Learning the evolutionarily stable strategy

The possibility that animals learn a “developmentally stable strategy” (DSS) (Dawkins, 1980) is an alternative in biological game theory to the idea that evolutionarily stable strategies (ESS) (Maynard Smith, 1972) are genetically determined. A learning rule is defined as a rule which assigns for every possible behaviour the probability of displaying that behaviour at each trial of a game as a function of previous payoffs. This report examines properties of the evolutionarily stable (ES) learning rule, i.e. the rule which, when adopted by a population, is uninvadable by a mutant with a different learning rule. The DSS is defined as the strategy used by individuals with the ES learning rule. With some simplifying assumptions, it is shown that the DSS is the ESS: the ES learning rule is a rule for learning ESSs. This and other properties of the ES learning rule suggested that an approximation to such a rule is the relative payoff sum (RPS) learning rule, which states that the probability of displaying a behaviour is equal to the cumulative payoff for that behaviour relative to the total sum of payoffs for the game. Residual payoffs and a memory factor are incorporated into the RPS learning rule to account for prior expectations of payoff and the decay of memory with time. Both features are adaptive. In simulations of several frequency dependent and frequency independent games using the RPS learning rule, the response of the simulated animals was consistent with the predictions of the ES learning rule. This analysis has shown how ESSs may be achieved by non-genetic means. The RPS learning rule is described in molecular terms utilizing synthesis, storage, and degradation of a substance which elicits the behavioural response. If the RPS learning rule is used by animals, it should be possible to identify within neurons substances whose synthesis is regulated by behavioural stimuli and which initiate alternative behaviours in proportion to their concentrations.     

A fast and symmetric DUST implementation to mask low-complexity DNA sequences.

The DUST module has been used within BLAST for many years to mask low-complexity sequences. In this paper, we present a new implementation of the DUST module that uses the same function to assign a complexity score to a sequence, but uses a different rule by which high-scoring sequences are masked. The new rule masks every nucleotide masked by the old rule and occasionally masks more. The new masking rule corrects two related deficiencies with the old rule. First, the new rule is symmetric with respect to reversing the sequence. Second, the new rule is not context sensitive; the decision to mask a subsequence does not depend on what sequences flank it. The new implementation is at least four times faster than the old on the human genome. We show that both the percentage of additional bases masked and the effect on MegaBLAST outputs are very small.     

The phylogeny of a species-level tendency: species heritability and possible deep origins of Bergmann's rule in tetrapods

One of the most widely recognized generalizations in biology is Bergmann's rule, the observation that, within species of birds and mammals, body size tends to be inversely related to ambient temperature. Recent studies indicate that turtles and salamanders also tend to follow Bergmann's rule, which hints that this species-level tendency originated early in tetrapod history. Furthermore, exceptions to Bergmann's rule are concentrated within squamate reptiles (lizards and snakes), suggesting that the tendency to express a Bergmann's rule cline may be heritable at the species level. We evaluated species-level heritability and early origination of Bergmann's rule by mapping size-latitude relationships for 352 species onto a tetrapod phylogeny. When the largest available dataset is used, Bergmann's rule shows significant phylogenetic signal, indicating species-level heritability. This represents one of the few demonstrations of heritability for an emergent species-level property and the first for an ecogeographic rule. When species are discretely coded as showing either Bergmann's rule or its converse, parsimony reconstructions suggest that: (1) the tendency to follow Bergmann's rule is ancestral for tetrapods, and (2) most extant species that express the rule have retained this tendency from that ancient ancestor. The first inference also generally holds when the discrete data or size-latitude correlation coefficients are analyzed using maximum likelihood, although the results are only statistically significant for some versions of the discrete analyses. The best estimates of ancestral states suggest that the traditional adaptive explanation for Bergmann's rule-conservation of metabolic heat-was not involved in the origin of the trait since that origin predates the evolution of endothermy. A more general thermoregulatory hypothesis could apply to endotherms and some ectotherms, but fails to explain why salamanders have retained Bergmann's rule. Thus, if thermoregulation underlies the origin of a Bergmann's rule tendency, this trait may have been continuously maintained while its cause changed. Alternatively, thermoregulation may not underlie Bergmann's rule in any tetrapod group. The results also suggest that many extinct groups not included in our analyses followed Bergmann's rule.     

Bergmann's rule in nonavian reptiles: turtles follow it,lizards and snakes reverse it

Abstract Bergmann's rule is currently defined as a within-species tendency for increasing body size with increasing latitude or decreasing environmental temperature. This well-known ecogeographic pattern has been considered a general trend for all animals, yet support for Bergmann's rule has only been demonstrated for mammals and birds. Here we evaluate Bergmann's rule in two groups of reptiles: chelonians (turtles) and squamates (lizards and snakes). We perform both nonphylogenetic and phylogenetic analyses and show that chelonians follow Bergmann's rule (19 of 23 species increase in size with latitude; 14 of 15 species decrease in size with temperature), whereas squamates follow the converse to Bergmann's rule (61 of 83 species decrease in size with latitude; 40 of 56 species increase in size with temperature). Size patterns of chelonians are significant using both nonphylogenetic and phylogenetic methods, whereas only the nonphylogenetic analyses are significant for squamates. These trends are consistent among major groups of chelonians and squamates for which data are available. This is the first study to document the converse to Bergmann's rule in any major animal group as well as the first to show Bergmann's rule in a major group of ectotherms. The traditional explanation for Bergmann's rule is that larger endothermic individuals conserve heat better in cooler areas. However, our finding that at least one ectothermic group also follows Bergmann's rule suggests that additional factors may be important. Several alternative processes, such as selection for rapid heat gain in cooler areas, may be responsible for the converse to Bergmann's rule in squamates.     

Simulation of Rapoport's rule for latitudinal species spread

Rapoport's rule claims that latitudinal ranges of plant and animal species are generally smaller at low than at high latitudes. However, doubts as to the generality of the rule have been expressed, because studies providing evidence against the rule are more numerous than those in support of it. In groups for which support has been provided, the trend of increasing latitudinal ranges with latitude is restricted to or at least most distinct at high latitudes, suggesting that the effect may be a local phenomenon, for example the result of glaciations. Here we test the rule using two models, a simple one-dimensional one with a fixed number of animals expanding in a northern or southerly direction only, and the evolutionary/ecological Chowdhury model using birth, ageing, death, mutation, speciation, prey-predator relations and food levels. Simulations with both models gave results contradicting Rapoport's rule. In the first, latitudinal ranges were roughly independent of latitude, in the second, latitudinal ranges were greatest at low latitudes, as also shown empirically for some well-studied groups of animals.     

The temperature-size rule in ectotherms: may a general explanation exist after all?

The majority of ectotherms mature at a larger size at lower rearing temperatures. Although this temperature-size rule is well established, a general explanation for this phenomenon has remained elusive. In this article, we address the problem by exploring the proximate and ultimate reasons for why a temperate grasshopper, Chorthippus brunneus, is an exception to the temperature-size rule. Using a complete set of life-history data to parameterize an established life-history model, we show that it is optimal for this species to mature at a larger size at higher temperatures. We also show that plasticity in adult size is determined by the relative difference between the minimum temperature thresholds for growth and development rates. The mechanism relates to aspects of the biophysical model of van der Have and de Jong. Ectotherms that obey the temperature-size rule are identified as having a higher temperature threshold for development rate than for growth rate; exceptions are identified as having a lower temperature threshold for development rate than for growth rate. The latter scenario may arise broadly in two ways. These are discussed in reference to the thermal biology of temperate grasshoppers and ectotherms in general.     

The 400 microsphere per piece "rule" does not apply to all blood flow studies

Microsphere experiments are useful in measuring regional organ perfusion as well as heterogeneity of blood flow within organs and correlation of perfusion between organ pieces at different time points. A 400 microspheres/piece "rule" is often used in planning experiments or to determine whether experiments are valid. This rule is based on the statement that 400 microspheres must lodge in a region for 95% confidence that the observed flow in the region is within 10% of the true flow. The 400 microspheres precision rule, however, only applies to measurements of perfusion to a single region or organ piece. Examples, simulations, and an animal experiment were carried out to show that good precision for measurements of heterogeneity and correlation can be obtained from many experiments with <400 microspheres/piece. Furthermore, methods were developed and tested for correcting the observed heterogeneity and correlation to remove the Poisson "noise" due to discrete microsphere measurements. The animal experiment shows adjusted values of heterogeneity and correlation that are in close agreement for measurements made with many or few microspheres/piece. Simulations demonstrate that the adjusted values are accurate for a variety of experiments with far fewer than 400 microspheres/piece. Thus the 400 microspheres rule does not apply to many experiments. A "rule of thumb" is that experiments with a total of at least 15,000 microspheres, for all pieces combined, are very likely to yield accurate estimates of heterogeneity. Experiments with a total of at least 25,000 microspheres are very likely to yield accurate estimates of correlation coefficients.     

Pair rule gene orthologs in spider segmentation

The activation of pair rule genes is the first indication of the metameric organization of the Drosophila embryo and thus forms a key step in the segmentation process. There are two classes of pair rule genes in Drosophila: the primary pair rule genes that are directly activated by the maternal and gap genes and the secondary pair rule genes that rely on input from the primary pair rule genes. Here we analyze orthologs of Drosophila primary and secondary pair rule orthologs in the spider Cupiennius salei. The expression patterns of the spider pair rule gene orthologs can be subdivided in three groups: even-skipped and runt-1 expression is in stripes that start at the posterior end of the growth zone and their expression ends before the stripes reach the anterior end of the growth zone, while hairy and pairberry-3 stripes also start at the posterior end, but do not cease in the anterior growth zone. Stripes of odd-paired, odd-skipped-related-1, and sloppy paired are only found in the anterior portion of the growth zone. The various genes thus seem to be active during different phases of segment specification. It is notable that the spider orthologs of the Drosophila primary pair rule genes are active more posterior in the growth zone and thus during earlier phases of segment specification than most orthologs of Drosophila secondary pair rule genes, indicating that parts of the hierarchy might be conserved between flies and spiders. The spider ortholog of the Drosophila pair rule gene fushi tarazu is not expressed in the growth zone, but is expressed in a Hox-like fashion. The segmentation function of fushi tarazu thus appears to be a newly acquired role of the gene in the lineage of the mandibulate arthropods.     

ATP-driven self-assembly of a morphogenetic protein in Bacillus subtilis

The N-end rule targets specific proteins for destruction in prokaryotes and eukaryotes. Here, we report a crystal structure of a bacterial N-end rule adaptor, ClpS, bound to a peptide mimic of an N-end rule substrate. This structure, which was solved at a resolution of 1.15 A, reveals specific recognition of the peptide alpha-amino group via hydrogen bonding and shows that the peptide's N-terminal tyrosine side chain is buried in a deep hydrophobic cleft that pre-exists on the surface of ClpS. The adaptor side chains that contact the peptide's N-terminal residue are highly conserved in orthologs and in E3 ubiquitin ligases that mediate eukaryotic N-end rule recognition. We show that mutation of critical ClpS contact residues abrogates substrate delivery to and degradation by the AAA+ protease ClpAP, demonstrate that modification of the hydrophobic pocket results in altered N-end rule specificity, and discuss functional implications for the mechanism of substrate delivery.     

Simulation of Rapoport's rule for latitudinal species spread

Rapoport's rule claims that latitudinal ranges of plant and animal species are generally smaller at low than at high latitudes. However, doubts as to the generality of the rule have been expressed, because studies providing evidence against the rule are more numerous than those in support of it. In groups for which support has been provided, the trend of increasing latitudinal ranges with latitude is restricted to or at least most distinct at high latitudes, suggesting that the effect may be a local phenomenon, for example the result of glaciations. Here we test the rule using two models, a simple one-dimensional one with a fixed number of animals expanding in a northern or southerly direction only, and the evolutionary/ecological Chowdhury model using birth, ageing, death, mutation, speciation, prey–predator relations and food levels. Simulations with both models gave results contradicting Rapoport's rule. In the first, latitudinal ranges were roughly independent of latitude, in the second, latitudinal ranges were greatest at low latitudes, as also shown empirically for some well-studied groups of animals.     

PREDICTING NUCLEAR GENE COALESCENCE FROM MITOCHONDRIAL DATA: THE THREE-TIMES RULE

Abstract.— Coalescence theory predicts when genetic drift at nuclear loci will result in fixation of sequence differences to produce monophyletic gene trees. However, the theory is difficult to apply to particular taxa because it hinges on genetically effective population size, which is generally unknown. Neutral theory also predicts that evolution of monophyly will be four times slower in nuclear than in mitochondrial genes primarily because genetic drift is slower at nuclear loci. Variation in mitochondrial DNA (mtDNA) within and between species has been studied extensively, but can these mtDNA data be used to predict coalescence in nuclear loci? Comparison of neutral theories of coalescence of mitochondrial and nuclear loci suggests a simple rule of thumb. The “three‐times rule” states that, on average, most nuclear loci will be monophyletic when the branch length leading to the mtDNA sequences of a species is three times longer than the average mtDNA sequence diversity observed within that species. A test using mitochondrial and nuclear intron data from seven species of whales and dolphins suggests general agreement with predictions of the three‐times rule. We define the coalescence ratio as the mitochondrial branch length for a species divided by intraspecific mtDNA diversity. We show that species with high coalescence ratios show nuclear monophyly, whereas species with low ratios have polyphyletic nuclear gene trees. As expected, species with intermediate coalescence ratios show a variety of patterns. Especially at very high or low coalescence ratios, the three‐times rule predicts nuclear gene patterns that can help detect the action of selection. The three‐times rule may be useful as an empirical benchmark for evaluating evolutionary processes occurring at multiple loci.     

WHEN RENSCH MEETS BERGMANN: DOES SEXUAL SIZE DIMORPHISM CHANGE SYSTEMATICALLY WITH LATITUDE?

Bergmann's and Rensch's rules describe common large-scale patterns of body size variation, but their underlying causes remain elusive. Bergmann's rule states that organisms are larger at higher latitudes (or in colder climates). Rensch's rule states that male body size varies (or evolutionarily diverges) more than female body size among species, resulting in slopes greater than one when male size is regressed on female size. We use published studies of sex-specific latitudinal body size clines in vertebrates and invertebrates to investigate patterns equivalent to Rensch's rule among populations within species and to evaluate their possible relation to Bergmann's rule. Consistent with previous studies, we found a continuum of Bergmann (larger at higher latitudes: 58 species) and converse Bergmann body size clines (larger at lower latitudes: 40 species). Ignoring latitude, male size was more variable than female size in only 55 of 98 species, suggesting that intraspecific variation in sexual size dimorphism does not generally conform to Rensch's rule. In contrast, in a significant majority of species (66 of 98) male latitudinal body size clines were steeper than those of females. This pattern is consistent with a latitudinal version of Rensch's rule, and suggests that some factor that varies systematically with latitude is responsible for producing Rensch's rule among populations within species. Identifying the underlying mechanisms will require studies quantifying latitudinal variation in sex-specific natural and sexual selection on body size.     

Extending Rapoport's rule to Pacific marine fishes

The mean bathymetric (depth) range of assemblages of marine fishes is negatively correlated with the depth at which the assemblage is found and negatively correlated with species richness. These findings support the creation of a new biogeographic rule patterned after the terrestrial Rapoport's Rules for Latitude and Elevation. Previous work on Rapoport's rule is extended to include this bathymetric rule and the basis for all known Rapoport's rules is generalized in hopes of broadening the search for other Rapoport's rules. Species richness is found to be correlated with Rapoport phenomena, consistent with previous studies. Moreover, local species richness is found to be strongly influenced by regional patterns of species richness (so-called macro-ecological factors), not just local influences such as productivity in the immediate area.     

Gloger's rule in plants: The species and ecosystem levels

Gloger''s rule posits that darker birds are found more often in humid environments than in arid ones, especially in the tropics. Accordingly, desert-inhabiting animals tend to be light-colored. This rule is also true for certain mammalian groups, including humans. Gloger''s rule is manifested at 2 levels: (1) at the species level (different populations of the same species have different pigmentation at different latitudes), and (2) at the species assembly level (different taxa at a certain geography have different pigmentation than other taxa found at different habitats or latitudes). Concerning plants, Gloger''s rule was first proposed to operate in many plant species growing in sand dunes, sandy shores and in deserts, because of being white, whitish, or silver colored, based on white trichomes, because of sand grains and clay particles glued to sticky glandular trichomes, or because of light-colored waxes. Recently, Gloger''s rule was shown to also be true at the intraspecific level in relation to protection of anthers from UV irradiation. While Gloger''s rule is true in certain plant taxa and ecologies, there are others where “anti-Gloger” coloration patterns exist. In some of these the selective agents are known and in others they are not. I present both Gloger and “anti-Gloger” cases and argue that this largely neglected aspect of plant biology deserves much more research attention.     

Learning to forage in a regenerating patchy environment: Can it fail to be optimal?

The behaviour of animals foraging along closed traplines of regenerating patches of food has been simulated using a learning rule that determines when an animal should leave the patch at which it is currently feeding to search for another one. The rule causes the animal to stay at the patch as long as it is feeding faster than it remembers doing. The foraging behaviour of one animal, and of two or more animals together, feeding in traplines containing patches of the same and of differing types has been simulated, and in all cases the foraging behaviour generated by the rule allowed the animals to exploit the food very efficiently. The learning model is also responsible for indirect social interactions among animals sharing the same trapline because the feeding of each animal reduces the availability of food for the others. This causes a population of animals to disperse themselves, on average, among patches of food according to the ideal free distribution. The relationship between the learning model and conventional optimal foraging models is examined and it is shown that it is pointless to try to account for learned behaviour in the context of optimal foraging theory.     

A mixed dispatching rule approach in FMS scheduling

Short-term scheduling in flexible manufacturing systems (FMSs) is a difficult problem because of the complexities and dynamic behavior of FMSs. To solve this problem, a dispatching rule approach is widely used. In this approach, however, a single dispatching rule is usually assigned for all machines in a system during a given scheduling interval. In this paper, a mixed dispatching rule which can assign a different dispatching rule for each machine is proposed. A search algorithm which selects an appropriate mixed dispatching rule using predictions based on discrete event simulation is developed for this approach. The search algorithm for the mixed dispatching rule is described in detail. The effectiveness (in meeting performance criteria) of the mixed dispatching rule and the efficiency of the search algorithm relative to exhaustive search (complete enumeration) is demonstrated on an FMS model. The mixed dispatching rule approach performs up to 15.9% better than the conventional approach, and is 4% better on average. The statistical significance of the results is dicussed.     

The Positive Inside Rule Is Stronger When Followed by a Transmembrane Helix

The translocon recognizes transmembrane helices with sufficient level of hydrophobicity and inserts them into the membrane. However, sometimes less hydrophobic helices are also recognized. Positive inside rule, orientational preferences of and specific interactions with neighboring helices have been shown to aid in the recognition of these helices, at least in artificial systems. To better understand how the translocon inserts marginally hydrophobic helices, we studied three naturally occurring marginally hydrophobic helices, which were previously shown to require the subsequent helix for efficient translocon recognition. We find no evidence for specific interactions when we scan all residues in the subsequent helices. Instead, we identify arginines located at the N-terminal part of the subsequent helices that are crucial for the recognition of the marginally hydrophobic transmembrane helices, indicating that the positive inside rule is important. However, in two of the constructs, these arginines do not aid in the recognition without the rest of the subsequent helix; that is, the positive inside rule alone is not sufficient. Instead, the improved recognition of marginally hydrophobic helices can here be explained as follows: the positive inside rule provides an orientational preference of the subsequent helix, which in turn allows the marginally hydrophobic helix to be inserted; that is, the effect of the positive inside rule is stronger if positively charged residues are followed by a transmembrane helix. Such a mechanism obviously cannot aid C-terminal helices, and consequently, we find that the terminal helices in multi-spanning membrane proteins are more hydrophobic than internal helices.     

Can Rapoport's rule explain tree species richness along the Himalayan elevation gradient,Nepal?

Rapoport's rule applied to an elevation gradient predicts a positive correlation between elevation ranges and elevation. This is supposed to be caused by the increasing magnitude of the climatic extremes at higher elevations, and thus, it is deduced that species richness should decrease with increasing elevation. The distribution of 614 tree species was used to test Rapoport's elevational rule along a gradient from 100 to 4300 m a.s.l., in the Nepalese Himalaya. The relationship between species richness and elevation was analysed by using generalized linear models (GLM). Generalized additive models (GAM) were used to examine the relationship between elevational range and the elevational mid-point of a species along the gradient. The widest elevation ranges are observed at mid-elevations, and narrow elevation ranges are observed at both ends of the gradient. This does not support Rapoport's elevation rule, as proposed by Stevens. There is a peak in species richness between 900 and 1000 m, and not in the tropical lowland as projected by Rapoport's elevation rule.     

Bivalent inhibitor of the N-end rule pathway.

The N-end rule relates the in vivo half-life of a protein to the identity of its N-terminal residue. Ubr1p, the recognition (E3) component of the Saccharomyces cerevisiae N-end rule pathway, contains at least two substrate-binding sites. The type 1 site is specific for N-terminal basic residues Arg, Lys, and His. The type 2 site is specific for N-terminal bulky hydrophobic residues Phe, Leu, Trp, Tyr, and Ile. Previous work has shown that dipeptides bearing either type 1 or type 2 N-terminal residues act as weak but specific inhibitors of the N-end rule pathway. We took advantage of the two-site architecture of Ubr1p to explore the feasibility of bivalent N-end rule inhibitors, whose expected higher efficacy would result from higher affinity of the cooperative (bivalent) binding to Ubr1p. The inhibitor comprised mixed tetramers of beta-galactosidase that bore both N-terminal Arg (type 1 residue) and N-terminal Leu (type 2 residue) but that were resistant to proteolysis in vivo. Expression of these constructs in S. cerevisiae inhibited the N-end rule pathway much more strongly than the expression of otherwise identical beta-galactosidase tetramers whose N-terminal residues were exclusively Arg or exclusively Leu. In addition to demonstrating spatial proximity between the type 1 and type 2 substrate-binding sites of Ubr1p, these results provide a route to high affinity inhibitors of the N-end rule pathway.