# A Vision for the Future of Scholarly Publishing

In many ways, the Research Works Act has been a blessing (see excellent link round up here). It has taken the moderately complacent but always grousing scientific community and whipped our feelings about the current state and cost of scientific publishing into a white hot fury. Ideas are bandied about, critiques given, and people begin to take action.

So what is the way forward? Certainly we are not getting away from journals in the near term. Or ever, really, as they are fabulous final curated repositories scientific results. They are the end point and gold standard. And I think we’re all coming to the conclusion that a PLoS-like model is a great way to go. Science must end up in an open access repository at the end of the day.

But a final resting place aside, what should the future look like so that research results can be disseminated rapidly and openly? How can we fold in peer review as a part of the process, as it is one of the hallmarks of the scientific quality control.

So I’ve been dreaming. A vision of the future of scientific publishing. What if arXiv, reedit, PLoS, pubcreds, slashdot’s commenting system, figshare, Data One, and Web 2.0 had a baby? This lead to an idea – a concept – a proposal.

So, here’s my vision of the future. It’s not the only vision, and there is substantial room for discussion, but, it’s a start… Consider this a SciFi musing on scholarly publishing.

I sit down with my morning cup of coffee and log into SciX. I am presented with several options on the main screen:

Submit a Paper
Revise a Paper
Review the Reviewers

So, what happens when I click on each of those? Let’s follow each one, one by one.

OK, so, I click on “Read a Paper”. I’m taken to a screen that shows different scientific disciplines and a search box. I click on my discipline of interest, as I’m just browsing. I am presented with a list of subdisciplines, a search box, and a list of papers below that with several sorting options (# of reviews, submission date, review score, etc.) I click on my subdiscipline, and am presented with just a list of papers which I can sort by various criteria and, again, a search box. I sort so that I can see the latest submissions and find one that piques my interest. I click on it, read it, maybe even view some of its supplemental videos or such. I have a strong opinion about it – I think it’s good, but has a few flaws that need to be corrected before it should be accepted by the community. The paper already has one review filed. I read it, and it’s OK, but it misses some key things. So I click review.

I write a brief review, just like a normal paper. I click that my review should remain anonymous. I also need to select one option from the following list:

This paper is fraudulent/not a paper (flag for review).
This paper is not acceptable in its current form (reject).
This paper is good, but requires some large revisions (major revisions).
This paper is acceptable, but requires some changes (minor revisions).
This paper is acceptable as is.

As I think there are some serious flaws, but like the work, I select the major revisions option.

At that moment, it just so happens that I get an email from SciX. The email contains the latest papers in my chosen disciplines and sub-disciplines that have received at least two more acceptable reviews than rejection reviews. I.e., reject is a score of -1, major revisions is a score of 0, and any acceptable score is +1.

OK, great. Let’s move on. Let’s say I wanted to submit a paper. The submission process is the same as any other site except, today when I click on submit, a screen comes up that denies me the ability to submit. It reads that I currently do not have a review to submission ratio of 3:1. I’m all good on reviewing reviews (more on that later), but I need to file more original reviews myself! I grumble about it, bemoaning my days in grad school when I only had to keep up with 1:1, but it’s right, so I go and file one more review before I come back and submit my paper in the usual way – except for that embedded video. After submitting, I like to the doi on my website and CV.

OK, it’s several weeks later. I have received two major revisions reviews on my paper. I’ve done the revisions, and thought carefully about the reviewers responses. So I go back to SciX and click on Revise a paper. I upload the revised version. I then upload an individual response to each reviewer. They are both anonymous, so I don’t know who they are. However, once I hit ‘resubmit’, they are sent an email. It tells them that I have responded to their reviews and submitted a revised version. They have two weeks to look at the revision and the responses. If they do nothing, the paper will be marked as “acceptable as is”. If they wish, though, they can go and submit a secondary review. This review also includes an option of “Did not respond to my review at all.” If both reviewers select this for more than two rounds of resubmission, my paper is booted and I have to start over again.

A few weeks later, both reviews come back positive, and my paper is included in the next email out. I have also received two additional ‘acceptable’ reviews of the paper with no comments attached. I list the score on my CV. I also hit “submit to journal” and select PLoS One. The system generates the proper submission, and attaches the review history. All I do is fill in a cover letter.

I have another paper to submit, but, I know I’m down on my number of “reviewing the reviewers”, so, I click on that option. I am brought to a screen with five reviews. For each review, I also have the title and abstract of the paper. For each review, I am asked to select one of the following options:

Review is fraudulent/someone padding their bank/unrelated to paper (flag)
Review is cursory. Email reviewer for more detailed review.
Review is acceptable, but laced with inappropriate invective. Count as half-review.
Review is fully acceptable.

I quickly go through and click acceptable for all of them, except one that merely says “No.” with “Reject” selected. Clearly, not fair to the author or the community.

With this finished, I go and submit my next short paper. It’s a brief note, but one that I feel important to get out into the literature.

After all of this, I go to my profile page. I check my list of papers, note their current scores and number of downloads and citations, and update those on my website and CV.

So, that’s it. That’s my simple vision. Open access and transparency from hitting the ‘publish’ button to reading and writing reviews. And a reputation based economy so that papers are only marked accepted when the weight of reviews say so, but anyone can still look at them and the comments that others have made about them.

Thoughts?

UPDATE I’m tremendously excited about F1000′s announcement of their new F1000 Research which is being discussed across the interwebs. I fear that their model of post-publication peer review will end up suffering the same fate as PLoS One, though – comments on highly controversial or touted articles, but most of the rest going without comment or notice. The above vision solves that problem.

Gowers’s How might we get to a new model of mathematical publishing?
Gowers’s more modest proposal
This excellent thread at Math 2.0
Nikolaus Kriegeskorte’s excellent The Future of Scientific Publishing

# A Need to Understand Climate Change’s Indirect Effects

We know that warming, storms, drought, acidification, and the myriad of other effects of climate change will impact natural ecosystems. Most of our studies have concentrated on direct effects, though. For example, if you change temperature, you alter herbivore grazing rates. But what about indirect effects? For example, I’ve found that increased intense storm frequency may remove kelp which will have an indirect effect on the structure of kelp forest food webs.

So, I did a little experiment. I went to Web of Knowledge and searched the following term: “climate change” AND “impact”. I got 21,310 entries. Then I searched again using this query: “climate change” AND “impact” AND “indirect effect”.

The search returned 35 entries.

Surely, this must be a mistake. So instead of “indirect effect” I went with just “indirect”. 506. Better. If I took out the word impact I went up to 1,202. So, at maximum, 5.6%.

OK, maybe this was because I was looking at EVERYTHING. So I filtered it down to just Environmental Sciences and Ecology. “climate change” AND “impact”: 9,248. “climate change” AND “impact” AND “indirect”: 173. Removing impact got me to 689. Only 7.5%.

I’m guessing there are other careful ways of filtering, but, either way, I’m pretty surprised that even at this point, the study of the indirect of climate change still accounts for so little of our knowledge. Pretty interesting. Although I’m heartened by the fact that this literature seems to be increasing exponentially.

# Running R2WinBUGS on a Mac Running OSX

I have long used JAGS to do all of my Bayesian work on my mac. Early on, I tried to figure out how to install WinBUGS and OpenBUGS and their accompanying R libraries on my mac, but, to no avail. I just had too hard of a time getting them running and gave up.

But, it would seem that some things have changed with Wine lately, and it is now possible to not only get WinBUGS itself running nicely on a mac, but to also get R2WinBUGS to run as well. Or at least, so I have discovered after an absolutely heroic (if I do say so myself) effort to get it all running (this was to help out some students I’m teaching who wanted to be able to do the same exercises as their windows colleagues). So, I present the steps that I’ve worked out. I do not promise this will work for everyone – and in fact, if it fails at some point, I want to know about it so that perhaps we can fix it so that more people can get WinBUGS up and running.

Or just run JAGS (step 1} install the latest version, step 2} install rjags in R. Modify your code slightly. Run it. Be happy.)

So, this tutorial works to get the whole WinBUGS shebang running. Note that it hinges on installing the latest development version of Wine, not the stable version (at least as of 1/17/12). If you have previously installed wine using macports, good on you. Now uninstall it with “sudo port uninstall wine”. Otherwise, you will not be able to do this.

Away we go!

1) Have the free version of XCode Installed from http://developer.apple.com/xcode/. You may have to sign up for an apple developer account. Whee! You’re a developer now!

2) Have X11 Installed from your system install disc.

` echo export PATH=/opt/local/bin:/opt/local/sbin:\$PATH\$'n'export MANPATH=/opt/local/man:\$MANPATH | sudo tee -a /etc/profile `

4) Open your terminal and type

` sudo port install wine-devel `

5) Go have a cup of coffe, check facebook, or whatever you do while the install chugs away.

7) Open your terminal, and type

``` cd Downloads wine WinBUGS14.exe ```

8 ) Follow the instructions to install WinBUGS into c:Program Files.

9) Run WinBUGS via the terminal as follows:

` wine ~/.wine/drive_c/Program Files/WinBUGS14/WinBUGS14 `

10) After first running WinBUGS, install the immortality key. Close WinBUGS. Open it again as above and install the patch. Close it. Open it again and WinBUGS away!

11) To now use R2WinBugs fire up R and install the R2WinBUGS library.

12) R2WinBugs should now work normally with one exception. When you use the bugs function, you will need to supply the following additional argument:

` bugs.directory='/Users/YOURUSERNAME/.wine/drive_c/Program Files/WinBUGS14' `

filling in your username where indicated. If you don’t know it, in the terminal type

` ls /Users `

No, ~ will not work for those of you used to it. Don’t ask me why.

# Food Web Structure and Changing Diversity at Two Levels

This is part of a larger series of open notebook posts about how food web structure modifies the effects of predator extinctions. For an introduction and list of other posts, see here.

OK, last but on two-level food webs for the moment. I’ve examined how food web structure can change the effects of predator or prey extinctions on both top-down and bottom-up control. A number of folk (including me) have theorized that changes in diversity at two trophic levels should interact – that the consequences of predator diversity loss should change as prey species are lost.

So bearing in mind our master food web and the little 2-level sliver of it we’re thinking about, let’s interrogate this idea. (And yes, that use of the word interrogate goes out to Scott Richmond).

Let's zoom in on one part of the general food web

Thinking about Extinction in Our Framework Thus Far

Thinking about what I’ve put together thus far, I’m not so certain that changing diversity at two trophic levels should influence predation or energy transfer beyond our understanding what’s happening with one trophic level. The simple probabilistic equations that I’ve shown to describe energy transfer and predation both rest on thinking about the average consequences for individual species. Each equation rests on taking a mean value of the probability of, say, being eaten over all prey when predators go extinct. If prey are going extinct as well, that should’t affect the outcome.

Why? Think about it this way. Let’s say you have a food web of 3 predators and 3 prey, and each trophic level is losing one species. For prey species a, the probability that it will be eaten does not change. This is because implicit in asking the question of what are the consequences of extinction for species a, we are asking what are the consequences for species a in all food webs in which it exists. Thinking further, what is, say p(eaten) for a species that does not exist? It’s not 1, but it cannot be 0 either. We just don’t think about it. This argument works as well when thinking about energy transfer.

So, I’d argue, that to understand p(eaten) we simply use the equations derived to understand p(eaten) under predator loss and to understand p(energy) we use the equations derived to understand energy transfer under prey species loss.

Well that chain of logic is uncomfortable. I don’t like where it led at all. I guess tacitly it suggests that maybe the variance of p(eaten) and p(energy) should somehow change… But I haven’t so much thought about variance other than thinking it would work in a similar way to means. Maybe I’m missing something. What is the proper way to calculate variances here? How do simultaneous extinctions affect this variance?

Still, even for the mean value of p(eaten) I’m no so sure. Let’s go draw some webs and see if this plays out.

Webs show that my Logic is Correct. Great.

Let’s start with our 2 predator, 2 prey food web with 1 of each going extinct.

Aaaaand – yeah, those results match exactly with what would be predicted from p(eaten) and p(energy) looking at predator or prey loss independently. The variance is larger – doubled, actually (from 0.125 to 0.25). Interesting. What about something more radical, say, a 3 predator, 3 prey web with 2 predators and 1 prey going extinct.

Yup, still the same as the single-level results, although, here the variance only increases slightly (by a factor of 1.03125).

So, clearly, the single-level results are true for the mean. The variance is still…yeah, I don’t quite have that figured out.

Comparison with the Experimental Literature

So, this result, that you can predict the average effects of changing diversity at two trophic levels at the same time by looking at the results for changing diversity of just one trophic level – does it agree with the experimental literature? Let’s think about one of my favorite examples – Lars Gamfeldt’s excellent 2005 Ecology Letters piece.

In this paper, Lars (LARS!) shows that he wishes I was working on the paper we are collaborating on rather than writing this entry.

Sorry, rather, Gamfeldt shows that prey and consumer species richness can interact. The key quote from the abstract is “…prey richness did not increase resistance to consumption when consumers were present. Instead, our results indicated enhanced energy transfer with simultaneous increasing richness of consumers and prey.”

I find this heartening. Here, p(eaten) was determined by consumers, as predicted. The second statement is curious as well and hearkens to Figure 4 of the paper where total biovolume (predators and prey) is clearly the highest when all 3 predators and prey are present. This is clear evidence that energy transfer into this food web is at its highest here. It drops, though, as consumer richness, but not prey richness, changes. Which, actually, we’d predict based on our in initial examination of energy transfer in the presence of predator loss alone. So…Gamfeldt’s results do appear to echo what I’ve shown here. And for anything with less than 3 consumers shows a consistent relationship for producer loss.

Ah ha. So…I admit, intuitively, I still think that under loss at both levels, p(energy) and p(eaten) should be products of the results from both the prey and predator equations together. But they don’t appear to be (otherwise for the 2-2 web with 1 loss at each level, we’d have p(eaten) and p(energy) = 0.5625). Hrm. This bears more thinking – at least for p(energy) why one does not have to incorporate diversity at both trophic levels. Clearly there’s something a little more complex that needs to be represented in a general equation for p(energy | Er, Ep) though. And likely p(eaten) as well. Hope to come back to that later.

That, and I’m starting to (unsurprisingly) see that some meta-analysis to compare predictions to observed results is going to be necessary, and that figuring out the right metric is going to be non-trivial.

# Prey Loss in Different Food Web Structures: We’ve Been Here Before

This is part of a larger series of open notebook posts about how food web structure modifies the effects of predator extinctions. For an introduction and list of other posts, see here.

OK, only two more entries (I think) on simple two-level food webs before we jump into the great unkown (and you’ll see how unknown it is). So far I’ve been talking about the consequences of losing predator species for predation and energy transfer. But, what about losing prey? And what about losing both? In this entry, I’m going to show that we already know how to think about prey loss and food web structure. We just have to stand on our head. So, keeping our “Master Food Web” in mind, and that we’re zooming on on a particular component, let’s think about loss of prey.

Let's zoom in on one part of the general food web

Who will be eaten?

First, the obvious nice result. If prey go extinct, this does not change the probability that they prey trophic level will be under control. No predation links have been deleted. Therefore, p(eaten) is still 1.

Huh? Yeah, really. Think about it. This is an obvious answer, but, well. It’s a rather nice one!

What’s the probability that energy will get to predators?

So, energy transfer is the thing to focus in on. Sure, energy will still enter the prey trophic level, but the probability of energy getting to some of the predators after some prey go extinct may now be 0. Oops!

The wonderful thing is, p(energy) can be defined using exactly the same framework as p(eaten). We just have to stand on our heads. Let’s first look at a familiar 2-predator 2-prey web with 1 extinction.

It’s quite similar to what we’ve seen before with predator loss with a mean p(energy) of 0.75 across all prey extinction scenarios. However, what’s different is that we’re now interested in what PREDATORS have no prey, not what prey have no predators. This implies that we can merely flip the equations from before, replacing predators and prey as follows.

Let’s assume Er extinctions of our resource species (i.e., prey), Sr is our maximum resource species richness, and Di from before now becomes the out degree of predator i – their number of prey. We can simply revisit our earlier framework for the following two equations.

p(energy | Er) = 1-dh(0; Di, Sr-Di, Sr-r)   (4)

$p(energy | E_{r}) = 1-sum_{D=1}^{S_{r}}{p(eaten|E_{r}, D)F(D)}$     (5)

Simple, no? And no extra explanation needed!

# A Probabilistic Approach to Predator-Prey Relationships: Worth All of the Hoo-Ha?

This is part of a larger series of open notebook posts about how food web structure modifies the effects of predator extinctions. For an introduction and list of other posts, see here.

So, in my last post (notebook entry?), I introduced a new framework for understanding how the food web structure of a predator-prey food web can affect the consequences of extinction for the ability of predators to control their prey. Nice, no? But two things stick out. 1) Really? I mean, this is pretty and such, but does this match anything we’ve seen in nature? 2) So…what if we don’t know the precise structure of a food web, but, rather, just some statistical properties, like linkage density, or degree distribution? What’s your fancy theory going to do for us now?

So, keeping our “Master Food Web” in mind, and that we’re zooming on on a particular component, I’ll address those two questions with a little simulation, a little probability math, and hopefully have you convinced, excited for more, and coming up with all of your own spin off ideas. Or, you can show me how I’m full of it.

Let's zoom in on one part of the general food web

First, a quick review for those of you who didn’t commit to memory the discussion from last time. We’re interested in knowing the change in the probability of prey being eaten given some number, E, of predator extinctions. I showed that we can calculate the average probability of extinction for each prey item if we know it’s number of predators (Di for prey item i) and the diversity of predators (Sp) using the density function of the hypergeometric distribution (dh) such that

p(eaten | E) = 1-dh(0; Di, Sp-Di, Sp-E)     (1)

We can then average this over all prey to get the average probability of being eaten for all prey. And, remember, if it’s just predator extinctions we’re concerned with, then the probability of energy getting to the predator trophic level is the same as p(eaten).

Verification
Great, so, can we trust this approach? Consider the results of a totally awesome paper by Finke and colleagues where they were able to manipulate diet breadth of three species of parasitoid. Broadly, the found that with all generalists, diversity didn’t matter bupkiss for the control of prey. But with specialists, mixtures of parasitoids were better able to control prey. So, one would predict that as average number of prey consumed per predator increases, the relationship between number of predator species and the probability of prey being eaten should go from being linear to quickly saturating at 1.

So, let’s take three food webs. In web 1, we have all specialists. In web 2, we have one specialist, and two predators that eat two prey. In web 3, we have all generalists.

Based on the insights of Finke et al.’s work, we would predict that in web 1, we should have a nice linear relationship between predator species richness (that’s species left after extinction). In web 2, we should start to see some curvature, as p(eaten) increases at lower levels of predator species richness. And in web 3, the only time we should see a value other than 1 is if there are no predators left – total predator extinction! And, indeed, that’s precisely what we see in the figure below.

And to see this over a much wider range of possible food webs, here’s a figure showing curves for all possible five predator, five prey food webs. I’ve colored the lines for each simulation by linkage density (that’s number of feeding links divided by total number of species). I’m plotting this with E on the x-axis again (brain flip!) for my own clarity. If you want to follow along at home, here’s the simulation code.

As you can see, the higher linkage density, the more quickly saturating the relationship.

Getting Away from Specific Food Web Structures
OK, but, we don’t always know the diet of every single species in a food web. Indeed, we often only know the general statistical properties of a web. Robust though that data may be, how can we incorporate it into our the framework we have here?

Now, Di seems to be the place where statistical properties of a food web may enter the picture. It would be great if we could somehow use the average value of Di, or maybe it’s mean and variance, or the power coefficient, or something. The sticking point is that this is a nonlinear equation, so, Jensen’s inequality says, “Nope!” to just plugging in something in place of Di. However, we can use the knowledge that Di is limited to be equal to or less than Sp, and that Di is discrete. We can then just apply some simple probability math – namely, how to estimate a mean from an arbitrary discrete distribution. Let’s assume that the in-degree distribution of the prey (i.e., their number of predators) follows some statistical distribution, F(D). We can then get the average value of p(eaten) with the following:

$p(eaten | E) = 1-sum_{D=1}^{S_{p}}{p(eaten|E, D)F(D)}$     (3)

So, as long as you know the degree distribution, the number of predators and prey, you can plug in anything you’d like. Simplicity itself, no? You can also use this approach to solve for other moments, such as the variance or more. I like it. OK, onwards to thinking about prey extinction, and then to more hairy territory.

# A Probabilistic Look at Predators, Prey, and Extinctions

This is part of a larger series of open notebook posts about how food web structure modifies the effects of predator extinctions. For an introduction and list of other posts, see here.

To begin tackling the question of “How does the structure of a food web influence the consequences of extinction? let’s begin by thinking about how changes in the number of predator species in a simple 2-level predator-prey food web can influence 1) the probability of prey being eaten and 2) the amount of energy transfered to the predator group. Looking back at our “Master Food Web”, we’re zooming in on, say, the consequences of extinction in group E for group C.

Let's zoom in on one part of the general food web

I’m going to begin by thinking about whether we can solve this problem if we know the specific structure of a food web. Later on, I’ll start talking about working from food web network properties such as degree distribution.

The first thing to realize is that we’re talking about probabilities. What’s the probability of a prey item being eaten? What’s the probability of energy getting to the predator trophic level? It’s this probabilistic thinking that’s at the centerpiece of the framework I’m going to lay out.

A Probabilistic Framework for Food Webs and Predation

Let’s establish some ground rules for this framework. For an arbitrary topology (i.e., network structure), we can calculate the probability of an individual prey species being eaten quite simply. If there are any links between a prey item and any predator, that probability is 1. If there are no links, it is 0. Let’s call this p(eaten). Control of a group of prey species can therefore be described as the average value of p(eaten) across the whole group of prey. If everyone has a predator, it’s 1. If no one has a predator, it’s 0. If half of the species have a predator, it’s 0.5. And one should be able to calculate variance, etc., from that information.

And just like that, we have a new network metric. p(eaten), which, really, is p(connected to the network by an incoming edge) if you want to get technical.

Before we jump into numbers, let’s look at some examples of how this p(eaten) metric works. First, a simple system with 2 predators, 2 prey. One predator eats one prey. One predator eats two prey. What’s the average p(eaten) if 1 predator goes extinct?

The above figure shows 2 different possible configurations. When the generalist is knocked out, one prey item escapes consumption. p(eaten) for that extinction scenario is 1/2. When the specialist is knocked out, neither prey item escapes consumption. p(eaten) is 1. So, what’s the average probability that a prey item will be eaten if 1 predator is going extinct? It’s just the average of results from the two scenarios: 0.75.

To hammer this home, consider the figure below for a three predator, three prey food web with two specialists and one generalists. I’ve drawn all possible configurations for both the 1 predator extinction and the 2 predator extinction scenarios. Underneath each scenario is its p(eaten) and in bold to the left is the average p(eaten) for that number of extinctions.

A Hypergeometric Approach to Predator-Prey Relationships. Whoah. You said Hypergeometric.

OK, so, the framework should be fairly clear at this point. Now, for that arbitrary topology, what will be the probability that a prey item will be eaten if some number, E, predators go extinct? First, we can calculate this for a single prey item, let’s call it prey item i, if we know the number of predators who eat it – the prey in-degree, Di.

Let’s say there are Sp predators. Some number of them, Di, eat a single prey. We want to know the probability that, if E predators go extinct, of those that remain, what is the probability that none of them are predators of our prey item. This is p(not eaten). And then 1-p(not eaten) = p(eaten) for our little prey item.

OK, so, given all of the possible combinations of predator extinctions, what is p(not eaten)? How do we find it?

This is actually a special case of the hypergeometric distribution. Remember it from intro probability and statistics? No? OK. So. Briefly, let’s say you are drawing balls from an urn. Some are white, some are black. What’s the probability, if you draw X balls, that N of them will be black? This can be expressed as dh(N; # black, # white, X) since we’re using the distributions probability density function. If you want to get into the details of it, see here.

In the case of our prey item, N=0 – no predators are left that eat the prey. The number of draws is the number of species left after extinction: Sp-E. Black balls are predators of our prey item (Di), white balls are those that are, well, not. So, the probability that an individual prey item will not be eaten given E extinctions is

p(eaten | E) = 1-dh(0; Di, Sp-Di, Sp-E)   (1)

To determine the average probability that a prey item will be eaten, we just average this over all prey.

And if you want to get all gory with this, we can actually write down a function for the probability of being eaten given E extinctions:

$p(eaten | E) = 1 - overline{ frac{ {{ S_{p}-D_{i} }choose{ S_{p}-E }} }{ {{ S_{p} }choose{ S_{p}-E }} }}$

N.B. In putting this together, I’ve also realized that we can use a slightly more intuitive general equation (but the gory details version is uglier). That is, rather than thinking about the probability of having 0 predators left after E extinctions, what is the probability of having all Di predators of a prey item removed by extinction. This is still p(not eaten). And it leads to the following very similar, and potentially more understandable, equation. Any preferences in the peanut gallery?

p(eaten | E) = 1-dh(Di; Di, Sp-Di, E)   (2)

A Last Note on Energy Transfer from Prey to Predators

The nice thing about this averaged function is that it is simultaneously both the average probability that the prey trophic level will be under control by predators and the average probability that energy entering the food web via prey will make its way up to the predator trophic level. Basically, p(prey eaten) = p(energy gets to predator).

A Final Note of Wonder and some R Code

So, the thing that amazes me the most about the results above is that it all hinges on the prey. One actually doesn’t need to know anything about the diet of individual predators. Instead, one only needs to know how many things eat each prey item. This makes the framework easy to code up computationally, and easy to similate, as instead of coming up with all possible adjacency matrices, one can just look at all possible combinations of Di given some number of total predators. To demonstrate how this can be nice, here’s the R code I use to calculate p(eaten):

```#Sp is the diversity of the predators
#E is the number of extinctions
#prey.vec is the in-degree (# of predators) of each prey species

pEaten<-function(Sp, E, prey.vec) {
#see ?dhyper for more on hypergeometric distributions in R
1-mean(dhyper(prey.vec,prey.vec, Sp-prey.vec, E))
}

#If you find the 0 predators remaining formulation more intuitive
pEaten2<-function(Sp.max, E, prey.vec) {
1-mean(dhyper(0,prey.vec, Sp.max-prey.vec, Sp.max-E))
}
```

Great, and thus end-eth the big information boom. This is the kind of thinking that will underlie everything as I move forward, so read and digest this. If there is something that isn't clear, let me know. Once you start to think about the probability of connections, I think it becomes a good bit more transparent. I'll talk validation and generalization to statistical network probabilities in my next post.

# #SciFund is OVER!

After 45 days, with \$76,230 raised from 1440 people, I am a pretty proud papa.

My own project hit 70% bringing in \$4,600 for kelp forest research. While not complete, it funds one full round of sampling trips and a little extra, so, I’m super excited! And now the data from RocketHub and #SciFund participants begins to flow in. Time to start doing some analyses on what worked, what didn’t, and begin to lay out the future of crowdfunding in science!

# Food Web Network Structure and Extinction: The Start of an Open Notebook

So, we know that species are going extinct at a pretty stunning rate. Mostly by human activities. The natural question is, will this affect the function of the natural world? You may well say ‘Duh! Of course!’ as a first instinctive pass, but, the issue isn’t so clear cut – will species that survive simply take up the slack? What’s the value of a ‘species’ anyway?

Starting in the late ’90s the field of diversity-function research has tackled this topic, largely using manipulations plant species number. And the results are pretty conclusive – what you change plant diversity, you affect how the natural world works.

But note I said plants.

A bunch of us in the early to mid ‘aughts wondered if changes in the number of top predator species, or herbivores, or intermediate predators, or other species other than plants and algae might also alter the way the natural world worked in an analogous way. Emmett Duffy outlined a number of reasons we could expect changes in diversity at different trophic levels to produce either the same results as changes in plant diversity or maybe not!

So we went out and did the experiments, and found – well, sometimes diversity affected function one way, sometimes another. It all seemed to depend on something about each individual experiment. I was involved in this by examining about whether losses of predator diversity affected the impact of herbivores on their plant or algal prey – so called trophic cascades.

And in looking at the relationship between predator diversity and trophic cascades we really did see every kind of result one could imagine.

Fortunately, there seemed to be some predictability here which can be seen both by comparing different experiments or looking at some of Deborah Finke’s awesome work in a variety of systems. That one could predict the effect of changing levels of diversity if they knew the relative number of omnivores, specialists, or within-trophic level predation (so called intraguild predation). But these insights were all pretty qualitative. There’s no real quantitative guide here as to when diversity will do what.

Leaving this, I went off and did some work looking at how climate change may alter the network structure of food webs. And promptly did a palm-to-the-forehead. Food web network ecology has done a brilliant job of deriving metrics to describe the structure of, well, food webs. And the structure of food webs seems to influence the effects of species going extinct on trophic cascades or any other function one would care to measure.

Clearly, these two fields needed to come together.

So this is what I’m doing for my postdoc here at NCEAS. I am slowly but slowly trying to figure out how to link food web network theory with biodiversity-ecosystem function.

A general food web to consider for other entries in this series.

What’s my goal? Simple. Look at the food web to the left. In it, different trophic levels have different colors. But, heck, even within a trophic level, we may split things into finer trophic groups based on their diet and types of interactions – something we do all the time qualitatively (e.g., by saying there’s a brown food web of detritivores and a green food web of consumers of living tissue) and can even now do quantitatively.

What I want to be able to do is say, let’s take this food web. If we know some structural properties of the web, can we then predict the effects of a change in diversity within any trophic group on the flow of energy and control of consumption within the web.

For example, if some number of species go extinct in F, will consumption of A increase or decrease? If some number of species in C go extinct, will G accumulate more or less energy?

I realize this doesn’t take some important things into account – interaction strengths or the abundance of each individual species. I think the former can be folded in later. I’d also note that I am trying a very different approach than qualitative modeling and think that problems of indeterminacy in predictions may be dealt with by using a probabilistic framework from the start. With respect to abundances – I’m hoping the results can translate into predictions of biomass, but, we shall see…

In the coming weeks, I’m going to try and open up my lab notebook, and lay out the theory I’m developing to answer these sorts of questions. I’ll be honest, I’m doing this for myself as much as anything. I have a lab notebook full of scribbles – some blind alleys, some promising leads. Writing it out will force me to focus my arguments and spot weaknesses (or have you spot weaknesses)! I’ve got some of this nailed, and some of it I may stumble around a bit with. And, heck, I’m always game to hear thoughts from the peanut gallery.

As I answer different pieces of the puzzle, I’ll put links to them in this entry. So, let’s start this open notebook and see where it goes!