From Lévy to Brownian: a computational model based on biological fluctuation

Background

Theoretical studies predict that Lévy walks maximizes the chance of encountering randomly distributed targets with a low density, but Brownian walks is favorable inside a patch of targets with high density. Recently, experimental data reports that some animals indeed show a Lévy and Brownian walk movement patterns when forage for foods in areas with low and high density. This paper presents a simple, Gaussian-noise utilizing computational model that can realize such behavior.

Methodology/Principal Findings

We extend Lévy walks model of one of the simplest creature, Escherichia coli, based on biological fluctuation framework. We build a simulation of a simple, generic animal to observe whether Lévy or Brownian walks will be performed properly depends on the target density, and investigate the emergent behavior in a commonly faced patchy environment where the density alternates.

Conclusions/Significance

Based on the model, animal behavior of choosing Lévy or Brownian walk movement patterns based on the target density is able to be generated, without changing the essence of the stochastic property in Escherichia coli physiological mechanism as explained by related researches. The emergent behavior and its benefits in a patchy environment are also discussed. The model provides a framework for further investigation on the role of internal noise in realizing adaptive and efficient foraging behavior.     

Feller processes: the next generation in modeling. Brownian motion, Lévy processes and beyond

We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of Lévy processes. Brownian Motion is one of the most frequently used continuous time Markov processes in applications. In recent years also Lévy processes, of which Brownian Motion is a special case, have become increasingly popular. Lévy processes are spatially homogeneous, but empirical data often suggest the use of spatially inhomogeneous processes. Thus it seems necessary to go to the next level of generalization: Feller processes. These include Lévy processes and in particular brownian motion as special cases but allow spatial inhomogeneities. Many properties of Feller processes are known, but proving the very existence is, in general, very technical. Moreover, an applicable framework for the generation of sample paths of a Feller process was missing. We explain, with practitioners in mind, how to overcome both of these obstacles. In particular our simulation technique allows to apply Monte Carlo methods to Feller processes.     

Lévy flight and Brownian search patterns of a free-ranging predator reflect different prey field characteristics

1. Search processes play an important role in physical, chemical and biological systems. In animal foraging, the search strategy predators should use to search optimally for prey is an enduring question. Some models demonstrate that when prey is sparsely distributed, an optimal search pattern is a specialised random walk known as a Lévy flight, whereas when prey is abundant, simple Brownian motion is sufficiently efficient. These predictions form part of what has been termed the Lévy flight foraging hypothesis (LFF) which states that as Lévy flights optimise random searches, movements approximated by optimal Lévy flights may have naturally evolved in organisms to enhance encounters with targets (e.g. prey) when knowledge of their locations is incomplete. 2. Whether free-ranging predators exhibit the movement patterns predicted in the LFF hypothesis in response to known prey types and distributions, however, has not been determined. We tested this using vertical and horizontal movement data from electronic tagging of an apex predator, the great white shark Carcharodon carcharias, across widely differing habitats reflecting different prey types. 3. Individual white sharks exhibited movement patterns that predicted well the prey types expected under the LFF hypothesis. Shark movements were best approximated by Brownian motion when hunting near abundant, predictable sources of prey (e.g. seal colonies, fish aggregations), whereas movements approximating truncated Lévy flights were present when searching for sparsely distributed or potentially difficult-to-detect prey in oceanic or shelf environments, respectively. 4. That movement patterns approximated by truncated Lévy flights and Brownian behaviour were present in the predicted prey fields indicates search strategies adopted by white sharks appear to be the most efficient ones for encountering prey in the habitats where such patterns are observed. This suggests that C. carcharias appears capable of exhibiting search patterns that are approximated as optimal in response to encountered changes in prey type and abundance, and across diverse marine habitats, from the surf zone to the deep ocean. 5. Our results provide some support for the LFF hypothesis. However, it is possible that the observed Lévy patterns of white sharks may not arise from an adaptive behaviour but could be an emergent property arising from simple, straight-line movements between complex (e.g. fractal) distributions of prey. Experimental studies are needed in vertebrates to test for the presence of Lévy behaviour patterns in the absence of complex prey distributions.     

What ecological factors favor the shift from distyly to homostyly? A study from the perspective of reproductive assurance

Aims Distyly is one of the most widespread floral polymorphisms promoting cross-fertilization. Evolutionary transition from obligate cross-fertilized distyly to predominantly self-fertilized homostyly is frequently documented in various groups. However, empirical studies concerning the ecological factors connected with this transition are still lacking. Primula chungensis, suggested to be evolving from distyly to homostyly, provides an ideal model for the study of the ecological factors concerned with this transition. We study P. chungensis to understand if autonomous self-fertilization would provide reproductive assurance for the self-fertilized homo-styled morph in the field.Methods The incompatibility features of P. chungensis were tested with hand-pollination experiments. We compared the capacity of autonomous self-fertilization between the distylous and homo-styled morph of P. chungensis in the field by excluding the pollinators with bags. In addition, the degrees of herkogamy of some P. chungensis plants were between the short-styled and homo-styled morphs. These plants were studied to understand whether they were able to obtain greater reproductive assurance when the herkogamy in the flowers was reduced.Important findings All three morphs of P. chungensis were highly self- and intra-morph compatible. The degree of herkogamy positively correlated with the capacity for autonomous self-fertilization. A negative correlation between the degree of herkogamy and the magnitude of pollen limitation was found, but no significant correlation was found between the degree of herkogamy and the contribution of cross-fertilization to overall fertilization. This study suggests that reducing the degree of herkogamy can significantly increase the reproductive assurance for a self-compatible plant. Our results provided evidence that the homo-styled morph of P. chungensis had the highest capacity for autonomous self-fertilization and the highest seed production in the field, because autonomous self-fertilization provided reproductive assurance for the homo-styled morph. This may cause selection towards the transition from distyly to homostyly.     

Lévy Flights and Self-Similar Exploratory Behaviour of Termite Workers: Beyond Model Fitting

Animal movements have been related to optimal foraging strategies where self-similar trajectories are central. Most of the experimental studies done so far have focused mainly on fitting statistical models to data in order to test for movement patterns described by power-laws. Here we show by analyzing over half a million movement displacements that isolated termite workers actually exhibit a range of very interesting dynamical properties –including Lévy flights– in their exploratory behaviour. Going beyond the current trend of statistical model fitting alone, our study analyses anomalous diffusion and structure functions to estimate values of the scaling exponents describing displacement statistics. We evince the fractal nature of the movement patterns and show how the scaling exponents describing termite space exploration intriguingly comply with mathematical relations found in the physics of transport phenomena. By doing this, we rescue a rich variety of physical and biological phenomenology that can be potentially important and meaningful for the study of complex animal behavior and, in particular, for the study of how patterns of exploratory behaviour of individual social insects may impact not only their feeding demands but also nestmate encounter patterns and, hence, their dynamics at the social scale.     

Behaviour during elevated water temperatures: can physiology explain movement of juvenile Atlantic salmon to cool water?

1. Temperature governs most physiological processes in animals. Ectotherms behaviourally thermoregulate by selecting habitats with temperatures regulating their body temperature for optimal physiological functioning. However, ectotherms can experience temperature extremes forcing the organisms to seek temperature refuge. 2. Fish actively avoid potentially lethal temperatures by moving to cool-water sites created by inflowing tributaries and groundwater seeps. Juvenile Atlantic salmon (Salmo salar) of different age classes exhibit different behavioural responses to elevated temperatures (>23 °C). Yearling (1+) and 2-year-old (2+) Atlantic salmon often cease feeding, abandon territorial behaviour and swim continuously in aggregations in cool-water sites; whereas young-of-the-year (0+) fish continue defending territories and foraging. 3. This study determined whether the behavioural shift in older individuals (2+) occurred when basal metabolic rate, driven by increasing water temperature, reached the maximum metabolic rate such that anaerobic pathways were recruited to provide energy to support vital processes. Behaviour (feeding and stress responses), oxygen consumption, muscle lactate and glycogen, and circulating blood lactate and glucose concentrations were measured in wild 0+ and 2+ Atlantic salmon acclimated to water temperatures between 16 and 28 °C. 4. Results indicate that oxygen consumption of the 2+ fish increased with temperature and reached a plateau at 24 °C, a temperature that corresponded to cessation of feeding and a significant increase in muscle and blood lactate levels. By contrast, oxygen consumption in 0+ fish did not reach a plateau, feeding continued and muscle lactate did not increase, even at the highest temperatures tested (28 °C). 5. To conclude, the experiment demonstrated that the 0+ and 2+ fish had different physiological responses to the elevated water temperatures. The results suggest that wild 2+ Atlantic salmon employ behavioural responses (e.g. movement to cool-water sites) at elevated temperatures in an effort to mitigate physiological imbalances associated with an inability to support basal metabolism through aerobic metabolic processes.     

Using likelihood to test for Lévy flight search patterns and for general power-law distributions in nature

1. Ecologists are obtaining ever-increasing amounts of data concerning animal movement. A movement strategy that has been concluded for a broad variety of animals is that of Lévy flights, which are random walks whose step lengths come from probability distributions with heavy power-law tails. 2. The exponent that parameterizes the power-law tail, denoted micro, has repeatedly been found to be within the Lévy range of 1 < micro 相似文献   

Making Young from Old: How is Sex Designed to Help?

Gametogenesis and syngamy are shown to incorporate, as key elements in their design, structures and processes that help to prevent age-related deterioration that accumulates in adult somas from being transferred directly to newly formed offspring. As such, in addition to producing new gene combinations, sex increases the separation of germ and soma. It follows as a central prediction that offspring of a species that has recently abandoned sex will manifest early in life some of the dysfunctions that formerly manifested only much later in life. These dysfunctions, which can include early onset of age-linked diseases such as cancer, should impede transitioning to non-sex, and therefore would help to account for sex’s maintenance. Evidence is reviewed, and found generally to support the hypothesis.     

How do ecologists select and use indicator species to monitor ecological change? Insights from 14 years of publication in Ecological Indicators

Indicator species (IS) are used to monitor environmental changes, assess the efficacy of management, and provide warning signals for impending ecological shifts. Though widely adopted in recent years by ecologists, conservation biologists, and environmental practitioners, the use of IS has been criticized for several reasons, notably the lack of justification behind the choice of any given indicator. In this review, we assess how ecologists have selected, used, and evaluated the performance of the indicator species. We reviewed all articles published in Ecological Indicators (EI) between January 2001 and December 2014, focusing on the number of indicators used (one or more); common taxa employed; terminology, application, and rationale behind selection criteria; and performance assessment methods. Over the last 14 years, 1914 scientific papers were published in EI, describing studies conducted in 53 countries on six continents; of these, 817 (43%) used biological organisms as indicators. Terms used to describe organisms in IS research included “ecological index”, “environmental index”, “indicator species”, “bioindicator”, and “biomonitor,” but these and other terms often were not clearly defined. Twenty percent of IS publications used only a single species as an indicator; the remainder used groups of species as indicators. Nearly 50% of the taxa used as indicators were animals, 70% of which were invertebrates. The most common applications behind the use of IS were to: monitor ecosystem or environmental health and integrity (42%); assess habitat restoration (18%); and assess effects of pollution and contamination (18%). Indicators were chosen most frequently based on previously cited research (40%), local abundance (5%), ecological significance and/or conservation status (13%), or a combination of two or more of these reasons (25%). Surprisingly, 17% of the reviewed papers cited no clear justification for their choice of indicator. The vast majority (99%) of publications used statistical methods to assess the performance of the selected indicators. This review not only improves our understanding of the current uses and applications of IS, but will also inform practitioners about how to better select and evaluate ecological indicators when conducting future IS research.     

Georgy Gause’s shift from ecology and evolutionary biology to antibiotics research: reasons,objectives, circumstances

Georgy Gause (1910–1986) is best known for his contribution to ecology and evolutionary theory. His book “The Struggle for Existence” (1934) inspired generations of ecologists. Yet his scientific interests were diverse, embracing many aspects of the life sciences and medicine. The most notable shift in his research took place in the early 1940s when he began to study antibiotics and discovered Gramicidin S. Superficially, this shift looked like an attempt to switch from purely theoretical to applied research during the years of World War II, but Gause’s decision may also have been seriously affected by the “Great Purge” and the growth of Lysenkoism. Personal factors played a significant role in his career too. In this article, we propose four factors which drove Gause to switch his focus from ecology to antibiotics: the inner logic of his scientific research, Stalin’s science policy and the growth of Lysenkoism, the sociopolitical influence of World War II, and personal relationships. We will also show how all these factors are interdependent to some extent.     

How many scientists does it take to change a paradigm?: New ideas to explain scientific observations are everywhere—we just need to learn how to see them

The scientific process requires a critical attitude towards existing hypotheses and obvious explanations. Teaching this mindset to students is both important and challenging.People who read about scientific discoveries might get the misleading impression that scientific research produces a few rare breakthroughs—once or twice per century—and a large body of ‘merely incremental'' studies. In reality, however, breakthrough discoveries are reported on a weekly basis, and one can cite many fields just in biology—brain imaging, non-coding RNAs and stem cell biology, to name a few—that have undergone paradigm shifts within the past decade.The truly surprising thing about discovery is not just that it happens at a regular pace, but that most significant discoveries occurred only after the scientific community had already accepted another explanation. It is not merely the accrual of new data that leads to a breakthrough, but a willingness to acknowledge that a problem that is already ‘solved'' might require an entirely different explanation. In the case of breakthroughs or paradigm shifts, this new explanation might seem far-fetched or nonsensical and not even worthy of serious consideration. It is as if new ideas are sitting right in front of everyone, but in their blind spots so that only those who use their peripheral vision can see them.Scientists do not all share any single method or way of working. Yet they tend to share certain prevalent attitudes: they accept ‘facts'' and ‘obvious'' explanations only provisionally, at arm''s length, as it were; they not only imagine alternatives, but—almost as a reflex—ask themselves what alternative explanations are possible.When teaching students, it is a challenge to convey this critical attitude towards seemingly obvious explanations. In the spring semester of 2009, I offered a seminar entitled The Process of Scientific Discovery to Honours undergraduate students at the University of Illinois-Chicago in the USA. I originally planned to cover aspects of discovery such as the impact of funding agencies, the importance of mentoring and hypothesis-driven as opposed to data-driven research. As the semester progressed, however, my sessions moved towards ‘teaching moments'' drawn from everyday life, which forced the students to look at familiar things in unfamiliar ways. These served as metaphors for certain aspects of the process by which scientists discover new paradigms.For the first seven weeks of the spring semester, the class read Everyday Practice of Science by Frederick Grinnell [1]. During the discussion of the first chapter, one of the students noted that Grinnell referred to a scientist generically as ‘she'' rather than ‘he'' or the neutral ‘he or she''. This use is unusual and made her vaguely uneasy: she wondered whether the author was making a sexist point. Before considering her hypothesis, I asked the class to make a list of assumptions that they took for granted when reading the chapter, together with the possible explanations for the use of ‘she'' in the first chapter, no matter how far-fetched or unlikely they might seem.For example, one might assume that Frederick Grinnell or ‘Fred'' is from a culture similar to our own. How would we interpret his behaviour and outlook if we knew that Fred came from an exotic foreign land? Another assumption is that Fred is male; how would we view the remark if we discover that Frederick is short for Fredericka? We have equally assumed that Fred, as with most humans, wants us to like him. Instead, perhaps he is being intentionally provocative in order to get our attention or move us out of our comfort zone. Perhaps he planted ‘she'' as a deliberate example for us to discuss, as he does later in the second chapter, in which he deliberately hides a strange item in plain sight within one of the illustrations in order to make a point about observing anomalies. Perhaps the book was written not by Fred but by a ghost writer? Perhaps the ‘she'' was a typo?The truly surprising thing about discovery is […] that most significant discoveries occurred only after the scientific community had already accepted another explanationLooking for patterns throughout the book, and in Fred''s other writing, might persuade us to discard some of the possible explanations: does ‘she'' appear just once? Does Fred use other unusual or provocative turns of phrase? Does Fred discuss gender bias or sexism explicitly? Has anyone written or complained about him? Of course, one could ask Fred directly what he meant, although without knowing him personally, it would be difficult to know how to interpret his answer or whether to take his remarks at face value. Notwithstanding the answer, the exercise is an important lesson about considering and weighing all possible explanations.Arguably, the most prominent term used in science studies is the notion of a ‘paradigm''. I use this term with reluctance, as it is extraordinarily ambiguous. For example, it could simply refer to a specific type of experimental design: a randomized, placebo-controlled clinical trial could be considered a paradigm. In the context of science studies, however, it most often refers to the idea of large-scale leaps in scientific world views, as promoted by Thomas Kuhn in The Structure of Scientific Revolutions [2]. Kuhn''s notion of a paradigm can lead one to believe—erroneously in my opinion—that paradigm shifts are the opposite of practical, everyday scientific problem-solving.A paradigm is recognized by the set of assumptions that an observer might not realize he or she is making…Instead, I propose here a definition of ‘paradigm'' that emphasizes not the nature of the problem, the type of discovery or the scope of its implications, but rather the psychology of the scientist. A scientist viewing a problem or phenomenon resides within a paradigm when he or she does not notice, and cannot imagine, that an alternative way of looking at things needs to be considered seriously. Importantly, a paradigm is not a viewpoint, model, interpretation, hypothesis or conclusion. A paradigm is not the object that is viewed but the lenses through which it is viewed. A paradigm is recognized by the set of assumptions that an observer might not realize he or she is making, but which imply many automatic expectations and simultaneously prevent the observer from seeing the issue in any other fashion.For example, the teacher–student paradigm feels natural and obvious, yet it is merely set up by habit and tradition. It implies lectures, assignments, grades, ways of addressing the professor and so on, all of which could be done differently, if we had merely thought to consider alternatives. What feels most natural in a paradigm is often the most arbitrary. When we have a birthday, we expect to have a cake with candles, yet there is no natural relationship at all between birthdays, cakes and candles. In fact, when something is arbitrary or conventional yet feels entirely natural, that is an important clue that a paradigm is present.It is certainly natural for people to colour their observations according to their expectations: “To a man with a hammer, everything looks like a nail,” as Mark Twain put it. However, this is a pitfall that scientists (and doctors) must try hard to avoid. When I was a first-year medical student at Albert Einstein College of Medicine in New York City, we took a class on how to approach patients. As part of this course, we attended a session in which a psychiatrist interviewed a ‘normal, healthy old person'' in order to understand better the lives and perspectives of the elderly.A man came in, and the psychiatrist began to ask him some benign questions. After about 10 minutes, however, the man began to pause before answering; then his answers became terse; then he said he did not feel well, excused himself and abruptly left the room. The psychiatrist continued to lecture to the students for another half-hour, analysing and interpreting the halting responses in terms of the emotional conflicts that the man was experiencing. ‘Repression'', ‘emotional blocks'', and ‘reaction formation'' were some of the terms bandied about.However, unbeknown to the class, the man had collapsed just on the other side of the classroom door. Two cardiologists happened to be walking by and instantly realized the man was having an acute heart attack. They instituted CPR on the spot, but the man died within a few minutes.The psychiatrist had been told that the man was healthy, and thus interpreted everything that he saw in psychological terms. It never entered his mind that the man might have been dying in front of his eyes. The cardiologists saw a man having a heart attack, and it never entered their minds that the man might have had psychological issues.The movie The Sixth Sense [3] resonated particularly well with my students and served as a platform for discussing attitudes that are helpful for scientific investigation, such as “keep an open mind”, “reality is much stranger than you can imagine” and “our conclusions are always provisional at best”. Best of all, The Sixth Sense demonstrates the tension that exists between different scientific paradigms in a clear and beautiful way. When Haley Joel Osment says, “I see dead people,” does he actually see ghosts? Or is he hallucinating?…when scientists reach a conclusion, it is merely a place to pause and rest for a moment, not a final destinationIt is important to emphasize that these are not merely different viewpoints, or different ways of defining terms. If we argued about which mountain is higher, Everest or K2, we might disagree about which kind of evidence is more reliable, but we would fundamentally agree on the notion of measurement. By contrast, in The Sixth Sense, the same evidence used by one paradigm to support its assertion is used with equal strength by the other paradigm as evidence in its favour. In the movie, Bruce Willis plays a psychologist who assumes that Osment must be a troubled youth. However, the fact that he says he sees ghosts is also evidence in favour of the existence of ghosts, if you do not reject out of hand the possibility of their existence. These two explanations are incommensurate. One cannot simply weigh all of the evidence because each side rejects the type of evidence that the other side accepts, and regards the alternative explanation not merely as wrong but as ridiculous or nonsensical. It is in this sense that a paradigm represents a failure of imagination—each side cannot imagine that the other explanation could possibly be true, or at least, plausible enough to warrant serious consideration.The failure of imagination means that each side fails to notice or to seek ‘objective'' evidence that would favour one explanation over the other. For example, during the episodes when Osment saw ghosts, the thermostat in the room fell precipitously and he could see his own breath. This certainly would seem to constitute objective evidence to favour the ghost explanation, and the fact that his mother had noticed that the heating in her apartment was erratic suggests that the temperature change was not simply another imagined symptom. But the mother assumed that the problem was in the heating system and did not even conceive that this might be linked to ghosts—so the ‘objective'' evidence certainly was not compelling or even suggestive on its own.Osment did succeed eventually in convincing his mother that he saw ghosts, and he did it in the same way that any scientist would convince his colleagues: namely, he produced evidence that made perfect sense in the context of one, and only one, explanation. First, he told his mother a secret that he said her dead mother had told him. This secret was about an incident that had occurred before he was born, and presumably she had never spoken of it, so there was no obvious way that he could have learned about it. Next, he told her that the grandmother had heard her say “every day” when standing near her grave. Again, the mother had presumably visited the grave alone and had not told anyone about the visit or about what was said. So, the mother was eventually convinced that Osment must have spoken with the dead grandmother after all. No other explanation seemed to fit all the facts.Is this the end of the story? We, the audience, realize that it is possible that Osment had merely guessed about the incidents, heard them second-hand from another relative or (as with professional psychics) might have retold his anecdotes whilst looking for validation from his mother. The evidence seems compelling only because these alternatives seem even less likely. It is in this same sense that when scientists reach a conclusion, it is merely a place to pause and rest for a moment, not a final destination.Near the end of the course, I gave a pop-quiz asking each student to give a ‘yes'' or ‘no'' answer, plus a short one-sentence explanation, to the following question: Donald Trump seems to be a wealthy businessman. He dresses like one, he has a TV show in which he acts like one, he gives seminars on wealth building and so on. Everything we know about him says that he is wealthy as a direct result of his business activities. On the basis of this evidence, are we justified in concluding that he is, in fact, a wealthy businessman?About half the class said that yes, if all the evidence points in one direction, that suffices. About half the class said ‘no'', the stated evidence is circumstantial and we do not know, for example, what his bank balance is or whether he has more debt than equity. All the evidence we know about points in one direction, but we might not know all the facts.Even when looked at carefully, not every anomaly is attractive enough or ‘ripe'' enough to be pursued when first noticedHow do we know whether or not we know all the facts? Again, it is a matter of imagination. Let us review a few possible alternatives. Maybe his wealth comes from inheritance rather than business acumen; or from silent partners; or from drug running. Maybe he is dangerously over-extended and living on borrowed money; maybe his wealth is more apparent than real. Maybe Trump Casinos made up the role of Donald Trump as its symbol, the way McDonald''s made up the role of Ronald McDonald?Several students complained that this was a ridiculous question. Yet I had posed this just after Bernard Madoff''s arrest was blanketing the news. Madoff was known as a billionaire investor genius for decades and had even served as the head of the Securities and Exchange Commission. As it turned out, his money was obtained by a massive Ponzi scheme. Why was Madoff able to succeed for so long? Because it was inconceivable that such a famous public figure could be a common con man and the people around him could not imagine the possibility that his livelihood needed to be scrutinized.To this point, I have emphasized the benefits of paying attention to anomalous, strange or unwelcome observations. Yet paradoxically, scientists often make progress by (provisionally) putting aside anomalous or apparently negative findings that seem to invalidate or distract from their hypothesis. When Rita Levi-Montalcini was assaying the neurite-promoting effects of tumour tissue, she had predicted that this was a property of tumours and was devastated to find that normal tissue had the same effects. Only by ‘ignoring'' this apparent failure could she move forward to characterize nerve growth factor and eventually understand its biology [4].Another classic example is Huntington disease—a genetic disorder in which an inherited alteration in the gene that encodes a protein, huntingtin, leads to toxicity within certain types of neuron and causes a progressive movement disorder associated with cognitive decline and psychiatric symptoms. Clinicians observed that the offspring of Huntington disease patients sometimes showed symptoms at an earlier age than their parents, and this phenomenon, called ‘genetic anticipation'', could affect successive generations at earlier and earlier ages of onset. This observation was met with scepticism and sometimes ridicule, as everything that was known about genetics at the time indicated that genes do not change across generations. Ascertainment bias was suggested as a much more probable explanation; in other words, once a patient is diagnosed with Huntington disease, their doctors will look at their offspring much more closely and will thus tend to identify the onset of symptoms at an earlier age. Eventually, once the detailed genetics of the disease were understood at the molecular level, it was shown that the structure of the altered huntingtin gene does change. Genetic anticipation is now an accepted phenomenon.…in fact, schools teach a lot about how to test hypotheses but little about how to find good hypotheses in the first placeWhat does this teach us about discovery? Even when looked at carefully, not every anomaly is attractive enough or ‘ripe'' enough to be pursued when first noticed. The biologists who identified the structure of the abnormal huntingtin gene did eventually explain genetic anticipation, although they set aside the puzzling clinical observations and proceeded pragmatically according to their (wrong) initial best-guess as to the genetics. The important thing is to move forward.Finally, let us consider the case of Grigori Perelman, an outstanding mathematician who solved the Poincaré Conjecture a few years ago. He did not tell anyone he was working on the problem, lest their ‘helpful advice'' discourage him; he posted his historic proof online, bypassing peer-reviewed journals altogether; he turned down both the Fields Medal and a million dollar prize; and he has refused professorial posts at prestigious universities. Having made a deliberate decision to eschew the external incentives associated with science as a career, his choices have been written off as examples of eccentric anti-social behaviour. I suggest, however, that he might have simply recognized that the usual rules for success and the usual reward structure of the scientific community can create roadblocks, which had to be avoided if he was to solve a supposedly unsolvable problem.If we cannot imagine new paradigms, then how can they ever be perceived, much less tested? It should be clear by now that the ‘process of scientific discovery'' can proceed by many different paths. However, here is one cognitive exercise that can be applied to almost any situation. (i) Notice a phenomenon, even if (especially if) it is familiar and regarded as a solved problem; regard it as if it is new and strange. In particular, look hard for anomalous and strange aspects of the phenomenon that are ignored by scientists in the field. (ii) Look for the hidden assumptions that guide scientists'' thinking about the phenomenon, and ask what kinds of explanation would be possible if the assumptions were false (or reversed). (iii) Make a list of possible alternative explanations, no matter how unlikely they seem to be. (iv) Ask if one of these explanations has particular appeal (for example, if it is the most elegant theoretically; if it can generalize to new domains; and if it would have great practical impact). (v) Ask what kind of evidence would allow one to favour that hypothesis over the others, and carry out experiments to test the hypothesis.The process just outlined is not something that is taught in graduate school; in fact, schools teach a lot about how to test hypotheses but little about how to find good hypotheses in the first place. Consequently, this cognitive exercise is not often carried out within the brain of an individual scientist. Yet this creative tension happens naturally when investigators from two different fields, who have different assumptions, methods and ways of working, meet to discuss a particular problem. This is one reason why new paradigms so often emerge in the cross-fertilization of different disciplines.There are of course other, more systematic ways of searching for hypotheses by bringing together seemingly unrelated evidence. The Arrowsmith two-node search strategy [5], for instance, is based on distinct searches of the biomedical literature to retrieve articles on two different areas of science that have not been studied in relation to each other, but that the investigator suspects might be related in some fashion. The software identifies common words or phrases, which might point to meaningful links between them. This is but one example of ‘literature-based discovery'' as a heuristic technique [6], and in turn, is part of the larger data-driven approach of ‘text mining'' or ‘data mining'', which looks for unusual, new or unexpected patterns within large amounts of observational data. Regardless of whether one follows hypothesis-driven or data-driven models of investigation, let us teach our students to repeat the mantra: ‘odd is good''!? Open in a separate windowNeil R Smalheiser     

Toward Système International d'Unité-traceable protein quantification: from amino acids to proteins

Here we present a demonstration of the proof of principle that absolute concentration of a protein within a mixture of other proteins can be measured with SI traceability. The method used was based on tryptic digestion of a protein followed by quantification using double exact matching isotope dilution mass spectrometry (IDMS) of the peptides released. To provide full SI traceability to measurements of protein concentration we demonstrated a method of SI traceable peptide quantification in which the peptide standards used were quantified by an amino acid analysis method that incorporated double exact matching IDMS and amino acid standards of known purity. The concentration of the protein was therefore determined based upon the concentration of tryptic peptides, which in turn had been quantified based upon amino acid standards. This allowed fully SI-traceable measurements of protein concentration to be made. Important caveats in the implementation of this approach are also discussed and examples of how these can have detrimental effects on the measurements are shown.     

Evolutionary consequences of extensive morph loss in tristylous decodon verticillatus (Lythraceae): a shift from tristyly to distyly?

The evolution of distyly from tristyly has occurred repeatedly, especially in the Lythraceae. However, the evolutionary forces involved remain unclear since species exhibiting transitional stages between tristyly and distyly have rarely been studied. The self-compatible, wetland perennial Decodon verticillatus (Lythraceae) may provide this transitional variation since populations commonly lack style morphs, particularly the mid-styled (M) morph. In dimorphic populations lacking the M morph, anthers positioned at the mid level in both the long- (L) and short-styled (S) morphs have lost their target stigma, setting the stage for either evolutionary repositioning of mid-level anthers to increase pollen export to L and S stigmas, or increased variability in mid-level anther position resulting from relaxed selection. We examined these two hypotheses by comparing floral morphology in eight dimorphic and ten trimorphic populations from throughout the species’ range. We found no evidence that loss of the M morph has led to evolutionary modification of mid-level stamens. While mid-level stamens of the S morph were 11.0 ± 4.0% (mean ± 1 SE) longer than those of the L morph in dimorphic populations, divergence in stamen length between morphs occurred to the same extent (10.4 ± 2.0%) in trimorphic populations and cannot be attributed to the absence of the M morph. Analyses of variability using median ratio tests revealed no difference in the variability of mid-level stamen length between dimorphic and trimorphic populations. Mid-level stamens were not more variable than long- and short-level stamens within dimorphic populations. The consistent divergence in mid-level stamens between the L and S morphs may reflect morph-specific differences in the optimal position of mid-level anthers for maximizing cross-pollination and avoiding self-fertilization.     

Binding of amphipathic α-helical antimicrobial peptides to lipid membranes: Lessons from temporins B and L

Temporins constitute a family of amphipathic α-helical antimicrobial peptides (AMP) and contain some of the shortest cytotoxic peptides, comprised of only 10-14 residues. General characteristics of temporins parallel those of other AMP, both in terms of structural features and biophysical properties relating to their interactions with membrane lipids, with selective lipid-binding properties believed to underlie the discrimination between target vs host cells. Lipid-binding properties also contribute to the cytotoxicity AMP, causing permeabilization of their target cell membranes. The latter functional property of AMP involves highly interdependent acidic phospholipid-induced conformational changes, aggregation, and formation of toxic oligomers in the membrane. These oligomers are subsequently converted to amyloid-type fibers, as demonstrated for e.g. temporins B and L in our laboratory, and more recently for dermaseptins by Auvynet et al. Amyloid state represents the generic minimum in the folding/aggregation free energy landscape, and for AMP its formation most likely serves to detoxify the peptides, in keeping with the current consensus on mature amyloid being inert and non-toxic. The above scenario is supported by sequence analyses of temporins as well as other amphipathic α-helical AMP belonging to diverse families. Accordingly, sequence comparison identifies ‘conformational switches’, domains with equal probabilities for adopting random coil, α-helical and β-sheet structures. These regions were further predicted also to aggregate and assemble into amyloid β-sheets. Taken together, the lipid-binding properties and structural characterization lend support to the notion that the mechanism of membrane permeabilization by temporins B and L and perhaps of most AMP could be very similar, if not identical, to that of the paradigm amyloid forming cytotoxic peptides, responsible for degenerative cell loss in e.g. prion, Alzheimer's and Parkinson's disease, and type 2 diabetes.