Maximize the benefit of Conference travel!

One of the best things you can do while travelling to a conference has nothing to do with the conference itself — visiting another University.

These days, with most airlines operating via a hub-and-spoke model, we rarely get direct flights to conferences. This is especially true if we live in small college towns or if most of the conferences we attend are overseas.

So why not visit a research group on your way to or from the conference?

Benefits

  • Often the meetings you have visiting a University are far deeper and more meaningful than at a conference
  • You get to visit laboratories/field sites and see their experimental setups in person.
  • You get to see the same project through different lenses, meeting lab techs, undergrads, PhD students, postdocs and Professors
  • You get to give a seminar to a usually quite large audience compared to a conference with multiple parallel sessions

Costs

  • Adding a few days to your trip takes time, and can be especially difficult for those with families
  • Landings and take-offs are the most carbon-intensive part of a flight, so if reasonable non-stop flights exist, there can be a substantial environmental cost by adding a stop-over
  • Additional financial costs, on top of what you incur from attending the conference, are, proportionally, fairly minimal and often easy to fund (see logistics below)

 

Last year I wrote a piece documenting that only 4% of conferences were using sustainable practices*. As a result, I’m always concerned about the environmental footprint of my travel.

But part of minimizing the impact of my travel is maximizing the professional benefit when I do choose to take long flights.

INFO_GRAPHIC_SustainableConferences

This week I just finished a wonderful visit to Hong Kong University, meeting with their Forensic Conservation Lab, hosted by the awesome Dr Caroline Dingle. It was a truly eye-opening experience to see all of the interesting genetic work they are doing to understand and combat illegal wildlife trade. It has been perhaps the most intellectually fulfilling trip I’ve ever been on, and to think it only happened because I chose to stop over from a workshop in China on my way back home to Australia. I think the cross-pollination between mathematics and forensics will lead to fruitful work that will hopefully reduce illegal wildlife trade and give us new ecological insights. The benefit will, therefore, hopefully, outway the costs.

Logistics

When looking for flights to the conference, take note of cheap and logistically comfortable stop-over cities. Then check which labs are based in those cities. Contact the lab you’d like to visit and ask if you can give a seminar the week before or after the conference. Usually, the flight is no more expensive than alternatives. The only additional expense is accommodation. But there are several avenues to fund this even if you don’t have grant money for it. Options include (1) if you tell a University that you want to visit them, and also let them know that the flight will be covered, they may cover accommodation or (2) they may volunteer to let you stay with someone in the department or (3) you can often ask your department or university if they’d cover a small accommodation expense. They’ll often do it because flights are the big expense for a short trip, and invited seminars can increase the exposure of their department’s research.

While many of us have focussed a lot on the hypocrisy of being an academic ecologist, I think we need to talk more about getting the most out of our activities that cause the greatest environmental damage. We need to maximise the environmental (and/or) societal benefit we attain per unit of environmental damage we do. So let’s not forget the benefits part.

So there you have it, some non-traditional advice on getting the most out of conferencing, in addition to all the great more conventional advice out there.


* although many conferences in Ecology and Conservation, especially ESA, were sustainable

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Risk of death by sharks vs. walking

In a comment on my previous post about shark attacks, I said that perhaps we should walk to the beach to lower our risk of death due to traffic fatalities. I’m glad Kevin Lawrence, correctly pointed out that in order to make that claim, I’d have to look at pedestrian fatality statistics.

Well, good thing I did. It turns out walking is way more dangerous than driving (per mile, but not per minute).

There are roughly 42 billion walking trips in the USA per year*. And on average those trips tend to be roughly about one mile*.  There are 5,376 pedestrian fatalities per year (compared to about 38,000 auto-accident fatalities in general, which likely includes the pedestrian figure). These figures leed to about 0.000000128 deaths per mile walked. This means that walking 0.08 miles has roughly the same fatality risk as one beach visit due to a shark attack. So your house would have to be less than 65 meters away from the beach for the walking trip (round trip) to be less dangerous than the beach visit.

In many cases, 65 meters is longer than the distance between the beach and our parked cars! The walk from your car to the beach might be more dangerous than dying from a shark attack***.

*based on this source http://www.pedbikeinfo.org/data/factsheet_crash.cfm

**based on the last table here http://www.pedbikeinfo.org/data/factsheet_crash.cfm

*** There are of course a lot of caveats here, as parking spots close to the beach might be in dedicated parking lots, and not involve crossing busy intersections. But even so, this number is quite stunning.

Promoting your papers more effectively

My most recent opinion article on the potential for human burials to save threatened species has received more media coverage than I am used to*. In this post I will talk about what I did to get the word out and how it differed from what I did in the past.

  1. I contacted my university’s communication & marketing department when the paper made it to the minor revision stage. I included a short 3 paragraph story about the article. They did a wonderful job modifying it into a press release and even included a video interview of me talking about the paper in a local cemetery. They uploaded the press release in a closed database prior to publication. Basically, journalists agree not to publish their stories before the paper actually comes out in exchange to see press releases ahead of time. For previous papers, I contacted the communications team well after the paper made it online. They sometimes turned it into a press release, but by then the article looked old. In addition, the marketing department had a lot of time to work with, which enabled them to shoot the creative cemetery video.
  2. I cold-emailed science journalists individually before the paper came out. This led to a piece in the Pacific Standard. While not all journalists responded positively, even the ones who declined often provided me with more direct contact information, so I could reach them more quickly in the future. Some of the journalists wished that they received my email earlier, citing that 36 hours prior to the paper’s release was more last minute than they usually like (especially given USA/Australia time-zone issues).
  3. I baked a cake that depicts the paper topic (from a box mix). This reached a whole different audience, even making it onto the baking section of Reddit. Several news stories included the cake in their pieces. My article got published the same day as our department morning tea, so I thought this might be a fun way to introduce the paper to my colleagues. I had no idea that this would add to the media coverage. 

 

The big moral of the story is to contact people well in advance of the article being published. There are many science stories competing for attention. See Meghan Duffy’s post on pitching a science opinion piece to different audiences, and the ensuing comments. While journalists want good stories, you need to make it easy for them, otherwise they will simply choose to write about something else. If the story seems old that is an added barrier. All of this publicity-chasing took a lot of work, but in the end I think it was worth it. I have received so many emails from everyday people thanking me for writing about the topic,. I am very happy I got the word out about Conservation Burials. It is a topic very dear to my heart.

*Coverage included: New Scientist, IFLscience, Australian Newspapers, radio, and podcasts

Online conferencing should be more convenient

If you’ve tried to watch (or organize) an online conference these days, you’ve probably gone through the pleasure of downloading fancy software [or going through a complex online membership/login process] just to get a seat in the audience. The software or website likely included all sorts of special features to make the talks feel more like you were watching them in person. You could press a button to raise your hand. You could ask questions using your microphone. Perhaps, you could even interact with other listeners.

Today I ask, “Is all of that worth it?”. Why not just stream the conference live on youtube (or similar website), with no login required, no required software to download, and no new tools we have to learn? Online conferencing needs to leverage its most powerful feature … convenience. In theory, I could decide to attend seconds before the conference. The only major obstacle to putting together an online conference via something like youtube is that speakers are in different locations, needing to stream their talks sequentially.

I have perhaps successfully joined 50% of the online conferences I wanted to watch. The most common reason I skipped was that I tried to download the conference software (or register in the online system) at the last minute and gave up at the first sign of required troubleshooting. Many of us are trying to watch the conference on work computers that have restrictions on the types of software we can download. Some people don’t, realistically, have the patience to download software we aren’t going to use on a regular basis.

Are there convenient, free, online conferencing options, requiring no login, keep the talks all in the public domain, and feature a live stream with minimal features? Could conferences stream from a website without any login or downloads required? I don’t see online conferencing taking off until watching the conference is literally as easy as clicking a link. Does this exist and many conferences are simply choosing not to use it? Or does the right tool simply not exist yet? Discuss in the comments.

Online conferencing will never replace everything we like about in-person meetings, so we need to stop pretending it will. Instead, if online conferences were more convenient, we would actually attend in droves. Only then can they be an integral part of reducing the environmental footprint of academic conferences. I think twitter conferences might be the most promising type of online conferencing, which avoids many of the pitfalls I talk about above. And I’m happy to be joining one in 2018.

What do you think about online conferencing?

Practice what you preach, and preach what you practice

A few weeks ago we published a correspondence paper in Nature Ecology & Evolution pointing out how few academic conferences engage in sustainable practices. This week we put it all in perspective in the University of Queensland’s “Small Change Blog“. An excerpt from our blog post is below

We have all been urged to reduce our greenhouse gas emissions for decades, as a way of avoiding runaway climate change.

One way to do this is to reduce the amount we fly. Air travel is a major source of carbon emissions. Roundtrip flights from Sydney to London total 35,000 kilometers. This trip emits more carbon than the average Australian motorist emits from two and a half years’ worth of driving …

See more here for the full blog post.

Is Theoretical Biology Dying?

While glancing through journal metrics recently for some of the most well known mathematical biology journals (with a bias towards ecology), I noticed something a bit disturbing. It appears that theoretical papers are declining in citations. Basically, the number of citations per article has been decreasing over the past 4-years in nearly every well respected theoretical biology journal I could think of. Some of the declines may not be statistically significant, but as a whole, the trend seems pretty clear (see the middle time-series plot in each of the graphs below – labeled “cites per doc” – from scimago).

SCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country Rank

The above journals range in how “theoretical” they are. Some might argue that the first three aren’t really theory journals at all, but I left them up there anyway since they are theory friendly journals.

I have three alternative hypotheses for the downward trend in per article citation

  1. Scientists have started to avoid reading/citing pure theory in biology
  2. The best and most influential theoreticians now team up with empiricists to publish high impact science papers, this means some of the best ideas, that would have gone to theory journals in the past, are now components of papers in Science, Nature, & other more general biology journals. In other words, data is being used to test some of the most promising ideas and the leftover ideas that couldn’t be tested against data go to the theory journals.
  3. Citations per article might be declining in biology in general, and hence the decline in theoretical biology is expected. This might be explained by something like the mean length of reference lists declining (possibly due to journal page limits or increased motivations to publish short zippy letter style papers)

Or perhaps it’s a combination of all three of these. Looking at some top ecology and general biology journals (below) it seems like hypothesis three might be the most likely. Cell, TREE, and Ecology Letters all seem to be declining. So it isn’t that the top journals are eating up all the citations of lower ranked journals. One might think that with an increasing number of articles published each year, that perhaps the top papers benefit the most from this (given how citations tend to be distributed), but this doesn’t seem to be the case, as far as I can tell.

 

SCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country RankSCImago Journal & Country Rank

I’m not so sure how general journals (outside of biology) stack up on this list, so maybe it is that biology journals are being cited less. I’m not so sure what to make of this. What do you think might be the cause of the perhaps general downward trend of cites/article? Or maybe it isn’t a trend at all, and this is all happening just by chance? I haven’t done any statistics to back anything I said up so it would be interesting to get a hold of some raw data (which scimago, doesn’t seem to share online) and analyse these hypotheses a bit more rigorously. Feel free to discuss in the comments.

————

Jeremy Fox has written quite a bit about theory and its value (and perceived value) in ecology, see the following:

Should theory published in general ecology journals have to be realistic? especially see Brian McGill’s comment, which might be considered an alternative hypothesis to the ones above. He basically argues that simple, general models might be for the most part fully explored, and hence the majority of what is left in theory journals these days is complex models, which aren’t so general. Complex models for specific situations should probably involve some data. If I were to continue Brian’s logic, if theory journals are now publishing more data-free complex model papers, they might be deservedly uncited.

Ecologists think general ecology journals only want realistic theory and they don’t like that

Uber is to YouTube as Conservation Scientists are to Mathematicians

Recently I organized sessions at two strikingly different conferences (1) The Society for Mathematical Biology (SMB) meeting and (2) The International Congress for Conservation Biology (ICCB). Both featured quantitative approaches, but presentation styles and modeling philosophies differed remarkably between the two conferences. You might be surprised to find out that the conservation scientists at ICCB were, on average, using more “complex” mathematical models than the mathematicians at SMB. How can this be? Shouldn’t mathematicians be analyzing more complicated equations? Answer: No, and it has to do with a trade-off between model “complexity” and model “transparency/tractability,” which I will explain below using YouTube video and Uber driver ratings.

Uber utilizes a 5-star rating system. When you take a trip in an Uber vehicle, you rate the experience from one to five stars (five being good and one being terrible).  Uber then displays the mean rating across the driver’s most recent 1000 trips. Similarly, drivers rate passengers the same way. These ratings are then used to determine whether drivers and passengers are allowed to remain on Uber.

YouTube’s rating system is quite different. They simply ask you to rate a video “thumbs up” or “thumbs down.” Youtube then displays the number of people who chose each option.

Why are these two rating systems so different and what do they have to do with model “complexity” and “transparency/tractability”? Uber’s model of a driver’s performance is complex: there are five choices for how to rate your driver, meaning each rating provides more detailed information than the like/dislike approach employed by YouTube. This creates a new challenge. Uber must now present more complex data to their customers. They opt for taking the mean, which removes information. Surely, a driver with 1 star and 1,000 trips means something very different from a driver that has 1 star and only one trip. But displaying the mean makes it easier for riders to digest the meaning of the rating.  One could potentially opt for a complex display that doesn’t remove such info, [e.g. a frequency distribution (histogram) of star ratings for each driver]. This type of information is provided by some websites, such as Yelp and Amazon, but in general, this approach is mostly avoided because a distribution is more difficult to understand than a single number such as 4.6-star rating.

XKCD comic on the 5-star rating system https://xkcd.com/1098/

The added complexity of the star rating system creates another issue. What exactly does a 4-star experience entail? One person might give 1 star for a small mistake. Others might reserve a one-star rating for things as extreme as physical violence. Model complexity introduces a new form of ambiguity, undermining the true meaning of a displayed star rating.

YouTube initially started with a 5-star rating system, but then they realized that the vast majority of people were rating a video either 1 or 5 stars anyway. So they ditched their 5-star rating system for the thumbs up, thumbs down approach. Netflix and other companies have followed suit. So what makes this system so great. (1) the viewer of the rating gets complete information and (2) there is less ambiguity as to what the rating means.

You might be thinking at this point, “why would Uber opt for this more complex and less transparent rating system?” I can’t answer this question, but I can take a guess based on my observations of conservation scientists and mathematicians at my last two conferences. Mathematicians are obsessed with understanding “why” things are true, while conservation scientists are obsessed with projecting the consequences of our actions onto the future state of the environment. For a decision maker, “understanding” only really matters when it leads to better decisions. Model complexity may in some cases improve predictability even if it is too complex to understand completely.

Since Uber uses its ratings to determine the fate of a driver’s employment, they are likely interested in predicting who will be a good long-term driver. A fine grain rating system might be required to make these predictions well (and there may be far more sophisticated things, behind the scenes, rather than calculations of mean star ratings, to do such predictions). At Uber, users can’t select drivers based on their rating so transparency to users may not be so important anyway.

To summarize Uber may be more like a Conservation Scientist and YouTube might be more like a mathematician.

 

 

 

 

 

 

Conferences Need Environmental Policies

Scientists have been preaching about sustainable conferencing for decades, yet our new study out in Nature Ecology & Evolution shows that few conferences have taken any action to lessen the environmental impact of their meetings. We assessed advertised environmental impact policies of 116 academic conferences across 18 scientific disciplines and 31 countries. The major findings were
  • only 4% of 116 conferences assessed advertised carbon offset options.
  • only 9% of conferences advertised any sustainable practice to mitigate or lessen the environmental impact of their meeting
  • Sustainability Science conferences were no exception, with 0 out of 10 advertising carbon offsets and only 1 out of 10 advertising any action that could be classified as a component of sustainable conferencing
  • Ecology & Conservation was the only field where carbon-offset options were common place, but still, only half of conferences in this field advertised sustainable practices
We point to the rapid turnover of organizing committees as both an opportunity and a challenge for sustainable conferencing. Societies can facilitate consistent sustainable practices by creating policies and guidelines that make organizer jobs as easy as possible. For more information see
Holden, M.H., N. Butt, A. Chauvenet, M. Plein, M. Stringer & I. Chadès. (2017). Academic conferences urgently need environmental policies. Nature Ecology & Evolutiondoi:10.1038/s41559-017-0296-2 (open access link available for 1st month http://rdcu.be/uOoO ).

How to organize a diverse conference, symposium or workshop

This year I took my first stab at organizing a couple of symposia for international conferences. In each symposium, one in math and one in conservation biology, I was determined to achieve a diverse set of speakers. Below, I will focus my advice on gender diversity, but it also applies to other types of diversity as well. While I am by no means an expert on this topic, I did achieve my goal, and I thought it would be valuable to share how I did it.

Here are some common challenges to organizing a gender diverse symposium

  1. Women on average turn down invitations at a higher rate than men
  2. Even if you invite many women, the women you invite may be more famous/senior than the men you invite (due to unconscious bias) and hence be especially more likely to say no
  3. Female professors that you invite may ask if male students or postdocs can go in their place

Note that unconscious bias, which creates challenge two, increases the chance you will experience challenge three.

Solution: Start by inviting only women until you meet your diversity target

This means starting your search early because you will send fewer invites out per time step. For example, if your diversity target is a 50:50 gender ratio*, and the symposium has eight spots, you might start by inviting four or more women. If less than four say yes, you invite a few more. At this point, you might be asking, “Why can’t I just invite four men and four women from the start, and if all the men say yes, and all the women say no, then I only invite women from then on.” Often, near the symposium proposal submission deadline, you start scrambling for a last minute speaker or two to fill the final empty slots. If four women didn’t say yes yet, it will be a lot tougher to stay devoted to your cause when you are desperate to accept anyone relevant to your symposium topic. If you’ve already proactively combatted your unconscious bias and secured four female speakers, your unconscious bias at “panic-o-clock” will not undermine your goal of achieving gender diversity.

If you follow this solution diligently, challenge number three (women suggesting their male students) is not an issue; you can easily accept the male students without compromising diversity. However, imagine you didn’t follow the solution above, and you already have 4 men speaking. In this case accepting another male will throw off the gender balance of your symposium. Of course, you could choose not to let him speak, but I don’t think that is a good solution. It’s beneficial to give students an opportunity to speak in a symposium [career stage is an important part of diversity]. Also, it’s good for gender equity to give early career researchers (ECRs), mentored by women, opportunities to succeed. Advancing the careers of ECRs advised by women is an important piece of gender equity because professor performance can hinge on the success of their students and postdocs.

Lastly, if your unconscious bias is preventing you from thinking of good women to invite, you can find female researchers (and other underrepresented minorities) in ecology, evolution, and conservation, using the following list. Be sure to invite post-docs, and pre-tenured faculty (remember challenge two above). You can also search for grad students here. Another strategy is to read recently published papers related to your symposium topic and take note of the authors’ likely gender. It’s of course really easy to find fantastic female scientists, engineers, and mathematicians to speak at conferences.

When I take active efforts to create a gender diverse symposium, I believe that I increase speaker quality. I can easily fall into the trap of inviting the first eight people who come to mind. Being more conscientious about whom I invite means I read extra papers, come up with new ideas for the symposium theme, and end up inviting more relevant and exciting speakers. These are often speakers who I have never met, and possibly didn’t even know about before creating the symposium. It is truly win-win.

The above strategy worked for me, but perhaps you have different strategies (or disagree completely). Please share in the comments.


 

*One might decide to set the target as matching the gender ratio of those working in the given field of research rather than 50%. In my math-bio symposium, I chose specifically to still shoot for a 50:50 gender ratio (or more female) because I know other symposia will likely be more male dominated than the already skewed gender ratio of the field. Shooting for the higher target helps to combat this. Plus, shouldn’t we aim for the ideal ratio, not a ratio perpetuating a status quo that underrepresents women? I, of course, found plenty of great women to speak at my math symposia, despite a skewed gender ratio in math. However, the advice in this blog can apply to any target, not just 50%.

 


Related posts by others

A more business & technology oriented post about diversifying conference panels by Stephanie Goodell. She has a lot of great advice that translates to academic conferences.

Diversify EEB by Gina Baucom A piece describing the list of female and underrepresented scientists that I link to in this post.

Edit: more links below from Jabberwocky Ecology

Advice on diversifying seminar series 

Advice on diversifying conferences

The Anthropogenic Allee Effect: the importance of doing the math

In 2006, Franck Courchamp, and colleagues, proposed a fundamental idea in conservation called the “anthropogenic Allee effect.” It is named after the classic “Allee effect” in ecology, where populations above a certain threshold size persist and below this size go extinct* (due to the inability to locate mates for example). However, even if we assume populations grow fastest when there are few individuals (the opposite of an ecological Allee effect), changes in human behaviour can drive small populations extinct. This can occur when humans are willing to pay more for products derived from rare species.

Take a hypothetical harvested fish population that obeys the following assumptions

  1. Fishing effort increases if the price consumers are willing to pay for fish is higher than the cost required to extract the fish from the ocean
  2. Harvesters decrease effort when cost is higher than price
  3. Fishers and fish behave like particles of gas randomly bumping into each other in space
  4. The price people are willing to pay for fish stays the same through time

As fishers remove fish from this population, the population size eventually gets small enough that individuals are too expensive to locate and harvest. This leads to a stable equilibrium population size, where below it harvest is too costly and above it harvest is profitable (see fig 1A, blue line is cost per unit harvest, red line is price per unit sold).

AAE

Now if we modify assumption (4) and make price per unit harvest higher when the species is less abundant we can create a second equilibrium (price and cost intersect again at low population sizes). Now, harvest is profitable when (1) the species is abundant (because cost of harvest is low) and (2) when the species is rare (because consumers are willing to pay a high price for harvested individuals). Therefore, species with initial population sizes below the unstable equilibrium in Fig. (b) will be harvested to extinction. Initial population sizes above this equilibrium will lead to sustainabe harvest and eventually the population will approach the stable equilibrium on the right.

So is this classic argument correct? It turns out, not exactly. This is a one dimensional argument for a two dimensional model (of both fish and fishers), and while it appears intuitively correct, it is a mistake to ignore harvest effort explicitly. Today I posted a preprint on ArXiv (edit: now out in J. Theor. Biol.), which demonstrates that when you actually do the math, the classic anthropogenic Allee effect models can generate a rich set of previously undiscovered dynamics. Even abundant populations can be driven to extinction, as long as there is a small minimum price people are willing to pay when the population is very abundant.   For example, in one scenario, initial population sizes and harvest effort in the small shaded area (in Fig. 2) cycle, but persist, while populations outside the shaded area go extinct. Note that large populations to the right of the grey area are destined to extinction.**

Figure 2. More complicated population dynamics are possible than Fig. 1 suggests. Traditional theory would say all population sizes to the right of the first black circle will persist, but actually a large percentage of such initial population sizes can lead to extinction.

Homoclinic

Jeremy Fox, has a nice list of good and bad reasons for choosing a research project. One of the good ones is

Develop the mathematical version of some verbal idea or hypothesis. Ecology is chock-a-block with influential ideas that haven’t been much developed mathematically. Often, when you try to do the math, you’ll discover key implicit assumptions that weren’t previously recognized, or else you’ll discover that the assumptions don’t actually imply the conclusions they are thought to imply. At worst, you’ll at least make the idea much more precise, and so much more testable. Now, if only someone had had a project idea along these lines back in 1979 or so…

Graphical arguments, based on models, to gain intuition can lead to great ideas, but it is eventually important to follow that up with some math [and/or simulation]. In this case, we have revealed a potential mechanism for populations deterministically crossing an Allee threshold, which would be impossible to intuit just from looking at the model. It’s is hard to tell whether the idea presented here is what drives some harvested populations to extinction (price abundance relationships are difficult to come by), but it seems like a promising mechanism to test, one that I hope will lead to interesting discussions.

*This is actually called a “Strong Allee Effect.” There are also non-threshold Allee effects where population growth rate is reduced at low densities, but is not negative.

**This figure is for a population with linear growth (in the absence of harvest). The green-red dotted loop is what we call in dynamical systems theory, a “homoclinic orbit.” It is broken if we add density dependent growth, but the dynamics in that case are similar. The grey area still exists in the density dependent case (although it isn’t a closed oval), and inside the grey area, populations spiral into the equilibrium.

 

Reference:

Holden, MH, and Eve McDonald-Madden. (2017). High prices for rare species can drive large populations extinct: the anthropogenic Allee effect revisited. J Theor Biol. 429, 170-180.