Do Not Log-Transform Count Data, Bitches!

ResearchBlogging.org OK, so, the title of this article is actually Do not log-transform count data, but, as @ascidacea mentioned, you just can’t resist adding the “bitches” to the end.

Onwards.

If you’re like me, when you learned experimental stats, you were taught to worship at the throne of the Normal Distribution. Always check your data and make sure it is normally distributed! Or, make sure that whatever lines you fit to it have normally distributed error around them! Normal! Normal normal normal!

And if you violate normality – say, you have count data with no negative values, and a normal linear regression would create situations where negative values are possible (e.g., what does it mean if you predict negative kelp! ah, the old dreaded nega-kelp), then no worries. Just log transform your data. Or square root. Or log(x+1). Or SOMETHING to linearize it before fitting a line and ensure the sacrament of normality is preserved.

This has led to decades of thoughtless transformation of count data without any real thought as to the consequences by in-the-field ecologists.

But statistics has had a better answer for decades – generalized linear models (glm for R nerds, gzlm for SAS goombas who use proc genmod. What? I’m biased!) whereby one specifies a nonlinear function with a corresponding non-normal error distribution. The canonical book on this was first published ’round 1983. Sure, one has to think more about the particular model and error distribution they specify, but, if you’re not thinking about these things in the first place, why are you doing science?

“But, hey!” you might say, “Glms and transformed count data should produce the same results, no?”

From first principles, Jensen’s inequality says no – consider the consequences for error of the transformation approach of log(y) = ax+b+error versus the glm approach y=e^(ax+b)+error. More importantly, the error distributions from generalized linear models may often be far far faaar more appropriate to the data you have at hand. For example, count data is discrete, and hence, a normal distribution will never be quite right. Better to use a poisson or a negative binomial.

But, “Sheesh!”, one might say, “Come on! How different can these models be? I mean, I’m going to get roughly the same answer, right?”

O’Hara and Kotze’s paper takes this question and runs with it. They simulate count data from negative binomial distributions and look at the results from generalized linear models with negative binomial or quasi-poisson error terms (see here for the difference) versus a slew of transformations.

Intriguingly, they find that glms (with either distribution) always perform well, while each transformation performs poorly at some or all values.

Estimated root mean-squared error from six different models. Curves from the quasi-poisson model are the same as the negative binomial. Note that the glm lines (black solid) all hang out around 0 as opposed to the transformed fits.

More intriguingly to me are the results regarding bias. Bias is the deviation between a fit parameter and its true value. Bascially, it’s a measure of how wrong your answer is. Again, here they find almost no bias in the glms, but bias all over the charts for transformed fits.

Estimated mean biases from six different models, applied to data simulated from a negative binomial distribution. A low bias means that the method will, on average, return the 'true' value. Note that the bias for transformed fits is all over the place. But with a glm, bias is always minimal.

They sum it up nicely

For count data, our results suggest that transformations perform poorly. An additional problem with regression of transformed variables is that it can lead to impossible predictions, such as negative numbers of individuals. Instead statistical procedures designed to deal with counts should be used, i.e. methods for fitting Poisson or negative binomial models to data. The development of statistical and computational methods over the last 40 years has made it easier to fit these sorts of models, and the procedures for doing this are available in any serious statistics package.

Or, more succinctly, “Do not log-transform count data, bitches!”

“But how?!” I’m sure some of you are saying. Well, after checking into some of the relevant literature, it’s quite straightforward.

Given the ease of implementing glms in languages like R (one uses the glm function, checks diagnostics of residuals to ensure compliance with model assumptions, then can use Likliehood ratio testing akin to anova with, well, the Anova function) this is something easily within the grasp of the everyday ecologist. Heck, you can even do posthocs with multcomp, although if you want to correct your p-values (and there are reasons to believe you shouldn’t), you need to carefully consider the correction type.

For example, consider this data from survivorship on the Titanic (what, it’s in the multcomp documentation!) – although, granted, it’s looking at proportion survivorship, but, still, you’ll see how the code works:

library(multcomp)
### set up all pair-wise comparisons for count data
data(Titanic)
mod <- glm(Survived ~ Class, data = as.data.frame(Titanic), weights = Freq, family = binomial)

### specify all pair-wise comparisons among levels of variable "Class"
### Note, Tukey means the type of contrast matrix.  See ?contrMat
glht.mod <- glht(mod, mcp(Class = "Tukey"))

###summaryize information
###applying the false discovery rate adjustment
###you know, if that's how you roll
summary(glht.mod, test=adjusted("fdr"))

There are then a variety of ways to plot or otherwise view glht output.

So, that's the nerdy details. In sum, though, the next time you see someone doing analyses with count data using simple linear regression or ANOVA with a log, sqrt, arcsine sqrt, or any other transformation, jump on them like a live grenade. Then, once the confusion has worn off, give them a copy of this paper. They'll thank you, once they're finished swearing.

O’Hara, R., & Kotze, D. (2010). Do not log-transform count data Methods in Ecology and Evolution, 1 (2), 118-122 DOI: 10.1111/j.2041-210X.2010.00021.x

My Dissertation in Under 7 Minutes

ResearchBlogging.org
I recently attended the DISCCRS symposium for recent PhDs of a wide variety of disciplines whose work (past or present) deals with climate change. The week-long meeting was phenomenal, seeding me with thoughts, ideas, and basically making me feel quite good about the work I’m doing (if also very pessimistic about how society is dealing with Climate Change). Perhaps one of the most interesting exercises of the whole thing was something we had to do as a sort of getting-to-know-you. We had to present our dissertation in 7 minutes.

That’s right. 6 years of blood, sweat, and tears in 7 minutes. Oh, and for a totally non-specialist audience.

I thought this was an amazing challenge. Granted, I only ended up really presenting on 3 of my chapters (see papers below). But I really liked the results.

Apologies for the sound quality – the acoustics of the room were pretty bad. Props to The Urban Matador for some sound editing. And malaprops to me for not annunciating or projecting as much as I usually do. Bad scientist. Bad! Bad!

Also, please note that this is with a particular emphasis on how our work relates to climate change.



Byrnes, J., Reynolds, P., & Stachowicz, J. (2007). Invasions and Extinctions Reshape Coastal Marine Food Webs PLoS ONE, 2 (3) DOI: 10.1371/journal.pone.0000295

Byrnes, J., Stachowicz, J., Hultgren, K., Randall Hughes, A., Olyarnik, S., & Thornber, C. (2005). Predator diversity strengthens trophic cascades in kelp forests by modifying herbivore behaviour Ecology Letters, 9 (1), 61-71 DOI: 10.1111/j.1461-0248.2005.00842.x

Byrnes, J., & Stachowicz, J. (2009). The consequences of consumer diversity loss: different answers from different experimental designs Ecology, 90 (10), 2879-2888 DOI: 10.1890/08-1073.1

Our Future: Hot n’ Tasty?

Climate change. It’s going to wreak no small amount of havoc on mother nature (and if you’re reading this but think all of this climate change stuff is poppycock, please visit Skeptical Science and then come back). How good of a guide is our intuition for what will happen?

This is a great question when it comes to predator-prey relationships and the food chain. One may well think that, heck, from first principles we know that adding heat to a system speeds things up. So, you know, things should continue just as they are – just faster, and maybe with some range-limits and annual timing moved around a bit.

This is quite a sensible proposition. It’s also wrong.

Biomass of phytoplankton and zooplankton under different temperature regimes. Images from Wikipedia.

Recent work from Mary O’Connor and colleagues in PLoS Biology as well as Oliver Beveridge and colleagues in the Journal of Animal Ecology points out some intriguing and non-intuitive effects of heating up food webs – in two completely different systems no less.

O’Connor et al. examine the relationship between phytoplankton and their predators under nutrient enriched conditions. While the little green guys grow more quickly (per capita primary production goes up with increasing temperature), this doesn’t matter to voracious copepods. Their metabolism is sped up even faster, leading to more and more copepods and less and less phytoplankton at higher temperatures.

But what about layering a little complexity on top of that? Beveridge et al. look at a three-level food chain, with bacteria at the bottom, a protozoan consumer, and a ciliate top predator. They cross a manipulation of number of links in the food chain against an increase in temperature and let things run for 6 weeks. While cranking up the heat leads bacteria activity to pick up markedly (and even moreso when their consumer is around), temperature crossed with food chain length does some funny things.

Density of different organisms under conditions of differing food chain length and temperature. Note, if you like the knitted bacteria, you can find the patterns at loxosceles - http://loxosceles.org/crafty/bacterium.html.

Depending on the number of links in the food chain, the relationship between temperature and bacterial density is positive, negative, or U-shaped. In contrast, their consumer, Colpidium, increases where it’s warm when there are no predators, but markedly declines with temperature when it’s predator is around. It’s predator, Didinium, increases in density only at intermediate temperatures. Again, shifts in metabolism and predation rates throughout the food chain appears to be key.

Together, the two studies suggest a dynamic interplay between metabolic activity, rates of predation, and population dynamics. Different levels of a food chain can be affected in very different ways. The simple faster-herbivore-kill-kill scenario is sadly discredited. Rather, we need an understanding of how warming will affect different types of organisms’ rates of growth, death, and predation. Only then can we determine climate change’s dynamic impact on food webs.

O’Connor, M., Piehler, M., Leech, D., Anton, A., & Bruno, J. (2009). Warming and Resource Availability Shift Food Web Structure and Metabolism PLoS Biology, 7 (8) DOI: 10.1371/journal.pbio.1000178

Beveridge, O., Humphries, S., & Petchey, O. (2010). The interacting effects of temperature and food chain length on trophic abundance and ecosystem function Journal of Animal Ecology, 79 (3), 693-700 DOI: 10.1111/j.1365-2656.2010.01662.x

The Conservation Horizon

ResearchBlogging.orgEvery so often, a conservation problem rears its head that, upon reflection, we realize we had some inkling of even decades ago. Global warming, biofuels, overfishing, etc. The information was there, but scarce, buried in obscurity, or seemingly counterintuitive. Why not try and recognize the crucial questions early, before the lobster is out of the trap, so to speak? (What, I’m a marine biologist!)

Businesses has recognized the need to spot emerging trends with scant information and regularly engages in an exercise called Horizon Scanning. Recently, a group led by William Sutherland decided to appropriate the approach for conservations issues in 2010. With a panel of academics, horizon scanning experts, and representatives of various organizations they identified 61 possible issues and then through voting, discussion, and evaluation winnowed the list down to 15 issues which are of potentially great import, but we don’t have a ton of information on.

Below I have listed the 15 with a little information. I also couldn’t resist, and have included a little color coding. – Red means something that we are fairly certain can and will be problematic, and needs more research now. – Yellow means something that either has mixed positive and negative aspects, and hence needs more exploration before it is adapted more widely, or we just don’t know enough about this issue. – Green are developments that seem largely positive, although we have yet to quite grasp their full implications.

  • Microplastic Pollution – Where is all of our plastic waste going? In the oceans, the SEAPLEX project is paving the way forward on this. But across the land, where is the plastic going? What happens as degraded plastics get incorporated into out soils?
  • Nanosilver in wastewater: In general, we have no ideas what nanomaterials do once released into the environment. Fortunately, there’s a huge research initiative beginning to address this.
  • Synthetic meat: Solve world hunger! Allow even vegetarians to eat meat! While this is synthetic meat is expensive now, look for the price to come down. PETA has even announced a $1 million prize for the first marketed in vitro meat.
  • Artificial life: This isn’t a-life in terms of simulations on your computer, but rather, starting with basic building blocks, and building a totally new from scratch. Very cool. Imagine custom-designed vaccine or fuel making organisms. But the potential for unanticipated results (I mean, heck, we don’t even entirely understand how all of the machinery of DNA works yet) or misuse is enormous.
  • Stratospheric aerosols: Proposed as a possible counter-force against global warming, sure, it’ll cut-down on insolation. However, putting things in the sky will not solve our CO2 problem and its related issues, such as acidification. Add to that potential issues for plant photosynthesis and acidic rain or other consequences or particular matter in the atmosphere, and you have giant blinking caution light.
  • Biochar: A process of burning plant material without oxygen, biochar creates solid carbon that can then be buried in soils, permanently sequestering carbon. As a bonus, some of the byproducts are great at generating energy. However, this only works if it is widespread across the globe. But, what will the consequences of adding so much locked up carbon to soils around the globe? This radical rebalancing of C:N ratios could have large and unanticipated consequences for plant diversity and productivity, particularly if this is rolled out globally without proper research in its impact.
  • Mobile sensing technology: With the advent of cellular networks tapped into los internets coupled with real-time image and data-processing, we can deploy all sorts of autonomous sensors around the globe and get data. Cameras, microphones, light-probes, temperature-probes – the list is endless, and the data that can be acquired is stunning. And this is to say nothing of citizen-science efforts that use texting to report sightings of animals or recreational fishing catch.
  • Deoxygenation of the oceans: While hypoxic zones in the ocean have always been with us, the increase in the size and duration of these zones has been quite troubling. Why, where, and when these zones form is a key question, particularly as many models predict warming will promote their formation, size, and duration.
  • Changes in denitrifying bacteria: I had not previously heard of this, but it makes sense. Nitrogen in ocean sediments is turned into inert N2 by bacteria. However, in some estuaries, declines in primary productivity, and hence the organic detritus, have caused a switch from denitrification to nitrogen fixation. This means that rather than absorbing excess nitrogen, these estuaries become a net exporter of nitrogen into the surrounding waters. Another biogeochemical cycle run amok. But how widespread this phenomena is, whether its impacts are local or global, and more remain unknown at present.
  • High-latitude volcanism: Guess what is under those receding ice sheets? You guessed it! Volcanos! Volcanos whose eruptions have, until now, been contained. This is already causing problems in Iceland. How many volcanos there are? How bad are they? What will they do to the atmosphere? Good questions all!
  • The invasion of lionfish in the Caribbean: Lionfish are pretty. They’re also highly invasive, and have spread all the way from Rhode Island to Columbia. They’re voracious predators, and their long-term impact on the already impacted Caribbean reef system is only just being understood. This one seemed a little specific compared to the other issues, but, I can see how the impact could be large.
  • Trans-arctic dispersal: As the Arctic sea-ice melts and opens up the fabled Northwest Passage, they also open up a road for a new transarctic interchange of biota. Not only this, but rapid shipping across the passage will further facilitate homogenization across both the Atlantic and Pacific sides of the Arctic.
  • Assisted colonisation: This is basically the movement of species to areas not current in their range by humans. There are a lot of good intentions behind this idea – to keep a species’ distribution moving faster than a shift in its habitat due to climate change, to restore lost ecological function provided by a sister taxa (see Pleistocene rewilding), or to transplant a species out of a place where it will otherwise be driven extinct. As with any invasive species problem, though, the potential unintended consequences are enormous, and cannot always be adequately discovered with pre-transplant research.
  • Impact of reduced deforestation on non-forested ecosystems: There are a number of efforts going on to reduce the clearing of tropical rainforests. While on its face, this is wonderful, there are some unintended consequences. First, in the 2 years until some restrictions cut in, many countries may accelerate the pace of destruction. Second, eliminating deforestation does not eliminate the demand for land. Efforts to clear rainforests may be shifted to other habitats, some of which may actually be more effective carbon sinks.
  • Large-scale international land acquisition: I also found this one rather curious. To shore up their food supply, many nations are buying vast swaths of land in developing countries. This has the benefit of providing work in those nations, as well as a more consistent food supply. It may also lead to more easily enforced environmental regulations if there are only a few major landholders However, it has the cost of turning sometimes natural lands into agriculture. It may also reduce access and ownership by local peoples (colonialism round 2?) causing some intense conflicts in the face of local environmental catastrophes.

All in all, an intriguing list. Given that it’s conservation concerns, it’s not too surprising that much of this list is somewhat disheartening. But, there is a ton of fodder for new research here. This is not to mention the benefits of thinking about and taking action on these issues NOW, before many of them become part of the global status quo.

Sutherland, W., Clout, M., Côté, I., Daszak, P., Depledge, M., Fellman, L., Fleishman, E., Garthwaite, R., Gibbons, D., & De Lurio, J. (2010). A horizon scan of global conservation issues for 2010 Trends in Ecology & Evolution, 25 (1), 1-7 DOI: 10.1016/j.tree.2009.10.003

Sea Stars on Acid

ResearchBlogging.org

As an ecologist working in temperate climes, I’ve been following the ocean acidification field with some interest. It’s always been obvious to me how acidification has enormous ramifications for coral reefs and other tropical marine ecosystems. They exist in warm waters already, often close to their thermal maxima. Acidifying the water around them at any creatures using calcium carbonate seems like a recipe for disaster.

How not to do acidification research on Pacific salmon.  Photo from <a href='http://www.simpledailyrecipes.com'>simple daily recipes</a>.

How not to do acidification research on Pacific salmon. Photo from simple daily recipes.

But what about up north in colder climes? There, what is the relative importance of acidification versus changes in temperature? Do changes in physiological rates due to warming compensate for costs of acidification due to CO2 increase? This is particularly interesting along the Pacific Coast of North America, as in many regions, upwelling already drives annual fluctuations in pH – sometimes to levels not predicted to be widespread until 2050 (Feeley et al 2005 Science).

The recent paper by Gooding, Harley, and Tang in PNAS puts an interesting spin on this. Their work shows that, under scenarios where both temperature and CO2 increase, the feeding and growth rates of sea stars actually increases.

Sadly, some folk in the non-science world seem to be taking this as evidence that either global warming is a lie, or will make the world a shiny happier place. The real answer is far from it.

The truth lies in the fact that the sea stars used here don’t have a ton of calcified body parts. Indeed, they may just be compensating with more wet tissue mass, although this currently remains unclear.

With respect to organisms that rely on calcified skeletons (e.g., sea urchins) we know that their larvae floating about in the ocean will react more poorly than expected to increased heat stress if they grow up in a high CO2 world (O’Donnell, Hammond, and Hoffman 2009 Marine Biology). And if hard-bodied prey (i.e. mussels) react more poorly to acidification than they gain from increased physiological rates due to heightened temperature, things get tricky. The particular sea star studied here, Pisaster ochraceus, for example, is already a voracious consumer of hard bodied prey. If it gets a boost while it’s prey is weakened, the consequences could be quite large.

The future of the intertidal?  Image modified from <a href='http://www.marinebio.net/marinescience/03ecology/tpmid.htm'>marinebio.net</a>.

The future of the intertidal? Image modified from marinebio.net.

I do wonder if there is hope, though. If in some regions there are already regular pulses of acidified waters, one would guess that organisms possess some machinery for dealing with this annual event. While they may not possess adaptations that allow them to deal with long-term acidification – not yet – perhaps these may serve as Gould’s Spandrels. While on average calcifying organisms may not perform well underacidified conditions – even with a boost from temperature – one wonders if the raw genetic variation is out there waiting to be tapped. A hopeful thought for some grim research.

Gooding, R., Harley, C., & Tang, E. (2009). Elevated water temperature and carbon dioxide concentration increase the growth of a keystone echinoderm Proceedings of the National Academy of Sciences, 106 (23), 9316-9321 DOI: 10.1073/pnas.0811143106

I’m an Editor?

So, someone over at researchblogging.org was decidedly foolish, and asked me to be one of their new editors-at-large for Biology. That means, every Thursday, I’ll be posting the three biology (typically ecology and evolution) research paper reviews linked through researchblogging.org that I enjoyed the most. My first post is up, and hopefully there will be many more to come!

New Ideas in Ecology and Reviewing

ResearchBlogging.orgRecently on ecolog-l, there has been a thread going around about journal publishing – open access v. pay-for access, impact factor, elitism, reviewing, etc. The central question seems to be, is the publication system somehow broken? Do we need to fix it? Is the model of journals such as PLoS Biology or The Open Ecology Journal not enough?

I think the answer is that in the realm of experimental or solid theoretical work, yes, the open access model of science publishing is alive and well (although I often wished that more of the journals out there, such as Research Letters in Ecology, got more attention – but the question of why to submit in a new journal, and what makes a journal high on ones priority list is a whole different ball of wax).

What seems to not have as clear a home in the world of Open Access science is short novel opinion pieces. True, PLoS One and others may have some room for forum, review, and opinion articles. But it is not their mission. Indeed, even in the world of non-open access, the primary publishing point for these sorts of articles is the Trends series, such as Trends in Ecology and Evolution. Articles there are often high-impact and intriguing. But, not open access and can be long-in-the-publishing-cycle (which is not as ideal for ideas types of papers).

Now, one might say, if you want a short, rapidly published, open access opinion piece – well, that’s called a Blog. But this does not have the cachet of a formally published journal (even an online-only one).

So, I’ve been intrigued to see the emergence of Ideas in Ecology and Evolution. It’s mission is to be quick (5 days from acceptance to publication), idea focused, very open to peer-reviewed commentary, and open access. Their entire publishing model is laidout by Lonnie Aarssen, the journal’s editor, in this opening editorial. Some seems like relatively standard stuff. For example, the criteria for publication are:


(i) The paper must present a genuinely novel idea or commentary.
(ii) The new idea /commentary must be well-argued and plausible.
(iii) The paper must demonstrate the potential for the new idea /commentary to impact significantly on the subject area or broader discipline.
(iv) The paper must clearly differentiate the idea or commentary from any previously published similar ideas or commentaries.
(v) A new idea must be accompanied by a proposal for testing the idea, even if it is completely impractical with current technology. Testability may be addressed directly, e.g. through empiricism, or in terms of the consilience of inductions.

But then it gets interesting. What is perhaps most intriguing (and most controversial) is how the journal attempts to speed up the initial review process and ensure that all ideas are given a fair shot, rather than try to maintain ‘prestige’ of a journal. It begins with the premise that the current review system is somewhat broken, and that referees have little incentive to be speedy in their reviews or easily embrace new ideas that are counter to dogma. So, it proposes to whopping changes to the system. 1) Referees are paid for their job (current $150). 2) No blind reviewing. Reviewers are fully credited when a paper is published. Not only that, but 3) “If the paper is accepted for publication, each referee is entitled to publish his/her views on the paper as a response article – peer reviewed by both the editors and the author.” Although, reviewers are also allowed to merely click through a standard form and submit no written comments if they wish, in order to speed up the process.

In their own words “Ideas in Ecology and Evolution represents a completely transparent peer-review publication model that rejects elitism, guards against sources of publication bias, and serves to break down traditional barriers to the release of creativity…

Lofty stuff. Assuming that this bias against new ideas is real. I have to admit, I’m skeptical. Reviewers are rigorous and sometimes slow. And yet, I am highly skeptical of the idea of buying objectivity. When I review, I always strive for editorial objectivity, money or no. I like the idea of publishing commentaries and reviews along with papers – I’ve long wished that more journals would allow access to general reviewer comments. But my skeptical side really has to wonder if paying reviewers might make them actually less objective and more likely to accept a paper. I’m just not sure if I would feel comfortable being paid good money, reading something, and then giving it a thumbs down.

Also intriguing, authors pay a $400 submission fee up front (which goes towards reviewers) and $300 afterwards if accepted. The up front fee is indeed novel, and I admit, I can see many an author blanche at the idea of paying $400 for a possible rejection. It also ups the ante on the question of whether introducing money into the reviewing system will actually change objectivity.

This far, not much has been published there – one paper on parasites in behavior research and a response by one of the reviewers. Will there be more? Is this The Way? Or, is there an even more streamlined semi-peer reviewed meta-blog more the way to go for this sort of thing (something to think about, folk)? And how ethically sound is the journals reviewing policy? I am indeed curious.

Aarssen, L. (2008). Ideas in Ecology and Evolution – A new open-access model dedicated to the rapid release of creativity in peer-review publication Ideas in Ecology and Evolution, 1, 1-9 DOI: 10.4033/iee.2008.1.1.e

snails going nom nom nom = productive diverse tidepools?

ResearchBlogging.orgThe “gold standard” experimental design for asking how do changes in biodiversity change ecosystem function has been to randomly assemble communities of varying species richness, but equal abundance, and examining differences in function from one level of richness to the next.

But let’s be honest. Changes in diversity due to impacts by man will not be random. In many ways, the early (and much maligned) designs of Tilman and colleagues are really more relevant to realistic biodiversity change scenarios than random assembly experiments. Sure, the mechanism behind diversity’s effect may not be as clear, but the end results sure are.

When it comes to changes wrought due to runaway trophic cascades (e.g., overfishing -> release of small predators -> removal of their grazer prey), the recent article by Altieri et al. provides a pretty compelling* example of some of the counterintuitive changes from real-world changes in ecosystem function.

The authors look at the consequences of increasing densities of grazers in intertidal tidepools for 6 months. They find that, while increasing grazer density decreases the biomass of algae (natch!), that total productivity (here defined as mg of Oxygen produced per hour per square meter) stays constant. So, the amount of oxygen produced per hour per gram of algal biomass has actually gone up. Wild, eh? What is more striking is that 1) this appears to be due to pools that have a more even even distribution of species having higher biomass specific rates of productivity (see Figure 2 from the paper below) and that increasing the abundance of grazers actually increases species evenness. It does not, however, effect the number of species per pool.

The authors argue that, by changing evenness in a non-random manner, we can see that realistic changes in biodiversity can indeed alter how ecosystems function. More intriguingly, changes in function may bee counterintuitive. Heck, if I looked at a pool full of lush green algae versus one which, while it had a pretty even mix of species, was grazed down to the dregs, I’d say that the lush pool was more productive. But I’d be wrong.

I do admit, I am curious if this is all just an Ulva (the dominant seaweed) story. But, then again, any competitive dominant is going to alter the function of all other species in the surrounding community. By ensuring that no one species can dominate, grazers boost total function. And what is more, those changes really depend here not so much on the number of species, but how evenly distributed they are across a landscape.

I remain curious as to how work like this can better tie into ecological forecasting. We can often understand some of the basic implications of an human impacts – changes in abundance of key players or the response of sensitive species. I wonder how this work on non-random changes to community properties such as evenness and diversity will enhance our ability to predict and understand the more profound, yet also less intuitive, changes to ecosystems.

* – Full disclosure, I have worked with most of the authors at one time or another, and they are a motley, loveable, and brilliant bunch of folk.

Altieri, A., Trussell, G., Ewanchuk, P., Bernatchez, G., & Bracken, M. (2009). Consumers Control Diversity and Functioning of a Natural Marine Ecosystem PLoS ONE, 4 (4) DOI: 10.1371/journal.pone.0005291

when NOT to MANOVA

ResearchBlogging.org
And now its time for a multivariate stats geek out.

The statistics that we use determine the inferences we draw from our data. The more statistical tools you learn to use, the more likely you are likely to slip on a loose bit of data, and stab yourself in the eyeball with your swiss-army-knife of p values. It’s happened to all of us, and it is rarely due to willful misconduct. Rather, it’s a misunderstanding, or even being taught something improperly.

I was given a sharp reminder of this recently while doing some work on how to breakdown some repeated measures MANOVAs- useful for dealing with violations of sphericity, etc. However, I fell across this wonderful little ditty by Keselman et al – Statistical Practices of Educational Researchers: An Analysis of their ANOVA, MANOVA, and ANCOVA Analyses (yes, as an Ecologist, I love reading stats papers from other disciplines – I actually find it often more helpful than reading ones in my own discipline).

Now, everything in my own work was A-OK, but I found this note on the usage of MANOVA fascinating. (bolded phrases are mine)

In an overwhelming 84% (n = 66) of the studies, researchers never used the results of the MANOVA(s) to explain effects of the grouping variable(s). Instead, they interpreted the results of multiple univariate analyses. In other words, the substantive conclusions were drawn from the multiple univariate results rather than from the MANOVA. With the discovery of the use of such univariate methods, one may ask: Why were the MANOVAs conducted in the first place? Applied researchers should remember that MANOVA tests linear combinations of the outcome variables (determined by the variable intercorrelations) and therefore does not yield results that are in any way comparable with a collection of separate univariate tests.

Although it was not indicated in any article, it was surmised that researchers followed the MANOVA-univariate data analysis strategy for protection from excessive Type I errors in univariate statistical testing. This data analysis strategy may not be overly surprising, because it has been suggested by some book authors (e.g., Stevens, 1996, p. 152; Tabachnick & Fidell, 1996, p. 376). There is very limited empirical support for this strategy. A counter position may be stated simply as follows: Do not conduct a MANOVA unless it is the multivariate effects that are of substantive interest. If the univariate effects are those of interest, then it is suggested that the researcher go directly to the univariate analyses and bypass MANOVA. When doing the multiple univariate analyses, if control over the overall Type I error is of concern (as it often should be), then a Bonferroni (Huberty, 1994, p. 17) adjustment or a modified Bonferroni adjustment may be made (for a more extensive discussion on the MANOVA versus multiple ANOVAs issue, see Huberty & Morris, 1989). Focusing on results of multiple univariate analyses preceded by a MANOVA is no more logical than conducting an omnibus ANOVA but focusing on results of group contrast analyses (Olejnik & Huberty, 1993).

I, for one, was dumbstruck. This is EXACTLY why more than one of my stats teachers have told me MANOVA was most useful. I even have advised others to do this myself – like the child of some statistically abusive parent. But really, if the point is controlling for type I error, why not do a Bonferroni or (my personal favorite) a False Discovery Rate correction? To invoke the MANOVA like some arcane form of magic is disingenuous to your data. Now, if you’re interested in the canonical variables, and what they say, then by all means! Do it! But if not, you really have to ask whether you’re following a blind recipe, or if you understand what you are up to.

This paper is actually pretty brilliant in documenting a number of things like this that we scientists do with our ANOVA, ANCOVA, and MANOVA. It’s worth reading just for that, and to take a good sharp look in the statistical mirror.

H. J. Keselman, C. J. Huberty, L. M. Lix, S. Olejnik, R. A. Cribbie, B. Donahue, R. K. Kowalchuk, L. L. Lowman, M. D. Petoskey, J. C. Keselman, J. R. Levin (1998). Statistical Practices of Educational Researchers: An Analysis of their ANOVA, MANOVA, and ANCOVA Analyses Review of Educational Research, 68 (3), 350-386 DOI: 10.3102/00346543068003350

Rum, Sea Squirts, and the Lash!

ResearchBlogging.org
“But assuming that the would-be scientist managed to avoid, or survive, the potentially dire consequences of scurvy, dysentery and malaria, that his ship was not sunk in bad weather or driven onto an uncharted rock or reef, and that his journals and specimens were not destroyed by shipboard fungus, insects, rodents or cow or sheep urine, he still had several major problems to overcome in order to undertake remotely adequate deep sea research.”

Wow. There really is no more fun left in marine science. That’s the conclusion one must reach after reading Anthony Rice’s Marine science in the age of sail, part of a wonderful special issue of Zoologica Scripta entitled In Linnaeus’ Wake: 300 Years of Marine Discovery.

Worth checking out. And it makes me pose the question, if you wanted to get into marine science then, would you rather spend 5 hours manually bringing in your sounding lines using a capstan and a crew of surly sailors, or study the intertidal? Followup: why then did it take until the 20th century for the study of the intertidal to take off?

Possible answer: Chanties and Rum. That’s my hypothesis, and I’m stickin’ to it.

(although, for 5 hours?)

Anthony L. Rice (2009). Marine science in the age of sail Zoologica Scripta, 38, 25-31 DOI: 10.1111/j.1463-6409.2007.00305.x