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).


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.


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.



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.

The REAL risk of dying from shark attacks vs. car accidents: the importance of basic fractions

It is summer time here in Australia and hence I find myself at the beach quite a bit. So naturally I want to talk about gruesomely dying in the jaws of a shark. Biologists often claim that the risk of dying from a shark attack is so inconsequentially low that any rational person would ignore it, in comparison to the many risks we take doing mundane activities like driving or taking selfies. Often the statistics quoted go something like this

Number of shark attack deaths pear year: 1

Number of car accident deaths per year: 38,300*

This indeed says that deaths from shark attacks are incredibly rare, but it says absolutely nothing about the relative risk of dying from a shark vs. a car. The numbers are meaningless without an appropriate denominator (that pesky number at the bottom of a fraction). The denominator here is “years”, as the statistic is “deaths per year”, but is that the correct choice for identifying the risk of death when choosing between activities? I don’t think so. There are many people who never venture into the ocean, and of those who do, most visit only a few times per year. In comparison, the average person in the US drives nearly every day. In other words, how many times do people really have the opportunity to encounter a shark?

So below I calculate a more meaningful statistic, the probability of death per instance of exposure (or at least a very rough estimate). Doing so, we can determine the distance one would have to drive in order to obtain the same chance of dying as someone going to the beach and dying from a shark attack. It starts with the numbers below

exposure source
Beach visits / year in USA 110 million (1.1 x 108) National Oceanic Atmospheric Administration
Miles driven / year in USA 3.1 trillion (3.1 x 1012) US Department of Transportation


The risk of dying from a shark attack in a given beach visit is therefore roughly 1 in 110 million and the probability of dying per mile driven is approximately 38,300 in 3.1 trillion (or roughly 1 in 81 million). What does this mean? These numbers are quite close, the risk of death from driving 0.74 miles (or 1.2 km) is about as high as dying from a shark during a beach visit.*

Now you can look at these numbers and think, the risk of dying from a shark attack is so low … it is equivalent to less than a mile (or a little over one km) of driving. Alternatively, you can look at these numbers and say wow … the statistic, “1 death from a shark attack vs. 38,300 deaths from car accidents” really makes the risk of dying from sharks sound a lot more inconsequential than the calculations above. Which camp you find yourself in might depend on how much you drive or visit the ocean without using a car. I’m gladly happy to visit the beach and take such a small risk, completely ignoring the chance of being eaten by a shark, but perhaps the risk isn’t as inconsequential as I once thought. Whatever your thoughts, the reminder here is that it is important to think about the appropriate denominator when talking statistics (there is almost always some assumed denominator, whether we realize it or not … absolute numbers are often misleading).

Photo of great white on surface with open jaws revealing meal.

This oldtime photo of a great white shark is provided by googlesite user TheBrockenInaGlory


*These calculations required some assumptions. First we assumed the numbers from the above sources were true. We also assumed that everyone at the beach goes in the water, which likely isn’t true – the risk of dying due to a shark attack might be more like the risk of driving one or two miles if for example only half of beach goes ever go past ankle-deep in the ocean. We also assumed that shark attacks and auto-accidents occur at a fixed rate for all individuals. This is of course untrue, by driving safely or taking safety precausions in the ocean you can reduce your risk of dying in either situation. We are merely looking at averages here.


Conservation needs to embrace more efficient peer review

Conservation is a crisis discipline. Species are going extinct at an unprecedented rate and therefore scientists and policy makers must act quickly to save them. The peer-review process is useful for quality control, but unfortunately a barrier for quickly disseminating information needed to make the best conservation decisions.

One challenge is that papers are often submitted and rejected from several journals, sometimes over the course of multiple years, before finally getting published. As a paper continues to get rejected, reformatted, and re-reviewed, conservation scientists (authors, reviewers and editors) each waste dozens of hours that could be allocated towards new conservation projects. In addition, policy makers must wait to get the latest credible information.

Solution: peer-review should be done for multiple journals in parallel. Imagine sending out your paper for peer-review and getting back detailed feedback along with a list of journals for which your paper is a good fit. Moreover, the service in charge of this centralized peer-review process contacts the appropriate journals and asks them whether they want the paper to be submitted. After you correct your manuscript, you send it to the interested journal, alongside a response to reviewer comments. If the journal rejects the paper, it is immediately sent to the next journal down your list. No more excessive reformatting, or unnecessary re-reviews, just a more efficient peer review process.

Now what if I told you this system already exists! A non-profit called Axios Review does exactly this, but shockingly the journals which have signed up are mostly pure biology journals, such as Ecology LettersEcology, and American Naturalist. With the exception of Frontiers in Ecology and the Environment, most of the big name conservation journals, such as, Conservation Letters, Conservation Biology, Biological Conservation and Journal of Applied Ecology, are surprisingly not lining up to be officially associated with this type of service. Axios boasts some impressive statistics: once submitted to an interested journal, 85% of their papers get accepted, and half of these accepted papers are not sent for additional review by the journal. On average, a paper going through Axios gets accepted after 1.8 rounds of review (the norm is closer to 5).

I should note that I have yet to use the service myself (partially because of the lack of conservation oriented official target journals), so this blog post is not meant as an endorsement of Axios specifically. Many ecologists already endorse the service, which is likely cost effective for authors.* I am a bit frustrated that conservation seems slow to join the party. If not Axios, we need to think how else we can reform peer-review.

Time is the most important resource in conservation! The peer-review process should reflect this.


*Cost Efficacy for Authors: The fee of 250 USD per article** is no more than the cost of one day of postdoc labour in many developed countries. So the service is likely cost effective, given that authors spend more than one day reformatting and re-submitting a paper.

**Edit: the fee is 250 USD when bought individually, and as low as 200 USD when bought in bulk