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Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

• I briefly summarize Michael Savageau's "Biochemical Systems Analysis" papers, published in volumes 25 and 26 of the journal. • These papers kickstarted Biochemical Systems Theory, which originated many of the core concepts and tools of Systems Biology. • I identify the most relevant developments in Biochemical Systems Theory since 1969. Michael Savageau's Biochemical Systems Analysis I, II, III papers, published in volumes 25 and 26 of the journal, kickstarted a research programme that originated many of the core concepts and tools of Systems Biology. This article briefly summarizes these papers and discusses the most relevant developments in Biochemical Systems Theory since their publication. [ABSTRACT FROM AUTHOR]

• I briefly describe the Boolean modeling approach to investigate gene regulatory networks (GRNs). • I discuss the foundational contributions by the three seminal manuscripts more than 15 years ago. • Finally, the applications of the Boolean modeling approach to the large-scale omics data is discussed. Boolean modeling is a mathematical modeling framework used for defining and studying gene-regulatory networks (GRNs). It serves as a means to develop mechanistic models, offering insights into the trajectories and dynamic properties of GRNs. In this review, I delve into seminal papers published in the Journal of Theoretical Biology that have spearheaded this field. Additionally, I explore the application of these modeling methods in the current era of data-intensive science. [ABSTRACT FROM AUTHOR]

In the recent work of Ullah et al. (2012a) , the authors developed an effective method to simplify reversible Markov chains by removal of states with low equilibrium occupancies. In this paper, we extend this result to irreversible Markov chains. We show that an irreversible chain can be simplified by removal of states with fast leaving rates. Moreover, we reveal that the irreversibility of the chain will always decrease after model simplification. This suggests that although model simplification can retain almost all the dynamic information of the chain, it will lose some thermodynamic information as a trade-off. Examples from biology are also given to illustrate the main results of this paper. [ABSTRACT FROM AUTHOR]

Scientific theories seek to provide simple explanations for significant empirical regularities based on fundamental physical and mechanistic constraints. Biological theories have rarely reached a level of generality and predictive power comparable to physical theories. This discrepancy is explained through a combination of frozen accidents, environmental heterogeneity, and widespread non-linearities observed in adaptive processes. At the same time, model building has proven to be very successful when it comes to explaining and predicting the behavior of particular biological systems. In this respect biology resembles alternative model-rich frameworks, such as economics and engineering. In this paper we explore the prospects for general theories in biology, and suggest that these take inspiration not only from physics, but also from the information sciences. Future theoretical biology is likely to represent a hybrid of parsimonious reasoning and algorithmic or rule-based explanation. An open question is whether these new frameworks will remain transparent to human reason. In this context, we discuss the role of machine learning in the early stages of scientific discovery. We argue that evolutionary history is not only a source of uncertainty, but also provides the basis, through conserved traits, for very general explanations for biological regularities, and the prospect of unified theories of life., (Copyright © 2011. Published by Elsevier Ltd.)

Abstract: Hamilton''s famous rule was presented in 1964 in a paper called “The genetical theory of social behaviour (I and II)”, Journal of Theoretical Biology 7, 1–16, 17–32. The paper contains a mathematical genetical model from which the rule supposedly follows, but it does not provide a link between the paper''s central result, which states that selection dynamics take the population to a state where mean inclusive fitness is maximized, and the rule, which states that selection will lead to maximization of individual inclusive fitness. This note provides a condition under which Hamilton''s rule does follow from his central result. [Copyright &y& Elsevier]

Environmental stochasticity is known to be a destabilizing factor, increasing abundance fluctuations and extinction rates of populations. However, the stability of a community may benefit from the differential response of species to environmental variations due to the storage effect. This paper provides a systematic and comprehensive discussion of these two contradicting tendencies, using the metacommunity version of the recently proposed time-average neutral model of biodiversity which incorporates environmental stochasticity and demographic noise and allows for extinction and speciation. We show that the incorporation of demographic noise into the model is essential to its applicability, yielding realistic behavior of the system when fitness variations are relatively weak. The dependence of species richness on the strength of environmental stochasticity changes sign when the correlation time of the environmental variations increases. This transition marks the point at which the storage effect no longer succeeds in stabilizing the community. [ABSTRACT FROM AUTHOR]

Admissible measures of diversity allow specification of the number of types (species, alleles, etc.) that are “effectively” involved in producing the diversity (the “diversity effective number”, also referred to as “true diversity”) of a community or population. In metacommunities, effective numbers additionally serve in partitioning the total diversity (symbolized by γ ) into one component summarizing the diversity within communities (symbolized by α ) and an independent component summarizing the differences between communities (symbolized by β ). There is growing consensus that the β -component should be treated in terms of an effective number of “distinct” communities in the metacommunity. Yet, the notion of distinctness is shown in the present paper to remain conceptually ambiguous at least with respect to the diversity within the “distinct” communities. To overcome this ambiguity and to provide the means for designing further desirable effective numbers, a new approach is taken that involves a generalized concept of effective number. The approach relies on first specifying the distributional characteristics of partitioning diversity among communities (among which are differentiation, where the same types tend to occur in the same communities, and apportionment, where different types tend to occur in different communities), then developing the indices which measure these characteristics, and finally inferring the effective numbers from these indices. Major results: (1) The β -component reflects apportionment characteristics of metacommunity structure and is quantified by the “apportionment effective number” of communities (number of effectively monomorphic communities). Since differentiation between communities arises only as a side effect of apportionment, the common interpretation of the β -component in terms of differentiation is unwarranted. (2) Multiplicative as well as additive methods of partitioning the total type diversity ( γ ) involve apportionment effective numbers of communities that are based on different apportionment indices. (3) “Differentiation effective numbers” of communities exist but do not conform with the classical concept of partitioning total type diversity into components within and between communities. (4) Differentiation characteristics are measured as effective numbers of distinct types (rather than communities) from the dual perspective, in which the roles of type and community membership are exchanged. This is relevant e.g. in studies of endemism and competitive exclusion. (5) For Shannon-Wiener diversity, all of the differentiation and apportionment effective numbers are equal, with the exception of those representing additive partitioning. (6) Under either perspective, that is dual or non-dual, measures of compositional differentiation (as originally suggested for the assessment of β -diversity) do not figure in the partitioning of total diversity into components, since they do not build on the intrinsic concept of diversity. [ABSTRACT FROM AUTHOR]

Abstract: Reliable functioning is crucial for the survival and development of the genetic regulatory networks in living cells and organisms. This functional reliability is an important feature of the networks and reflects the structural features that have been embedded in the regulatory networks by evolution. In this paper, we integrate this reliability into network reconstruction. We introduce the concept of dependency probability to measure the dependency of functional reliability on network edges. We also propose a method to estimate the dependency probability and select edges with high contributions to functional reliability. We use two real examples, the regulatory network of the cell cycle of the budding yeast and that of the fission yeast, to demonstrate that the proposed method improves network reconstruction. In addition, the dependency probability is robust in calculation and can be easily implemented in practice. [Copyright &y& Elsevier]

Abstract: This paper examines the role of other-regarding behavior as a mechanism for the establishment and maintenance of cooperation in resource use under variable social and environmental conditions. By coupling resource stock dynamics with social dynamics concerning compliance to a social norm prescribing non-excessive resource extraction in a common pool resource, we show that when reputational considerations matter and a sufficient level of social stigma affects the violators of a norm, sustainable outcomes are achieved. We find large parameter regions where norm-observing and norm-violating types coexist, and analyze to what extent such coexistence depends on the environment. [Copyright &y& Elsevier]

Abstract: The flux-summation theorem (FST) is a central principle of metabolic control analysis. It describes how the control of flux through any metabolic pathway of arbitrary complexity is distributed among the component reaction steps. Two issues concerning the FST are discussed in this paper. First, it has been suggested that the theorem could, in principle, be inapplicable under certain conditions, i.e. the sum of the control coefficients of all the enzymes supporting a pathway could exceed unity. Such conditions have not been found in any species so far studied, so in practice the FST is always applicable. I argue that applicability of the FST is a precondition for phenotypic robustness and therefore for survival. Second, the FST provides a basis for explaining dominance that renders Fisher''s ‘modifier genes’ hypothesis otiose. Some recent misunderstandings of metabolic control analysis have led to the claim that this explanation is flawed and therefore that Fisher''s hypothesis can and should be reinstated. Here, these suggestions are refuted. [Copyright &y& Elsevier]

Abstract: It has recently been proposed [Dediu, D., Ladd, D.R., 2007. Linguistic tone is related to the population frequency of the adaptive haplogroups of two brain size genes, ASPM and Microcephalin. Proc. Natl Acad. Sci. USA 104(26), 10944–10949] that genetically coded linguistic biases can influence the trajectory of language change. However, the nature of such biases and the conditions under which they can become manifest have remained vague. The present paper explores computationally two plausible types of linguistic acquisition biases in a population of agents implementing realistic genetic, linguistic and demographic processes. One type of bias represents an innate asymmetric initial state (initial expectation bias) while the other an innate asymmetric facility of acquisition (rate of learning bias). It was found that only the second type of bias produces detectable effects on language through cultural transmission across generations and that such effects are produced even by weak biases present at low frequencies in the population. This suggests that learning preference asymmetries, very small at the individual level and not very frequent at the population level, can bias the trajectory of language change through the process of cultural transmission. [Copyright &y& Elsevier]

Abstract: DEBtox (Dynamic Energy Budget in toxicology) models have been designed to analyse various results from classic tests in ecotoxicology. They consist of a set of mechanistic models describing how organisms manage their energy, when they are exposed to a contaminant. Until now, such a biology-based modeling approach has not been used within the regulatory context. However, these methods have been promoted and discussed in recent guidance documents on the statistical analysis of ecotoxicity data. Indeed, they help us to understand the underlying mechanisms. In this paper, we focused on the 21 day Daphnia magna reproduction test. We first aimed to clarify and detail the model building process leading to DEBtox models. Equations were rederived step by step, and for some of them we obtained results different from the published ones. Then, we statistically evaluated the estimation process quality when using a least squares approach. Using both experimental and simulated data, our analyses highlighted several statistical issues related to the fitting of DEBtox models on OECD-type reproduction data. In this case, particular attention had to be paid to parameter estimates and the interpretation of their confidence intervals. [Copyright &y& Elsevier]

Abstract: The complexity–stability relation is a central issue in ecology. In this paper, we show how the sampling method most often used to parameterize an ecological community, can affect the conclusions about whether or not complexity promotes stability and we suggest a sampling algorithm that overcomes the problem. We also illustrate the importance of treating feasibility separately from stability when constructing model communities. Using model Lotka–Volterra competition communities we found that probability of feasibility decreases with increasing interaction strength and number of species in the community. However, for feasible systems we found that local stability probability and resilience do not significantly differ between communities with few or many species, in contrast with earlier studies that, did not account for feasibility and concluded that species-poor communities had higher probability of being locally stable than species-rich communities. [Copyright &y& Elsevier]

Abstract: Human and animal trails on steep hillsides often exhibit dramatic switchbacks and shortcuts. Helbing et al. have recently examined the emergence of human trail systems on flat terrains while Minetti and Margaria established the effect of gradients on human metabolic efficiency. In this paper we use these ideas to develop a semi-quantitative theoretical model of the behaviour of humans moving on a terrain with relief. The model determines the direction of movement by minimising metabolic cost per unit of distance in a desired direction. The structure of the theory resembles the Landau Theory of Phase Transitions, much used in theoretical physics. We find that both hairpin bends (switchbacks) and shortcuts appear as efficient strategies for downhill walkers, while uphill walkers retain switchbacks. For weakly inclined slopes, the best strategy involves walking directly uphill or downhill. For sufficiently steep slopes, however, we find that the best strategy should undergo a transition to a broken symmetry solution corresponding to the switchback trail patterns typical of rugged environments. The critical slope at which this transition takes place should be less steep for uphill and downhill walkers. The theory should be amenable to empirical investigation. Amongst other applications, this model will enable us to generalize the work of previous authors to real landscapes, eventually permitting the reconstruction of ancient patterns of movement in archaeological landscapes. [Copyright &y& Elsevier]

Abstract: The stability of a folded single-stranded nucleic acid depends on the composition and order of its constituent bases and may be assessed by taking into account the pairing energies of its constituent dinucleotides. To assess the possible biological significance of a computed structure, Maizel and coworkers in the 1980s compared the energy of folding of a natural single-stranded RNA sequence with the energies of several versions of the same sequence produced by shuffling base order. However, in the 2000s many took as self-evident the view that shuffling at the mononucleotide level (single bases) was conceptual wrong and should be replaced by shuffling at the level of dinucleotides (retaining pairs of adjacent bases). Folding energies then became indistinguishable from those of corresponding shuffled sequences and doubt was cast on the importance of secondary structures. Nevertheless, some continued productively to employ the single base shuffling approach, the justification for which is the topic of this paper. Because dinucleotide pairing energies are needed to calculate structure, it does not follow that shuffling should not disrupt dinucleotides. Base shuffling allows determination of the relative contributions of base composition and base order to total folding energy. The potential for secondary structure arises from pressures acting at both DNA and RNA levels, and is abundant throughout genomes—with a probable primary role in recombination. Within a gene the potential can often be accommodated, and base order and composition work together (values have the same negative sign) in contributing to total folding energy. But sometimes protein-coding pressure on base order conflicts with the pressure for secondary structure and the values have opposite signs. Total folding energy can be deemed of potential biological significance when the average of several readings is significantly less than zero. [Copyright &y& Elsevier]

Abstract: In this paper the problem of designing experiments for the Monod model, which is frequently used in microbiology, is studied. The model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, environmental research, pharmacokinetics, and plant physiology. The designs presented so far in the literature are local optimal designs, which depend sensitively on a preliminary guess of the unknown parameters, and are for this reason in many cases not robust with respect to their misspecification. Uniform designs and maximin optimal designs are considered as a strategy to obtain robust and efficient designs for parameter estimation. In particular, standardized maximin D- and E-optimal designs are determined and compared with uniform designs, which are usually applied in these microbiological models. It is demonstrated that maximin optimal designs are substantially more efficient than uniform designs. Parameter variances can be decreased by a factor of two by simply sampling at optimal times during the experiment. Moreover, the maximin optimal designs usually provide the possibility for the experimenter to check the model assumptions, because they have more support points than parameters in the Monod model. [Copyright &y& Elsevier]

A novel method is described for solving systems of differential equations pertaining to organism development, where this development is assumed to be directly influenced by fluctuation in measurable environmental variables. The system parameters are written as functions of these variables and, because these functions involve the accumulation of “environment time” (e.g., “day-degrees”), the system is therefore regulated by the prevailing environmental conditions. This method contrasts with the more usual descriptions of development along a time-line. The parameters of the differential equations involved are estimated by modelling data, which show evidence of changes in the dependent variable(s), i.e. the components of the system. They are expressed in terms of their response to continuous fluctuations in one or more independent, environmental variables. Accumulated thermal time (including day-degrees) or more complex units may be derived by using either linear or nonlinear functions. Critical environmental parameters such as the basal thresholds of a given developmental process or parameters describing a nonlinear relationship with the environment may then be estimated. This paper develops the methodology of this environmentally driven approach to describing organism development in general terms, and gives a specific example of its application with reference to the cellular development within the secondary vascular tissues in the stems of young hybrid aspen trees. [Copyright &y& Elsevier]