Tuesday, May 1, 2007

Independent Project done

I finished up my independent project over the weekend. I ended up going back to my original idea - using Mantel tests to test for niche complementarity in understory flycatchers at La Selva. The data was collected primarily by my advisor, Tom Sherry, in the 1970s with some recent observations collected in 2000 and 2003. The data included habitats, foraging heights, diet (order/family of arthropods consumed, as determined from gut contents), and prey size (again from gut contents) of 15 species. The hypothesis was that birds that were similar in one niche dimension - e.g., habitat - would differ in another niche dimension - e.g., diet - or, at the least, not be similar in more than one.

I took the compiled data, imported it into R, and calculated dissimilarity values for all pairs of species (e.g., 1 vs 2, 1 vs 3, 2 vs 3, and so on...) for each niche parameter. These values were then compiled into matrices, which were then run through Mantel tests. Mantel tests allow you to test for correlations between two matrices - essentially they're like Pearson's correlation coefficients on steroids. Each pair of matrices (diet and habitat, diet and prey size, etc.) was tested for correlations.

As it turned out, there was no correlation between either food-related parameter (diet or prey size) and any other parameter. Oddly enough, though, I found a significant and positive correlation between habitat and foraging height. That is, species that overlap in habitat also overlap in foraging height, and conversely species that occupy different habitats have different foraging heights. Rather counterintuitive, contrasting with both theory and our hypotheses. However, this was a preliminary study, and we're in the process of collecting additional data and obtaining some old data that is currently in another lab, so perhaps this will help. It is true that the gut content sample size is very low - but LSU has an extensive collection, so perhaps we can improve power by boosting the sample size (now there's an idea - but for later).

Thursday, April 19, 2007

Framing Science

There's a heated debate going on in the science education corner of the blogosphere this week over how best to convey scientific knowledge to non-scientists. Matthew Nisbet (a communications prof) and Chris Mooney (a science writer and author of two excellent books on the intersection between science, politics and the media) wrote an article for this week's Science entitled "Science and Society: Framing Science" (you can access the article here ).

They start out with a good point: despite the near-universal acceptance of the existence of phenomena such as global warming and evolution amongst scientists, most Americans - even many college-educated Americans - doubt the veracity of these reports, with viewpoints strongly associated with individual politics. They cite polls showing that while 75% of Democrats agree that global warming is attributable to human activities, only 23% of Republicans accept what is - according to the latest IPCC report - widely considered to be nearly as close to "fact" as is possible to say in science (~97% odds). Similarly, only 27% of Republicans and 42% of Democrats or Independents believe in evolution according to a 2005 Harris poll (I've heard as low as 23% belief across the board in other studies - the lowest level of all developed nations), and a full 45% (!!!) believe that humanity was created by God less than 10,000 years ago (last numbers from this webpage). I read recently (sorry, can't find the citation) that the average American has approximately an 8th-grade level of scientific knowledge (if that). There's no doubt that scientists need to find better and more effective ways to communicate scientific knowledge to the general public, both in school and to adults via the media.

However, there's a hearty debate over how best to go about this. Although in actuality the debate is quite complex, it seems to boil down to this: do we teach science and the scientific method in all it's intricate (though - to many people - boring) details, or do we find a way to "re-frame" science in a way to make it more accessible to non-scientists. Nesbitt and Mooney argue for the latter, going so far as to say: "In short, as unnatural as it might feel, in many cases, scientists should strategically avoid emphasizing the technical details of science when trying to defend it". They stress that rather than emphasizing data - and actually educating people about the scientific method, processes, etc. - we should find ways to "package" information in ways that are "relevant" to people's lives (i.e., speak to the pocketbook).

In the other corner, you have scientists such as P.Z. Myers - a highly-renowned evolutionary scientist and blogger at Pharyngula, and - gasp! - an atheist. He argues, in essence, that we should not "dumb down" science, nor should we have to find a way to repackage and make excuses for evolutionary theory so as not to offend biblical literalists.

Think scientists are just dull, mellow, soft-spoken people locked up in their labs? You should see the jabs going around the blogosphere right now!

Anyway, as for me - well, I'm still waffling. The idealist in me says that we need to improve science education right from the beginning - back in elementary and junior high school. Teach kids the "hows" and the "whys" and find a way to keep it interesting. I don't think we should just toss out the "meat" of science to come up with fluff that will fit within the 30-second soundbite format of modern news. I believe we need to increase scientific knowledge as a whole, so that people can understand the difference between a "theory" and a "hypothesis", can understand why scientists are so reluctant to say something is "absolutely true", and can understand the method behind the results. This is supported by some recent studies (e.g., this paper, which found that in the US - unlike in other developed nations - level of scientific knowledge was the primary factor influencing variation in attitudes towards science.

But yet, I'm aware that many (most?) non-scientists just tune-out discussion of what they consider "boring" details - in this fast-paced information world, they just want the bottom-line. And I think there's a place for the Bill Nye's and the Mythbusters, who make science fun and thus more accessible. We certainly need to improve our skills at writing and speaking to the lay public. But I would caution against going for the soundbite, and softening down your results, at the expense of further diminishing public understanding of science. There has to be a happy medium in there somewhere...

Thursday, April 12, 2007

Stilla's Sense of Snow

...ok, so it wasn't snow exactly, but as I'm sure you all noticed it was bloody cold last weekend! I woke up Sunday morning - on the Florida coast near Pensacola, mind you - to find ice on the windshield and sleet collected on the cycad plants. Ice - in Florida - in April!!! I tried to find historical weather data for Pensacola to see if I could calculate the probability of temperatures <40 in the first week of April, but couldn't find any free data. I imagine the probability's pretty low, though.

I'm slowly poring through the Bayesian papers and book. It's quite complicated - both theoretically and practically - but we've had a local Bayesian expert, Chuck Bell, speaking to our Phylogenetics class, which has been helpful. He uses Bayesian stats in a different manner (specifically for phylogenetic tree selection, which uses somewhat different techniques and software programs than ecological analysis), but his lectures have been a huge help in understanding the theory behind the techniques (and learning how to read all that Greek code - ok, Latin, but it looks like Greek to me!).

Tuesday, April 3, 2007

On objectivity

I just read a great quote by Stephen Jay Gould - one of my favorite recent (though recently deceased and greatly missed) evolutionary scientists. I practically grew up reading his work - he published monthly columns in Natural History magazine (back when it used to publish semi-technical pieces), and I always admired his abilities for insight, self-reflection, making connections between evolutionary concepts and popular culture references, and in turn explaining complicated theories in terms many laymen could relate to.

Anyway, here's the quote: "The most erroneous stories are those we think we know best - and therefore never scrutinize or question." This was a frequent theme of Gould's (see, e.g., his well-known and oft-cited "Spandrels of San Marcos" paper), and also a frequent topic of interest to me (e.g., discussed in this blog post from earlier this year: Ch. 2, Gotelli and Ellison)

The scientific method is dependent, among other things, upon objectivity, and scientists tend to pride themselves on their ability to approach a system or a question with no pre-conceived notions or biases. But yet, we're all human, and as such we naturally tend to make assumptions, prefer evidence which supports our conclusions, and fail to question that which we "know" to be true, despite our best efforts to the contrary. I'm not saying that all scientists are biased - not by any means! - just that -we have to continually work to question our presumptions.

This is an especially relevant topic at this point in my career, as I'm delving deeper and deeper into one obscure corner of the literature, and at this point in time, as I'm reviewing proposals by other scientists at similar points in their careers. I catch myself viewing general ecological questions through the filter of my particular study system and organism, while failing to consider alternate viewpoints - often just because they never crossed my mind! In reviewing proposals and published papers, I find other scientists doing the same thing - looking only at the influences of one particular set of forces, or one particular group of organisms, while not taking into consideration other forces that could be equally, or of greater, importance. To give an example, imagine that you want to study plant-herbivore interactions. I as a bird person tend to focus on the roles avian predators have on controlling insects while failing to recognize the roles of parasitoids, while a recent frog paper I read built exclusions that did not exclude birds, but then failed to recognize their likely role in altering insect abundances.

So, I'm going to copy that quote (and save it in yet another Notepad file somewhere on my Desktop, Megan!) in an attempt to remind myself to question my assumptions and filters...

Thursday, March 29, 2007

This and that...

I'm finally back, after a several-week blogging hiatus. The last few weeks have been incredibly hectic, between working out the final details of my experimental design, writing 3 proposals, and generally preparing for my field season which will begin May 7 (getting permits, equipment, etc etc). Oh yeah, then I took a few days off to go to Big Bend NP in Texas - a much-needed break in an incredibly beautiful spot!!!

I'm beginning the process of learning Bayesian analysis techniques. I contacted Jackie Mohan, a candidate for the EBIO dept's Global Change position, regarding good intro texts, and she made several recommendations. Several of the papers she recommended were helpful and provided a good introduction, especially "Alternatives to statistical hypothesis testing in ecology: A guide to self teaching" by Hobbs and Hilborn (Ecological Applications 16(1): 5-19; 2006).

I also purchased several Bayesian Analysis textbooks (thank goodness for cheap used textbook websites - how did I ever manage to get through undergrad without the internet?!?) and am starting to work through them. Interestingly, we've been discussing Bayesian techniques quite a bit in my Phylogenetics class as well, and we even have an "expert" in the use of likelihood and Bayesian techniques for phylogenetic studies speaking to our class next week.

Tuesday, March 6, 2007

Losing Ground

If you haven't already read the 3-part series "Losing Ground" featured in the Times-Picayune, do so now! There is an excellent interactive graphic as well, explaining the issues clearly and concisely for those who have little time for extensive, non-scholarly reading (e.g., students).

The bottom line is, wetlands have been and are currently being lost at a rate far more rapid than most people had realized. Those maps of Louisiana's coastline that we're all familiar with, showing miles of intricately webbed marshes protecting New Orleans from storm surge? Turns out those are based on 1930s data, and the modern-day picture is disturbingly worse.

Think we still have a long time - maybe 30-50 years, beyond most of our lifespans - to solve the problem? Think again - turns out we have 10 years to restore wetlands before they're too far gone to repair.

Think solving the problem is too expensive? Well, yes, $45 billion is a big number, but here are a few points to consider to put this number into perspective:
> $45 billion = 5-8 months in Iraq at recent (pre-surge) spending rates of ~$6-9 billion/MONTH (source: http://usgovinfo.about.com/library/weekly/aairaqwarcost.htm)
> Louisiana is critical to the nation's oil and gas industry infrastructure, with 19 active refineries (15% of total refining capacity in the country), thousands of miles of pipelines, and the closest access to the huge offshore oil-drilling industry (source: http://www.lmoga.com/industryoverview.html). Whatever your opinion may be re: our dependence on oil, currently the nation's economy is inextricably linked to petroleum prices.
> Estuaries are critical to the seafood industry. Louisiana is the largest producer of crawfish in the world, and also exports huge quantities of oysters, catfish, and other seafood nationally and globally (source: http://en.wikipedia.org/wiki/Louisiana)
> The Mississippi River is an important shipping channel and New Orleans is a crucial access point and port, with ~80 million tons/year passing through (source: http://www.yearontheriver.com/stories/rvr_nav.php)
> This isn't even getting into all the qualitative, difficult-to-quantify reasons why New Orleans and southern Louisiana are crucial to the United States - culturally, musically, et al. - nor does it touch on the fact that we are the United States of America, and we as a country didn't shirk at spending huge sums to rebuild Manhattan post-9/11, San Francisco post-Loma Prieta (or post-1906), Chicago post-fire, etc.

OK, stepping off the soapbox - what does this have to do with biostats or science in general? Well, the need for "proper" science, for thorough studies and full understanding of all potential impacts of action has hindered our actions to this date, and brought us to the point we are at today. While it's true that as scientists we need to be cautious and objective and understand impacts of potential conservation and restoration measures, when do the dangers of inaction or postponement of action outweigh the need for urgent action? How many pilot studies need to be done before we accept the data and act on it? I'm torn, because as a scientist I say we need to fully understand the processes before acting, but as an environmentalist and concerned citizen I say that we need to do something about this, and fast. And I'm concerned that science and the lengthy process of conducting studies and writing reports is all too commonly abused by politicians who benefit from retaining the status quo (see this book for an excellent summary of this abuse, particularly as perfected by the current administration)...while meanwhile opportunities are slipping out of our hands. See this quote in the first TP article for just one example:

"In a convoluted process, restoration projects proposed by a local sponsor must undergo a series of studies of their economic and ecological benefits and detriments. Congress must approve the studies, which can take three to five years. Then, in a separate process, the corps must seek money in its annual budget to conduct them."

In all, it can take over 10 years for any - even small - restoration action to occur, by the time all studies and bureaucratic processes have been completed. We don't have 10 years...

So, where do we draw the line? When - if ever - should the slow, cautious steps prescribed by the scientific method be overruled by the need for urgent action? Who should make the decisions regarding when or how - scientists (ecologists, engineers, wetland biologists?)? Politicians? Committees?

Friday, March 2, 2007

Independent Project

After speaking with Mike Guill re: Bayesian stats earlier this week, I've decided to change my independent project. I'm really interested in learning more about Bayesian analysis - I like the philosophical concepts behind the techniques (directly testing the hypothesis rather than the data, using prior information to come to a conclusion). I'm curious to see for myself how the analysis works (I can't really fully understand a technique like this until I've done it myself), and just how influential informative priors are on the outcomes. So, rather than analyze Tom's dataset of niche breadths for competitive exclusion, I'm going to revisit an old dataset of mine comparing arthropod abundance and defenses and avian insectivore foraging success in two Costa Rican forests.

This data was collected to test one component of an avian life-history theory which my lab has been working on. Birds - like many other organisms - have a distinct latitudinal gradient in demographic rates (most notably clutch size, but also survival et al.) wherein tropical birds have "slow" life-histories (low reproduction, high survival, low metabolic rates) and temperate birds have "fast" life-histories (high reproduction, low survival, high metabolic rates). Hypotheses have been proposed to explain this since the early 1900s, but none fully explain the observed patterns.

We suspect that food limitation is at the root of this gradient. Specifically, we cite references showing that tropical insectivorous birds face strong food limitation - contrary to popular belief - due to the low seasonality (lack of a seasonal "flush" of resources), low population densities of arthropods, and strong predator pressure (due to many species of insectivorous birds feeding on arthropod prey) leading to development of strong anti-predator defenses (physical, chemical, and behavioral) by arthropods. These forces should be strongest in so-called "perhumid" moist tropical rainforests with limited seasonality, moderate in dry-seasonal tropical forests, and weakest in temperate areas.

I sought to test this by comparing arthropod population densities and defenses in a moist tropical forest (La Selva, go figure) and a dry-seasonal forest (Palo Verde), both in Costa Rica. I also observed insectivorous birds and recorded various measures of foraging success & movement rates. I originally analyzed this data using univariate parametric and non-parametric statistics (t-tests, ANOVA, Chi-square, Kolmogorov-Smirnov) and also ran it through a multivariate MANOVA, but found few significant results.

I'm very curious to see if Bayesian analysis will produce similar results. I also have several references upon which I based my hypotheses from which I can draw data for prior distributions, and I want to test the influence of several different informative and non-informative priors.

Monday, February 26, 2007

Of Caterpillars and Compounds...

The theme du jour is the influence of plant defenses (particularly secondary compounds) on caterpillar growth and anti-predator defense in tropical forests (primarily at BCI and La Selva). Over the weekend, I read a proposal seeking to document the influences of mixtures of similar plant compounds in anti-herbivore (specifically, caterpillar) defense. This study focused primarily on the intraplant chemical level, looking at which compounds or compound mixtures best deterred caterpillars. I followed this up by reading an article for Journal Club today focusing on the role of plant quality (supposably including secondary compounds, though these weren't investigated directly - more on this later) in influencing caterpillar growth rates and anti-predator defenses. And I myself have focused more on the next trophic level up - namely, the role of diverse arthropod defenses (which are presumably due to some combination of bottom-up - i.e., plant-driven - and top-down - i.e., predator-driven) on limiting food availability to insectivorous birds. I found this to be interesting and thought-provoking reading - for all the time I've spent thinking about the relationship between caterpillars and birds in terms of top-down selection for anti-predator defenses and bottom-up food limitation acting to reduce metabolic and foraging rates and population densities of the birds, I've spent very little time thinking about other - namely, plant-driven - selective forces driving caterpillar defensive trait evolution. This adds a whole new level of questions to my research. Funny how ecological research feels a bit like jumping down the rabbit hole sometimes - the more you learn, the more new worlds of ideas and questions open up.

The other interesting aspect of reading these two papers back-to-back was the contrasts in methodological techniques and quality. The proposal I read was directly testing the roles of secondary compounds on herbivory, by synthesizing the compounds and adding different concentrations and mixtures to leaves which are then offered to caterpillars, allowing direct testing of causation. The second paper, however, primarily investigated the role of nutrient quality on caterpillar growth, discovered that nitrogen and water did not fully explain the regressions, and from there made a leap to saying that the residuals are likely therefore explained by secondary compounds. They did throw in a few other related experiments - e.g., exposing caterpillars fed on different leaves to ant predators - but it seemed they were confusing correlation for causation. Another problem I had with the methods of this paper is that they arbitrarily broke continuous characters (e.g., leaf-expansion rate, number of spines on a caterpillar) into dichotomous categories, and worse, did not explain the justification for the divisions. Dividing the data into discrete classes allowed them to use ANOVA and t-tests which produced significant differences between groups, but I can't help but wonder if that isn't partially just a construct, a result of their categorizations rather than reflecting biological reality. I wonder if keeping the data continuous and using single and/or multiple regressions wouldn't have better reflected reality - and if the significant results they found would still appear this way. As scientists we're taught to strive for that p<0.05 value, but I wonder if we don't sometimes rearrange and reclassify our data in ways not completely reflecting the complexity of nature in order to reach that holy grail...

Wednesday, February 14, 2007

Spring has sprung

Spring is here (so early!), or at least so it seemed yesterday. The great egrets are staking out territories, reuniting with or courting new mates, and gutting and refurbishing their old nests down at the rookery at Audubon Park. I love seeing the birds (displaying males, primarily) fanning out their lacy, snow-white plumes almost peacock-like. It's sad to think how we nearly lost this species - and so many others - a century ago, though I can see why people wanted those gorgeous plumes for themselves. Crows are building nests and songbirds are belting out their amorous songs from the treetops, while young couples walk arm-in-arm below, acting out their own courting rituals on this St. Valentin's Day (we like to think we're so different from the "lower animals", but are we really?)

Anyway, what does this have to do with stats? Absolutely nothing! I just don't have anything all that interesting to say about today's reading. The Verzani book is certainly practical, and is a good introduction to programming in this language - which is fairly different (less object-oriented) than some other programs I've worked with. But it's straight-forwardness (is that a word?) which makes it so useful for learning the code leaves little to comment upon!

Monday, February 12, 2007

Dissertation Hypotheses!!

So, I've spent a lot of time trying to hone down my ideas/questions regarding the causes of declines in tropical insectivorous understory birds into specific, testable hypotheses. That's a lot harder than it sounds!! Well, at least it was for me - I find coming up with the question(s) - and more than that, valid, testable, bivariate (yes/no) questions to be one of the most difficult parts of the scientific method. The field work's the fun part, and I find even the analysis (seeing the results coming together) and the writing to be easier. Anyone else find this as well?

Anyway, here are the hypotheses that I've developed at this point. I likely won't test all of these questions now (too much for one project), but will choose between the most relevant and testable. Seeing as I'm about to go present them to Tom (wish me luck!), and we're discussing hypothesis-framing in class tomorrow, this seems like a good time to put them out there for comment. So, here goes - let me know what you think!

Dissertation questions/hypotheses:

Overarching: 1) what mechanisms are responsible for the decline of understory insectivorous birds in tropical rainforest?

2) Does a trophic cascade exist (can one exist w/in such a highly diverse environment), and if so what are the strengths of the various direct and indirect effects (model this w/ path analysis, per Lee)

(note: LS = La Selva)

Hyp 1) Abundance of leaf-litter and understory arthropods is greater in absence of disturbance by large mammals (peccaries) => top-down trophic cascade.

- Test: sample leaf-litter and understory arthropods w/in and outside peccary exclosures at LS (very high density of peccaries) and Tirimbina (no peccaries).

Hyp 2) Food limitation is a primary influence on demographic rates of understory insectivores => bottom-up effects

- Test: provide supplemental food (mealworms) in proportions sufficient to equalize biomass/ha of exclosures, measure demographic parameters (I expect post-fledging success rate and adult survival rate to be most influential). Build matrix population model and do sensitivity analyses to determine which parameter most influences pop. Growth/decline rate. Prediction: post-fledging success

Hyp 3) Antwren (a group of birds which have disappeared at La Selva, but not at other sites) losses at LS are due to "loss" of vine and dead-leaf tangles (can't measure loss per se - no historic records - but can compare current biomass/cover at sites w/ and w/o full insectivore guild)

- measure vine/leaf tangle (biomass? percent cover?) at La Selva and compare with sites where antwrens still persist (Tirimbina or Pipeline Road = low density, Bartola or BCI = high density)

- Prediction: I can’t think of any mechanism that would drive loss of leaf tangles at LS and not at the other sites – unless Pentaclethra has increased it’s proportion of canopy cover in the last 40 years (which I doubt).

Hyp 4) Nest predation is a primary influence on demographic rates

- Observe nests (White-breasted Wood-wren probably - easiest to find and observe), use cameras – who the heck are the predators, since there are so few snakes there these days???

- Include fledging success as a parameter in sensitivity analyses (see hyp #2)

Hyp 5) In absence of other guild/trophic-level members, remaining species widen their realized niches and fulfill role of absent species, maintaining similar effects on next-lower trophic level (=arthropods)

- Quantify niches (foraging height, strategy, prey consumed) of insectivores (white-breasted wood-wren and/or chestnut-backed antbird) at several sites. Prediction: niche width LS > Tirimbina > Bartola/Plastico (also, or conversely, antwrens BCI > Tirimbina > Bartola/Plastico)

- Establish bird exclosures at LS (w/in and outside peccary exclosures), Plastico, Tirimbina (BCI and/or Bartola?). Quantify arthropods w/in and outside exclosures. Prediction: differences b/w avian exclosures & controls should be similar at all sites (assumes peccary exclosures do not limit avian access).

Hyp 6) Avian predators limit arthropod populations, but to a lesser degree than resource (plant/detritus/other arthropod) availability (per Dan Gruner)

- difference b/w (avian exclosure w/in peccary exclosure and avian exclosure outside) should be > than difference between (avian exclosure w/in peccary exclosure and control w/in peccary exclosure),; quantify influence of birds on arthropods

(Hyp 7 – pesticides from surrounding banana plantations drifting into forest and influencing arthropods directly and/or birds indirectly (e.g., estrogen-mimics lowering fertility?)? Want to wait to run some tests on litter/arthropod samples I collect over spring break – not sure about this as of yet)

Wednesday, February 7, 2007

JV Ch. 3, Bivariate data

This chapter discussed methods for plotting 2+ sample data, looking for correlations, linear regression, etc. (strange to be discussing linear regression prior to learning how to do a t-test! Usually it's the other way around...)

They discussed some odd graphical methods (odd in that I've never seen or heard of them before) - like qqplots. I still don't grasp when you would use these, or how to read them. To me, it seems easier to compare density plots or - better yet - boxplots. Lee got us into using boxplots in his stats class last fall, and I'm really beginning to see just how useful they are for viewing the spread and means/medians of data.

I'm glad to see that Pearson correlation coefficients can be calculated so easily! I'll need to calculate a bunch of them for my independent project, and I can't recall using them before. One less thing to worry about :)

Monday, February 5, 2007

G&E Ch. 3

This chapter discussed summary stats - mean, sd, se, cv, median, mode, and all that jazz. Mostly stuff we've discussed in many classes before - and in Ch. 2 of JV - but they made a few interesting points. The descriptions of the different kinds of means (arithmetic vs. geometric vs. harmonic) and when they're used was interesting - we used geo. means in a pop. ecology/analysis class I took a couple years ago, but I never really understood why. I also liked the description of degrees of freedom - finally, it makes sense. That's what I like about this book so far (as I've said before) - they give good, easy-to-understand descriptions of basic things that, generally, are assumed to be understood (yet rarely/never explained) in other stats books.

Then later in the chapter they bring up Bayesian stats again a couple times, but never follow up... Why don't we have a Bayesian stats class here? I'm not even aware of any current faculty who have much experience with Bayesian stats, with the exception of their use in systematics (correct me if I'm wrong)...I'll have to read up, because it seems that they're becoming more common...

Monday, January 29, 2007

Ch. 2, Gotelli and Ellison

Ch. 2 discussed random variables and probability distributions. I found this chapter really helpful. In the last several stats classes I've taken, we've discussed and/or used various types of probability distributions (Poisson, log-normal, etc.), but I've never really understood "what" they are/what they're based upon, nor in what cases they should be used. I've marked the pages with tables 2.3 and 2.4 - they have good, concise summaries of when and how to use each distribution.

On a side note, I really like the way these guys write. It's very accessible and easy to understand, unlike other stats texts I've read (e.g., Sokal and Ralph is a great example of an unreadable book!). They're pretty funny, too - I like the offhand comments like "In our continuing series of profiles of dead white men in wigs..." (p. 26). Keeps your attention.

The discussion of discrete vs. continuous variables reminded me of a paper I read for Phylogenetics class tonight, on the use of qualitative and quantitative variables in phylogenetic/cladistic analysis. Stevens (1991) argued that most traits used in cladistic analysis are quantitative/continuous, even some of those that were classed as discrete. Often, the classes/character states are determined arbitrarily by the analyst - and, no big surprise here, are defined in such a way as to fit their preconceptions of what the phylogenetic order should be. We like to think of science as objective, yet it's becoming more and more clear to me just how much our backgrounds and preconceptions influence our thinking, often without us even realizing (re: Journal Club today). Anyway, back to the topic of discrete variables - I think it's difficult to find discrete classes when measuring character states within a population, because there's so much individual variation. Even things seemingly quite discrete like color can vary - is that flower pale pink or white with a slight tinge? But when you're dealing with outcomes of trials, it is possible to have discrete variables - e.g., a coin toss can only be heads or tails (well, unless it lands on it's edge, which is extremely unlikely - but hey, when you're dealing with Ecology, it seems there's an exception for every rule). Interesting stuff...

Wednesday, January 24, 2007

Independent Project ideas

I've been kicking a few ideas around for the independent project. Ideally, I was hoping to be able to analyze some of my own data. However, the data I collected last summer has already been analyzed as fully as I believe it could/should be. I'll be collecting more data over spring break, but I'm concerned that will be too late to begin the project.

Instead, I think I'll work with the niche breadth and complementarity dataset of Tom's, which I began working with last fall but was put on hold while we waited for some samples from Tom's former advisor. The dataset includes information on foraging height, arthropod species consumed, habitat, maneuvers used, substrate, et al. for about a dozen species of rainforest-dwelling insectivorous birds in Costa Rica (mostly in or near La Selva). We're testing to see whether there is an inverse relationship between habitat and food specialization in this guild resulting in niche diffferentiation. That is, we expect that species that consume similar diets will be separated spacially (by habitat, height, etc.) and vice versa. We intend to combine this with a phylogenetic analysis (perhaps phylogenetic independent contrasts? need to look into this further) to identify which differentiation (habitat vs. food) developed first - the prediction is that similar species will differentiate spatially fairly rapidly, while specialized food habits will take longer to involve.

We plan to test this using Mantel tests, which can be run using an add-on package for R which you can download from CRAN. I haven't looked into this yet, but had good success with the VEGAN package which I used last summer, and I expect this will be similar.

Monday, January 22, 2007

Introduction to Probability

The first chapter of Gotelli and Ellison discusses probability. Probability is defined as the expected frequency with which events occur. However, this itself is dependent upon the scale of the investigation - the more you understand about a process, the less "stochasticity" there is. They make an interesting point on p. 11 - random/stochastic events are, in reality, processes that we are unable or unwilling to measure. Under this view, everything can be measured if you look close enough - yet this doesn't seem to agree with quantum physics, where the closer you get to a particle, the more random it's behavior and very existence seems to be. Hmmm....

Complex events = sequences of simple events (in coding, = OR, probabilities additive)
Shared events = multiple simultaneous occurrences of simple events (= AND, probabilities multiplicative)

This chapter also discusses conditional probabilities, e.g. P(A|B), and the Bayes theorem, which provides a way of measuring conditional probabilities. Essentially, conditional probability and Bayesian analysis involves narrowing down all possible outcomes of an event based on prior knowledge. So, if there are 10 different possible outcomes of A, and 10 different outcomes of B, but only 3 outcomes of A that also include outcome X of B, then you're limited to those 3 possibilities for A. This seems to me a legitimate method of narrowing down possible outcomes - I don't fully understand the controversy re: Bayesian analysis (given, of course, that the data you're introducing into the analysis are relevant and complete).

My First Post

Well, I've been reading blogs for several years now. During that time I've thought and talked about starting my own blog, even went so far as to get a domain space last summer (manakinescapades.com), but never found the time to actually post anything. Now, thanks to Mike Guill's Biostats and Experimental Design class, I'm actually going to begin regularly keeping a blog. For now I'll probably mostly post about readings for Biostats, dissertation ideas, Spanish assignments, and occasional random thoughts on (liberal) politics, New Orleans, and life in general.

I spent the last half an hour messing with the settings on this site, and still can't get the "oh-so-easy" Hello/Picasa picture-sharing software to work...maybe later. For now I'm off to class...later, a real post for biostats...