Genetical ESS-models. I. Concepts and basic model

Evolutionarily Stable Strategies (ESS) in phenotypic models are used to explain the evolution of animal interactive behaviour. As the behavioural features under consideration are assumed to be genetically determined, the question arises how underlying a genetical system might affect the results of phenotypic ESS-models. This question can be fully treated in terms of ESS-theory. A method of designing Genetical ESS-Models is proposed, which transfers the question of evolutionary stability to a "lower" level, the genetical basis. Genetical ESS-models - although nonlinear even in the simplest cases - can be analysed in a way that is familiar to ESS-theorists and yield immediate results on gene pool ESSs, which then may or may not maintain ESSs on the phenotypic level. Moreover, general results can be obtained to characterize evolutionarily stable gene pool states and their interrelation with commonsense, phenotypic ESSs. This part of the article presents the basic concepts and an outline of the method of genetical ESS-models. It gives, as a demonstration, a complete analysis for phenotypic two-strategy models (linear or nonlinear) based on a diploid, diallelic single-locus system under random mating. The results in this case suggest that a phenotypic ESS should indeed be expected to evolve but, maybe, only after passing through a succession of temporarily stable states.     

Tychastic Viability

Tychastic viability is defined in an uncertain dynamical framework and used for providing a “viability risk eradication measure”, first, by delineating the set of initial conditions from which all evolutions satisfy viability constraints, second, for the other “risky” initial states, by introducing their duration index. This approach provides an alternative to the stochastic representation of chance and these two measures replace the statistical measures (expectation, variance, etc).     

Predictive landscapes hidden beneath biological cellular automata

To celebrate Hans Frauenfelder’s achievements, we examine energy(-like) “landscapes” for complex living systems. Energy landscapes summarize all possible dynamics of some physical systems. Energy(-like) landscapes can explain some biomolecular processes, including gene expression and, as Frauenfelder showed, protein folding. But energy-like landscapes and existing frameworks like statistical mechanics seem impractical for describing many living systems. Difficulties stem from living systems being high dimensional, nonlinear, and governed by many, tightly coupled constituents that are noisy. The predominant modeling approach is devising differential equations that are tailored to each living system. This ad hoc approach faces the notorious “parameter problem”: models have numerous nonlinear, mathematical functions with unknown parameter values, even for describing just a few intracellular processes. One cannot measure many intracellular parameters or can only measure them as snapshots in time. Another modeling approach uses cellular automata to represent living systems as discrete dynamical systems with binary variables. Quantitative (Hamiltonian-based) rules can dictate cellular automata (e.g., Cellular Potts Model). But numerous biological features, in current practice, are qualitatively described rather than quantitatively (e.g., gene is (highly) expressed or not (highly) expressed). Cellular automata governed by verbal rules are useful representations for living systems and can mitigate the parameter problem. However, they can yield complex dynamics that are difficult to understand because the automata-governing rules are not quantitative and much of the existing mathematical tools and theorems apply to continuous but not discrete dynamical systems. Recent studies found ways to overcome this challenge. These studies either discovered or suggest an existence of predictive “landscapes” whose shapes are described by Lyapunov functions and yield “equations of motion” for a “pseudo-particle.” The pseudo-particle represents the entire cellular lattice and moves on the landscape, thereby giving a low-dimensional representation of the cellular automata dynamics. We outline this promising modeling strategy.

     

Multiple Treatment Comparisons in Linear Models When the Standard Error of a Difference is not Constant

Users of analysis of variance (ANOVA) procedures are accustomed to an ANOVA table, followed by a table of means. When the underlying linear model is variance‐balanced, i.e. the standard error of a difference is constant for all pairwise comparisons, non‐significant differences can be indicated by underlining. Unfortunately, when the design is unbalanced, it may turn out to be impossible to consistently represent all significant differences by standard underlining procedures. This paper proposes simple approaches, which allow a “connected lines” representation of treatment comparisons in the unbalanced case. The price for the improved display of results is a potential need to set‐aside some significances and report them separately. Experience shows that often all significances can be displayed by underlining, especially when variance‐imbalance is moderate. Alternatively, a “broken lines” representation can be used, which is guaranteed to allow a display of all significances. This type of display seems particularly suitable for implementation as a letters representation into statistical packages for linear models.     

Genetical ESS-models. II. Multi-strategy models and multiple alleles

The problem of evolutionarily stable strategies (ESS) in sexual populations can be investigated by means of genetical ESS-models which link common sense, phenotypic ESS-models to an underlying genetical system. Thorough results are obtained for multi-strategy models in diploid, panmictic populations on the basis of multi-allelic, one-locus systems. A sexual population will be maintained at a phenotypic ESS if this can possibly be produced by the genotypes currently existing. If there is enough allelic variation, the corresponding gene pool may either be an ESS itself, or belong to an attracting, continuous set of states, which all determine the same evolutionarily stable population. The latter case allows new alleles to enter and spread in the gene pool without disturbing the phenotypic ESS. If a phenotypic ESS cannot be established, ESSs of the genetical model may be found which give rise to stable populations alternatively. Since these depend on the phenotypes determined by the currently existing genotypes, they may be destabilized by the occurrence of new mutations. In this sense, they are less durable than populations maintained at a phenotypic ESS and can be expected to evolve, in the long run, towards a phenotypic ESS.     

Graph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates

This paper derives new results for certain classes of chemical reaction networks, linking structural to dynamical properties. In particular, it investigates their monotonicity and convergence under the assumption that the rates of the reactions are monotone functions of the concentrations of their reactants. This is satisfied for, yet not restricted to, the most common choices of the reaction kinetics such as mass action, Michaelis-Menten and Hill kinetics. The key idea is to find an alternative representation under which the resulting system is monotone. As a simple example, the paper shows that a phosphorylation/dephosphorylation process, which is involved in many signaling cascades, has a global stability property. We also provide a global stability result for a more complicated example that describes a regulatory pathway of a prevalent signal transduction module, the MAPK cascade.     

Metrics for evaluating representation target achievement in protected area networks

Global conservation targets (e.g. Aichi Target 11) have helped drive a dramatic expansion of the global protected area (PA) network. Credible metrics have an important role to play in evaluating and expanding PAs to achieve conservation outcomes and objectives. For metrics to be useful and adopted, they need to be transparent, easy to understand, and easy to implement. We present two complementary metrics, “mean protection gap” and “mean target achievement”, for evaluating representation target achievement in PA networks along with the R package “ConsTarget” that calculates and plots both metrics. We use Australia's proposed Commonwealth Marine Reserve network as a case study to demonstrate the application of these metrics. We recommend the metrics be used to evaluate the progress towards building representative PA networks in line with Aichi target 11's goals.     

A new method for describing predator-prey relations in discontinous environments

I propose a new method for anlysing predatorprey interactive systems in discontinuous environments. The basic index used here is a generalized version ofLloyd 's (1967) “interspecies mean crowding”, which is defined as the number of individuals of one species existing in a given patch per that of the other species in either the same or different patches at either the same or different times. Four indices are derived from different combinations of the numbers of the prey and the predator in habitat patches. Then, the correlation coefficients between the numbers of individuals in patches in both different locations and times are derived by modifying the above new indices. Using this technique, dynamical changes of the joint distributions of the numbers of predators and prey which reflect variation in local conditions, can readily be described. As an example, this method was applied to an analysis of the outcomes of a multi-patch version of theLotka-Volterra model of predator-prey interactions.     

Reprogramming cell fates: reconciling rarity with robustness

The stunning possibility of “reprogramming” differentiated somatic cells to express a pluripotent stem cell phenotype (iPS, induced pluripotent stem cell) and the “ground state” character of pluripotency reveal fundamental features of cell fate regulation that lie beyond existing paradigms. The rarity of reprogramming events appears to contradict the robustness with which the unfathomably complex phenotype of stem cells can reliably be generated. This apparent paradox, however, is naturally explained by the rugged “epigenetic landscape” with valleys representing “preprogrammed” attractor states that emerge from the dynamical constraints of the gene regulatory network. This article provides a pedagogical primer to the fundamental principles of gene regulatory networks as integrated dynamic systems and reviews recent insights in gene expression noise and fate determination, thereby offering a formal framework that may help us to understand why cell fate reprogramming events are inherently rare and yet so robust.     

Two-enzyme active transport in vitro with ph induced asymmetrical functional structures.: III. Discussions based on numerical treatments of the time-dependent evolutions

Three complementary models have been considered in which pH gradients (step function. linear pH or linear H^?) impose asymmetry on a two-enzyme mixture. If the “combined pH dependences” of enzymes is pro-asymmetrical, the pH gradient induces an asymmetrical distribution of potential activities (“latent” asymmetry of functional structure). When substrate is added, “developed” asymmetry of effective activities appears which results in “substrate space wave” and pumping when the catalysed reaction couple is “inversible”. It is shown that only one steady state exists for a given boundary condition and is attained when the “combined effective activity” of enzymes is nil: the stationary flux with symmetrical boundaries or the stationary load with moving boundaries is proportional to “effective global activities” of enzymes. “Equivalent square models” could be proposed that would be able to describe “functional” or “permanent” structure pumps as well. These models belong to the thermodynamic branch and the asymmetrical “space wave” substrate concentration profiles obtained must be distinguished from dissipative structures. It appears that such primary active transport pumps are chemical equivalents of heat pumps.     

A general-purpose electronic model for arbitrary configurations of neurons

This paper describes a general-purpose electronic model for simulating the electrical activity in small groups of nerve cells arranged in arbitrary configurations. The model consists of 44 realizations of two basic modules (the “cell”, and the “axon with synapses”) which can be connected together in various arrangements by way of snapper-capped wires. The activity of the individual units is displayed via flashing lights atop the constituent cells; also there are taps on each cell from which one can obtain and display more detailed information concerning the electrical activity of each and all cells, including the graded “generator” potential of the triggering section, on for example an oscilloscope. The modules include realistic approximations to basic mechanisms of neuronal activity, but the main advance over previous models is the emphasis on and ability to deal with the network context of neuroelectric signals.Illustrative applications to mutually-inhibiting centers and to our ladder net theory for reticular-like networks are presented. The primary advantages of the electronic model are: actual physical representation of various configurations, asynchronous timing, flexibility with respect to overall configuration and with respect to network parameters, immediate turnaround, and cost.     

Reconciling neuronal representations of schema,abstract task structure,and categorization under cognitive maps in the entorhinal-hippocampal-frontal circuits

Learning leads to a neuronal representation of acquired knowledge. This idea of knowledge representation was traditionally developed as a “cognitive map” of spatial memory represented in the hippocampus. The framework of cognitive mapping has been extended in the past decade to include not only spatial memory, but also non-spatial factual and temporal memory. Following this conceptual advancement, a line of recent neurophysiological research discovered such knowledge representations not only in the hippocampus, but also in the entorhinal cortex and frontal cortex. Although the distinct terms “cognitive map,” “schema,” “abstract task structure” or “categorization” were used in these studies, it is likely that these terms can be reconciled as a common mechanism of learned knowledge representations. Future experimental work will be required to differentiate the parametric nature of knowledge representations across brain areas.     

Analysis of evolution: evolutionary rates, independence and treeness.

Populations that separate according to a given pattern of fissions (a “tree” of descent) and evolve independently after fissions have a patterned variance—covariance matrix which reflects the history of fissions. Spectral analysis of the matrix can help reconstruct the pattern; multivariate analysis techniques can be used to test if an observed matrix is compatible with a given tree of descent, and with the assumption of constant or of variable evolutionary rates. We call these tests of “treeness” and discuss evolutionary implications, giving also an example on human evolution. The methods can be used more generally to test if a loss of information is involved in using a tree as a formal representation of any particular set of data.     

Social is Emotional

This is a biological approach to the philosophy of mind that feeds an investigation of the phenomena of “social” and “emotional”, both of which are widespread in nature. I scrutinize the non-dualistic Darwinian concept of the continuity of mind. For practical reasons, I address mind at different levels of organization: The systemic mind are the properties of which a common, coherent evolution works upon. Separated from this is “language-mind”: the crystallization of thought in words, which is a strictly human phenomenon. As the phenomenology of the body is a theory of philosophy that lie beyond language it can—to a certain extent—be extrapolated across a species boundary. In the process the phenomenology of the body comes to resemble biosemiotics and with this tool, I investigate a field study of social play behavior in canids. This leads to a possibility to study the non-human experience of emotion as “locally meaningful phenomena”.     

Two enzyme active transport in vitro with ph induced asymmetrical functional structures: I. The model and its analytical treatment

A class of systems is characterized by the asymmetrical distribution of a sink and a source reaction, the asymmetry of the global chemical equation (energy liberation) and by an asymmetrical one-wave space profile. These systems belong to the family of primary chemical cells and can deplete and enrich the media they separate. A “ one way ” transport-reaction chain is needed for specific “ real ” active transport. A two enzyme model of this class is described in which the spatial asymmetry is due to a (diffusive) pH gradient; this distribution of “ potential ” enzyme activities is called the “ functional structure ”. Equal potential enzyme activities and absence of reactive back action on local pH are assumed in the “ square model ” version of the pump. Analytical expressions of the enzymatic diffusion reactions are derived for zero and first order kinetics, i.e. in function of substrate concentrations. Tables of equations are presented. The intrinsic properties of the pump are characterized by (dimensionless) transport reaction parameters, (membrane composition); the “ potential ” activity is controlled by the pH gradient; the “ effective ” pumping is also a function of the substrate concentrations on the boundaries.     

Limitations of perturbative techniques in the analysis of rhythms and oscillations

Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are “sufficiently weak”, an assumption that is not always valid when perturbative methods are applied. In this paper, we identify a number of concrete dynamical scenarios in which a standard perturbative technique, based on the infinitesimal phase response curve (PRC), is shown to give different predictions than the full model. Shear-induced chaos, i.e., chaotic behavior that results from the amplification of small perturbations by underlying shear, is missed entirely by the PRC. We show also that the presence of “sticky” phase–space structures tend to cause perturbative techniques to overestimate the frequencies and regularity of the oscillations. The phenomena we describe can all be observed in a simple 2D neuron model, which we choose for illustration as the PRC is widely used in mathematical neuroscience.     

Characterization of topological keystone species: Local,global and “meso-scale” centralities in food webs

An important question in the network representation of ecological systems is to determine how direct and indirect interactions between species determine the positional importance of species in the ecosystem. Here we present a quantitative analysis of the similarities and differences of six different topological centrality measures as indicators of keystone species in 17 food webs. These indicators account for local, global and “meso-scale” – intermediate between local and global – topological information about species in the food webs. Using factor analysis we shown that most of these centrality indices share a great deal of topological information, which range from 75% to 96%. A generalized keystone indicator is then proposed by considering the factor loadings of the six-centrality measures, which contains most of the information encoded by these indices. However, the individual ordering of species according to these criteria display significant differences in most food webs. We simulate the effects of species extinction by removing species ranked according to a local and a “meso-scale” centrality indicator. The differences observed on three network characteristics – size, average distance and clustering coefficient of the largest component – after the removal of the most central nodes indicate that the consideration of these indices have different impacts for the ranking of species with conservational biology purposes. The “meso-scale” indicator appears to play an important role in determining the relative importance of species in epidemic spread and parasitism rates.     

Ecopharmacognosy and the responsibilities of natural product research to sustainability

The recently developed term “ecopharmacognosy” is defined as the study of sustainable, biologically active, natural resources. As a philosophical approach, it provides a conceptual framework for developing new strategies and new scientific perspectives which may improve future global food and health care product accessibility and assure beneficial outcomes. In this brief article some facets of how the precepts of ecopharmacognosy may apply in developing new medicinal products may be developed, based on sustainability and the use of integrated technologies.Although from a medicinal agent perspective, plants remain a primary source of global health care, these resources are not being pursued by major pharmaceutical companies as sources of new agents, and essentially all tropical diseases, as well as most microbially based diseases, remain outside the scope of their drug discovery programs. Countries and regions therefore must address their own drug discovery needs for “local” and some global diseases. In addition, the cost of drug importation is so high that development of local resources, i.e. traditional medicines, may be the only rational alternative approach. At the same time, network pharmacology is exploring the many diverse effects of both individual and complex natural products at the gene level, and this is offering new opportunities to rethink and restructure the core, long-standing, Western, magic bullet philosophy to drug discovery. Other ecopharmacognosy changes underway include the computer-aided design of natural product derivatives, based on molecular docking, which is providing targetable enzyme substrates, and remote sensing technologies which can assess natural materials non-invasively for critical constituents as a part of rethinking quality control strategies in the field. Furthermore, there are the hyphenated chromatographic and spectroscopic procedures to quantitatively analyze single and multicomponent plant mixtures for bioactive markers to enhance quality control and, thereby, patient care. The relationship of these evolving approaches will serve as practical examples to the philosophies of ecopharmacognosy. In summary, with respect to health care, ecopharmacognosy poses the long-term practical question for drugs, “How Green is Your Medicine?”