, known as Peto's Paradox, is at odds with this assumption. Finding the events responsible for this discrepancy can unveil mechanisms

Dengue is, in terms of death and economic cost, one of the most important infectious diseases in the world. So, its mathematical modeling can be a valuable tool to help us to understand the dynamics of the disease and to infer about its spreading by the proposition of control methods. In this paper, control strategies, which aim to eliminate the Aedes aegypti mosquito, as well as proposals for the

Clonal plants grow horizontally by producing multiple physiological individuals (ramets). We studied clonal growth in a homogeneous environment using a dynamic spatial model based on a stochastic cellular automaton. We investigated different growth forms from the aspect of ramet mortality. Non-steady-state and quasi-steady-state cases were defined, and we determined the number of steps suitable for

A novel nonlinear time-delayed susceptible-infected-recovered epidemic model with Beddington-DeAngelis-type incidence rate and saturated functional-type treatment rate is proposed and analyzed mathematically and numerically to control the spread of epidemic in the society. Analytical study of the model shows that it has two equilibrium points: disease-free equilibrium (DFE) and endemic equilibrium

Zika is a flavivirus transmitted to humans through either the bite of infected Aedes mosquitoes or sexual intercourse with infected individuals. In this paper, we present a mathematical model based on these two modes of transmission. Using the next-generation matrix method, a threshold parameter called basic reproduction number is determined. Sensitivity analysis of the basic reproduction number in

Measles, a highly contagious infection caused by the measles virus, is a major public health problem in China. The reported measles cases decreased dramatically from 2004 to 2012 due to the mandatory measles vaccine program started in 2005 and the goal of eliminating measles by 2012. However, after reaching its lowest level in 2012, measles has resurged again since 2013. Since the monthly data of measles

The original version of this article unfortunately contained a mistake.

The Extended Evolutionary Synthesis (EES) debate is gaining ground in contemporary evolutionary biology. In parallel, a number of philosophical standpoints have emerged in an attempt to clarify what exactly is represented by the EES. For Massimo Pigliucci, we are in the wake of the newest instantiation of a persisting Kuhnian paradigm; in contrast, Telmo Pievani has contended that the transition to

Research on symbiotic communities (microbiomes) of multicellular organisms seems to be changing our understanding of how species of plants and animals have evolved over millions of years. The quintessence of these discoveries is the emergence of the hologenome theory of evolution, founded on the concept that a holobiont (a host along with all of its associated symbiotic microorganisms) acts a single

In this article, some new aspects of unified cell bioenergetics are presented. From the perspective of unified cell bioenergetics certain subsequent stages of cancer development, from initiation stage, through transformation to metastasis, are analyzed. Here we show that after transformation, cancer cells are permanently exposed to reactive oxygen species, that causes continual random DNA mutations

Here, we present new theory and law of longevity intended to evaluate fundamental factors that control lifespan. This theory is based on the fact that genes affecting host organism longevity are represented by subpopulations: genes of host eukaryotic cells, commensal microbiota, and non-living genetic elements. Based on Tetz's theory of longevity, we propose that lifespan and aging are defined by the

The founders of modern biology (Jean Lamarck, Charles Darwin, August Weismann etc.) were organismic life scientists who attempted to understand the morphology and evolution of living beings as a whole (i.e., the phenotype). However, with the emergence of the study of animal and plant physiology in the nineteenth century, this "holistic view" of the living world changed and was ultimately replaced by

Evolutionary processes have been described not only in biology but also for a wide range of human cultural activities including languages and law. In contrast to the evolution of DNA or protein sequences, the detailed mechanisms giving rise to the observed evolution-like processes are not or only partially known. The absence of a mechanistic model of evolution implies that it remains unknown how the

Comprehending life history of migratory fish, onset of migration in particular, is a key biological and ecological research topic that still has not been clarified. In this paper, we propose a simple mathematical model for the onset of fish migration in the context of a stochastic optimal stopping theory, which is a new attempt to our knowledge. Finding the criteria of the onset of migration reduces

Georgy Gause (1910-1986) is best known for his contribution to ecology and evolutionary theory. His book "The Struggle for Existence" (1934) inspired generations of ecologists. Yet his scientific interests were diverse, embracing many aspects of the life sciences and medicine. The most notable shift in his research took place in the early 1940s when he began to study antibiotics and discovered Gramicidin

A mathematical model for the quantitative analysis of cancer-immune interaction, considering the role of antibodies has been proposed in this paper. The model is based on the clinical evidence, which states that antibodies can directly kill cancerous cells (Ivano et al. in J Clin Investig 119(8):2143-2159, 2009). The existence of transcritical bifurcation, which has been proved using Sotomayor theorem

Self-complementary circular codes are involved in pairing genetic processes. A maximal [Formula: see text] self-complementary circular code X of trinucleotides was identified in genes of bacteria, archaea, eukaryotes, plasmids and viruses (Michel in Life 7(20):1-16 2017, J Theor Biol 380:156-177, 2015; Arquès and Michel in J Theor Biol 182:45-58 1996). In this paper, self-complementary circular codes

One of the definitive characteristics of chordates (cephalochordates, vertebrates) is the somites, which are a series of paraxial mesodermal blocks exhibiting segmentation. The presence of somites in the basal chordate amphioxus and in vertebrates, but not in tunicates (the sister group of vertebrates), suggests that the tunicates lost the somites secondarily. Somites are patterned from anterior to

In this paper we are concerned with how aggregated outcomes of individual behaviours, during interactions with other individuals (games) or with environmental factors, determine the vital rates constituting the growth rate of the population. This approach needs additional elements, namely the rates of event occurrence (interaction rates). Interaction rates describe the distribution of the interaction

Homology of some RNAs with template DNA requires systematic exchanges between nucleotides. Such exchanges produce 'swinger' RNA along 23 bijective transformations (nine symmetric, X ↔ Y; and 14 asymmetric, X → Y → Z → X, for example A ↔ C and A → C → G → A, respectively). Here, analyses compare amino acids coded by swinger-transformed codons to those coded by untransformed codons, defining coding invariance

A new system for maintaining homogeneous gene expression in tissue and for destroying through apoptosis nonconforming cells is introduced. This functionality is called the "similarity comparison." Accordingly, the survival of mutated cells is hindered due to reduced gene expression. That, in turn, maintains the homogeneity of the tissue and prevents tumors from developing. The concept of the similarity

In this paper, we study the global properties of a computer virus propagation model. It is, interesting to note that the classical method of Lyapunov functions combined with the Volterra-Lyapunov matrix properties, can lead to the proof of the endemic global stability of the dynamical model characterizing the spread of computer viruses over the Internet. The analysis and results presented in this paper

Cellular automata are often used to explore the numerous possible scenarios of what could have occurred at the origins of life and before, during the prebiotic ages, when very simple molecules started to assemble and organise into larger catalytic or informative structures, or to simulate ecosystems. Artificial self-maintained spatial structures emerge in cellular automata and are often used to represent

Discussions of the survival determinism concept have previously focused on its primary role in the evolution of early unicellular organisms in the light of findings which have been reported on a number of diseases. The rationale for such parallel was in the view according to which multicellular organisms could be regarded as sophisticated colonies of semi-autonomous, single-celled entities, whereby

Polyploidy is a widespread feature of plant genomes. As a typical model of polyploidy, autopolyploidy has been postulated evolutionary dead ends and received little attention compared with allopolyploidy. For the limited data available so far, the evolutionary outcome of genome diversity in autopolyploids remains controversial in comparison with its diploid ancestors. In the present study, the effects

Hominin evolution in the African Pliocene and Pleistocene was accompanied and mediated by changes in the abiotic and biotic spheres. It has been hypothesized that such environmental changes were catalysts of hominin morphological evolution and speciations. Whereas there is little doubt that ecological changes were relevant to shaping the trajectories of mammalian evolution, testing specific hypotheses