Necessary and sufficient conditions for the existence of an optimisation principle in evolution

This paper presents a necessary condition for the existence of a numerical quantity optimised by evolution by natural selection, which also turns out to be a sufficient condition under rather general conditions. As a corollary, a related criterion with a particularly intuitive graphical interpretation in terms of pairwise invadability plots is obtained.     

Necessary and sufficient conditions for the existence of linear invariants in phylogenetic inference.

The necessary and sufficient conditions for the existence of linear invariants under semigroups of probability transition matrices are derived. It is found that a biologically meaningful nucleotide substitution model has linear invariants if and only if it is a submodel of one of the three most general models, which include the so-called balanced and unbalanced transversion models. Each of these three general models is a nucleotide substitution model with six parameters.     

Necessary and sufficient conditions for the existence of certain quadratic invariants under a phylogenetic tree.

Invariants are functions of the probabilities of state configurations among lineages, with expected values equal to zero under certain phylogenies. For two-state sequences, the existence of certain quadratic invariants requires a symmetric substitution model. For sequences with more than two states, the necessary condition for the existence of certain quadratic invariants in terms of independent events is much stronger than symmetry. For DNA sequences, only three parameters are allowed in the substitution model, which includes Kimura's two-parameter model as a special case.     

Quasi-equilibrium assumption in enzyme kinetics. Necessary and sufficient conditions and accuracy of its application for single-substrate reactions

Steady-state kinetics of compulsory-ordered single-substrate irreversible and reversible enzyme reactions with two, three, and arbitrary number of intermediates were observed. Necessary and sufficient conditions for application of the quasi-equilibrium assumption and restrictions of this assumption were found in cases of two and three intermediates in the equilibrium segment. For all cases, accuracy of the quasi-equilibrium assumption was evaluated.     

Necessary and sufficient conditions for R_{0} to be a sum of contributions of fertility loops

Recently, de-Camino-Beck and Lewis (Bull Math Biol 69:1341–1354, 2007) have presented a method that under certain restricted conditions allows computing the basic reproduction ratio $R_0$ in a simple manner from life cycle graphs, without, however, giving an explicit indication of these conditions. In this paper, we give various sets of sufficient and generically necessary conditions. To this end, we develop a fully algebraic counterpart of their graph-reduction method which we actually found more useful in concrete applications. Both methods, if they work, give a simple algebraic formula that can be interpreted as the sum of contributions of all fertility loops. This formula can be used in e.g. pest control and conservation biology, where it can complement sensitivity and elasticity analyses. The simplest of the necessary and sufficient conditions is that, for irreducible projection matrices, all paths from birth to reproduction have to pass through a common state. This state may be visible in the state representation for the chosen sampling time, but the passing may also occur in between sampling times, like a seed stage in the case of sampling just before flowering. Note that there may be more than one birth state, like when plants in their first year can already have different sizes at the sampling time. Also the common state may occur only later in life. However, in all cases $R_0$ allows a simple interpretation as the expected number of new individuals that in the next generation enter the common state deriving from a single individual in this state. We end with pointing to some alternative algebraically simple quantities with properties similar to those of $R_{0}$ that may sometimes be used to good effect in cases where no simple formula for $R_{0}$ exists.     

Empirical and counterfactual conditions for sufficient cause interactions

Sufficient-component causes are discussed within the deterministicpotential outcomes framework so as to formalize notions of sufficientcauses, synergism and sufficient cause interactions. Doing soallows for the derivation of counterfactual and empirical conditionsfor detecting the presence of sufficient cause interactions.The conditions are novel in that, unlike other conditions inthe literature, they make no assumption about monotonicity.The conditions can also be generalized and the conditions forthree-way sufficient cause interactions are given explicitly.The statistical tests derived for sufficient cause interactionsare compared with and contrasted to interaction terms in standardstatistical models.     

Necessary and sufficient condition for a model insect population to go to extinction

A necessary and sufficient condition on the parameters for a model population to become extinct is presented. The mathematical model describes an insect population with overlapping generations where the females are polyandrous and the males are subject to autosterilization. The relationship between the values of the parameters of the model and the time to extinction is illustrated.     

On necessary and sufficient conditions for group selection efficacy

The statement “group selection predominates over individual selection” is formulated within a class of patch-structured models. Conditions involving both “selfish” and “altruistic” predator characteristics are then shown to be necessary and sufficient for group selection predominance in this class of models. Maynard Smith's criterion M < 1 (Group selection, Quart. Rev. Biol., June 1976, pp. 277–283) is shown to be sufficient but not necessary for group selection predominance.     

Necessary and sufficient factors for the import of transfer RNA into the kinetoplast mitochondrion

The mechanism of active transport of transfer RNA (tRNA) across membranes is largely unknown. Factors mediating the import of tRNA into the kinetoplast mitochondrion of the protozoon Leishmania tropica are organized into a multiprotein RNA import complex (RIC) at the inner membrane. Here, we present the complete characterization of the identities and functions of the subunits of this complex. The complex contains three mitochondrion- and eight nuclear-encoded subunits; six of the latter are necessary and sufficient for import. Antisense-mediated knockdown of essential subunits resulted in the depletion of mitochondrial tRNAs and inhibition of organellar translation. Functional complexes were reconstituted with recombinant subunits expressed in Escherichia coli. Several essential RIC subunits are identical to specific subunits of respiratory complexes. These findings provide new information on the evolution of tRNA import and the foundation for detailed structural and mechanistic studies.     

Necessary conditions for isolation of tightly coupled higher plant mitochondria

A number of parameters associated with the isolation of plant mitochondria were carefully examined in the hope of optimizing the isolation technique. Dark-grown mung bean (Phaseolus aureus var. Jumbo) hypocotyls were used as the source of mitochondria. Necessary conditions for the isolation of tightly coupled plant mitochondria include: (a) gentle tissue disruption; (b) rigorous exclusion of contaminating particles from the mitochondrial fraction; (c) the use of an optimal grinding medium containing a high concentration of mannitol, 10 mm phosphate or triethanolamine buffer to maintain the pH above 7.2, ethylenediaminetetraacetic acid at 1 mm level, cysteine at a low concentration (0-5 mm), and a high concentration of bovine serum albumin (0.1-1.0%); and (d) the use of the proper wash and suspending medium consisting of mannitol, buffer, and bovine serum albumin at the same concentration as in the grinding medium.     

Necessary conditions for the method of inferring phylogeny by linear invariants.

It is known that if all the Markov transition matrices that govern the substitution of one nucleotide for another satisfy six linear constraints, then equations can be derived that permit one to infer evolutionary trees from nucleic acid sequences by the method of linear invariants. These sufficient conditions are also necessary. Any relaxation of them results in the loss of all linear invariants. Necessary conditions for any given set of linear invariants can be derived by examining conditions a matrix must satisfy to map a certain set of matrices into itself. To the extent that necessary conditions are incorrect, a method is not reliable. In a world where different parts of molecules evolve at different rates, the two-parameter model of Kimura may not be empirically distinguishable from the more general one treated here.     

Necessary conditions for avoiding incorrect polypeptide folds in conformational search by energy minimization

Low energy conformations have been generated for melittin, pancreatic polypeptide, and ribonuclease S-peptide, both in the vicinity of x-ray structures by energy refinement and by an unconstrained search over the entire conformational space. Since the structural polymorphism of these medium-sized peptides in crystal and solution is moderate, comparing the calculated conformations to x-ray and nmr data provides information on local and global behavior of potential functions. Local analysis includes standardization calculations, which show that models with standard geometry can approximate good resolution x-ray data with less than 0.5 Å rms deviation (RMSD). However, the atomic coordinates are shifted up to 2 Å RMSD by local energy minimization, and thus 2 Å is generally the smallest RMSD value one can target in a conformational search using the same energy evaluation models. The unconstrained search was performed by a buildup-type method based on dynamic programming. To accelerate the generation of structures in the conformational search, we used the ECEPP potential, defined in terms of standard polypeptide geometry. A number of low energy conformations were further refined by relaxing the assumption of standard bond lengths and bond angles through the use of the CHARMM potential, and the hydrophobic folding energies of Eisenberg and McLachlan were calculated. Each conformation is described in terms of the RMSD from the native, hydrogen-bonding structure, solvent-acessible surface area, and the ratio of surfaces corresponding to nonpolar and polar residues. The unconstrained search finds conformations that are different from the native, sometimes substantially, and in addition, have lower conformational energies than the native. The origin of deviations is different for each of the three peptides, but in all examples the refined x-ray structures have lower energies than the calculated incorrect folds when (1) the assumption of standard bond lengths and bond angles is relaxed; (2) a small and constant effective dielectric permittivity (ε < 10) is used; and (3) the hydrophobic folding energy is incorporated into the potential. © 1993 John Wiley & Sons, Inc.     

Ecological and evolutionary conditions for fruit abortion to regulate pollinating seed-eaters and increase plant reproduction

Coevolved mutualisms, such as those between senita cacti, yuccas, and their respective obligate pollinators, benefit both species involved in the interaction. However, in these pollination mutualisms the pollinator's larvae impose a cost on plants through consumption of developing seeds and fruit. The effects of pollinators on benefits and costs are expected to vary with the abundance of pollinators, because large population sizes result in more eggs and larval seed-eaters. Here, we develop the hypothesis that fruit abortion, which is common in yucca, senita, and plants in general, could in some cases have the function of limiting pollinator abundance and, thereby, increasing fruit production. Using a general steady-state model of fruit production and pollinator dynamics, we demonstrate that plants involved in pollinating seed-eater mutualisms can increase their fecundity by randomly aborting fruit. We show that the ecological conditions under which fruit abortion can improve plants fecundity are not unusual. They are best met when the plant is long-lived, the population dynamics of the pollinator are much faster than those of the plant, the loss of one fruit via abortion kills a larva that would have the expectation of destroying more than one fruit through its future egg laying as an adult moth, and the effects of fruit abortion on pollinator abundance are spatially localized. We then use the approach of adaptive dynamics to find conditions under which a fruit abortion strategy based on regulating the pollinator population could feasibly evolve in this type of plant-pollinator interaction.     

Thermodynamic stability of histone H3 is a necessary but not sufficient driving force for its evolutionary conservation

Determining the forces that conserve amino acid positions in proteins across species is a fundamental pursuit of molecular evolution. Evolutionary conservation is driven by either a protein's function or its thermodynamic stability. Highly conserved histone proteins offer a platform to evaluate these driving forces. While the conservation of histone H3 and H4 "tail" domains and surface residues are driven by functional importance, the driving force behind the conservation of buried histone residues has not been examined. Using a computational approach, we determined the thermodynamically preferred amino acids at each buried position in H3 and H4. In agreement with what is normally observed in proteins, we find a significant correlation between thermodynamic stability and evolutionary conservation in the buried residues in H4. In striking contrast, we find that thermodynamic stability of buried H3 residues does not correlate with evolutionary conservation. Given that these H3 residues are not post-translationally modified and only regulate H3-H3 and H3-H4 stabilizing interactions, our data imply an unknown function responsible for driving conservation of these buried H3 residues.     

Why psychiatric conditions are special: an evolutionary and cross-cultural perspective

In non-Western and premodern societies, approaches to sickness involved moral considerations laden with existential and spiritual implications. Healers and physicians had access to this aspect of their patient's lives, were expected to use it constructively, and often did so. The contemporary biomedical theory of disease no longer assigns to illness such metaphysical connotations. While general physicians are permitted - perhaps even advised - to avoid involvement in morally laden dialogues tied to illness and the self, such dilemmas are more prominent and qualitatively different in psychiatry, as psychiatric conditions often entail changes in self-conception, psychological disaffection, unacceptable behavior, and untoward personal reactions to social circumstances. Manifestations of psychiatric conditions can overwhelm an individual's control in areas of cognition, emotion, autonomy, social responsibility, behavior, and body functions - exactly those matters that "modern" individualistic minds are supposed to master. Consequently, psychiatric conditions challenge basic presuppositions of the modern, secular credo about personhood, disease, and behavior. They comprise a species of human problems ontologically distinct from the conditions handled by other medical disciplines.