Category Archives: Lab meeting summaries
Lilly started this week’s proceedings by pointing out new work by Tom Price and colleagues, recently published in Proceedings B. Tom and his colleagues studied a latitudinal cline in rates of polyandry in North America that covaries with the prevalence of sex ratio (SR), a meiotic-driving X chromosome. A selfish genetic element on the driving X causes sperm that carry Y chromosomes to die during development, which has two consequences for fathers carrying SR:
- All offspring sired by SR males carry the driving X (which is great for the selfish genetic element);
- Fathers only produce half as many sperm (which is terrible for dads who have to compete for fertilizations within females who mate more than once). This is why SR is a “selfish” genetic element — it improves its own fitness at a cost to its bearer).
Given that SR carrying males produce fewer sperm, females who mate more than once incite sperm competition that favours males who do not carry SR. This is a winning outcome for males who do not carry SR, as they are more likely to win in sperm competition by producing twice as many sperm. It also is a boon for polyandrous females, who are more likely to produce sons, which are rare when SR is prevalent and therefore have relatively high fitness. Price and his colleagues show that the elevated polyandry observed in regions of high SR prevalence is heritable, and argue that polyandry may frequently evolve to help reduce the intragenomic conflict imposed by selfish genetic elements.
Andy Dobson introduced himself to Science Drinks by explaining his research interest in parasite-host dynamics and his recent and ongoing modelling work with Stu Auld on virulence evolution, which has been constrained by processing power of late. Tim P. suggested that implementing subroutines in platforms other than R might accelerate things, and used the word “vectorized” to describe this, which I somehow found amusing. The discussion soon degenerated into some speculation of who has the most computer power and who has the most data, to slow down even the biggest and baddest of PCs. Think Robot Wars for stats nerds (I retain the copyright for this idea but am open to negotiating TV rights).
Adam then brought in a few figures to illustrate his ideas for upcoming grant applications. These are naturally Top Secret! We wouldn’t want anyone to steal his ingenious plan to secure a big research council grant.
Tim then mentioned an inspiring astro-physical story that was recently published in Science on one of Saturn’s moons, Enceladus. Summarizing this kind of work is dangerous for an entomologist, but your bloggy servant will have a go anyway: Luciano Iess and colleagues used telemetric data and Doppler radar antennae during flybys of Enceladus by the Cassini spacecraft to map the gravity field of Enceladus. Their findings indicate a magnetic anomaly near the south pole of Enceladus that is consistent with a large subsurface ocean 30-40 km deep(!). Wow! Amazing how some advanced number crunching can illuminate us about the state of one of Saturn’s moons from so far away, using tracking and careful measurements of the time taken to bounce radar signals off objects….
Each of the undergrads in attendance then took a turn presenting the latest discoveries: Gregor showed us some of his most recent findings on the phenologies of dance flies; Claudia showed us some intriguing and contrasting effects of body size and mass on the accumulation of resources by crickets, and Toby showed us data indicating that the relationship between compound eye facet size (which prevails in unspecialized eyes) and interommatidial angle may be disrupted among flies with derived “bright zones”. Watch this space for more in the coming weeks.
Andy then asked a provocative question: how does brood parasitism in birds (such as is seen in cuckoos) evolve in the face of imprinting, which is the phenomenon that leads many birds to identify with whatever rears them? We engaged in quite a lot of speculation without finding convincing answers. I did since find a handy webpage containing an expert answer from Naomi Langmore from ANU.
We wrapped up Science Drinks with a meaty paper by Mathieu Delcourt and colleagues in PNAS (not so hot off the press, but only recently read by me). Delcourt and his colleagues note that most populations tend to remain phenotypically stable over time in spite of strong directional selection (for example strong sexual selection for the increased expression of some sexual traits) and substantial genetic variance for the traits in question. Most of the time we assume that selection must be balancing on the character in spite of strong selection in one context (for example because overinvestment in a trait starves other important life history traits of resources). By measuring the genetic covariance between traits under sexual selection and total fitness, the authors here were able to use the multivariate Robertson-Price identity (also called the “secondary theorem of natural selection”, this equation is an alternative to the Breeder’s equation which Michael Morrissey and his colleagues note makes fewer assumptions) to demonstrate that in spite of substantial directional selection on male cuticular hydrocarbons (CHCs), there was little multivariate genetic covariation between these traits and fitness. Instead, their analysis of trait deviations revealed stabilizing selection on some aspects of genetic variance in CHCs. This work clarifies new methods for studying evolutionary responses (or the lack of them) in wild systems.
Attendees for the latest Science Drinks session at the William Wallace included:
Lilly started the session by introducing a paper on allometry in cervids by Lemaître and colleagues recently published in Biology Letters. Allometry is the study of scaling relationships, and is typically quantified by measuring the slope of the line fit between a log-transformed “body size” index and log-transformed trait values. But a review by MacLeod (2010) pointed out several problems with standard assumptions by scientists studying allometry, including that the best-fit line is straight. Lemaître and colleagues show that the allometric relationship between (log) body mass and (log) antler length in cervids is curved, with the increase in antlers leveling off once mass reaches about 110 kg. they argue that this curvilinearity may be explained by energetic constraints on investment in antlers among the largest species., and caution that researchers should be mindful of possible nonlinearities when assessing scaling relationships.
Adam shared a different comparative study, this one focusing on the lengths of telomeres in chimps and humans and recently published in the American Journal of Human Biology. Telomeres are a section of repetitive DNA that caps the end of each chromosome, and that tend to shorten progressively as an animal ages because with every cell replication, a tiny bit of the telomere at the very end of the chromosome cannot be copied. The enzyme telomerase can restore lost telomere, but because this kind of repair mechanism is costly, the length of telomeres may reveal both individual-level information about biological age and susceptibility to degenerative diseases, as well as species-level investment in somatic repair that has evolved in conjunction with maximum longevity (see Monaghan 2010 for a great review of telomere dynamics in a life history context). Tackney and colleagues (2014) predicted that because the maximum longevity of humans exceeds that of chimps, chimps might have shorter telomeres or faster rates of telomeric loss than humans. The computed the relative signals of telomeric and single copy gene signals (T/S ratios) in white blood cells, and found that while their estimates of telomeric loss for chimps (approx. 73 nucleotides per year lost) exceeded that of humans (approximately 40 nucleotides per year), these rates were not statistically distinguishable. Moreover, the chimp telomeres were actually longer, having a T/S ratio around twice that of humans. It’s unclear what the implications of this finding are, but it raises many intriguing questions about the complex relationship between longevity and investment in repair that concerns all students of life history.
Toby showed some new figures, hot off the printer, illustrating some of his Hons research findings about the relationships between eye facet size divergence (which involves adaptations for photosensitivity) and the angles between facets (which may limit acuity) in dance flies. Claudia showed off some new plots and tables of coefficients of her own, involving the study of courtship and mating as a function of diet and social environment in crickets. I don’t want to step on imminent punch-lines: both Toby and Claudia will submit their dissertations in a few short weeks, and we’ll have a chance to see summaries of their work then. Stay tuned!
I (Luc) wrapped up the session by calling attention to a paper just published as an “early-view” manuscript on the journal Evolution‘s homepage by Walker (2014). This paper deals with a problem that is well-known but still underappreciated: when dealing with observation data (unmanipulated experimentally), coefficients of regression analyses will be biased upwards if any of the predictors are correlated with other causal factors that have been omitted from the model through ignorance or negligence. Walker uses simulations to show that this upward bias can be substantial, and argues that the problem is especially acute if one seeks to interpret coefficients as evidence for causal relationships. He further argues that the problem is not necessarily avoided by having prior knowledge of the “right traits” to include in one’s model, and carefully measuring candidate rival traits that one can include as covariates. He writes,
“forty percent of the time an additional covariate is added, even using omniscient prior knowledge of effect size, the error in the estimate of the effect is worse than if the confounder had been left unmeasured”.
This is deeply unsettling research for someone like me who spends a lot of time trying to find patterns of covariance in observational data (much of it by necessity since some of our work is on organisms that do little in the lab except die). Walker does point to directed acyclical graphs (structural equation models) as promising some clarity concerning causal relationships in observational data, which is satisfying news given my recent obsession with them, but overall the MS is more cautionary than prescriptive:
“Unless a functional model generates very specific predictions of effect magnitude, observational data is better used for testing model assumptions and not the mere presence of an effect. For studies where experimental manipulation or functional modeling is not an option, we may have to be content with simply not knowing the magnitude of effects very precisely.”
Science Drinks kicked off with Gregor explaining exciting progress he has made in his honours project work. Gregor is using mapping techniques (GIS) to examine the phenology of dance flies across the UK, trying to find whether there is a difference in emergence times across dance fly species which display both conventional and reversed sex roles.
Luc then presented to the group a paper recently accepted in Evolution looking at age-dependent performance and senescence in sport (Lailvaux, Wilson & Kasumovic 2014). The authors used an extensive dataset on male and female professional basketball players to investigate sex differences in ageing and performance. The main results included a trend for earlier senescence in males, and evidence that different male performance traits showed varying rates of senescence. The Science Drinks group discussed the paper at length, especially how aspects of the data and game were controlled for in the analyses.
Whilst the paper made me realise how very little I know about basketball it prompted a long discussion about the use of sport stats (of which there are apparently huge repositories for some sports) in scientific analyses. Luc explained his ongoing interest in analysing sumo wrestling statistics and then went on to describe a paper he co-authored in 2004. This paper used data from cricket (the sport not the insect) to show that there was evidence of negative-frequency dependent success of left-handed batsman in the 2003 cricket World Cup. After the group chatted about cricket for a while I added both cricket and sumo wrestling to the quickly growing list of sports I know absolutely nothing about! The discussion then moved on to the group pondering what other sports may have large and detailed datasets, collected and published by enthusiasts, that could be used to answer biological questions.
Adam was next to speak and gave us a very interesting introduction to his work. His main interests are senescence and menopause in mammals and he currently uses a large dataset of human birth and death records to answer questions in this field. This dataset was collected from pre-industrial Finnish church records that are apparently extensive and very detailed. He is currently using the dataset to try and find the effect that number of children has on maternal fitness and survival. An issue that he has found in this system is that if a mother died, her offspring often died soon after, meaning the causal relationship is reversed (a lack of maternal care affects child survival, rather than the birth of children affecting mothers). The challenge of disentangling complex causal relationships appears to be a persistent problem for life history research.
Finally, Stuart talked us through some thoughts he was having in his own field of study using Daphnia to look at host-parasite coevolution. A major interest of his currently surrounds the idea that not every parasite will successfully infect a host and will instead simply pass through the host’s digestive system unharmed. He is looking into the cost of a failed infection on the parasite and how this affects both host and parasite population dynamics and coevolution.
Attendees: Luc Bussiere, Elizabeth Herridge, Toby Hector, Claudia Santori, Gregor Hogg
To start with, Luc discussed ongoing struggles he is having in presenting some statistical concepts to first year students. It turns out that lecturers often have just as much trouble writing lecture material as we do understanding it! We debated the issue of making the material engaging enough to keep everyone interested in a difficult subject, and considered the contrasting pressure of getting all the information across when the lecture is a pivotal point in the course. Luc will report back on how his lectures went later on….
Next onto science as Toby presented a paper that has found a novel method of looking at depth perception using jumping spiders (Depth perception from image defocus in a jumping spider, 2012). The authors report evidence for the first known example of an animal (the jumping spider) that uses defocused images as a primary mechanism for depth perception.
Claudia then shared an interesting paper on the convergent evolution between Cane Toads and the Madagascan plant Mother of Millions (Interacting Impacts of Invasive Plants and Invasive Toads on Native Lizards, 2012). In a case study on the blue tongue lizard (Tiliqua scinoides) it was observed that while these omnivorous lizards are threatened by the invasion of toads in north western Australia, conspecifics from other areas of Australia are less affected by the poison of the toads, including where the toads have yet to invade. Researchers noticed that this pattern was consistent with the geographic occurrence of an ornamental plant from Madagascar – Mother of Millions (Bryophyllum spp.), introduced in the continent around the same time as the cane toads.
This seems to be a remarkable case of convergent evolution, where the toxins produced by the Mother of Millions are chemically extremely similar to the bufotoxins produced by the toads. The lizards that were found to have evolved resistance to the plant toxins also turned out to be tolerant to the poison of the cane toad. Different individuals from various geographical areas were collected and injected with a sublethal dose of toxin, and changes in their locomotor performance were then observed. Lizards located in areas where neither Mother of Millions nor Cane Toads were present were found to have to lowest tolerance to the toxins. This supports the idea that both the Mother of Millions and the Cane Toads impose selection on bufadienolide resistance.
Finally Lilly discussed some of her ongoing work on sexual selection in dance flies!
Attendees: Claudia Santori, Tim Paine, Moha Abdelaziz Mohamed, Gregor Hogg, Lilly Herridge, Toby Hector, Luc Bussière, Nils Bunnefeld
After an unplanned relocation of the Nov 5 Science Drinks, we found ourselves back at the Wallace, where the smell of new varnish only somewhat made up for the lack of other renovation surprises. Spoiler: the newly renovated pub does not provide free house port on every table after all, at least not yet.
Before the whole crowd had assembled, the keen early arrivals started chatting about spatial autocorrelation, because why not? Both Gregor and Toby face this problem in different respects in their honours work: Gregor finds spatial autocorrelation in his geographic information about species distributions, while Toby faces similar problems when assessing morphological information from different positions on a single animal. As soon as they sat down, we asked Tim and Nils if and how they might have addressed similar issues involving transects (not trans sex) in their ecological work. They respectively pointed to couple of potentially helpful sources. Tim suggested consulting Mark McPeek‘s work on the evolution of dragonfly morphology, while Nils referred us to his better half Lynsey McInnes‘ work on geographic ranges. Very helpful pointers — we’ll expect a status update from Toby and Gregor in a few weeks once they have digested some of these papers.
Lilly’s contribution was recent paper by Dowling and colleagues, recently published in JEB, demonstrating trans-generational effects (not trans sex) of exposure to mates on offspring fitness in Drosophila melanogaster flies. They manipulated female exposure to sexual conflict by both manipulating access to males and by cauterizing the genitals of males in some treatments, so that while there were many males they could not mate and transfer ejaculate accessory gland proteins that are known to impose conflict. Intriguingly, the offspring of the cauterized multiple male treatment did worst of all. It seems like the mechanisms that might cause this are numerous, and worth further study.
Nils then provided a fascinating and long discussion involving both the humanities and sciences, both pure and applied, and which provoked some fairly nuanced philosophy as well as no small amount of depression in the author of this blog. However, because the exact topic is the subject of ongoing work that might just be subject to embargo, I have to write very little here (I know, the readership of this blog is hardly wide enough to pose a risk, but better safe than sorry!) This is a lesson in the benefits of experiencing science drinks in person! Some topics are too hot to summarize later on. Maybe we can link to the paper in due course….
Before anyone could escape for the evening, I asked the crowd for advice on a project proposal concerning cotton plants and Spodoptera caterpillars that a colleague from Bangladesh and I are writing for an upcoming travel grant. Tim and Moha both had some very good insight on the plant biology and herbivory that will be useful in refining our ideas, and suggested some references by Anurag Agrawal and Sharon Strauss that I need to follow up on.
So as you can see (at least for the unexpurgated components of this summary), Science Drinks is usually fun AND productive! Join us for the next session if you can…
For the second consecutive week, we were forced to relocate from the Wallace Pub on account of renovations. Instead we met at the Meadowpark. After dealing with minor matters related to our own research projects, we discussed the organization of a new initiative for the research group: Journal Pub (aka Beer Review).
As part of an effort to catch up to some of the information age, we’re devoting ourselves to collectively reading some new and classic papers in several corners of evolutionary biology. We’ll organize our efforts using the newest page on our website: Journal Pub. Navigate there to learn about the topics and papers under discussion prior to a particular Journal Pub session, or go there after a session to see the brief written summaries of the papers as well as some annotations of our discussions on each of them. So there’s a bit of wrangling ahead to wrap our heads around a lot of difficult concepts, but it’s exciting to think that we might collectively learn about some very big and important ideas rather productively and quickly.
The first Journal Pub (location TBC) will occur on Nov 26. I have taken the liberty to assign responsibility for chief and adjunct reviewers of each paper, though naturally anyone can read more than the focal assigned papers. Looking forward to the discussions!
Dr Luc Bussière, Dr Timothy Paine, Elizabeth Herridge, Thomas Houslay, Toby Hector, Sam Paterson, Claudia Santori, Hazel Smith, Gregor Hogg
Our bi-weekly research meetings continued last night at the William Wallace with a number of interesting topics and surprising revelations such as: ‘I got Hep B in Croy’ from Dr Paine, ‘Twitchers are crazy’ from Lilly and ‘We build houses’ from Luc as a rebuttal on the subject of behavioural response to poor environments.
DISCLAIMER: Some of the above may have been taken wildly out of context.
‘From egg to dead’
The centre of discussion was of Hazel’s summer research project looking at the effect of different life history traits on phenology in dance flies. This impressive undertaking involved her designing a model to test a range of life history parameters (with regards to longevity, mating frequency and physiology) with the hope of making some predictions that could be tested experimentally.
So far her work has focused on getting the model up and running with the aim now to test the rest of the life history parameters. As is often the case, the current model design is very complex but Dr Paine made some helpful suggestions on model simplification such as eliminating aspects of functions that include random variation (for example, in nuptial gift size) and on running sensitivity analysis.
We followed Hazel’s coherent presentation with a fuzzy discussion on plasticity. It got deep. It got so deep in fact that your humble scribe does not feel entirely comfortable leading you down the contorted and abstract path that followed. If you’re really keen though have a look at this paper by Samuel Scheiner on the genetics of phenotypic plasticity that Tom recommended. If that wasn’t enough, have a look at this paper by Emilie Snell-Rood on the costs and benefits of phenotypic plasticity, or there is always ol’ trusty!
‘Yes, surprisingly I am still married…’
Next Tom showing us some cool results from ‘his’ (Tom’s words not mine Mrs Houslay) work on the effect of diet on the chemical composition of male decorated crickets. An arduous undertaking but with some promising implications for his research.
‘Tessellation, a cool word to use when neatly packing your fridge’
We finished up with a discussion on the physics of eyes as Toby presented some problems on the size of facets in some male dance flies.
Any other business:
There was a quick tactical discussion on how to peer pressure Lilly’s sister into presenting her work to the group during her visit. She’s doing some interesting work on dwarf elephants in the Mediterranean, she must be so jealous she’s not studying flies in Scotland! I would also suggest having a look at a short video from the Quirks & Quarks podcast.
Finally Luc proposed a research group Movember team effort extravaganza with a clean shave group photo scheduled for Friday. Movember for those who don’t know is a charity that is based around the noble art of growing a moustache. Lilly, Hazel and Claudia clearly felt left out of this discussion but not to worry as ‘Mosistas’ are considered an integral part of the event!
A rather low-key science drinks on this occasion, as the mid-semester break meant a number of people are away (including our Fearless Leader, who is swanning about in Finland right now). Stu and I were joined by Claudia, Gregor and Toby to discuss a diverse set of topics, ranging from where best to set up camp on Mull to why I have just ordered a pint of maggots through the internet. We also managed to talk some science, including a general discussion on the peer review process and how it works, as well as why it sometimes doesn’t. Gregor outlined his plans for his project for the statistics module he’s taking, in which he’s hoping to do some work on random forests – a machine learning technique involving ‘forests’ of decision trees that is useful for ‘small n large p‘ problems (that is, problems that are high-dimensional but have a low sample size). This means that Gregor will – like the best of us – get to spend the vast majority of his time glued to RStudio. Luckily for him, there is a wealth of information out there to help him get started. Even more luckily, it turns out that R users of random forest techniques also like to party.
Last night we met for our usual biweekly Research Group meeting, in our new favourite location – the Wallace Pub.
Luc began the meeting by highlighting Dr Jan Lindstrom’s visit to Stirling on the 28th of October to take part in the BES Seminar series. Dr Lindstrom is set to give a talk alliteratively titled “Sexual selection, signalling and senescence in sticklebacks”.
The limelight then fell to Claudia who outlined the motivation behind her dissertation. Claudia’s dissertation is based on a pattern Tom observed whilst carrying out his PhD. By subjecting male crickets to different diet treatments, and controlling access to females across these treatments, Tom was able to show that male calling effort is affected by both these factors. However, it now falls on Claudia, to explain the patterns observed, and to ultimately try and answer the question: Why does the effect of diet on calling activity depend on mate availability?
Claudia presented a number of hypotheses, which she believes may play a part in explaining Tom’s observations, in particular the fact that males have increased calling effort at the beginning of the experiment followed by a sharp decline depending on the exact diet and mate availability combination. One idea is that females may become choosy when exposed to promiscuous males, and males consequently to reduce their calling effort if they sense a female is reluctant to mate. Alternatively, the males may themselves become choosy as they perceive mating opportunities to increase, with their keenness to mate and hence calling effort decreasing as the number of times they mate increases. Tom’s observations may also be explained if the males are running out of energy as the experiment progresses, although the exact processes governing this depletion of resources are probably complex in the light of the interaction between diet and female availability.
Over the coming weeks, Claudia will design an experiment which will give us some insight into the patterns observed by Tom. Further details of the exact experiment planned will be posted as the dissertation progresses.
Dr Luc Bussière
Dr Timothy Paine
Dr Moha Abdelaziz Mohammed
Dr Evangelos Spyrakos
Tuesday saw the second biweekly “Science Drinks” of the semester. These events consist of staff and students from many scientific backgrounds in Biological and Environmental Science getting together to discuss cool science over beer (or a soft drink of your choice). The only requirement for attending is to bring along a science question, conundrum or interesting story or paper. I will give a brief synopsis below outlining some of the anecdotes, stories and discussions that took place in our session on Oct 8.
The evening started (after a trip to the bar) with Luc telling us all about the strange and wonderful swarming habits of the Mormon cricket (really a katydid!). These large insects form huge aggregations and ‘march’ through western North America eating everything in their way. This behaviour is apparently driven by the desire for food and salt leading them to try and catch the katydid in front (and stay ahead of the hungry katydid behind!). Luc went on to tell us how it is Mormon belief that when these swarms came to ‘plague’ them, God sent seagulls that ate until they vomited allowing them, as the story goes, to continue eating the crickets. It’s a nice story, although the vomit may have a little more to do with the katydids repugnant taste.
In the first Science Drinks of the semester, two weeks ago, Tim made the bold suggestion that humans have no muscles in their fingers. This was idea was promptly shot down by most of the group. However after some quick research and lots time squeezing and staring at our fingers we discovered that he was in fact correct. Apologies were given to Tim and the rest of us learned something quite interesting about our fingers.
Three researchers who were new to Science Drinks then gave brief descriptions of their interests and work.
Jen described how she uses mathematics to model protandry in natural systems. This lead to a lengthy discussion about the possibility that protandry is a sexually antagonistic trait.
Moha gave us an outline of his work on the Brassicaceae genus Erysimum. He works on mainland North America and several islands comparing how ecological and genetic mechanisms cause speciation and radiation. One of his main interests is the potential impact of plant-pollinator interactions on these processes. Interestingly he commented that just a single plant species might have up to 150 different pollinator species from 6 orders associated with it.
Evangelos gave an outline of his work looking at light penetration into lakes using satellite imaging. He then went on to explain to us biologists the applications of applied physics, such as playing pool.
The first paper of the night was presented to us by Gregor. The paper written by Healy et al., was titled: Metabolic rate and body size are linked with perception of temporal information. The article was intriguing to all and led to a lengthy discussion into the potential mechanisms for such increased visual perception speeds. Gregor also highlighted that in the literature, regions of insect eyes that have greater perception speeds (associated with mate assessment) are often called “love spots”. This hypothesis of ‘slow motion’ vision could have an interesting implication for my own work on acute visual zones in the eyes of male dance flies.
We then pondered the potential for sexual dimorphism in sensory perception systems due to different energetic requirements between males and females. The reasoning was that “females are egg machines” and so males may have higher levels of energy to expend on the metabolic costs needed for greater sensory perception speeds.
Healy, K., McNally, L., Ruxton, G.D., Cooper, N. & Jackson, A.L. (2013). Metabolic rate and body size are linked with perception of temporal information. Animal Behaviour, 86, 685-696.
Link to paper: HERE
The second paper was presented by Tom and was titled ‘Repeatability of behaviour: a meta-analysis’. This paper made some interesting suggestions about the repeatability of behaviours and the recording of behaviours both in laboratory and field experiments. Key points included the authors’ findings that male behaviours were typically more repeatable than female behaviours, possibly because females are more variable in their mate choice (maybe due to some system of learning). The important difference between process and measurement error was also discussed.
Bell, A.M., Hankison, S.J. & Laskowski, K.L. (2009). The repeatability of behaviour: a meta-analysis. Animal Behaviour, 77, 771-783.
Link to paper: HERE
We finally discussed the importance of fitting appropriate lines and error bars to graphs. Most importantly, when a variable has a definite top or bottom bound (such as data which can only be between zero and one), an error bar should not extend higher or lower than the point to which the data is limited.