Ecology seems to me like a hodge-podge of different ideas. A result of this (or a manifestation or a cause?) is that we teach and learn ecology as a hodge-podge. The single overarching theme is levels of organization, typically as individuals, populations, communities, ecosystems, landscapes, and global issues, with a generous dose of climate, geology, and geography at the beginning. Applications, statistics, experimental design, and primary literature are scattered throughout.
Quick perusal of two evolution textbooks (Ridley, and Freeman & Herron) showed me that they do not have chapters on "The Physical Environment" or "Biomes" or "The Earth's Climate System." The evolution textbooks instead focus on the math and biology that is universal.
What if a book laid out ecology completely independently of natural history and environment? Would the books look the same? Do we need context? If we lead with context (e.g., a pond, a forest, a grassland) what do we gain, what do we lose?
Why do we lead with the physical environment? Perhaps because we have been ecologists for at least the past 2 my, and we know a lot?
What if we learned B = aM^z and dX/dt = aX - bX^2 before we learned that trees dominate the eastern US, and deep water bodies are dark?
This same question plagues the niche vs. neutral debate...in ecology. Evolutionary biologists learned long ago that it is both, in different measure. Ecologists and humans generally are plagued with the notion that niche matters. It makes it hard for us to think outside the box.
Wednesday, November 23, 2011
US Government as Central Dogma of Molecular Biology
Spoiler Alert: There is nothing new here. However, writing it helps to form the thoughts in my own head ....
Complex adaptive systems
A colleague of mine -- a very successful molecular biologist -- recently gave a Sigma Xi Researcher of the Year presentation. In it, he made the relative specific analogy relating the central dogma of biology to the operation of the U.S. federal government. It blew my mind. It was is SO cool to me, because I take seriously those "far fetched" analogies between different complex adaptive systems. I realize that others have made these analogies before, but they are cool to me, because I rarely hear them.
Social institutions, such as governments, are complex adaptive systems under selective pressures. Each governing institution acquires mutations which maybe retained or discarded. Each governing institution competes with other governing institutions for limiting resources. Different institutions exhibit different levels of survival and growth and spread. These institutions tend to be passed on from generation to generation because humans have written records, and also simply and more importantly, humans remember what they did yesterday and twenty years ago, and change is both intellectually challenging, and financially restricted.
Governments exhibit
-- phenotypic variation,
-- heritable phenotypic variation, insofar as governments persist and self-replicate,
-- fitness differences among variants.
As a consequence of these phenomena (1), governments tend to evolve. As you know, evolution does not always optimize performance. Rather, they undergo probabilistic responses to selective pressures,. It is possible for these responses to result in objects which are poorly suited for future conditions. Evolution is always backward-looking.
Social Darwinism? No, not in the original sense.
The above smacks a bit of "Social Darwinism." However, the earlier incarnation of that phenomenon was used as an excuse for greed and imperialism (2). In the past 50 years, however, strong evidence has accrued that cooperation can easily evolve and is an evolutionary stable state (3). All successful societies or nations rely heavily on within-group cooperation. It seems further that cooperation among nation-states provides increased fitness as well. This seems like a no-brainer, given that nation-states are themselves composed of interacting groups that cooperate as well as compete.
One of the primary requirements of the evolution of cooperation is that fitness of individuals within groups is increased through the cooperation. This central criterion is often easily met.
Another important criterion for the emergence and maintenance of cooperation is repeated interactions among the same agents so that "learning" can occur. Repeated interactions is the key difference between the standard Prisoner's dilemma game, where cooperation is not advantageous vs. games in which cooperation is advantageous. [I put "learning" in quotes, because it need not be learning in the usual sense of a cognitive process by an individual, but rather can be an adaptation to respond to cues given by cheaters that they are cheating. "Cheating" is defined as the receipt of benefits of cooperation without incurring the costs of cooperation and reciprocity.]
The ease with which cooperation can arise, and become a stable equilibrium does not exclude the possibility that cheating cannot also arise. However, under easily met conditions, if a "mutation" does give rise to cheating, it can be eliminated, or kept at low levels, depending on the conditions.
References cited
1. Endler, J. Natural Selection in the Wild. Princeton monographs.
2. Wikipedia, 2011, http://en.wikipedia.org/w/index.php?title=Social_Darwinism&oldid=461877577
3. Nowak, 8 December 2006, Science; Nowak et al. 26 August 2010. Nature.
Complex adaptive systems
A colleague of mine -- a very successful molecular biologist -- recently gave a Sigma Xi Researcher of the Year presentation. In it, he made the relative specific analogy relating the central dogma of biology to the operation of the U.S. federal government. It blew my mind. It was is SO cool to me, because I take seriously those "far fetched" analogies between different complex adaptive systems. I realize that others have made these analogies before, but they are cool to me, because I rarely hear them.
Social institutions, such as governments, are complex adaptive systems under selective pressures. Each governing institution acquires mutations which maybe retained or discarded. Each governing institution competes with other governing institutions for limiting resources. Different institutions exhibit different levels of survival and growth and spread. These institutions tend to be passed on from generation to generation because humans have written records, and also simply and more importantly, humans remember what they did yesterday and twenty years ago, and change is both intellectually challenging, and financially restricted.
Governments exhibit
-- phenotypic variation,
-- heritable phenotypic variation, insofar as governments persist and self-replicate,
-- fitness differences among variants.
As a consequence of these phenomena (1), governments tend to evolve. As you know, evolution does not always optimize performance. Rather, they undergo probabilistic responses to selective pressures,. It is possible for these responses to result in objects which are poorly suited for future conditions. Evolution is always backward-looking.
Social Darwinism? No, not in the original sense.
The above smacks a bit of "Social Darwinism." However, the earlier incarnation of that phenomenon was used as an excuse for greed and imperialism (2). In the past 50 years, however, strong evidence has accrued that cooperation can easily evolve and is an evolutionary stable state (3). All successful societies or nations rely heavily on within-group cooperation. It seems further that cooperation among nation-states provides increased fitness as well. This seems like a no-brainer, given that nation-states are themselves composed of interacting groups that cooperate as well as compete.
One of the primary requirements of the evolution of cooperation is that fitness of individuals within groups is increased through the cooperation. This central criterion is often easily met.
Another important criterion for the emergence and maintenance of cooperation is repeated interactions among the same agents so that "learning" can occur. Repeated interactions is the key difference between the standard Prisoner's dilemma game, where cooperation is not advantageous vs. games in which cooperation is advantageous. [I put "learning" in quotes, because it need not be learning in the usual sense of a cognitive process by an individual, but rather can be an adaptation to respond to cues given by cheaters that they are cheating. "Cheating" is defined as the receipt of benefits of cooperation without incurring the costs of cooperation and reciprocity.]
The ease with which cooperation can arise, and become a stable equilibrium does not exclude the possibility that cheating cannot also arise. However, under easily met conditions, if a "mutation" does give rise to cheating, it can be eliminated, or kept at low levels, depending on the conditions.
References cited
1. Endler, J. Natural Selection in the Wild. Princeton monographs.
2. Wikipedia, 2011, http://en.wikipedia.org/w/index.php?title=Social_Darwinism&oldid=461877577
3. Nowak, 8 December 2006, Science; Nowak et al. 26 August 2010. Nature.
Wednesday, November 9, 2011
Oops. Another poorly implemented assignment
For a graduate class I asked grad students to prepare for a Monday class by reading a text book chapter and writing down two research ideas complete with a very short literature based rationale. In class on Monday they began collaborating, and for Wednesday's class they wrote 2-3 page preproposals. In class on Wednesday, they reviewed each others' preproposals. I had given them more guidance (see Week 12 in the linked document), but this was the gist of it.
The preproposals were horrible. Although the grammar was fine, and some of the ideas might have been adequate, but the ideas were not well-supported by the weekly readings nor based on deep thinking about the material I had assigned. I think some of their ideas came from their own research projects, but they did not construct convincing arguments as to why anyone would invite a full proposal.
I need to break down the assignment into smaller, more explicit pieces. For example:
"From the material that you have read for this week,
1. What are the important topics in this area of this sub-discipline of ecology?
2. Of the important topics that you identified (for this week, within this area of this sub-discipline), which topics have a sufficient literature upon which you can build, that is, to build a convincing case that your new idea will also be important? [Cool ideas are cool, but they have to be based upon evidence, and evidence is presented in the literature. Mere cool ideas don't get published or funded. A well-reasoned cool idea gets both published and funded.]
3. How do you convince a reader that (a) this area of ecology is important and interesting, and (b) our research idea(s) is likely to bear fruit (i.e., become an important contribution)?"
I had students work in fairly large groups 3-5, and I think it is hard for each member to contribute in a substantial way to the writing. I think the groups should be 1-3 students in size. I will have to pick a size for next week. Perhaps individuals....
When I asked for feedback, students expressed the concern that, while they enjoyed it, they would have gotten more out of lecture. I think that is because they are used to being lectured to by bright, engaged faculty (my colleagues), often on topics not well covered in the reading. In contrast, I am letting Peter Morin lecture (through his text book), and I want the students to grapple -- get sweaty -- with the reading. That is why I assigned both exploratory and formal writing exercise, in order to enable them to dig into it. They did a poor job of it, because I did not give them enough guidance.
I think that they each need to do their own next week, and bag the group work. We will use class time for that. Maybe I will make pairs (but not 3's) optional....
The preproposals were horrible. Although the grammar was fine, and some of the ideas might have been adequate, but the ideas were not well-supported by the weekly readings nor based on deep thinking about the material I had assigned. I think some of their ideas came from their own research projects, but they did not construct convincing arguments as to why anyone would invite a full proposal.
I need to break down the assignment into smaller, more explicit pieces. For example:
"From the material that you have read for this week,
1. What are the important topics in this area of this sub-discipline of ecology?
2. Of the important topics that you identified (for this week, within this area of this sub-discipline), which topics have a sufficient literature upon which you can build, that is, to build a convincing case that your new idea will also be important? [Cool ideas are cool, but they have to be based upon evidence, and evidence is presented in the literature. Mere cool ideas don't get published or funded. A well-reasoned cool idea gets both published and funded.]
3. How do you convince a reader that (a) this area of ecology is important and interesting, and (b) our research idea(s) is likely to bear fruit (i.e., become an important contribution)?"
I had students work in fairly large groups 3-5, and I think it is hard for each member to contribute in a substantial way to the writing. I think the groups should be 1-3 students in size. I will have to pick a size for next week. Perhaps individuals....
When I asked for feedback, students expressed the concern that, while they enjoyed it, they would have gotten more out of lecture. I think that is because they are used to being lectured to by bright, engaged faculty (my colleagues), often on topics not well covered in the reading. In contrast, I am letting Peter Morin lecture (through his text book), and I want the students to grapple -- get sweaty -- with the reading. That is why I assigned both exploratory and formal writing exercise, in order to enable them to dig into it. They did a poor job of it, because I did not give them enough guidance.
I think that they each need to do their own next week, and bag the group work. We will use class time for that. Maybe I will make pairs (but not 3's) optional....
Sunday, November 6, 2011
Pathogen-mediated promiscuity
If the spread of (human) sexually transmitted diseases requires humans to have sex, wouldn't selection favor pathogens which increase our promiscuity? Very interesting...someone smart must have already thought of this and figured out the math...at some level...maybe there is something to add?
Can joy be modelled with a SIR disease model?
I guess the better question is how, and whether it would make sense or lead to interesting hypotheses. I just like the idea of modelling the spread of something wonderful using a model of something we think of as bad. :-)
Monday, May 16, 2011
Learning environments (more from "How Students Learn...")
Donovan and Bransford (2005) describe four types of environments, "centered on" learners, content, assessment, and community.
- Learner-centered environment. Here we start with what the learner knows, and help the student expand beyond that. Typically, we connect to that existing knowledge as a base, and build outward and upward. Occasionally, we have to carefully remove what was already built before building onward. Related to this, we have to provide manageable, yet challenging tasks, and give them the tools, so students feel challenged and empowered rather than hopeless and frustrated.
- Content- or Knowledge-centered environment. Here we begin with three questions: (i) what is important for students to know and be able to do? (ii) what are the core concepts we use for organization, and what are the case studies or detailed knowledge that embody those concepts? (iii) How will we know that students have mastered this knowledge and these concepts? Although items (i) and (iii) overlap with the Learner- and Assessment-centered approaches, item (ii) is the core. It appears critical that specific case studies be understood as exemplars of more general concepts, and that concepts provide a framework for understanding other specific cases. Here I will suggest that students understand that there are usually multiple conceptual frameworks by which we might perceive and understand a specific phenomenon. The authors contend that textbooks tend to focus on the facts and less on the conceptual frameworks. I observe that that is true for the ecology texts I am most familiar with.
- Assessment-centered environment. Formative assessment is essential because it makes the success and failure of learning clear to both students and teachers. Such assessments can help both students and teachers identify preconceptions, and to track change in understanding over time. Seeing this change over time helps students understand better where they are and how they got there. These assessments are tools students and teachers need to use in the service of building knowledge.
- Community-centered environment. In this environment, we create a place or context that rewards participation rather than correctness, because mistakes, preconceptions, and dogma are all good starting places for real learning. In addition, students are more engaged when participating, and this participation results in a positive feedback loop wherein participation begets enjoyment, enjoyment begets participation, and it all facilitates learning.
Principles of how students learn (from Donovan and Bransford (editors). 2005. How Students Learn....)
Notes to myself:
The introductory chapter of this NRC book summarizes an earlier NRC report How People Learn: Brain, Mind, Experience and School.
They describe three key principles:
1. New knowledge must connect to existing knowledge already learned.
2. Facts and conceptual framework go together, hand-in-hand. A framework with facts is relatively meaningless (an empty framework) and facts without a framework make no sense, cannot be retained, or recalled.
3. Metacognition (understanding tips, tricks, and principles of learning) helps facilitate learning.
One common trap that I fall into is that I fail to appreciate what a limited experience most students students have of the natural world. Therefore, I fail to connect to their existing knowledge base. To connect this to the principles above, I fail to give students enough facts for a new conceptual framework. I assume that they already have lots of facts in hand (what a maple tree looks like, or what a sow bug acts like). What I may want to do is say or ask:
The introductory chapter of this NRC book summarizes an earlier NRC report How People Learn: Brain, Mind, Experience and School.
They describe three key principles:
1. New knowledge must connect to existing knowledge already learned.
2. Facts and conceptual framework go together, hand-in-hand. A framework with facts is relatively meaningless (an empty framework) and facts without a framework make no sense, cannot be retained, or recalled.
3. Metacognition (understanding tips, tricks, and principles of learning) helps facilitate learning.
One common trap that I fall into is that I fail to appreciate what a limited experience most students students have of the natural world. Therefore, I fail to connect to their existing knowledge base. To connect this to the principles above, I fail to give students enough facts for a new conceptual framework. I assume that they already have lots of facts in hand (what a maple tree looks like, or what a sow bug acts like). What I may want to do is say or ask:
- "Here is a new conceptual framework, and here is how it works and what it is good for."
- "Here is a specific example of an empirical experiment that helped confirm the utility of this framework. This is how this example fits into this framework."
- "Here is another example...can you figure out how this example fits into the framework?"
- "Here are more examples. Go for it."
- "Can you find other examples?"
- "Can you imagine other ways to investigate the natural world using this framework?"
- "What do you like about this framework? What do you find confusing or frustrating about this framework?"
- "How might you modify this framework?"
Tuesday, April 26, 2011
Reflections on mathematical modeling (II)
Brain data dump...
levels of formalization:
Modeling data, modeling dynamics.
Learning by,
levels of formalization:
- what do previous data tell us - deterministic models (e.g., average, linear regression)
- what do previous data tell us - stochastic models (e.g., range, standard dev., standard error)
- increased sophistication (e.g., non-normal forms of stochasticity: null models, interesting parametric distributions).
- meta-analysis - combining previous empirical studies
- models with and without feedback or loops
Modeling data, modeling dynamics.
Learning by,
- copying,
- applying,
- combining,
- creating.
Friday, April 22, 2011
Discussing scientific papers in classes - what do we DO?
Should we demonstrate understanding during class time, or should we just jump ahead? I think we need to demonstrate understanding in class, if only to make sure people actually work at reading the assigned papers. However, we could even read the paper out loud, but that would not guarantee understanding. So, it seems to me that in each class we should address at least the following questions:
1. Is the question addressed in the paper interesting?
2. Do the data address the hypotheses?
3. Do the results support the conclusions?
4. What are the implications of the conclusions (or of the results)?
In class, we might start with #2, then #3, #4, and then maybe return to #1.
1. Is the question addressed in the paper interesting?
2. Do the data address the hypotheses?
3. Do the results support the conclusions?
4. What are the implications of the conclusions (or of the results)?
In class, we might start with #2, then #3, #4, and then maybe return to #1.
Pedagogical and scientific goals
I posit that understanding is the core value of mathematical modeling. There are (at least) two levels of understanding, the understanding of our own questions. The first aspect of understanding enhanced by modeling is making our spoken language precise with the aid of mathematics. The second aspect of understanding is providing an unambiguous structure to our ideas that the scientific community can use, that is, the development of useful theory.I like to think of the scientific process of knowledge creation as a 3D spring, coil, or spiral, where a single loop represents a complete cycle of the scientific process (question, hypothesis, test, interpretation), and progress occurs as we repeat the process through multiple cycles, traveling down length of the coils. Mathematical modeling can help us at different phases of a single coil.
I think that making ourselves formalize our conceptual models helps us see and understand our ideas to a greater degree. Formalization helps us become ever more specific and thereby operationalize our hypotheses and thereby generate more testable predictions. Going through the formalization process helps us understand what a mathematical model is and and how mathematical models provide structure to theory. The process helps show us and convince us of how models are used in Science.
Thursday, April 21, 2011
Reflection on teaching modeling, or why should non-modelers try to model?
At the moment, I believe that non-modelers (students or faculty) benefit from attempting to model simple systems. I believe that it helps them become better scientists.
I am near the end of a semester in which we tried to incorporate a little bit of modeling into an otherwise basic graduate level ecosystems course. I think I would like to reflect a bit.
For years I have helped teach a population/community grad course, where we included basic population and food web models, and a smidgen of other stuff. In that course, we started everyone out making the same assumption of ignorance for all, and we taught just enough for students to implement simple models in R. I am not sure how satisfactory it is. I think I want to teach more basic R so that students learn about R in a modeling context, not just their stats classes. I think by learning R they will learn about models even more effectively.
This semester (Winter/Spring 2011), in the ecosystems course, we started students thinking along two tracks, one of conceptual models of ecosystems and the other learning the R language. Our thought was that by the time they had learned enough about ecosystems, to create conceptual models, they would have learned enough R to begin formalizing their conceptual models. However, that has not been the case, for at least two reasons.
The first cause of sub-optimal pedagogy may have been that students new to a language (e.g., R) need to work with it at least three days/week (preferably 4-6), but I did not structure the assignments that way. They need both carrots and sticks, and assignments that require daily turn-around (e.g., automated release and deadlines, or email with 24 hours to upload answers). I would not even have to grade every one of them - just mark them turned in or not, perform spot checks, and provide detailed answers. Why didn't I do this? Several not-very-good reasons:
However, I think that forcing students to formalize their conceptual models has helped them see and understand their own conceptual models to a greater degree. Formalization helps them become ever more specific with regard to their conceptual model and this helps them generate more testable predictions. Formalization helps them understand what a mathematical model is and and how mathematical models provide structure to theory. The process helps show them how models are used in Science, and last, it helps them see indirect connections more clearly and accurately. Well, ... I hope it does all that.
I am near the end of a semester in which we tried to incorporate a little bit of modeling into an otherwise basic graduate level ecosystems course. I think I would like to reflect a bit.
For years I have helped teach a population/community grad course, where we included basic population and food web models, and a smidgen of other stuff. In that course, we started everyone out making the same assumption of ignorance for all, and we taught just enough for students to implement simple models in R. I am not sure how satisfactory it is. I think I want to teach more basic R so that students learn about R in a modeling context, not just their stats classes. I think by learning R they will learn about models even more effectively.
This semester (Winter/Spring 2011), in the ecosystems course, we started students thinking along two tracks, one of conceptual models of ecosystems and the other learning the R language. Our thought was that by the time they had learned enough about ecosystems, to create conceptual models, they would have learned enough R to begin formalizing their conceptual models. However, that has not been the case, for at least two reasons.
The first cause of sub-optimal pedagogy may have been that students new to a language (e.g., R) need to work with it at least three days/week (preferably 4-6), but I did not structure the assignments that way. They need both carrots and sticks, and assignments that require daily turn-around (e.g., automated release and deadlines, or email with 24 hours to upload answers). I would not even have to grade every one of them - just mark them turned in or not, perform spot checks, and provide detailed answers. Why didn't I do this? Several not-very-good reasons:
- I felt sorry for them,
- I wasn't 100% convinced that I should push programming and math that hard,
- it would have been more work for me,
- not everyone needed that kind of practice,
- those that needed that kind of practice COULD have done self-study.
However, I think that forcing students to formalize their conceptual models has helped them see and understand their own conceptual models to a greater degree. Formalization helps them become ever more specific with regard to their conceptual model and this helps them generate more testable predictions. Formalization helps them understand what a mathematical model is and and how mathematical models provide structure to theory. The process helps show them how models are used in Science, and last, it helps them see indirect connections more clearly and accurately. Well, ... I hope it does all that.
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