"x"
"1" "Interesting survey. I was originally a math major for the first two years of college. I switched to ecology as my environmentalism grew. There, the use of math pretty much stopped. I recall doing an ordination by hand and I did a good bit of modeling my senior year. In fact, my first paper is a simulation model. For grad school, however, I kept getting more fascinated in learning about natural history, ecology, and long-term environmental change. A stats class was required for my MS, but it was classical block design kind of stats, which was not useful for me. It was taught in the stats department and felt very detached from my research. I focused on learning more about different disciplines for my PhD and learning stats by analyzing my data. Unfortunately, I didn't do a post-doc and went straight into a heavy teaching position. Any stats knowledge or momentum stopped. Now back in the research world, I am way behind, especially as Bayesian has taken over.
So, a long intro to suggestions: my experience reflects what I see in the ecological world: statisticians and modelers that I work with/know are amazing in calculus, linear algebra, etc, etc. But, their knowledge of ecology is rather low [not all, but most] and the simulation models used in my mind do not reflect what we know about the ecology of systems. The more natural ecologists seem short on stats and such and rely on cookbook approaches to their work. It all seems messy. I guess I do not know how to combine the two disciplines (natural history & field ecology with stats & modeling) in a normal program. Some people can do it, but they are a rarity. I would merge as much as possible in classes, but knowledge in one aspect will be lost for the other. "
"2" "Don't do it to theoric, try to relate it with applications and examples"
"3" "More statistics and programming courses "
"4" "Not more teaching, but better teaching: less oriented towards theory, more towards practice.
More courses like \"The R Book\" rather than mathematical demonstrations
"
"5" "It would be really useful if basic mathematical concepts were introduced in first year ecology, with increasing complexity as students progress into higher level courses. Economics seems to to this much better than Ecology does currently."
"6" "Implemented early on in the University education. "
"7" "I also think basic programming should be part of ecological training, but I think it's best if this is separate from learning statistics and mathematics so students don't become overwhelmed and feel like they aren't learning anything well. (My first stats course also taught R concurrently, and I only felt comfortable with both after taking courses that specialized first in statistics--with all math actually being done by hand/with hand-held calculators, and then one that specifically taught R.)"
"8" "My feeling is that mathematical understanding and statistics is highly variable amongst young ecologists. I'd consider myself \"competant\" and no more, yet am frequently asked for help across the department. The degree of skill level in young ecologists varies primarily with the PI's mathematical level - maybe training for older researchers would be useful!
"
"9" "Confidence in programming is increasingly important!"
"10" "Any mathematical training should be directly applied to biology. Thus, courses should not be taken with students from other programs."
"11" "Research in ecology is based on statistics - it's the only way to make sense of the natural world with all its complications. Not teaching wannabe ecologists stats and the relevent mathematical theories (and how to carry them out (programming) as well as why they work (& thus when they're suitable) is to massively underequip them for life as an ecologist. However, there is a balance to be struck - of all the sciences, ecology is the most rooted in field observation and so field skills, etc, are also vitally important. Pure statisticians are useful, as are pure naturalists, but to be a good ecologist you must be both, and the training should reflect this duopoly"
"12" "Mathematical training should begin as early as possible, even in introductory biology courses. Ecology is often summarized as the study of the \"distribution and abundance\" of organisms and the null hypothesis is usual that the distribution is random and the abundance is changing randomly. We should emphasize even at an elementary level how random draws from probability distributions can create patterns and how directional changes can occur from random walks.
At the graduate level I think we should be trained to at a minimum be able to read a basic methods paper published in Ecology, JoE, etc. Most stat methods papers however rely on a level of mathematics that that average student does not have and probably won't acquire without a course in linear algebra. I have invested a large amount of time in self study to be able to understand basic statistical papers and am surprised how few of my peer are able to process these papers.
I've often heard people say that you should learn statistics as you need them. I think this leads to the situation where people try to solve every problem with the tools they have instead of learn what tools actually are appropriate for the problem. I am constantly amazed at how reluctant people are to even learn about basic logistic regression methods - they'd rather assume that an ANOVA or a t-test is appropriate.
I think as meta analysis becomes more common and more important to what we do that proper statistical methods will become more important. Improper methods can still yield qualitatively correct result, but parameter estimates and effect sizes will be wrong.
Thank you for conducting this survey - its a very important topic for advancing ecology."
"13" "I think all PhD students should have an understanding of the basics of linear algebra. I find it very odd that some biologists work with large sets of data but don't have an understanding of what vector or a matrix is (much less how to use them). "
"14" "We should start studing mathematics and statistics earlier like at undergraduate level"
"15" "Maybe add a course in \"philosophy of modelling/science\". I mean to learn about the different approach to answer an ecological question and how to chose the appropriate approach in statistics for example (model inference, hypothesis testing, data mining..). I missed a course on how to develop a methodology at the interface between the ecological question, the data set and the broad diversity of method available. Then we can look in more details into models.
Also, I think that the students need really applied example to get into the theory. And yes a computing course run in parrallel is required I guess."
"16" "integrated with ecology"
"17" "Integrate mathematical an statistical training with R programming from year 1 of biology programs. Theoretical training and practical application goes hand in hand."
"18" "From a palaeontologist point of view, more training in understanding and use of applied statistical methods (related to palaeoecology, palaeobiogeography, morphometrics, phylogenetic analyses) on both undergraduate and graduate levels would be a significant advantage during the university study programmes."
"19" "The real issue is not about gaining a better mathematical background. Most of us have had quite good exposure to mathematics through our education. What is missing are course that refresh students on what they have learned in the past and make sure the can apply it to ecological inquiries. So, what is currently needed are courses that initiate the students to basic ecological modeling applied to problems such as Lotka-Volterra dynamics. "
"20" "It should be applied for ecological research! The undergraduate stats-courses we had, were quite far from making anyone understand a) why would an ecologist need stats and b) what could they be used for...and c) provided absolutely no overview of different types of maths used in different ecological research.
I think that a good solution could maybe be a combination of a) assuring that all students are at the same level of \"pure maths\", b) a general undergraduate course \"different types of ecological research questions and what kind of maths to use\" and c) targeted graduate courses of using different maths for different types of ecological research. For example, one could assume a certain level of pre-university math, clearly defining what is expect from participants of any maths in ecology-course, and provide a possibility for an additional rehearsal course. No point to have courses where 50% of students drop off because the lack knowledge... But then, undergraduate courses should give an understanding on what mathematics is used in ecology and especially graduate courses should be targeted to dealing with different ecological questions, not as courses for \"statistics\" or \"linear algebra\" but more question oriented courses; e.g. \"study designs\", \"analysing experimental data\", \"analysing observational data\", \"analysing movement data\", \"time-series analysis\", \"species distribution models\", you name it...That could help people to get an overview of the existing methodology in their field(s). "
"21" "What is really needed is further integration of mathematics into the whole of ecology curriculum rather than additional stand alone courses. For graduate students this may mean that short workshop refresher courses will be needed between semesters or at the beginning of graduate level courses."
"22" "I took several mathematics courses as an undergraduate. Unfortunately they all focused strictly on math for math's sake. A more applied approach to undergraduate mathematics would have engaged myself and several friends more than the strict math strategy. An application based math curriculum could teach the underlying mathematics, engage ecology students, and teach the mathematical foundations of ecological theories all at once.
Thanks for putting this together-Cheers."
"23" "Especially emphasize the importance of statistics to undergrads who consider a carreer in science. They are the ones who still have time to adjust an do extra courses to have a firm basis. In my opinion there are plenty of classes available, but as long as students do not see the necessity they will not be motivated to follow them "
"24" "greater availability of refresher courses (webinars in particular) that are free, and the recognition from employers that time is needed to stay current"
"25" "Include machine learning topics and focus not only on theory, but also on practical issues (e.g. math- and stat-oriented programming)."
"26" "I selected \"Other\" for the math areas to represent differential equations."
"27" "i think the trouble starts in high school; people become biologists because they cant do the math.
problem gets amplified in college when math and stat courses are unconnected to anything biologists/ecologists might do"
"28" "A lot of people, specially in South America seek the biology/ecology careers because they think it has nothing to do with math!!! Colleges and Universities should make clear from their degree descriptions that this is not the case and have the math required instead of trying to make people happy by lowering the level down so much!"
"29" "Integrate the stas and maths into ecological teaching by embedding in examples that students can relate to"
"30" "Learn R"
"31" "It is important to have classes where applied examples that are relevant are used. However I feel I learned much more in classes where there was a mix of biologists/ecologists and other areas, such as people in engineering, statistics, mathematics and computer science."
"32" "The course described by Hobbs and Ogle (2011) titled \"introducing data-model assimilation to students of ecology\" would be an excellent start! "
"33" "It would be great if somebody (or everybody) set up a youtube channel where we could submit \"how to\" videos of coding particular statistics, or using particular types of maths. For example, I recently was trying to learn about determining lambda from a Leslie matrix (i.e. determining the dominant eigen value). It would be wonderful to have an ecology youtube channel where I could go and find information about population ecology, matrix calculations, etc. There are some videos like this, but it would be great to have a collection of videos that are specifically geared for ecologists (using examples from ecology, etc). Also, having somebody walk through the steps of building a model in R would be great, or performing path analysis, etc. The data could be available online, and anyone could follow along with the videos to teach themselves particular materials as needed. "
"34" "Training related to specific program (e.g. R) would be most useful
There is probably high potential for distance-based learning, especially when using a program like R, and I would be very keen to take part in that"
"35" "at minimum, students need a basic biostats knowledge (including ANOVA and non-parametrics when ANOVAs are not appropriate) *AND* the knowledge of one statistical package - how to enter data, how to run appropriate analyses, and interpretation of the output. This should be required at the Master's level and above."
"36" "One increasingly needs them for everything, even if not using them in own work.
Try reading a recently published paper in anything other than strictly nomenclatural matters..."
"37" "Undergraduates should be taught Bayesian statistics as a starting point. Classical frequentist statistics are much less intuitive, and tend to instill an obsession with p-values which is hard to break. And so they should be taught after introducing Bayesian, as a class of sometimes useful techniques, but in the understanding that their philosophical underpinning are fairly abstract.
We also need more training in the conducting of and interpretation of simulation studies, in addition to classical analytical models. Simulation and numerical techniques will be increasingly important in ecology, and so teaching some of the underlying theory and techniques for gaining insight from increasingly complex studies would be good. So perhaps some courses also in algorithm theory, complexity theory, and information theory to add to your list above. For example, I took a course in Markov Chain Monte Carlo (MCMC) techniques from my statistics department which was very valuable."
"38" "I wish that there had been some training in modeling in my courses that went beyond the basic Lotka-Volterra models. I had a decent understanding of them, but it felt very arbitrary. It seemed like something I would need to know for the exam and would never be of much use to me in the real world. I never did very well in pure math classes, because they also never seemed to be of much use. It wasn't until the why and what for was taught to me that math started to make sense, and I consequently excelled in statistics and physics courses."
"39" "More applied statistics courses, more applied math courses. No need for too much theory- we get that in high school and undergrad- but my MA definitely didn't offer enough math to see me through my thesis, never mind my career."
"40" "I was lucky enough to have modules in both my graduate and undergraduate course which covered stats and calculus, I don't think that's common though - especially in an applied way, which is so much more useful."
"41" "More calculus in biology content courses
Require/strongly recommend linear algebra for undergrads interested in ecology"
"42" "I found that my undergraduate mathematics course was too difficult, and graudate courses too easy. Ideally a mathematics course would be run by a biologist, so that we can see the direct applicability of the maths (in my undergrad course the mathematics, taught by a mathematician, were NEVER related to anything applicable - we focused on deriving the equations rather than using them...)."
"43" "I find it much more interesting when these courses involve actual ecological data and problems."
"44" "For faculty and post-doc level: short workshops and working with successful mentors
also fully-funded summer workshops for students (undergrad and grad level)"
"45" "More advanced statistical classes, particularly on modelling. Most classes are taught at an introductory level and I have found it difficult to find a suitable class that speaks to my needs now I'm a graduate student."
"46" "Anyone getting an education in ecology or environmental science would be well-served to complete math through at least Calc I and a good mathematical modeling course (in bio dept). Multivariate and nonparametric stats courses would be ideally taken too. "
"47" "Math training for ecologists should differ in some degree for the rote method that is used to teach engineers, etc. Applied mathematics would seem to fit this idea nicely."
"48" "Mostly ecologists need a working understanding of statistics and experimental design. The focus should be on stats, stats, stats!! From junior year of undergrand through the PhD, and even through professional development during the a post-doc."
"49" "Mathematical training that is directly relevant to ecological applications. Many statistics courses that I have taken were outside of the biological discipline. Therefore, there was not discussion about what is currently used in my own field and no examples that I could directly apply o my own research questions. "
"50" "The mathematical training needs to be specifically tailored for ecologists in such a way that they can see the relevance of quantitative skills from the very beginning. Too many students choose ecology because they think it is a science that doesn't require maths, and too often they are not exposed to the importance of quantitative methods until too late in their training. Instead there are simply general requirements for a maths course that students take reluctantly, and rarely pay too much attention to until it is too late."
"51" "I think basic ecology courses should focus on more conceptual ideas and introduce some of the basic math - the goal should be to cultivate interest in the subject and not intimidate students with equations. Upper-level ecology courses should make a point of including more math, and math courses themselves should be a required part of the curriculum. An ecological modeling course or a biomathematics course would be a good required course to demonstrate how theory and math intertwine."
"52" "We need open source web based training. This can help people from all over the world!"
"53" "Need courses at PhD level about statistics:
analysis of variance,
significancy of the results,
sampling representativity, etc
i.e. : training in applied statistics for data processing in order to increase confidence in the results"
"54" "I double-majored in math and biology, and I'm finding that it put me at a huge advantage compared with the math-abilities of my peers."
"55" "I finished my undergraduate in 1998, did a Master's in 2001, and will be finishing my PhD this year. Because I spent the interim years working in the private sector, I did not use statistical software much. I understand the theory quite well, but the software has always been my weak point. I'm now teaching myself R -- mainly because the course schedules for formal classes did not fit with my overseas field schedule -- and it is a struggle. There is a LOT of training material out there -- the worst part for me has been sifting through it to quickly find what I need and do it. To me statistics is a tool and does not tell the whole story on its own -- I'm not a fan of modelling and find it too abstract and imperfect to get across to land managers in developing countries. My math training is adequate -- it is really software that I need help with. "
"56" "There definitely needs to be more emphasis of math/stats/programming in the ecological fields. I think we are slowing getting there, but the vast majority of people graduating with a Master's degree, and some with Ph.Ds are not getting stats/math emphasized in their curriculum. I've seen a lot of people get into this field because they want to 'work outside, make a difference, play with {insert charismatic ungulate species}. They do not understand that math and stats should be a core piece of knowledge and they treat it as something to avoid like the plague. "
"57" "During my education, it seems to have been tough to (a) make a statistics course broadly applicable such that it's useful at the moment and potentially in the future, while (b) supplying specific enough problems and case studies such that the concepts can be fully understood, recalled, and applied if a student runs into a similar topic in the future. In my opinion, that's been a fundamental problem that should I think should be addressed in statistics courses."
"58" "More focus should be put on statistical courses that teach the foundations of statistics (e.g., what is a probability distribution, how is a P-value calculated and what does it mean, what is the difference between a deterministic and a stochastic model, etc.) instead of courses that essentially jump right in to conducting statistical tests.
An undergraduate program in ecology should require (at least):
1 Probability course
1 Statistical foundations course
1 Applied biostatistics course"
"59" "Curriculum should be as practical as possible, with real life examples. I indicated that training in mathematics should be done seperately from programming to gain a good understanding of the concepts. However in programming it cannot really be done without any mathematics or statistics. The programmes incorporate this in developing models, therefore ofcourse to some extent mathematics and statistics should be part of programming becasue that is the only way how you can understand when your model is not working or gives spurious results and be able to fix it."
"60" "To fully understand the underpinnings of current ecological theory, as well as its future development, a strong mathematical background is key. Despite the fact that my PhD is in Quantitative Biology (6 grad level stats/math courses + biology courses) and I have actually published a model, I still feel that I am unprepared for what I would like to do. In my experience, most ecology curricula (both undergraduate and graduate) at the average state schools only offer a \"biometry\" course or two which may cover only basic stats or at most some experimental design with a little exposure to some multi-variate techniques. Most of my colleagues are 'self-taught' to some degree depending entirely upon which tools become necessary for completing theses projects. I would strongly recommend more required coursework as undergraduates taken within the context of math departments on more advanced topics such as linear algebra or differential equations in addition to biometry offered in biology departments. "
"61" "The problem is that students in ecology are math-phobic. They are terrified of math. How do we change that? It has to start earlier than undergraduate. It has to start in early years of math training.
If you start to require to much math in ecology you may lose some great minds that have the potential to be quantitative with the right training.
I don't know what the solution is but perhaps integrating the math into ecology courses in the right way might work."
"62" "I think statistical training is imperative for ecologists. I have a BS in pure math, and an MS in biometry, and this background has given me many skills to correctly carry out statistical analyses for non-standard experimental designs. I feel that many people are intimidated by math, and limit themselves to easy, uninteresting, and often incorrect statistical analyses because of it. Courses in mathematics and statistics may help alleviate these fears. "
"63" "During my under and graduate studies, I was able to choose if I had to take statistic classes or not and in my case I did most of them. This is why I believe I had enough courses. However, what I'm missing is training (I don't remember what I have done 10 years ago).
"
"64" "math & stats should be both merged and separate. some to focus exclusively on the principles, and others to help you apply it. (also, \"other\" = masters student)
"
"65" "I find that my students are fairly weak in basic ecological thinking. When trying to be up on the latest trends (and the latest statistical techniques), they fail to get appropriate background in ecology. They THINK they need more math, but I think they need more ecology."
"66" "Take my answers with a grain of salt. I graduated in 1973 (BS) and got my doctorate in 1984. Since then I have seen a degradation in the understanding of the mathematics in those I hire and mentor and an increased reliance on model output as an \"answer\" instead of a \"clue.\" I attribute the latter to a lack of depth in the underlying math and stats used to generate the model. A secondary affect is that the user is seldom able to identify a model operating outside its basic parameters and limitations, also leading to bad results. Education is layered. Biology, then ecology, then a mathematical representation of each, then the ability to statistically analyze each, and finally the ability to predict (model) within each. Today's educators tend to jump to the end."
"67" "Basic statistics should be taught at the undergraduate level, and more advanced statistics, including novel approaches and modeling should be taught at the graduate level."
"68" "Offering both theoretical and applied classes with biological context can take the equations and turn them from esoteric minutia to problem-solving tools. Perhaps this can be done in a semester, but I feel that a year-long series in experimental design and linear models, multivariate statistics and stochastic models - all in R or a homogenous language would go very far in most applied ecology/fisheries/natural resource graduate programs. If this were a common curriculum for M.S. students and first-year PhD students, perhaps there would be less headaches later in the analysis and publication processes."
"69" "Q9: initially separate, then merged.
Ways for instructors in mathematical ecology to connect with each other would be most welcome (e.g., web site, occasional meeting), to share materials and strategies."
"70" "Ecologists should take higher-level probability and at least intro programming courses. Topics should include: PCA, Maximum entropy models, Vector machines, neural networks, and matrix modeling. Ecologists should be able to use R, Matlab, Python (extra credit) and these will help them use open source programming software like GRASS and QGIS.
This is more applicable to large scale ecology. Not sure this is applicable to phisiological ecology, for example. "
"71" "The teacher of statistics should be an ecologist with good knowledge of statistics, not a professional mathematician. Also, tie the theory with real ecological examples. "
"72" "My undergraduate training as a biologist (with an ecology speciality) did not require any mathematics or programming classes. There was one required basic \"intro to using computers\" class which I forever resent having to take, and would have liked to take a more advanced mathematics or programming class instead of the basic one. Program flexibility is a general gripe, but I certainly think more math and programming classes are needed for ecologists, not just general computer skills. I think having those classes would have given me the basic skills and confidence to move forward in my graduate work, but instead I am floundering in my attempts to do modelling and programming, with an immense learning curve and long hours reading journal and text book content somewhat out of my current realm of understanding."
"73" "Don't be afraid of the numbers. Math is not a scarey topic. It seems to me the word math scares people away from taking the upper level math courses necessary to understand mathematical models and programming."
"74" "I took as much math as I could in grad school and it's been very useful, but it wasn't required. Had to self-teach programming and a lot of 'modern' stats -- having more official background in these would be useful...actually it might be more useful to have ESA or another organization offer regular short courses on these things (affiliated with meetings?) because it's often hard for faculty to fit time to develop courses on these things in addition to other responsibilities, and the uses and applications change rapidly. Also, training needs to continue beyond undergrad and grad school, and right now, for example, I do this on my own, but short courses would be useful for professionals, too.
I sometimes think there's not enough effort put into career development of working ecologists and faculty as there should be, in addition to training of the next generation. The more comfortable and up to date my peers are on these skills, the more they will teach and practice them, too."
"75" "R"
"76" "Integrate mathematics/statistics with ecology"
"77" "Integrate it with the ecology courses students are taking. It doesn't do much good for an undergraduate to take a calculus course, when they will promptly forget material that they perceive as non-relevant. Instead, use the math in projects and assignments in ecology classes, so students will a) be exposed to the actuality of the field, and b) see how the math is useful. "
"78" "Let's start incorporating R at an early stage"
"79" "The question about combining math and statistics classes with programming was vague. I see no problem with math and statistics being taught within the frameworks of Matlab and R, but to me computer programming implies things like Python and C++, and I answered accordingly."
"80" "It should be early and plentiful. Practical knowledge in implementing models is becoming more and more important, so it's essential that people get trained well in theory and practical applications."
"81" "I didn't really understand \"What percentage mathematics, statistics, and programming should approximately cover of the university curriculum\" - very odd grammar.
However, I do feel that biology programs should require more math. My undergraduate degree only required one semester of calculus. I took 3 semesters of calculus, linear algebra, and statistics...and I am very glad I did!
I don't regularly use calculus (in fact, I have forgotten enough that I have to go back to the books to follow differential equations) but linear algebra has been very useful and probability/statistics is essential for anyone in the sciences."
"82" "Three suggestions/observations:
1. Statistics classes must move away from P-values and arbitrary judgments about \"significance.\" These approaches have roots going back over 100 years and are now only of historical importance. Current/modern methods should be taught and taught well.
2. Statistics classes should move to likelihood and stop the focus on various least squares methods. The backbone of statistical theory and application is Fisher's likelihood. This is true also for the Bayesian approaches. The gross emphasis on least squares, while the more useful likelihood approaches, is hard to justify.
3. Relatively few professors in the biological sciences have any grasp of analysis theory in the broad sense. The advice given to grad students and post-docs is often very misguided. This lack of basic understanding hurts undergrads and well as others."
"83" "I am constantly astounded by the fact that most PhD students in my department has 1 quarter of statistics training and then that is it. That is what they go forth with in their career. That particular course in statistics isn't even a requirement for my department. I think considering how important and involved with statistics ecologists are, there is very little training and people expect others to know all the right kinds of statistical models when in reality, I would estimate that less than 10% of ecologists can be identified as statisticians. A stronger emphasis, both in undergrad and grad, needs to be placed on math and statistics. So many undergraduates who are thinking about graduate school have no idea that they will be required to do math and there are so many who don't even have a basic math background."
"84" "The questions in this survey could be improved. For example: \"Do you think more mathematics classes (statistics not included) during the ecological curriculum would be good?\" -Potential answers vary from university to university and from bachelor's to master's to PhD.
I feel like you are trying to put everyone into one box. Not everyone who studies plants or insects, for example, would have the same aptitude or interest in math as someone who wants to create models, just like modelers wouldn't necessarily have the aptitude for the skills required by taxonomists or field workers."
"85" "1. Teach mathematical and statistical modelling by first doing simple analysis on a sample dataset manually from first principles rather than just using a statistical software to compute the answer. The answers should later be compared with the same analysis using a software.
2. Teach using open access softwares.
3. Try to find guest faculty who are willing to teach a course that they are very good in (teaching). That increases the options of instructors for a course."
"86" "Qual o investimento das universidades nas formações dos ecologistas na área da matemática. Eu estudo em uma universidade de boa qualidade, porém totalmente desfalcada na formação de seus estudantes na área da estatística ecológica, modelos matemáticos e biometria."
"87" "There is much too little emphasis on mathematics in training for ecologists. Over the course of my degree programs, I have taken several basic and advanced stats classes and have done very well, but these still seem to be insufficient. This is often because they are mostly based on theory and there is a disconnect when it comes to actually applying these methods to real data sets. For example, a vast majority of my stats training focused on parametric methods based on the Gaussian distribution, but probably only 10% of my data have adhered to assumptions that would allow me to analyze them using traditional methods. In addition, because unexpected problems are encountered with data (even in well-designed experiments), it is often necessary to use much higher-level techniques than are taught in stats courses or even than colleagues are familiar with, forcing a researcher to turn to primary stats literature in order to deal with data that cannot be analyzed in any standard way. However, as ecologists (especially those that are early-career) are typically not also statisticians, I think that this lends itself to mistakes that are not caught because reviewers are also not familiar with these non-traditional techniques. There is an emphasis by reviewers to analyze data in the most appropriate way, but a dearth of resources guiding a researcher to actually apply these statistical methods to real ecological data."
"88" "There is almost 0 training in programming. Of all things, this needs to change. Algorithmic thinking is key to solving novel ecological problems with big data sets. We need to begin teaching this along with a solid foundation in statistics and math that teaches us that both of these are evolving disciplines, not a set of rules set in stone."
"89" "On a routine basis, I encounter limitations in my math background. Because I teach ecology, my limitations may become my students' limitations Once one leaves graduate school, the opurtunities for addressing limitations are rare. Post-graduate course offerings (e.g. remedial math for ecologists) might be helpful. Course offerings geared towards teaching math in an ecological context would also be helpful.
"
"90" "People going into ecology programs often have no idea how much math is necessary. It may be advisable to make a course in the math - statistics, linear algebra, etc available the summer before beginning regular studies for those that need to 'catch up' as it were."
"91" "At least some courses should be designed to help ecologists bridge their knowledge with mathematicians, because ecologists will never be able to learn mathematics to that same level. "
"92" "Make it friendly, because it's so necessary and so many don't realize it while they have the chance."
"93" "Teach approximation in mechanistic models & teach simulation.
Many ecologists even with a strong knowledge of mathematical models lack the ability to transition between models by limits and approximations. One should be able to flow smoothly between an individual based model and a stochastic differential equation, a nonlinear model and a linear one, from a spatial & non-spatial, etc.
Second, everyone should have a go at trying to simulate the data they expect before conducting the experiment. The assumptions needed to make the simulation need not be \"true\", but are supposed to be \"consistent\" with the pattern we expect to see. If things work out as expected on the simulation, it's no guarantee, but if the proposed analysis doesn't work on the simulation, it definitely won't work in reality. I think being able to describe the process as a simulation clarifies thinking about the potential process involved, implicit assumptions we are making and the statistical methods we use to analyze it. This approach is also accessible by computer without advanced mathematical knowledge (though that is often a valuable short-cut to avoid searching big parameter spaces of possible behavior).
"
"94" "Population estimation methods "
"95" "Flexibility in the degree requirements, i.e., to include probability/linear algebra as counting towards a Biology BSc, if the student so chooses. Flexibility at the graduate level, so that taking an introductory probably course (even if it's a 200-level course) could count towards graduate requirements, if the student so wishes."
"96" "At an undergraduate level, I believe our basic math skills should be strengthened across the board. If a student is going to go on to use mathematical and statistical modeling extensively (and really, I would argue that there isn't much ecological science that doesn't), then more specific techniques should be easier to come by because they will (hopefully) be integrated into graduate coursework. I strongly believe that is would be useful have some sort of \"historical to current techniques and applications\" survey course giving students some broad context for what is out there to be used and how it fits together."
"97" "The training must be done by other ecologists. I believe the best way for ecologists to learn math is to learn through applications to real biological problems. In this sense, course like mathematical biology or theoretical ecology are a good venue."
"98" "Definitely more statistics for ecology undergraduates is required. More mathematics classed may be necessary also, but should be specifically appplied to techniques and questions typically found in ecology."
"99" "I have taken a couple of classes in ecological modeling because I can see it's usefulness as an important tool in ecological research. However, it is very difficult and painfully slow because few classes in coding or math are required or taught at the undergraduate level for ecologists. Trying to learn at the graduate level is really tough and most people quit unless they have a strong motivation for continuing. I would like to have had more coding, mathematical modeling, and even more stats classes as an undergraduate. "
"100" "There needs to be a serious discussion of fractals..."
"101" "Unfortunately such courses are often relegated to people who actually do not specialize in these subjects. Mathematics, statistics should be taught in a more practical fashion using the real world examples. And it is very important to make a student understand the finer nuances."
"102" "having comprehensive workshops with models and practical usage with results should be made to practiced or should be the part of the students curriculum in both undergraduate and graduate programs which makes one understand how to use these methods and finally their ultimate use to obtain results for their own work.. "
"103" "Unless we apply what we learn, we never really learn. While training ecologists, math should be used hands on and preferably using examples from fields that ecologists are interested in. Along with theory emphasis should be on a lot of practical applications using questions or systems of interest."
"104" "make it more informative and more interesting"
"105" "There has to be enough courses through the UG and PG. Along side this, there should also be project work separately dedicated for learning modeling for each semester.
At least in India, there is lack of good faculties, who actually understand the mathematics. It would also be good to conduct such courses online and make it available as transferable credit . "
"106" "mathematical training should involve applying theory to ecological problems - this makes it much easier for the students to understand the concepts"
"107" "I really wish I had taken more math and stats courses as an undergrad (and had more opportunities to do so now as a grad student), and I'm really thankful I took a programming course on a whim. I think a lot of ecological concepts are at least somewhat intuitive, so they are a lot easier to pick up later than the fundamental math/stats that turns data into concept!"
"108" "I wish I'd taken more math as an undergrad. I think requiring a course in computer science wouldn't be bad either. Now I feel like I have so much that I'd need to learn/re-learn to really do any modeling that I am better off collaborating with a more skilled person while keeping a big-picture understanding of what is happening."
"109" "To me, it is probably my mental block, however, I feel that an ecologist can always go to a mathematician and ask for modelling his/her ecological stuff. Instead of going for a mathematical education (except a very basic mathematics), an ecologist should be taught basic understanding of statistics from its ecological application point of view. somewhere in the feat of doing a good quantification ( unnecessarily, may be for getting the paper published!), ecologists may leave the true ecology study and does only hard mathematics, though the phenomenon he wants to explain is very very simple. many of the mathematical models do not work in natural systems. I think, mathematics is just for giving the ideal situations and thus ecologists should work to see what kind of fluctuations are there in field from that particular model and till what extent. "
"110" "Every scientist should be required to take courses in linear algebra, maybe include a second course in applied mathematics--the kind engineers and computer scientists take. "
"111" "In general, almost 90% of the students are scared of Mathematics and this feeling which develops in early age lasts till they write their thesis. Thus in order to make it understandable, different teaching patterns should be innovated. This will greatly help ecologists and researchers. "
"112" "I think taking math courses in the first year of a biology degree is pretty much useless. At that stage, the majority of students think that the class is useless, the purpose is to weed students out of the sciences, and do the minimum to pass or get a semi-decent grade. When we realize we need math is after we have taken the courses! I think university level math for biologists should be taught in third or fourth year, and graduate school."
"113" "it should be explained early in the bachelor degree WHY it so important, especially for those who wants to pursue graduate studies"
"114" "The training should be interactive i.e. the real field based problems of an ecologist should be guided by the expert to help in decision making process."
"115" "Offer statistics classes that are serious about understanding why the statistics are used under different circumstances and why they work. Just having the students work through a Jump (statistical package) tutorial DOES NOT count. It would be best to simultaneously learn how to program the statistical concepts learned in R.
Higher math beyond calculus would also be good. I stopped there, and now I really regret it, as I work with ecological modelling."
"116" "It would be nice before using the mathematical formula and equations to know the accuracy or preciseness in the real world. Most of the students just copy-cat the equations without even understanding the parameters used."
"117" "From the very beginning understanding 1. the concepts behind models, 2. why the model, and 3. how the model helps tease out what u r looking for is needed. But, more than often the approach of courses is such that the candidate gets bogged on by the \"numbers\" and equations, not really understanding the \"why\" behind it and loses interest before understanding."
"118" "statistics usinf free software (e.g., R)"
"119" "If applied field of Ecology needs any mathematical representation to understand any consequence , that should be a good aspect , but I strongly think that theoritical places donot or cannot rather need any mathematical explanation , it might decrease the interest of Ecology and behavioural biology to the students. "
"120" "Availability of simple and user-friendly softwares desgned for ecologists very often mask the reasoning and theory behind using a particular function. For me personally, the logic seems clear but confusion begins when dealing with the nitty gritties of those functions. As a student, it would be better if the theory and underlying calculations/steps carried out by the softwares are taught at the UG/PG level beyond t-tests and ANOVA. "
"121" "I'd suggest more focus at undergrad level on fundamentals of probability and risk, and on unifying concepts such as linear models, less on teaching tons of different statistical tests. And don't teach GLMMs to anyone who hasn't demonstrated mastery of both GLMs and LMEs!
"
"122" "Please arrange a mathematical training for the ecologists, at least to point the application of basic mathematical methods in ecological modelling.
"
"123" "Undergraduates should be required to take calculus 1, 2, and 3 (learn up through multi variate calculus, e.g. double/triple integration). This basic background will pay dividends in most any field they pursue after the undergraduate level."
"124" "Training programme should be organized for ecologists."
"125" "Concurrent teaching of stats with programming (i.e R) is the most helpful."
"126" "I guess emphasize the ways that mathematics expands the amount and type of science that you can do"
"127" "My programming training was limited to specific software packages for statistics. Now I wish I had also been trained more generally in computer programming.
In my graduate studies, I felt that excellent statistical training was available to me. However, the training available in other aspects of mathematics was limited and honestly the programs weren't very good.
I feel that a lot of my difficulties with math go back to my undergraduate training. Calculus was presented as a series of abstract mathematical 'tricks' without mention of applied applications. The fact that I could move the integer and obtain the slope of a line didn't seem very interesting to me, so I took the bare minimum required and moved on to other classes. If applications of what I was learning had been presented, my comprehension would be better and I would have been likely to move on to other courses like linear algebra and graph theory that would be a big help to me now.
As an early career scientist, I would be eager to take more training in mathematics if it was available to me."
"128" "Upon entering graduate school, there need to be different suggested curricula for students from liberal arts backgrounds and technical backgrounds. Each has it's strengths and weaknesses in terms of foundational ecology and mathematics."
"129" "We're currently involved in a NSF-sponsored Biomathematics program inspired by ideas generated through the US National Institute for Mathematiocal and Biological Synthesis (NimBios). This is well worth looking at..."
"130" "This is a tricky topic. I think in the U.S. we tend to have more coursework than in other countries, so there's a lot of opportunity to take modeling/stats/math courses. However, as a statistician friend of mine said, even a 4 month long course is only a toe in the door--most of what you actually learn you do so through actively programming/using stats/etc. I feel like folks coming from a more quantitative background (e.g., scientific programming and engineering) have a huge advantage when it comes to being modelers or quantitative ecologists. However, I sometimes see those folks have a lack of understanding and appreciation for the natural world, which should truly be the background for a good ecologist (in my humble opinion). I personally wish I had had a stronger quantitative background as an undergrad, but I am coming from a liberal arts background where I studied anthropology, german, spanish, economics, creative writing, and literature as well as biology, and I don't regret any of that."
"131" "Connect it to the ecology; don't have a pure math class and then an ecology class that just assumes an understanding of the pure math. Make it a merged curriculum. The math, stats and programming should all be introduced and developed in service of actual problems in ecology."
"132" "Leave more room for naturalists/biologists. It is sad to see how ecology and conservation biology are becoming more so the realm of mathematicians and physicists.Without empirical understanding of the natural world (often with MANY hours spent monitoring the study origanis in the field), we often end up with fancy but rather useless models that distract from the tough reality of today: unprecedented loss of biological diversity."
"133" "As an undergraduate, the only requirements for my ecology degree were one semester of calculus (no integrals) and basic stats. Now I am trying to catch up with the state of the art, especially with multivariate analyses and species distribution modeling.
Let's raise the bar in our math education. "
"134" "This is a tough question. Some scientists have very little need for math while others have a strong need. I certainly did not anticipate where my research would go, even at the start of my PhD. taking a math course (and statistics for that matter) without applying it to one's current research is often not effective. I personally forgot most of what I learned if it was not immediately relevant."
"135" "I would have preferred to have more applied mathematics (e.g. applied statistics) with clear ecological examples during the first years, and then more theoretical mathematics (e.g. calculus and linear algebra) for the master; instead of the opposite."
"136" "Need to have much more training on using statistical software such as R."
"137" "Organizing more mathematical summer schools for students but and also for researchers would be great."
"138" "I think mathematics should be teach early in ecologic studies, and in all fields (statistics, modelling, etc) even if it does not correspond to the particular educational program."
"139" "- Couple with examples of relevant applications for ecologists
- Applying to research projects at advanced level courses"
"140" "I think it is important that ecologists not only take classes on statistics, but that they take statistics courses taught by ecologists. Being taught by someone who understands the math but also knows how you will be using it in the field makes a huge difference in learning the methods well, and I think make statistics easier and more fun to learn."
"141" "As for me ecologist must stay ecologist ! Field ecologist skills (species determination) are by far more important in ecologist course ! Mathematic is a field by it own, i agree to work with mathematitian or statistician but i don't want to began one of them !
"
"142" "Most of my mathematical train has come through self study, mainly due to frustation with my level of understanding of statistics. I don' t think statistics should be taught as a series of 'magical' tests, I think you should understand the underlying maths, at least to some degree. In future I think all undergraduate ecology courses should expect reasonable maths skills at entry and should develop these skills as you progress. Ecology can't be considered a non mathematical subject anymore. "
"143" "Mathematics should be integrated into the science courses. I have seen and experienced may instances where students know the math and they know the ecology but they have no experience connecting the two. In many cases students don’t seem to have a way to know whether the output their program/statistical package gives them has any logic. Models that predict 1000 or 10000 years into the further present un-testable hypotheses and un-testable hypotheses are rather useless in ecology."
"144" "While some of Ecology is becoming more mathematical (e.g. modelling), expectations for statistics is becoming nearly ubiquitous. One can choose to be or not be a modeller and learn what they need to follow through, but at this point, it isn't math like Calc or Linear Algebra that is required -- those are optional and one can still be an ecologist but lots of good stats is simply not optional.
"
"145" "All ecologists need to be conversant in math/stats. Not all of them need to be fluent or even very good. There are still multiple paths that ecologists can follow. However, students should be aware that more and more of these paths require a solid understanding of math/stats. The number I suggested above (40%) is misleading. Some students should have 60-70% of there training in math/stats, whereas others should have 10-20% (many, however, would probably benefit from something in-between these two extremes, hence my suggestion). It all depends on what path they intend to follow."
"146" "One way to reach those who are reluctant regarding statistics, especially at the undergraduate level, may be approach the subject as \"data visualization.\" This aspect frames the beginning of any set of analyses anyway, and is a great way to introduce the cool capabilities of programming software like R."
"147" "Should have courses at least through ODE"
"148" "need training in bayesian stats"
"149" "more"
"150" "Some on line training modules should be available by taking some examples so that students like me who is not from Mathematics background will get some help for the same. "
"151" "Should be taught at a more fundamental level (eg undergrad)"
"152" "I think practical examples are always important for understanding mathematical concepts. Turn typical ecology-related data analysis problems into exercises in programming / statistics / mathematics. This is how I have had concepts stick through my own learning (i.e. patching up holes in my knowledge that should have been filled during university courses). This is not to say that I hadn't come across some of these mathematical topics at earlier times; just that they were learned through the mathematics dept. and thus did not include a link to biological / ecological problems that I would encounter later in my career."
"153" "it could be interesting to propose formation and training course for ecologist in job and out of the university since a long time "
"154" "As far as mathematics courses per se, I think the 2 semesters of calculus that are common (with maybe 1 semester of linear algebra becoming more common) are sufficient. I think the improvement to be made here is more about working the specific elements of these that frequently come up in ecological theory into ecology classes.
Statistical and computer literacy are two things that I think undergraduate curricula should emphasize more across all sciences. "
"155" "Mathematical training for ecologists should begin at the undergraduate level and should include both theoretical studies and applicative studies (courses such as programming and modeling for ecological theories)."
"156" "Seek out classes that challenge you to use open-source statistics programs such as R."
"157" "I would like to see a general biomodelling course made core in undergraduate degrees for students oriented towards ecologists. Statistics and/or first year calculus is insufficient for ecologists."
"158" "Scientific programming as second language."
"159" "I think it would be really hard to design a universal program of math for all ecology students, since people's needs vary so widely. I think everyone ought to have (probably by the end of their undergrad degree):
-Calculus: basic, maybe multivariate
-Linear algebra
-Statistics: basic probability and stats, general linear models, maybe generalized linear models. Focus should be on application to real data, model selection, and parameter estimation more than significance testing. I basically had to relearn statistics once I started doing research.
-***Programming.*** Ecologists NEED to learn how to program and to do it well. I took a single intro to programming class as an undergrad, and it gave me an immense leg up once I got to grad school. Anyone starting a career now is going to spend a huge part of it writing computer programs to analyze data, and there are things you just won't learn if you teach yourself: program structure, object-oriented thinking, good style, version control systems, unit testing. See www.software-carpentry.org."
"160" "Good lecturers are critical. The ability to effectively convey concepts to increase comprehension is vital. If they cannot communicate their knowledge to students they are almost useless."
"161" "Having studied in Britain and France, I think that the British statistics training was more applied and straightforward. I understand the value of a more theoretical background which the French system is trying to give the students. However, I think that in practice, many students were lost in the course and didn´t really know \"what this is for\". I suggest to start with a more practical, applied approach... and give more theoretical background at a later stage."
"162" "Online forums and weekly workshops on biostat. "
"163" "I think it's vital to try and integrate as much as possible mathematical training with learning about natural history and ecology. I initially found my introductory math courses not terribly relevant (since they mostly focused on physics and engineering applications). It wasn't until my second year when I started taking population ecology courses that I began to see the relevance, and it wasn't until the end of my degree that I really started getting into math in a major way. I think the best way to understand the effectiveness (and limitations) of modelling is to connect learning about how to effectively model a process at the same time as you learn about the process itself.
"
"164" "Mathematics must be a part of the curriculum at both the undergraduate and graduate levels. User friendly books on mathematics and stats designed specifically for ecologists would be helpful. Since advances occur frequently a website that helps researchers (especially those not enrolled in academic programs and work independently) acquaint themselves with latest techniques would also be useful. Free online courses would be great."
"165" "I'm all in favour of statistical training, and just enough programming training so we can use R. But I dislike the growing trend toward mathematical ecology (i.e., theoretical modelling). It's new and fancy and high-tech ... and it is not real life. There is no substitute for going outside and observing nature. It's old-fashioned, low-tech, and real life. I know my opinion makes me sound crotchety, but in fact I'm quite computer-savvy (I'm webmaster on a couple sites), young (if mid-30's is young), and use lots of computer power in my research on phylogenetics and climate change macroecology."
"166" "bayesian as well as frequentist theory
structural equation modelling
food web theories
multivariate analyses
R programming
teached by biologists and not mathematicians"
"167" "The knowledge on how mathematical models are constructed and also, the use of models (simulation) in cursus of university could be very helpfull for ecologists. Practical works are necessary i think."
"168" "have to be linked with its use in statistics"
"169" "Mathematics should be used at a good percentage of about 40% for biology."
"170" "A strong background in mathematics should be provided during the first years of studies in biology, so that when the students in biology specialize in ecology, they already have basics knowlegdse in mathematics (in linear algebra especially) and can then follow courses dedicated to advances mathematics for ecology."
"171" "Ted Case's book"
"172" "I do not think more statistics are needed at Undergrad or postgrad, but better training, less tied to specific programmes and using programming based methods (i.e. perhaps R or S). I think there should be more formal toes between maths and biology, particularly ecology, at undergrad level. I certainly missed an opportunity when I opted for another science instead of maths to get credits during my undergrad. I think the idea to mix programming and mathds teaching is a great idea as it helps learning to use these skills practically."
"173" "The core improvement lies in the undergraduate curriculum: many new ecology undergraduates lack a sound mathematical basis. In order to get more mathematically able ecologists, any curriculum should accept that there is 'catch-up' work to do, in which aspects that should normally have been taught at secondary school are rehearsed (even basic algebra work). Acknowledging that this is the case, instead of immediately pushing on with fairly advanced subjects, will prevent three quarters of the ecologists to avoid models for the rest of their careers after they have wrestled past the first quantitative courses.
In addition, a programming course (e.g. languages such as R, python or C) should be compulsory in any undergraduate degree in the life sciences. This will also allow one to add numerical analyses/simulations to the toolbox of current undergraduates, allowing one to shift focus away from the mathematically tractable models only.
During the early graduate stage, students should learn how to specify a model from scratch, as opposed to learn how to analyse/extend already existing models. Model specification and simplification is a skill itself that is not easy to master to newcomers, and any theoretical ecology book teaches analysis, but not how to apply insights to novel problems."
"174" "The problem I have is that - by necessity, I'm reasonably confident on statistics. I've had to use it all the time and now teach it. The problem is that I dropped maths at age 16 and now lack the main underpinnings of some very basic topics - it is the patchiness of my maths that limits me most."
"175" "I think based on my own background and what I know from other people that statistics are way underrepresented in undergraduate studies in biology as a whole. It is practically impossible to be a successful scientist without a good understanding of statistics. I don't necessarily think it's important to understand all of the underlying maths, but a thorough grounding in the basics seems to be missing.
My undergraduate training was not in Ecology, but Animal Behaviour and Welfare. This means my statistical background had a measuring behaviour leaning rather than an ecological field data leaning."
"176" "Training needs to start with a problem or question based on a real-life example, preferably amusing, or something that students are likely to encounter, or easily relate to. It should guide students through defining models in words before using equations, to make classes accessible and not too scary for the less mathematically-oriented students. It should explain why learning more maths will be helpful in doing ecological research in the future."
"177" "A lot of statistics courses focus on using prepared data and being able to carry out a set practical (of a partiocular class of models) on the prepared data. Many students (myself included) would benefit from having the ability to discuss the finer details of their data with a stats expert and while this si not always possible, in a lot of cases, simply being able to work with a data set they provide themselves, might help. Even if it's just a made up data set with some of the same characteristics of the data that they are likely to encounter, I feel it would give them a better understanding and a stronger connection to the underlying data and the process of statistical modelling. "
"178" "It has to be taught in a context relevant to and understood by the ecologist. For example, if a teacher is just using algebra and equations alone to explain a mathematical technique, at least 75% of students (particularly undergrad!) will either switch off, give up or get confused as to why they are having to learn this. Most going into a biological undergrad degree won't even realise how much math and statistics they are going to have to learn. If, however, the technique is demonstrated using an ecological question or theory, I think more people will reposnd positively to the training and see how it can be useful. "
"179" "Although I did not feel that ecologists should spend more time learning stats (as opposed to maths), I feel that courses could be much better designed, and would be much more effective, if the students had better maths and/or programming skills."
"180" "Linear algebra!!!"
"181" "More departments need statistical consultants, not necessarily better-taught stats in ecology (though we need that, too). If nothing else, actual statisticians could keep up with trends and assist in modeling and programming, and could do it much more efficiently than ecologists. Ecologists are good at asking questions. Statisticians are good at analyzing the answers to those questions. We would all be better off if we had better access to each other, instead of insisting that all ecologists become programmers. "
"182" "At least some basics in linear algebra, differential (and difference) equations and probability. Within statistics there is need for basic maximum likelihood theory and possibly some Bayesian modelling.
To accomplish that some calculus would be required to master the above subjects. "
"183" "Stochastic processes"
"184" "It should be applied i.e. trained with respect to meaningful examples from the field of biology/ecology. And it should comprise basics as well as useful and up to date methods in a way that can be grabed by students without spending the entire week just for that single course.
In my own studies I just had \"pure\" maths lessons at the mathematic faculty. We never really learned what the stuff is good for and where it will be useful later on. We also didn't have ANY statistics at all! I"
"185" "Introduction as an undergraduate to modern statistics, to equip a student properly to deal with non-normal error distributions, pseudoreplication, and non-parametric techniques based on resampling, rather than rank-based statistics. My undergraduate statistical education left me under equipped to properly analyse real research data."
"186" "I said above that programming should be separated rather than merged but really I believe that having some of both would be best."
"187" "I think a solid understanding of mathematics is hugely important, and I am only discovering this now! I would not have been interested in just pure mathematics, but I think a more applied (and relevant for ecology) mathematics and statistics course would be very useful"
"188" "How to use 'R' for ecological research- statisitics, plotting graphs, modelling etc. It is a free resource, but the programming element is off-putting. Courses at undergraduate and graduate level would be hugely helpful. I know I definitely would have benefitted from it as an Ecology post-graduate student."
"189" "It should be a fundamental part of training for any ecologist. Repeatedly you see new ecologists running interesting experiments and then ruining them due to a poor understanding of the statistics and supporting mathematical theory. Mathematical training should be introduced at the start of an undergraudate degree programme instead of as an after thought just before final project deadlines, as is so often the case."
"190" "Should start year 1 of undergraduate to cover the basics before becoming more advanced in final years"
"191" "I wish someone had told me as an undergrad to take economics as well as computer programming courses as those two were the most helpful courses taken during my Masters studies and still could be developed further. "
"192" "Most of my statistical training has focussed on how to design experiments that fit a T-test or ANNOVA approach. This seems outdated, and isn't terribly useful. In my undergraduate course we touched on PCA analysis, but nothing more complex. It has been in more complex techniques where my training has been lacking. A course which dealt with experimental design, complex statistical techniques and computer modelling would be benificial."
"193" "Many ecological ideas have a mathematical basis or can be expressed in mathematical terms. Making the links between concepts and their mathematical basis explicit will help students understand how relevant theory is. If students can then explore how mathematical methods can be used to extend our understanding of ecology (or at least postulate extensions to existing theory), students at the start of their career will become much more receptive to mathematical ecology in general. At least that's my penny's worth..."
"194" "The problem is wider than ecology, it applies at least across the whole of the biological sciences. One issue is that many undergraduates in these subjects have not taken mathematics beyond basic school level, whereas physical scientists typically will be required to have studied mathematics to a higher level. The other issue is the generally low level of numeracy achieved by the basic school level mathematics today compared to a few decades ago (at least in the UK)."
"195" "More of it! Lots more! There is a huge gap in ecologists' biologists' and other life scientists' quantitative training and subsequent understanding. It is doing all of us and the field of quantitative ecology a huge disservice. Thank you."
"196" "I would think more statistical training for undergraduates and Graduates would be important."
"197" "Maybe there is a need to \"desecrate\" the use of mathematics and statistics in Ecology and more generaly in Life Sciences. Some of my colleagues use lots of models and statistical tests with too few critical views (on the models AND on the fact that they use models).
Mathematics and statistics are TOOLS and not METHODS in ecology. This is the big missing in our math&stat classes. Then some of us are like to focus more on the tool we used than the scientific reasoning (eg. for a presentation, an article, a simple discussion). "
"198" "When [deleted] started her PhD, she went on a multi-week stats course run by [deleted] that also included stats programming in R. Whatever the teaching style and course format were she said it was an excellent course (but she had a head for statistics), and multiple approaches to visualize the same problem were used to get an understanding of the problem. Unfortunately my basic maths is very poor, is a subject i just can't seem to get a grasp of, and thus have difficulties at my stage in life - a problem with I was taught pre-degree and entirely different issue."
"199" "Ecologist need more mathmatical training!"
"200" "Stats: There is a growing trend towards explaining in papers the reasoning behind chosen analytical approaches, with some sacrifice of brevity. I applaud this, and think it should be the norm. The same approach (\"Why did you choose this model?\") should be used in teaching.
Simulation modelling: Too many graduates seem to think that if a simulation model predicts that elephants are pink, then it must be true. They don't seem to appreciate that the model only expresses what you put into it; and that if anything surprising appears in the model output, its causes must be explored and explained in words."
"201" "http://www.amazon.com/How-Quantitative-Ecologist-Mathematics-Statistics/dp/0470699795/ref=sr_1_1?ie=UTF8&qid=1329839486&sr=8-1"
"202" "The fundamentals need to be taught at the most basic level - \"mathematics for ecologists\", \"statistics for ecologists\", \"bayesian inference for ecologists\" - an ecologist taught in these fundamentals would approach being sufficiently prepared for modern day ecology."
"203" "Though some basic mathematics & statistics are included in ecology courses but more emphasize should be given to teach how the knowledge of mathematics & statistics can be linked with practical ecological researches. "
"204" "I think the more math you know, the better...but I also feel like you can be an excellent ecologist with an average math background if you aren't trying to do modeling."
"205" "My main requirement would be to better understand the mathematics behind commonly used statistics - GLM, REML, multivariate. "
"206" "I have a very strong background in biology and ecology, but most of the positions out there need modelers, which I find frustrating. I want to find out how to supplement my doctoral training with modeling so I can have the tools I need to do the research required today."
"207" "Mathematical modelers should understand the importance of realistic assumptions made during the process. Too many models have limited applicability because axioms are not reasonable."
"208" "Many more courses at the undergraduate and graduate level need to be offered. Stats and modeling need not be merged but should both be offered at multiple levels (e.g. 200, 300, 400, and grad levels). Min requirements need to be raised for ecologists ESP. Having mandatory stats classes also frees up classtime in other courses to learn actual ecology or biology."
"209" "I was teaching ecologists for a while, a problem that I see in Gerrmany is that students chose ecology/biology exactly BECAUSE they do not like maths, and Biology is perceived as the discipline in Science were quantitative skills are least important.
Thus, increasing the maths is a question of offering courses, but also of explaining the students why they need this and showing them that they can do this. It may even be too late to start this at university, maybe one would need to start already in the biology classes in school, here it's really also a problem of attitude and expectation to some degree. "
"210" "Mathematical training should be full of example situations where an ecologist would need maths, so the maths can feel relevant to what ecologists are training for"
"211" "It would be good to form some mathematician to biology, to help ecologist"
"212" "Like in school, the most efficient training in math comes from practical work. If derived directly from a scientific problem, I believe that students are much more motivated to solve it by learning more mathematical tools."
"213" "I think mathematical training should be applied. I don't think that there should be more maths in ecology classes but more ecology in maths classes. I feel that education of mathematics can best be realized when it comes with ecological relevance."
"214" "On my opinion, mathematical training for ecologists should be based on ecological data and past studies. There should be a course where real data and publications are intensively studied. Students should get a better feeling for the challenges they have to face in future research.
Make courses more realistic and close to \"real\" life as a scientist. "
"215" "Not only the theory of analysing data but also and as a second main focus: How should experiments be designed? There is a really big lack in literature and training, at least for me."
"216" "Have courses jointly taught by mathematicians with some real-world experience in ecology and practitioners of ecology who happen to be quantitative. The courses I took were all theoretical, using hypothetical examples constructed from perfect data.
I also think it's important to start training ecologists to be \"bilingual\" in math: show the mathematical equations, but also the same equation as R code, to get in the habit of going back and forth between the two. We're usually taught to think about math in ecology in either mathematical notation or as code: to the instructor, it's equivalent. To the student, the translation can be overwhelming. "
"217" "It should be trainings in applied maths
I had a lot of heavy maths but this was totally unrelated to what I need as an ecologist.
Modelling and statistics should be a central part of an ecologists education"
"218" "There is a forced feeling that ecologists do ecology because they cannot do mathematics. I completely disagree with this. A mathematician who can provide good biology/ecology examples can definitely give better understanding of maths to ecologists. Ecologist always feel the nature, if mathematics can be made to feel, according to me, every ecologist would be very good at mathematics too. "
"219" "I am building simulation models. My studies of probability theory are proving most useful at the moment. "
"220" "More focus on practical problems and own research, using improved softwares (e.g. R)."
"221" "use R instead of commercial applications"
"222" "Definetly more statistics and especially the more sophisticated methods (study design and statistics behind, GLMs, GAM, LME,...), at least at the graduate level should be incorporated into studies. And since R is the most widely used softwarem, statistics should be directly taught using/teaching R. Though, it shouldn't be forgotton that biology/ecology students chose to study nature. Students should be able to apply methods and therefore need to understand the principles behind. Hence, courses should always focus on the ecological story behind to make it more appealing. Nonetheless, students do not have to fall in love with mathematics!"
"223" "I had 2 courses in calculus as an undergraduate, and then nearly completed a degree in statistics as a M.S. student in biology. During my statistics training, I would have benefited tremendously from skills in advanced calc and diff eq. as well as more linear algebra. I am now completing my PhD in ecology and am considering taking some [deleted] epidemiology/biostats courses or applied math m.s. courses because although I have more statistics training and skills than most of my fellow PhD students, I think I need more math skills to actually be successful at most of my research objectives. Moreover, I struggle to use ecology theory because I am not experienced in programs that solve complex dif eq. and have lacked the math skills to completely grasp the ecological modeling tools used by ecologists."
"224" "I recommend meta-studies on the needs, benefits and limits of using quantitative methods, statistics and computer-aided modelling in ecology. It should also point to general epistemology."
"225" "Taking a stats or math class is fine, but when you are not then using it in the context of your research how can you reinforce its uses? I took an undergrad stats class as well as a year of calculus. Then I had several field jobs and other jobs (in between the field jobs to pay the bills) that did not utilize any of my math or stats skills/knowledge. Several years later I went back to school for a Master's and was expected to remember it all. I took another stats class and learned how to use SPSS. Then more field work--none of which entailed me using stats--and other jobs that did not involve math, stats, etc. When I went back for my PhD they expected me to be a stats wizard. How? As a field tech you are not using those skills. In conservation non-profits I was not using those skills. And when I was back in school the stats classes very rarely were based on ecological models. So apparently the statisticians can be taught how natural systems work even if they have never actually been out in the field. But my field experience mattered virtually not at all (even though I was told I had to have it to be competitive in my field) since I was not strong quantitatively. Seems all sorts of bass-ackwards to me."
"226" "mathematical models and ecological theories might not be separated"
"227" "Mathematics are fundamental to ecologists, but most of them are aware of using it; so they reduce it to the minimum expression of familiar statistics. Then, when they are lecturers they are unable to deliver mathematics to undergraduates.
In the other hand, mathematics thinks they are the center of the universe, so the classes are too hard.
So, correcting this will attain a better training. Moreover, I propose much more exercises in modeling. "
"228" "I would have preferred the curriculum at my institution to be a little more full-featured in reviewing some basic math analysis topics (e.g., series expansions & manipulations) and much more broad in its coverage of statistical techniques beyond multivariate ANOVA and regression. An entire semester was allocated to the latter 2 topics, and it could have been condensed while still yielding a more concrete and less theoretical approach to variance & regression analysis. There was no course within my department covering information-theoretic or Bayesian techniques, and students who wanted to learn MARK or R were on their own."
"229" "I think any biologist looking to specialize in ecology and conservation should possess a minor in mathematics, such as myself. It is impossible to understand how ecological models apply and are crucial to conservation research and management without a strong background in mathematics. I think a typical minor, which covers calculus, differential equations, linear algebra, and electives in statistics, would go a long way to empower the next generation of researchers."
"230" "Rather than just teaching students how to do things like ANOVA/ttest, I think it is important to also present the linear model behind these. See for example chap 6 of MArc Kery's book Introduction to WinBUGS for Ecologists"
"231" "In my experience the mathmatical training was done in a lecture style with limited ability to practice techniques. I feel most statistical/mathmatical training should be provided in the situation it will be used (I.e. a computer room with examples of models etc so the training can be practiced whilst being taught as opposed to a taught lecture)"
"232" "go through the process of building a model and putting it in equations from examples based on real case-studies and biological issues."
"233" "Question: \"What percentage...\" - should depend on your emphasis. Would be good to have much more elective curses. "
"234" "In my four years of undergraduate study, only one class was wholly dedicated to teaching statistics. I feel I would be much more confident in my post graduate studies if I had a more substantial understanding of the mathematical and statistical theory. "
"235" "Thanks for a good initiative. Could we have a follow up of the results on this site once it is over?
One more comment: usually, the problem comes not only from to few hours of mathematical/statistical teaching, but also from the way these are teached. This is especially true in the first years of university where, maybe due to classes with students from mixed fields (ecology, molecular biology, sometimes medecine, etc), the courses can be very disconnected from the reality of our work. I think we need, as ecologists, to understand better why and how mastering not only complex modeling but also basic calculus can help us answer an ecological question."
"236" "Ecologists need applied mathematics. They do not aim to be mathematicians. Teaching shoud not begin by mathematical rigour but end, for those who wish to get deeply involved in mathematical modelling, with more and more rigorous understading of the mathematical background. For example, begining an undergraduate course in mathematical biology by the definition of sigma-algebra relying on the measure theory is useless and discouraging, while it is absolutely necessary to understand stochastic calculus (for instance for solving SDEs), later. Life is long ! "
"237" "I had teachings in maths and stats that were too theoretical and general. Courses specifically designed for the life sciences would be better."
"238" "The most useful statistics courses I attended in the past were the once that were very hands-on, used real ecological problems I could relate to and managed to explain concepts in simple plain English. "
"239" "remedial courses for professional practitioners e.g. working in consultancy, environmental agencies etc. who didn't get much training in maths or statistics as undergraduates or postgraduates, have worked for years without needing much and then find themselves increasingly having to either use ecological modelling or understand work by others."
"240" "training by ecologists, not \"pure mathematicians\""
"241" "It must be there! "
"242" "I think the key thing is to have courses in statistics for scientists. It is difficult to make the connection of \"usefulness\" between a straight mathematics course and analytical needs in science."
"243" "How to be a Quantitative Ecologist: The 'A to R' of Green Mathematics and Statistics. by Jason Matthiopoulos. Reviewed some draft chapters. Just ordered a copy @ Amazon. Brilliant."
"244" "some ideas from http://worrydream.com/KillMath/ would be a nice starting "
"245" "My studies did not include any programms exept excel (which really cannot be taken as a serious class!). There should be a state of the art overview within any math/stats course, teaching advantages/disadvantages and minimum introduction into several programms (e.g. short overviews in statistica, SPSS, R, sigma stat).
Ecology departments should have/employ a person that knows stats, preferrably one with mathematical background.
As datasets from fieldwork (especially with little n when working with animals) are normally small or patchy, one needs advice what to do, if normal statistical rules do not apply. These situations are usually not covered in materials (lowest n that is applicable)."
"246" "Get more stats in Zoology (and possibly Ecology) undergraduate programs. Spend more time on it, introduce R and linear models etc."
"247" "There is a danger in relying too much on mathematical/statistical modelling in ecology - it dumbs down the reality of what is observed and the interactions within the system. Too many of the graduates coming into my industry tinker with statistical modelling without actually understanding the ecological or mathematical processes and, although we have nice graphs to look at, much of the output is irrelevant and just plain wrong (that goes for much of the peer reviewed literature I have to wade through). "
"248" "Ensure that statistical/mathematical training is taught with relevance to the subject. The most difficult thing I found as an undergraduate doing the requisite statistics unit was not being able to translate the written problems to mathematical processes and hence solutions. I had a fantastic statistics lecturer who used lots of excellent examples to show how statistics is used to investigate and analyse data but when it came to doing the practicals on my own I struggled with interpreting and translating the written problems to numbers."
"249" "All ecologists must be taught R in classes prior to learning any statistical methods. All statistics should then be taught with R."
"250" "Given the nature of the field, and despite the outsourcing of modelling to specialists, it is good to at least understand what is going on within the model or behind the model, if not directly programming it yourself. This deeper understanding allows for better theory. It has taken me months of just focusing on stats/ math/ and models to just get up to speed with fundamentals that i wish had been given during undergrad. "