UNDESIRABLE CONSEQUENCES OF NEGLECTING NONLINEARITY: RESPONSE TO COMMENTS BY LIEFTING ET AL. (2013) ON ROCHA & KLACZKO (2012)

In response to our previous study, Liefting et al. argue, in defense of their work on latitudinal variation of developmental‐rate reaction norms (RNs), that (1) developmental rate (the reciprocal of development time: rate = time^?1) is a more biologically relevant variable than development time; (2) the linear RN model is a valid approximation; and (3) three experimental points suffice to estimate RN parameters. Here, we reply to their comments. First, we give evidence that the complexity of actual development challenges the appealing simplicity of developmental rate. Using the same analysis as Liefting et al. to test their hypothesis with development time, instead of rate, reveals a pattern that is the opposite of their conclusion. Second, we show that a quadratic model is consistent with the whole development‐time RNs and explains this contradiction. Third, with the quadratic model, we introduce two parameters to study plasticity: the RN shape (the quadratic coefficient) and RN local plasticity (the derivative of the RN function). The first showed a statistically significant correlation with latitude; and the second showed a continuous variation pattern where all localized patterns can be found (positive, negative, or nonsignificant correlations with latitude) but certainly cannot be generalized.     

RECONSTRUCTIONS OF THE GRANA-FRETWORK SYSTEM OF A CHLOROPLAST

The grana-fretwork system was reconstructed from serial sections representing 0.5 μm slice, in profile view, from the midregion of a chloroplast of Nicotiana tabacum. Reconstructions show grana in multiple strata. The fretwork integrates the grana in all three dimensions. Large grana are visualized as complex structures consisting of two or more eccentrically stacked solids that vary in height and diameter. The close spacing and overlapping positions of grana in the plastid explain why phase microscopy cannot be used to demonstrate adequately the numerous strata of grana within a chloroplast. The grana are not far enough apart to allow for successful optical sectioning of a plastid in face view. In profile view no distinct grana can be resolved because the grana-fretwork system has the aspect of a “honeycomb.” Thus, observations with a light microscope are not adequate to determine the arrangement of grana in a chloroplast, and the recently-proposed model showing all grana of a plastid to be arranged in a single spiral ribbon must be rejected as incompatible with properties of real plastids.     

EVOLUTION OF VIVIPARITY: A PHYLOGENETIC TEST OF THE COLD‐CLIMATE HYPOTHESIS IN PHRYNOSOMATID LIZARDS

The evolution of viviparity is a key life‐history transition in vertebrates, but the selective forces favoring its evolution are not fully understood. With >100 origins of viviparity, squamate reptiles (lizards and snakes) are ideal for addressing this issue. Some evidence from field and laboratory studies supports the “cold‐climate” hypothesis, wherein viviparity provides an advantage in cold environments by allowing mothers to maintain higher temperatures for developing embryos. Surprisingly, the cold‐climate hypothesis has not been tested using both climatic data and phylogenetic comparative methods. Here, we investigate the evolution of viviparity in the lizard family Phrynosomatidae using GIS‐based environmental data, an extensive phylogeny (117 species), and recently developed comparative methods. We find significant relationships between viviparity and lower temperatures during the warmest (egg‐laying) season, strongly supporting the cold‐climate hypothesis. Remarkably, we also find that viviparity tends to evolve more frequently at tropical latitudes, despite its association with cooler climates. Our results help explain this and two related patterns that seemingly contradict the cold‐climate hypothesis: the presence of viviparous species restricted to low‐elevation tropical regions and the paucity of viviparous species at high latitudes. Finally, we examine whether viviparous taxa may be at higher risk of extinction from anthropogenic climate change.     

SOLVING THE PARADOX OF STASIS: SQUASHED STABILIZING SELECTION AND THE LIMITS OF DETECTION

Despite the potential for rapid evolution, stasis is commonly observed over geological timescales—the so‐called “paradox of stasis.” This paradox would be resolved if stabilizing selection were common, but stabilizing selection is infrequently detected in natural populations. We hypothesize a simple solution to this apparent disconnect: stabilizing selection is hard to detect empirically once populations have adapted to a fitness peak. To test this hypothesis, we developed an individual‐based model of a population evolving under an invariant stabilizing fitness function. Stabilizing selection on the population was infrequently detected in an “empirical” sampling protocol, because (1) trait variation was low relative to the fitness peak breadth; (2) nonselective deaths masked selection; (3) populations wandered around the fitness peak; and (4) sample sizes were typically too small. Moreover, the addition of negative frequency‐dependent selection further hindered detection by flattening or even dimpling the fitness peak, a phenomenon we term “squashed stabilizing selection.” Our model demonstrates that stabilizing selection provides a plausible resolution to the paradox of stasis despite its infrequent detection in nature. The key reason is that selection “erases its traces”: once populations have adapted to a fitness peak, they are no longer expected to exhibit detectable stabilizing selection.     

LIMITS TO BEHAVIORAL EVOLUTION: THE QUANTITATIVE GENETICS OF A COMPLEX TRAIT UNDER DIRECTIONAL SELECTION

Replicated selection experiments provide a powerful way to study how “multiple adaptive solutions” may lead to differences in the quantitative–genetic architecture of selected traits and whether this may translate into differences in the timing at which evolutionary limits are reached. We analyze data from 31 generations (n = 17,988) of selection on voluntary wheel running in house mice. The rate of initial response, timing of selection limit, and height of the plateau varied significantly between sexes and among the four selected lines. Analyses of litter size and realized selection differentials seem to rule out counterposing natural selection as a cause of the selection limits. Animal‐model analyses showed that although the additive genetic variance was significantly lower in selected than control lines, both before and after the limits, the decrease was not sufficient to explain the limits. Moreover, directional selection promoted a negative covariance between additive and maternal genetic variance over the first 10 generations. These results stress the importance of replication in selection studies of higher‐level traits and highlight the fact that long‐term predictions of response to selection are not necessarily expected to be linear because of the variable effects of selection on additive genetic variance and maternal effects.     

THE EVOLUTION OF COSTLY MATE PREFERENCES II. THE “HANDICAP” PRINCIPLE

We use a general additive quantitative genetic model to study the evolution of costly female mate choice by the “handicap” principle. Two necessary conditions must be satisfied for costly preference to evolve. The conditions are (i) biased mutation pressure on viability and (ii) a direct relationship between the degree of expression of the male mating character and viability. These two conditions explain the success and failure of previous models of the “handicap” principle. Our model also applies to other sources of fitness variation like migration and host-parasite coevolution, which cause effects equivalent to biased mutation.     

THE EVOLUTION OF PHENOTYPIC CORRELATIONS AND “DEVELOPMENTAL MEMORY”

Development introduces structured correlations among traits that may constrain or bias the distribution of phenotypes produced. Moreover, when suitable heritable variation exists, natural selection may alter such constraints and correlations, affecting the phenotypic variation available to subsequent selection. However, exactly how the distribution of phenotypes produced by complex developmental systems can be shaped by past selective environments is poorly understood. Here we investigate the evolution of a network of recurrent nonlinear ontogenetic interactions, such as a gene regulation network, in various selective scenarios. We find that evolved networks of this type can exhibit several phenomena that are familiar in cognitive learning systems. These include formation of a distributed associative memory that can “store” and “recall” multiple phenotypes that have been selected in the past, recreate complete adult phenotypic patterns accurately from partial or corrupted embryonic phenotypes, and “generalize” (by exploiting evolved developmental modules) to produce new combinations of phenotypic features. We show that these surprising behaviors follow from an equivalence between the action of natural selection on phenotypic correlations and associative learning, well‐understood in the context of neural networks. This helps to explain how development facilitates the evolution of high‐fitness phenotypes and how this ability changes over evolutionary time.     

High-resolution crossover maps for each bivalent of Zea mays using recombination nodules

Recombination nodules (RNs) are closely correlated with crossing over, and, because they are observed by electron microscopy of synaptonemal complexes (SCs) in extended pachytene chromosomes, RNs provide the highest-resolution cytological marker currently available for defining the frequency and distribution of crossovers along the length of chromosomes. Using the maize inbred line KYS, we prepared an SC karyotype in which each SC was identified by relative length and arm ratio and related to the proper linkage group using inversion heterozygotes. We mapped 4267 RNs on 2080 identified SCs to produce high-resolution maps of RN frequency and distribution on each bivalent. RN frequencies are closely correlated with both chiasma frequencies and SC length. The total length of the RN recombination map is about twofold shorter than that of most maize linkage maps, but there is good correspondence between the relative lengths of the different maps when individual bivalents are considered. Each bivalent has a unique distribution of crossing over, but all bivalents share a high frequency of distal RNs and a severe reduction of RNs at and near kinetochores. The frequency of RNs at knobs is either similar to or higher than the average frequency of RNs along the SCs. These RN maps represent an independent measure of crossing over along maize bivalents.     

Plant volatiles activating specific olfactory receptor neurons of the cabbage moth Mamestra brassicae L. (Lepidoptera, Noctuidae)

Herbivore insects are suitable model organisms for studying how plant odor information is encoded in olfactory receptor neurons (RNs). By the use of gas chromatography linked to electrophysiological recordings from single RNs, screening for sensitivity to naturally produced plant odorants is possible in order to determine the molecular receptive ranges of the neurons. Using this method, we have in this study of the cabbage moth, Mamestra brassicae, classified 21 types of olfactory RNs according to their responses to odorants present in the host plants of Brassicae, in the related species of Arabidopsis, as well as in essential oils of nonhost plants like ylang-ylang. Most of the RNs were tuned to one or a few structurally similar compounds, showing minimal overlap of their molecular receptive ranges. Whereas some RNs displayed a novel tuning, others were tuned to the same compounds as neurons in other insect species. We also found colocation in the same sensillum of 3 RN types with the same response characteristics and tuning as 3 colocated types described in heliothine moths living on different host plants. The presence of similar RN types across different insect species implies conservation or reappearance of the RN types, independent of the evolution of host plant ranges.     

THE EFFECT OF A PARTIAL BARRIER ON THE MOVEMENT OF A HYBRID ZONE

Computer simulations of clines (Brues, 1972; Endler, 1977) as well as theoretical arguments (Nagylaki, 1975), have shown that steps in gene frequencies will be pulled to partial barriers (areas of reduced gene flow) if they form within approximately a cline width of the partial barrier. The behavior of a hybrid zone between two chromosomal taxa (“Moreton” and “Torresian”) of the acridine grasshopper Caledia captiva in southeast Queensland has been analyzed and found to comform qualitatively with a model of altered gene flow patterns. Clines in four enzyme systems were analyzed for 1983 and 1986 along a transect across the hybrid zone. The clines have shifted towards an area of regenerating forest, while homozygote frequencies have increased at this point. This forest barrier has broken the continuity of the spatial distribution of C. captiva, forming population islands in part of the hybrid zone, and thus reducing the amount of gene flow. The distance between the barrier and the original cline is approximately of the order of a cline width, so that they would be expected to interact. Historical information suggests that the secondary contact between the “Moreton” and “Torresian” taxa occurred very recently (1844–1940), due to the intensive land-clearing activities during the European settlement.     

THE ORIGIN OF AN ORGAN: PHYLOGENETIC ANALYSIS OF EVOLUTIONARY INNOVATION IN THE DIGESTIVE TRACT OF FLIES (INSECTA: DIPTERA)

The cardia, a prominent digestive tract organ consisting of several specialized cell types, occurs throughout the “higher” or muscoid flies, division Schizophora of order Diptera. Phylogenetic analysis of cellular organization in 65 insect species from 36 families indicates that this organ originated within the order Diptera from ancestrally undifferentiated tissues. “Lower” flies, suborder “Nematocera,” display little or no epithelial cell specialization at the corresponding site. Scorpionflies of the outgroup order Mecoptera are similarly unspecialized. Intermediate levels of cellular specialization occur in Tabanomorpha, Asilomorpha and Aschiza, dipteran taxa that diverge between “Nematocera” and Schizophora. The distribution of epithelial characteristics suggests that the cardia evolved through a sequence of simple tissue transformations, combining changes in epithelial configuration with local differentiation of cell structure and function. The evolution of locally specialized cell types implies the emergence of structural genes and regulatory mechanisms through the modification of an ancestral genome that had not supported such extensive differentiation. Comparison of localized gene expression in Drosophila melanogaster with that in other fly species having greater or lesser degrees of cell specialization may provide a practical model system for studying specific patterns of mutation associated with such evolutionary innovation.     

PERSPECTIVE: THE PACE OF MODERN LIFE: MEASURING RATES OF CONTEMPORARY MICROEVOLUTION

We evaluate methods for measuring and specifying rates of microevolution in the wild, with particular regard to studies of contemporary, often deemed “rapid,” evolution. A considerable amount of ambiguity and inconsistency persists within the field, and we provide a number of suggestions that should improve study design, inference, and clarity of presentation. (1) Some studies measure change over time within a population (allochronic) and others measure the difference between two populations that had a common ancestor in the past (synchronic). Allochronic studies can be used to estimate rates of “evolution,” whereas synchronic studies more appropriately estimate rates of “divergence.” Rates of divergence may range from a small fraction to many times the actual evolutionary rates in the component populations. (2) Some studies measure change using individuals captured from the wild, whereas others measure differences after rearing in a common environment. The first type of study can be used to specify “phenotypic” rates and the later “genetic” rates. (3) The most commonly used evolutionary rate metric, the darwin, has a number of theoretical shortcomings. Studies of microevolution would benefit from specifying rates in standard deviations per generation, the haldane. (4) Evolutionary rates are typically specified without an indication of their precision. Readily available methods for specifying confidence intervals and statistical significance (regression, bootstrapping, randomization) should be implemented. (5) Microevolutionists should strive to accumulate time series, which can reveal temporal shifts in the rate of evolution and can be used to identify evolutionary patterns. (6) Evolutionary rates provide a convenient way to compare the tempo of evolution across studies, traits, taxa, and time scales, but such comparisons are subject to varying degrees of confidence. Comparisons across different time scales are particularly tenuous. (7) A number of multivariate rate measures exist, but considerable theoretical development is required before their utility can be determined. We encourage the continued investigation of evolutionary rates because the information they provide is relevant to a wide range of theoretical and practical issues.     

Equal frequencies of recombination nodules in both sexes of the pigeon suggest a basic difference with eutherian mammals.

The total number of recombination nodules (RNs) in the autosomal synaptonemal complexes (SCs) is statistically equivalent in oocytes and spermatocytes from the domestic pigeon Columba livia. The distribution on RNs along the three longest autosomes is also equivalent in oocytes and spermatocytes. The numbers of RNs show a linear relationship when plotted against SC length both in oocytes and spermatocytes. On the other hand, the ZW pair shows a single and strictly localized RN near the synaptic termini, but the ZZ pair shows unrestricted location of RNs (average 3.8). The ZW and ZZ pairs of the pigeon are euchromatic and do not show specific chromatin packing at pachytene in either sex. The lack of sex-specific differences in the number and location of RNs in the autosomal bivalents of C. livia and previous data on the chicken, suggest that the regulation of crossing-over is basically different in birds and mammals.     

A mathematical model for the batch reactor kinetics of algae growth

A mathematical model based on the Einstein law of photochemical equivalence is proposed to describe the batch growth of unicellular algae. The model was applied in an integrated form to cell concentration versus growth time data taken over an extended range of cell concentrations which include both the regions of “exponential” and “linear” growth. It is shown that a certain function of cell concentration contained in the integrated form of the model is linearly dependent on the growth time over both the “exponential” and “linear” growth regions.     

Is optimism optimal? Functional causes of apparent behavioural biases

We review the use of the terms ‘optimism’ and ‘pessimism’ to characterize particular types of behaviour in non-human animals. Animals can certainly behave as though they are optimistic or pessimistic with respect to specific motivations, as documented by an extensive range of examples in the literature. However, in surveying such examples we find that these terms are often poorly defined and are liable to lead to confusion. Furthermore, when considering behaviour within the framework of optimal decision theory using appropriate currencies, it is often misleading to describe animals as optimistic or pessimistic. There are two common misunderstandings. First, some apparent cases of biased behaviour result from misidentifying the currencies and pay-offs the animals should be maximising. Second, actions that do not maximise short-term pay-offs have sometimes been described as optimistic or pessimistic when in fact they are optimal in the long term; we show how such situations can be understood from the perspective of bandit models. Rather than describing suboptimal, unrealistic behaviour, the terms optimism and pessimism are better restricted to informal usage. Our review highlights the importance of choosing the relevant currency when attempting to predict the action of natural selection.     

THE MIGRATION PATTERNS OF THE PURPLE SANDPIPER CALIDRIS MARITIMA

Summers, R. W. 1994. The migration patterns of the Purple Sandpiper Calidris maritima. Ostrich 65: 167–173.

The Purple Sandpiper breeds largely in the Arctic, and winters (boreal season) on the rocky shores of the north Atlantic, further north than any other sandpiper. As the populations from Canada, Greenland, Iceland, Svalbard, Norway and Russia differ in wing and bill lengths it is possible to match measurements taken from breeding birds with samples of birds caught in winter. Ringing recoveries, especially from colour marked birds, have also helped to determine migration routes and wintering areas. Four populations move to the nearest ice-free coast. Two populations move south of the nearest ice-free coast, being replaced by larger birds from a more northerly population (“chain migration”). Only the north Canadian population is believed to migrate a long distance, “leap-frogging” other winter populations. These patterns are discussed in relation to theories for the migration patterns of waders.     

Beyond the GTP-cap: Elucidating the molecular mechanisms of microtubule catastrophe

Almost 40 years since the discovery of microtubule dynamic instability, the molecular mechanisms underlying microtubule dynamics remain an area of intense research interest. The “standard model” of microtubule dynamics implicates a “cap” of GTP-bound tubulin dimers at the growing microtubule end as the main determinant of microtubule stability. Loss of the GTP-cap leads to microtubule “catastrophe,” a switch-like transition from microtubule growth to shrinkage. However, recent studies, using biochemical in vitro reconstitution, cryo-EM, and computational modeling approaches, challenge the simple GTP-cap model. Instead, a new perspective on the mechanisms of microtubule dynamics is emerging. In this view, highly dynamic transitions between different structural conformations of the growing microtubule end – which may or may not be directly linked to the nucleotide content at the microtubule end – ultimately drive microtubule catastrophe.     

Movement of tropomyosin during regulation of vertebrate skeletal muscle: a simple physical model.

Using data obtained from (a) X-ray diffraction patterns of vertebrate skeletal muscle (b) three dimensional reconstructions from electron micrographs of in vitro aggregates of the thin filament proteins in the switched “on” and “off” positions (c) the analysis of the sequence of tropomyosin, a simple model can be proposed which may explain the geometrical arrangement of actin, tropomyosin and troponin during regulation. The “cooperative” behaviour exhibited by the thin filament can also be explained in terms of this arrangement.     

Robust mutant strain design by pessimistic optimization

Background

Flux Balance Analysis (FBA) based mathematical modeling enables in silico prediction of systems behavior for genome-scale metabolic networks. Computational methods have been derived in the FBA framework to solve bi-level optimization for deriving “optimal” mutant microbial strains with targeted biochemical overproduction. The common inherent assumption of these methods is that the surviving mutants will always cooperate with the engineering objective by overproducing the maximum desired biochemicals. However, it has been shown that this optimistic assumption may not be valid in practice.

Methods

We study the validity and robustness of existing bi-level methods for strain optimization under uncertainty and non-cooperative environment. More importantly, we propose new pessimistic optimization formulations: P-ROOM and P-OptKnock, aiming to derive robust mutants with the desired overproduction under two different mutant cell survival models: (1) ROOM assuming mutants have the minimum changes in reaction fluxes from wild-type flux values, and (2) the one considered by OptKnock maximizing the biomass production yield. When optimizing for desired overproduction, our pessimistic formulations derive more robust mutant strains by considering the uncertainty of the cell survival models at the inner level and the cooperation between the outer- and inner-level decision makers. For both P-ROOM and P-OptKnock, by converting multi-level formulations into single-level Mixed Integer Programming (MIP) problems based on the strong duality theorem, we can derive exact optimal solutions that are highly scalable with large networks.

Results

Our robust formulations P-ROOM and P-OptKnock are tested with a small E. coli core metabolic network and a large-scale E. coli iAF1260 network. We demonstrate that the original bi-level formulations (ROOM and OptKnock) derive mutants that may not achieve the predicted overproduction under uncertainty and non-cooperative environment. The knockouts obtained by the proposed pessimistic formulations yield higher chemical production rates than those by the optimistic formulations. Moreover, with higher uncertainty levels, both cellular models under pessimistic approaches produce the same mutant strains.

Conclusions

In this paper, we propose a new pessimistic optimization framework for mutant strain design. Our pessimistic strain optimization methods produce more robust solutions regardless of the inner-level mutant survival models, which is desired as the models for cell survival are often approximate to real-world systems. Such robust and reliable knockout strategies obtained by the pessimistic formulations would provide confidence for in-vivo experimental design of microbial mutants of interest.