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International Network for Next-Generation Ecologists.

Proficiency in mathematics and statistics is essential to modern ecological science, yet few studies have assessed the level of quantitative training received by ecologists. To do so, we conducted an online survey. The 937 respondents were mostly early-career scientists who studied biology as undergraduates. We found a clear self-perceived lack of quantitative training: 75% were not satisfied with their understanding of mathematical models; 75% felt that the level of mathematics was “too low” in their ecology classes; 90% wanted more mathematics classes for ecologists; and 95% more statistics classes. Respondents thought that 30% of classes in ecology-related degrees should be focused on quantitative disciplines, which is likely higher than for most existing programs. The main suggestion to improve quantitative training was to relate theoretical and statistical modeling to applied ecological problems. Improving quantitative training will require dedicated, quantitative classes for ecology-related degrees that contain good mathematical and statistical practice.

Basic tasks in ecological research and management often involve fairly advanced statistics, especially outside of experimental science. Typical examples include capture–recapture models to census populations (

Theoretical ecology has been using fairly advanced mathematics since the 1920s and 1930s (e.g.,

Examples of a tighter link between theory and data abound in population dynamics (e.g., population projection models,

Given the trend for more quantitative research in ecology, one might expect current ecology students to receive training rich in mathematics, statistics and programming. By mathematics, we mean both “pure” topics such as calculus, algebra, and probability, and more applied topics usual in theoretical ecology such as dynamical systems. By statistics, we mean techniques used for the collection, organization, and interpretation of data, covering therefore both exploratory (e.g., principal component analysis) and inferential statistical techniques (e.g., the linear model). Programming refers both to algorithms (e.g., the “for loop”) and their practical implementation (e.g., how to use R or Python). With the increase in the availability of advanced methods, quantitative training ought to focus on (i) understanding how these methods work and (ii) when to use them. However, many ecology students at the undergraduate or graduate level do not have the required background to formulate statistical or theoretical models, or even to understand their properties (

We designed this survey as a short online questionnaire (see

Key proportions presented in the paper, and differences between those proportions, are accompanied with their 95% asymptotically normal confidence intervals, using a binomial model (more complex CIs, e.g., Agresti–Coull, are available but those used here are sufficient given the large sample size,

Most respondents (84%) were trained as biologists (

Partitioning of the respondents with respect to (A) background (i.e., discipline of undergraduate studies), (B) geographic origin, (C) gender, and (D) employment status/level.

A survey such as this could be biased if the respondents predominantly liked or disliked quantitative approaches to ecology. As it was not possible to control the composition of participants with a voluntary survey, we attempted instead to assess the extent of this bias by asking respondents questions about their own feelings about mathematical and statistical training. To do so, we asked the respondents “Rate your feeling towards using equations” and “Rate your involvement in the process of ecological modeling in your field” (

(A) Distribution of “Feeling” variable (from 1: “really dislike” mathematics to 5: “really like”) and (B) Distribution of “Modeler” variable (1: “do not model” to 5: “specialist modeler”). See

The first question of the survey reveals that 96% of respondents use mathematics for statistics, 39% use mathematics for theoretical modeling and 24% for decision making overall (see supplementary graphs at

Most respondents use mathematics primarily for statistics (S), and some other for statistics+theory (S+T, 26%), and the remaining 11% for statistics+decision making (S+D) and 10% for statistics+theory+decision making (S+T+D). Pure theoreticians (T) are therefore negligible in the sample.

We asked respondents to assess whether they were satisfied with their understanding of models in their own field; the goal was to assess quantitative understanding in directly relevant areas for them rather than general theory. Based on the response to this question, 75% (CI [73.2;77.8]%) of respondents do not feel satisfied with their understanding of models (and likely with the mathematical training they received). To interpret this number, it is worthwhile to note that humans, including academics, are prone to over-rate their own abilities (

The “Modeler” score goes from 1 (“do not use models”, on the left) to 5 (“only use models”, on the right). Red color is associated to dissatisfaction with mathematical understanding and blue to satisfaction.

We asked: “In the general ecology courses you have followed, how would you describe the level of mathematics (in retrospect)?” with three possible answers: “Too low”, “Just right”, and “Too high”. We included “in retrospect” because it seems a common experience for ecology students to initially appreciate verbal descriptions of ecological theories and analytical tools, rather than a mathematical description of those same theories using equations. Quite often, students discover later that these concepts and tools involve some fairly advanced mathematics (

We asked whether there should be more mathematics and statistics in the ecological curriculum. We asked for opinions (“Do you think …”) instead of absolute answers (“Should …”) to allow for more personal inclinations in the responses. The overwhelming majority of respondents want more mathematics courses (91%, CI [89.1;92.9]%) and more statistics courses (95%, CI [93.6;96.4]%). Surprisingly, these percentages (90% for more mathematics and 95% more statistics) do not vary much across categories, and hold for the categories 1 and 2 of the “Feeling” variable (> 200 respondents), who therefore reported disliking the use of equations to construct mathematical models (Feeling = 1: “really dislike”, Feeling = 5: “really like”). More than half of respondents want more mathematics and statistics at both undergraduate and graduate levels (61% for mathematics and 76% for statistics). Additionally, 14% want more mathematics only at the undergraduate level, and another 16% desire more mathematics only at the graduate level. For statistics, 7% want more statistics only at the undergraduate level, and 11% only at the graduate level. In essence, respondents want more mathematical and statistical training. The opinions do not depend much on what people use mathematics for; we found only a 5% difference between respondents using mathematics for statistics-only or other purposes as well (

To assess what fraction of the university curriculum respondents thought was appropriate to devote to mathematics, statistics, or programming, we asked: “What percentage mathematics, statistics, and programming should approximately cover of the university curriculum of an ecologist, in your opinion?” Given the inherent interdisciplinary nature of ecology, the responses should produce a wide probability distribution whose median indicates the best approximation of a “consensus”. In our results, the median was 30% and the mean 28.3% (two modes at 20% and 30%,

(A) with respect to involvement in modeling (“Modeler” score, 1: no modeling to 5: specialist), (B) with respect to status/employment level.

After carefully evaluating the comments left by 250 out of the 937 respondents, we classified them into four categories (see

Teach mathematics for ecologists/biologists (36% of comments). Many respondents feel abstract mathematical/statistical classes, or teachers from pure or applied mathematics, do not bridge the gap between mathematics and application. Some respondents pointed out much of the theory/statistics taught is not particularly applicable to the empirical datasets gathered by ecologists.

Inform “mathematics avoiders” of the quantitative nature of ecology (33% of comments). Many ecology students come to ecology programs hoping to avoid mathematics. Many respondents feel we need to advertise early on to high school and undergraduate students the quantitative nature of ecology-related disciplines. Variant: make classes of mathematics/statistics compulsory.

Teach students how to program (14% of comments). Variant: Use R (

Personal experience in favor of mathematical training (11% of the comments). ‘I wish I had learned more mathematics, I encounter difficulties now’ or ‘I’ve been lucky to learn some mathematics, and that puts me at a huge advantage now.’

The last anonymous comment in the sample speaks for the general sentiment:

“

Overall, our results indicate that quantitative training in ecology is often insufficient and that arresting this insufficiency requires both extra classes and better integration of quantitative methods within existing programs. Most of our ecological respondents seem to agree with

Conveying the quantitative nature of ecology to high-school students and undergraduates before they specialize is non-trivial. The comments of our respondents indicate that many aspiring ecologists entered the discipline not only because they loved animal and plant life, but also because they were less inspired by other, more quantitative, physical sciences. We should strive to present more clearly the quantitative nature of the discipline earlier, perhaps as early as high-school (which highlights, in turn, the importance of incorporating more mathematics within ecological courses followed by future teachers). For undergraduate and later graduate students, combining math-intensive activities with fieldwork has also been suggested (

On the practical side, our results indicate that ecologists want mathematics and statistics to be taught by quantitative ecologists so that the curriculum is applied and relevant. This suggests that departments who provide quantitative training via service teaching from mathematicians may not provide the optimal training for their students. We also asked whether programming classes should be taught separately or merged with mathematics and statistics. The results did not show a strong preference (63% merged, 37% separated, with no trend according to respondents’ profiles). Merging classes would allow a clearer integration of programming with practical problems; separated programming classes would promote higher levels of programming ability. One respondent commented: “initially separate, then merged”. This appears to us as a sound proposition, because it allows students not to be overwhelmed at first by simultaneous struggles with computing and statistical/model thinking. As soon as some familiarity with computer programming is established, however, ecology/biology-driven courses help to show students the usefulness of programming (e.g.,

Note that we do not imply that basic knowledge in ecology, evolutionary biology, or any related discipline such as geography, physiology or molecular genetics should be replaced in undergraduate curricula by mathematics and statistics. Indeed we do not believe that adding more effective quantitative training precludes the teaching of these fields, and that they would necessarily loose time in favor of quantitative disciplines. Currently, many biological courses require rote learning in e.g., anatomy, morphology, or taxonomy, especially at the undergraduate level. Though memory has to be trained and a background in these biological sub-disciplines is important, the amount of time spent on memorization tasks could likely be reduced. Of course, this holds only true for the majority of undergraduate biology students, some of which will choose ecology at various points in their curriculum; we are certainly not suggesting that veterinarians learn less anatomy. Likewise, taxonomy is very valuable to various fields of biology, and the knowledge of biological diversity should be encouraged: we simply mean that a fraction of the energy applied to remember precisely lists of organisms, organs, tissues, or chemical reactions could be diverted towards learning mathematics, statistics and programming. The fundamentals of these quantitative disciplines are highly transferable to the world of employment in many fields. In some cases, integration with biological courses is possible, see below. One-third of quantitative disciplines seems a good balance for the university curriculum of an ecologist, but specialization can be as late as the master level. Given that biology curriculums make compromises between different specialties, the right fraction of quantitative classes at the undergraduate level, when specialization is late, will likely be found on a case-by-case basis. How best to inferface with physics and chemistry is another open debate (

Ecology is moving into an increasingly quantitative era (

Contains the 937 questionnaire answers. The first column provides names for variables.

Free comments left by 250 respondents.

The first column is the suggestions ID in “Suggestion.txt” file, and the 4 remaining columns correspond to the 4 categories referred to in the main text. See legend after comment sign # in the file for more details.

We thank our colleagues who took the time to answer the survey (special thanks to the nodes list of the International Network of Next Generation Ecologists (INNGE), for beta-testing of the questionnaire), and all those who participated in the survey diffusion. FB also thanks NG Yoccoz for discussions and literature, and V Hausner, M Neby Olsen for advice on surveys. TP thanks about 30+ undergraduate ecology students from UQAR for discussions of this manuscript. Thanks also to R McKinnon, CP Doncaster, A Rahlin, G Simpson, and E Ward for comments on previous versions.

The authors declare that they have no competing interests.

The following information was supplied relating to ethical approvals (i.e., approving body and any reference numbers):

The questionnaire was anonymous and voluntary, no identifying questions needing approval were asked. The guidelines of Norwegian research ethics (country of first author’s institution) were followed (http://www.etikkom.no/en/In-English/Committee-for-Research-Ethics-in-the-Social-Sciences-and-the-Humanities/).