tag:blogger.com,1999:blog-38524876637989428642024-03-13T14:57:55.829-04:00One ecologist's viewExploratory writing on topics ecological.Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.comBlogger39125tag:blogger.com,1999:blog-3852487663798942864.post-9999250504347779012014-04-10T15:46:00.000-04:002014-04-10T18:03:15.469-04:00Based on the insight from Lev Ginzburg<div class="userContentWrapper aboveUnitContent" data-ft="{"tn":"K"}" style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 11px; line-height: 14.079999923706055px; margin-bottom: 15px; margin-top: 15px;">
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<span class="userContent">A simple ratio-dependent explanation of logistic growth...with R of course.</span></div>
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Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-41754165330013994602014-04-10T15:44:00.000-04:002014-04-10T15:44:12.777-04:00Evolution and ecosystem dynamics: Implementing a simple example from Ellner et al. 2011, Ecology Letters, <span style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;">An example of measuring the relative importance of evolutionary and ecological dynamics.</span><br style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;" /><a href="http://rpubs.com/hankstevens/13258" rel="nofollow nofollow" style="background-color: white; color: #3b5998; cursor: pointer; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px; text-decoration: none;" target="_blank">http://rpubs.com/hankstevens/13258</a>Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-19959669383153999752014-04-10T15:42:00.002-04:002014-04-10T15:42:39.403-04:00Vitousek et al. 1998. Insights from a simple nitrogen budget model<span style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;">An implementation of a simple nitrogen budget model:</span><br style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;" /><a href="http://rpubs.com/hankstevens/vitousek1" rel="nofollow nofollow" style="background-color: white; color: #3b5998; cursor: pointer; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px; text-decoration: none;" target="_blank">http://rpubs.com/hankstevens/vitousek1</a><br style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;" /><br style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;" /><span style="background-color: white; color: #333333; font-family: 'lucida grande', tahoma, verdana, arial, sans-serif; font-size: 13px; line-height: 18px;">from Vitousek, P. M., Hedin, L. O., Matson, P. A., Fownes, J. H., & Neff, J. (1998). Within-system element cycles, input-output budgets, and nutrient limitation. In M. L. Pace & P. M. Groffman (Eds.), Success, Limitations, And Frontiers Of Ecosystem Science (pp. 432–451). Springer, New York.</span>Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-65406279025477824802013-03-25T15:45:00.000-04:002013-03-25T15:49:38.130-04:00The Physiology/Life-history Nexus: life history a la Ricklefs and Wikelski (2002)Ricklefs and Wikelski (2002) present a conceptual model linking genotypes, phenotypes, performance, and demography to evolutionary responses in the context of the environment.<br />
<br />
It is a little mushy because they define life-history in as a set of ... physiological adaptations, and then argue that "physiology mediates the relationship between life-history and the environment" (R&W p. 463).<br />
<br />
Demography refers to traits of populations, where the state variable is typically population size, <i>N</i>, and we may characterized rates of change of <i>N</i> due to birth rates, death rates and migration. In contrast, life history refers to traits of individuals, especially individual probabilities of survival and death, lifespan, and the sizes and number of offspring in one bout of reproduction and over an organism's lifetime.<br />
<br />
I think they take it for granted that their readers know that <i>life history</i> refers literally to the history of <i>"</i>significant" events in the life of an average individual of a population, focused exclusively on those events, such as clutch size or lifespan, that govern population demographic rates. For instance, different <i>life history stages</i> refer to elements of a life cycle are relatively recognizably distinct, and which might be characterized by different probabilities of death or survival, birth, or different average fecundities. Thus distinct life history stages are characterized by individuals having different properties. The study of life histories includes the study of traits of individuals related directly to survival and reproduction. The traits of interest most commonly include:<br />
<ul>
<li>lifespan and senescence;</li>
<li>age at maturity; </li>
<li>metamorphosis between stages;</li>
<li>age-specific or stage-specific probabilities of survival or death;</li>
<li>number of seeds, eggs, or offspring per bout of reproduction (e.g., mast event, clutch, or litter);</li>
<li>semelparity <i>vs.</i> iteroparity </li>
<li>average size of individual seeds, eggs, or offspring;</li>
<li>lifetime reproductive success. </li>
<li>body size.</li>
</ul>
<i>Life history strategies</i> are set of these traits that seem to us to optimize fitness in a particular context. For instance, <i>r-</i>selection is a life history strategy characterized by early onset of reproduction and large numbers of offspring and which often maximizes fitness in highly unpredictable environments. This strategy can maximize fitness when adult survival (and therefore future reproduction) is unpredictable. At the other end of the <i>r vs. K</i>-selection continuum, <i>K-</i>selected species are characterized by delayed onset of reproduction, and multiple bouts of reproduction (iteroparity). The <i>K</i>-selected strategy tends to maximize fitness in predictable environments. These two life history strategies seem to represent to ends of a continuum in which many of the above life history traits seem to covary.<br />
<br />
The study of life histories focuses on the proximate (e.g., phsyiological) and ultimate (evolutionary) causes of variation and covariation in the above traits. <br />
<br />
<i>Non-sequitor: Why do we have the impression that aggregate properties (ecosystem variables, diversity, N) exhibit patterns and are suitable objects of study? (I ask this, I think, because of Ricklefs' focus on individuals and species).</i><br />
<br />
The five principles of Ricklefs and Wikelski (2002):<br />
<ol>
<li>individuals respond to variation in their environments.</li>
<li>responses are constrained by the allocation of limited resources among competing functions, </li>
<li>individual organisms assume alternative physiological states at different stages in their life cycles because these states are incompatible.</li>
<li>individuals might also assume different states as phenotypic responses to the environment,</li>
<li>the assumption of one or another state can be modulated by demography, especially reproductive value (future reproductive potential).</li>
</ol>
Specific points <br />
<ul>
<li> It seems to me that their primary point is that we need to study physiology in order to understand life history. </li>
<li>I could not determine whether they were implying that the environment caused covariation in life history traits, or the covariation was due primarily to physical constraints on different components of organisms' physiologies.</li>
<li>Figures I and II in Box 1 seems orthogonal or perpendicular to life history traits. That is, we might imagine that a particular life history strategy such as r-selected traits occupies the phenotype box but different points on the <i>r-K</i> continuum lie perpendicular to the figure, extending out of and into the page.</li>
<li>I thought it was odd that they chose to not mention tradeoffs that might arise through "simple" laws of conservation of matter and energy.</li>
</ul>
Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-20457028198376773722013-03-07T09:50:00.000-05:002013-03-07T09:50:22.185-05:00Organisms are built in four dimensionsHere is, I think, one observation, expressed in various and complementary ways:<br />
<ul>
<li>All species exhibit an average relative fitness, <i>w</i>, of approximately $w = 1$.</li>
<li>On average, all organisms leave approximately one descendent.</li>
<li>Over its lifetime, an organism does the work (joules) required to leave approximately one descendent.</li>
<li>Over its lifetime, an organism must do the work required to build another organism of the same size. </li>
</ul>
Let<br />
<ul>
<li>A be the total amount of work required to produce a descendent.</li>
<li>R be the rate of that work, and</li>
<li>T be the time over which the work is done, then</li>
</ul>
RT = A<br />
<span style="font-size: small;"><span style="font-family: inherit;"><br /></span></span>
<span style="font-size: small;"><span style="font-family: inherit;">My "observation" above implies that A depends strongly on body size: It takes longer to build a large organism</span></span><span style="font-size: xx-small;"><span style="font-size: small;"><span style="font-family: inherit;">.</span></span></span><br />
<br />
A 3-D organism has to propagate itself through time, at a velocity
sufficient to maintain and replicate itself. The 4-D integral of that mass-time event
is directly proportional to the mass of the organism. The rate or velocity
measured at any instant in time, $t$, will be a 3-D slice of the 4-D
mass-time event. As the event is proportional to the size (mass or
volume) of the organism, the 3-D slice will scale to the 3/4 power of
the 4-D event or size of the organism. Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-5319906205196948672012-11-11T04:29:00.001-05:002012-11-11T04:29:40.098-05:00Thinking like an ecologist<a href="https://docs.google.com/document/d/1ZLyQL2_5nFpPixFqNbvIsLLeSAhzlwN5rFSxhi-GoF0/edit" target="_blank">Here is some advice</a> for budding young ecologists--useful or not useful?Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-84203237855635424072012-09-03T19:22:00.005-04:002012-09-03T19:22:51.148-04:00A blueprint for ecology<span style="font-size: small;"><span style="font-family: Times,"Times New Roman",serif;"><span id="internal-source-marker_0.4040886250851754" style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><span id="internal-source-marker_0.4040886250851754" style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;">Scheiner (and Willig's) general theory of ecology</span></span><br />
<span style="font-size: large;"><span style="font-size: small;"> Scheiner 2012, QRB; Scheiner and Willig 2011 monograph</span></span><br />
<h4>
<span style="font-size: small;"><span id="internal-source-marker_0.5811040491142698" style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;">Domain</span></span></h4>
<span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">The spatial and temporal patterns of the distribution and abundance or organisms, including causes and consequences.</span></span><br />
<h4>
<span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;">Principles</span></span></h4>
<ol>
<li><span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Organisms are distributed unevenly in space and time. </span></span></li>
<li><span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Organisms interact with their abiotic and biotic environments.</span></span></li>
<li><span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Variation in the characteristics of organisms results in heterogeneity of ecological patterns and processes.</span></span></li>
<li><span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">The distributions of organisms and their interactions depend on contingencies.</span></span></li>
<li><span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Environmental conditions are heterogeneous in space and time.</span></span></li>
<li><span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Resources are finite and heterogeneous in space and time. </span></span></li>
<li><span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Birth rates and death rates are a consequence of interactions with the abiotic and biotic environment.</span></span></li>
<li><span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">The ecological properties of species are the result of evolution. </span></span><span style="font-size: large;"></span></li>
</ol>
<h2>
<span style="font-size: small;"> </span></h2>
<h2>
<span style="font-weight: normal;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;">Stevens' general theory of ecology</span></span></span></h2>
<h4>
<span style="font-size: small;"><span id="internal-source-marker_0.5811040491142698" style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;">Domain</span><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"> </span><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"> </span></span></h4>
<span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Life: its constituent entities, causes, and consequences.</span><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;"> </span></span><br />
<h4>
<span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;">Principles</span></span></h4>
<ol style="margin-bottom: 0pt; margin-top: 0pt;">
<li style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">All entities are systems, with some internal complexity.</span></span></li>
<li style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">All entities change.</span></span></li>
<li style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Some entities may have inputs and outputs.</span></span></li>
<li style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">All rates of change, including inputs and outputs, are influenced directly by physical factors.</span></span></li>
<li style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Some entities interact.</span></span></li>
<li style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><span style="font-size: small;"><span style="background-color: transparent; color: black; font-family: Ubuntu; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">All observers must choose specific temporal and spatial scales at which to make observations.</span></span></li>
</ol>
<span style="font-size: small;"><br /></span>
<span style="font-size: small;"><span style="font-family: Times,"Times New Roman",serif;"><br /></span></span>Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-3026005842435774692012-06-10T09:13:00.001-04:002012-06-27T15:48:52.171-04:00Basic desiderata (Jaynes)From <a href="http://en.wikipedia.org/wiki/Edwin_Thompson_Jaynes" target="_blank">E.T. Jaynes</a> with G.L. Bretthorst (2003) Probability theory: the logical of science. Cambridge University Press, Cambridge.<br />
<br />
Consider that we build a robot that thinks like us, except that it cannot make qualitative judgements. It can use only Aristotelian logic. What sort of fundamental desirable properties would its thinking have? <br />
<br />
Desiderata I. Degrees of plausibility are represented by real numbers.<br />
<br />
Desiderata II. Qualitative correspondence with common sense.<br />
<br />
Desiderata III. Consistency:<br />
<ul>
<li>IIIa. If a conclusion can be reasoned out in more than one way, then every plausible way must lead to the same result.</li>
<li>IIIb. The robot always takes into account all of the evidence it has relevant to a question. It does not arbitrarily ignore some of the information, basing its conclusions only on what remains. In other words, it is not ideological.</li>
<li>IIIc. The robot always represents equivalent states of knowledge by equivalent plausibility assignments. That is, if in two problems the robot's state of knowledge is the same (except perhaps for the labeling of propositions), then it must assign the same plausibilities in both.</li>
</ul>
....<br />
<br />
I (HS) will note that IIIb makes this robot a Bayesian, just like the rest of us.<br />
<br />
<br />
<br />Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-55716864719761419122012-06-03T08:58:00.002-04:002012-06-27T15:42:13.162-04:00Will Bayesian statistics become too easy?<div class="statusUnit">
<div class="tlTxFe">
A Bayesian approach to
statistical inference has become increasing popular since the advent of
increased desktop computing power and the development of tailored software. This is a
really really good thing. However, I am concerned that it may, in the not very distant future, become too easy, and too much like frequentist methods as they are currently learned and used by life science undergraduate and graduate students. I am concerned that, in order to make Bayesian methods more accessible, they will be dumbed-down --made too easy-- and their value lost.</div>
<div class="tlTxFe">
</div>
<div class="tlTxFe">
Part of the benefit of a Bayesian approach is
that it more accurately reflects how Science is done. In a nutshell, the Bayesian approach consists of <br />
<ol>
<li>Prior
beliefs: ideas, knowledge, and explicit assumptions about our system, </li>
<li>Collection of new data. </li>
<li>Using the new data to update our beliefs.</li>
</ol>
The result of a Bayesian analysis is not a simple yes-no, significant-not significant kind of answer, but rather a probability distribution that reflects our most informed guesses about our variable of interest. </div>
<div class="tlTxFe">
<br /></div>
<div class="tlTxFe">
I believe that there are two potential pitfalls in the over simplification of a Bayesian analysis. I believe that the less serious of these pitfalls concerns the results, the posterior distribution of each model parameter. Each of these distributions is really a massive collection of independent guesses at the parameters of interest, given all of our assumptions and the newly collected data. Thus the result is not "an answer" but rather thousands of answers, with some answers more likely than others. In our efforts to satisfy ourselves, editors, and readers, we may try too hard to simplify our results. <br />
<br />
Although we may try too hard to simplify our results, I think there is a greater danger that we will try to simplify the prior knowledge and that assumptions that we start with. In my limited experience, ecologists and statisticians are very quick to fall back into the use of the "uninformative prior," as if this is somehow "unbiased." Statisticians recognize that all priors come with a point of view, so there is no such thing as an objective uninformative prior, sometimes more accurately called a reference prior. However, I see us taking the lazy route too often and using a supposedly unbiased reference prior that reduces the tendency to take seriously the literature we read. Lots of data will overwhelm a weak prior. However, it is my experience that priors derive their weakness out of our tendency to not take seriously the quantitative nature of our literature.<br />
<br />
As evidence that Bayesian analyses can be made easy, I can point to the numerous specialized programs for population genetics and phylogenetics that are based upon Bayesian approaches. I have seen many students use these with very little notion of what they are doing.<br />
<br />
As learning in general is essentially a Bayesian process, my fears are not too serious. Nonetheless, ecologists need to take their priors seriously. Statisticians can help by encouraging us to make our beliefs both informed and explicit. In the end, it will only strengthen our science.<br />
<br />
<br /></div>
</div>
<span class="fbTimelineFeedbackLikes tlFLC324978000909761"></span><span class="UIActionLinks UIActionLinks_bottom" data-ft="{"tn":"=","type":20}"><button class="like_link stat_elem as_link" data-ft="{"tn":">","type":22}" name="like" title="Like this item" type="submit"><span class="default_message"></span></button></span>Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-8458580104491339972012-05-29T13:10:00.000-04:002012-05-29T13:11:17.290-04:00Fundamental units?<h3 dir="ltr" id="internal-source-marker_0.4196594078262619">
<span style="background-color: transparent; color: #666666; font-family: Arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline;">What are the fundamental units in E & E?</span></h3>
<span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Part
of the trick to unifying or connecting things is to figure out what the
“things” are that can be connected and need connecting. Here I list the
elements or “things” that are at the core of ecology and which need
connection. We should think of these as the primary state variables of
the most distinct subdisciplines:</span><br />
<ul style="margin-bottom: 0pt; margin-top: 0pt;">
<li style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Ecosystem
variables: elements tracked by ecosystem scientists, such as carbon, or
nitrogen; these might be described by the mean, variance and dynamics
of grams per meter squared.</span></li>
<li style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Individual
physiological rates: elements tracked by physiologists, such as body
mass, resting and active metabolic rates, or the fat reserves in
migratory songbirds.</span></li>
<li style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Populations:
elements tracked by population and community ecologists, and
evolutionary biologists; these might be tracked as the mean and variance
and the dynamics of </span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">N</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">, the number of individuals.</span></li>
<li style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">Genes: the elements tracked by evolutionary biologists; these tend to be tracked by either copy number, </span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">N</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">, or frequency, </span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">p</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">.</span></li>
</ul>
<span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><br />
<span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">We
can use similar conceptual and mathematical tools and equations to
study all of these. Complicating factors are numerous and in many cases
shared across subdisciplines. For instance, one could study
“disturbance” in any of these subdisciplines, but but it is the </span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">consequence</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">
of disturbance that is usually of primary interest. The physical
landscape is an important factor as well, whether in landscape ecology,
metapopulation dynamics, or in niche partitioning. Again, it is the </span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">consequence</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"> of the landscape more than the landscape itself which is usually of primary interest. </span><br />
<span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><br />
<span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">These elements (ecosystem variables, populations and genes) can be and often are linked in classic </span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">levels of biological organisation</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">
(e.g., cells, tissues, organs, organ systems, etc.). While this is a
comfortable approach, it is not the best we can do. This LBO approach
requires the instructor to create all the meaning, connection, and
disciplinary thinking and structure. Instead, the Core Elements approach
reinforces the type of disciplinary thinking of of ecology and
evolutionary biology generally. </span><br />
<span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><br />
<span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">The primary cross-cutting feature of these elements that scientists tend to study are </span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">statics</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"> and </span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: italic; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">dynamics</span><span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">,
corresponding to pattern and process. For each element type, we can
measure a static pattern such as the amounts of carbon in the atmosphere
and the oceans, the abundance an invasive species in its introduced
range and its native range, or the relative frequency of rare genotypes
in the wild. By the same token, we can measure the dynamics or processes
of a system, such as the rate of flow of carbon from the atmosphere to
the oceans, how metabolic rate varies with body mass, population growth
rate of an invasive species, or changes in particular allele frequency
in response to El Nino events. </span><br />
<span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;"></span><br />
<span style="background-color: transparent; color: black; font-family: 'Times New Roman'; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline;">We
often equate pattern with description and process with mechanism, but
this is a misleading distinction. We can describe patterns and
processes, and use either of such descriptions in either
hypothesis-generation or hypothesis falsification/confirmation. </span>Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-45446932237079112812012-03-23T15:08:00.001-04:002012-03-24T12:09:59.754-04:00On Robert Ricklefs (2012), American Naturalist Presidential AddressI am one of those ecologists that thinks like a theoretical physicist -- I want to maximize the ratio of explanatory power to the number of parameters in a model. I look for ways to simplify and unify phenomena. I am bad with details. Therefore, I have tremendous respect for and feel humbled by innovative ecologists that emphasize natural history. Robert Ricklefs is a prime example of this type of ecologist. His presidential address to the American Society of Naturalists, recently published in Am Nat, is a rich cornucopia of discussion material.<br />
<br />
A somewhat useful summary comes from the penultimate page:<br />
<div style="text-align: left;">
"<i>Neither niche theory nor neutral theory provides a satisfying narrative for ecological communities, and the defense of one or the other (sometimes both) by ecologists has at times slowed progress toward understanding biodiversity."</i></div>
<br />
Earlier in the paper, he argues pretty emphatically that neutral theory is a waste of ecologists' time, because there are examples of it not explaining observed patterns, and because some of its assumptions and/or predictions are not realistic, even in principle. He also argues that niche theory (as typified by Lotka, Hutchinson, MacArthur, Lack, Elton, Gause, and others) is highly limited in its usefulness. <br />
<br />
I would say the same thing about natural history, that natural history <i>alone</i> does not provide a satisfying narrative for ecological communities, because, unfortunately, words can sometimes be horribly ambiguous and non-quantitative. I would
also argue that we need mathematics because it is the least ambiguous
language we have, and that its quantitative nature underlies the nature
Ricklefs wants us to spend more time observing.<br />
<br />
I heartily agree with his sentiment that we need to spend more time observing nature. The scientific culture needs to find ways to reward useful, organized, and detailed observation of natural history. However, I don't think we should throw the baby out with the bath water. <br />
<br />
Josh Tewksbury is one of many examples of an ecologists that seems to have equal respect for, and grasp of, both natural history and theory. Long ago, I had the pleasure of listening to a talk of his at Miami University, in which introduced his thinking about ecology as the combination or unity of natural history, theory, and experiment. He was a bit more dogmatic about it, or perhaps just enthusiastic. Regardless, it struck a positive chord with me, because I think his goal is the goal of all ecology and evolutionary biology. I guess I think not everyone needs to do it all, nor all at once. <br />
<br />
<br />Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0Oxford, OH 45056, USA39.5069974 -84.74523139.482494900000006 -84.784713000000011 39.5314999 -84.705749tag:blogger.com,1999:blog-3852487663798942864.post-58046919294608244972012-01-22T06:44:00.000-05:002012-01-22T06:44:22.054-05:00The Cockroach(<i>Inspired by my wife's habit, on Fridays in October, of providing ghastly Halloween treats and poetry in our kids' school lunches. On this day, she provided rubber cockroaches, and we had to come up with some poetry to match the theme.</i> <i>Lacking true creativity, I usually provide different words to poems our kids already knew. Here I update the Raven for my daughter, in the school lunchroom.</i>)<br />...<br />Open here I flung the lunchbox, when, so quickly it did outfox,<br />In there was a stately Cockroach, of the saintly days, once happier.<br />Not the least obeisance made he; not a minute stopped or stayed he;<br />But with mien of lord or lady, perched upon my Twinkie wrapper.<br />Perched upon this food-like substance, digging at my Twinkie wrapper,<br />Perched, and sat, and nothing more.<br /><br />Then this tawny roach beguiling, my sad fancy into smiling,<br />By the buzzing stern decorum of the countenance it wore,<br />"Though your back is made of rubber, thou," I said, "art sure no tubber!<br />Ghastly, creepy, and icky cockroach, wand'ring from the lunchroom store.<br />Tell me what the insect name is on thy lunchroom's Plutonian floor."<br />Quoth the cockroach, "Nevermore."<br /><br />Startled at the stillness broken by reply so aptly spoken,<br />"Doubtless," said I, "what it utters is its only stock and store,<br />'Scaped from some unhappy master, whom unmerciful disaster<br />Taught him speech, not love nor laughter, till his songs one burden bore,<br />Till the words bereft of hope, so that melancholy burden bore<br />Of life, "No---nevermore."<br /><br />"Prophet!" said I, "thing of evil--prophet still, if roach or devil!<br />By the old school building 'round us--by these four walls we both adore--<br />Tell this soul with sorrow laden, if, within the distant snacktime,<br />It shall consume a chocolate iced cake, whom the angels name Ding Dong---<br />Clasp and covet a rare delicious iced cake, whom the angels name Ding Dong?<br />Quoth the cockroach, "Nevermore."<br /><br />And the cockroach, never skitt'ring, still is sitting, still is sitting<br />On the pallid Twinkie food-like substance, me wishing I had more;<br />And his 'tennae moving, sensing, like a demon's sword in fencing.<br />Flourescent lights o'er him dancing throws his shadow on the floor;<br />Like my hope (to eat that Ding Dong) is also dashed on the floor,<br />To be lifted---nevermore!Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-8594801063229161832011-11-23T15:11:00.001-05:002011-11-23T15:35:59.487-05:00Too much or too little?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.<br />
<br />
Quick perusal of two evolution textbooks (Ridley, and Freeman & Herron) showed me that they <i>do not</i> 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.<br />
<br />
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?<br />
<br />
<i>Why</i> 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?<br />
<br />
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?<br />
<br />
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.<br />
<br />
<br />Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-45267162761113945982011-11-23T12:30:00.001-05:002011-11-23T14:46:08.463-05:00US Government as Central Dogma of Molecular Biology<span style="font-size: x-small;"><i>Spoiler Alert</i>: There is nothing new here. However, writing it helps to form the thoughts in my own head ....</span><br />
<br />
<b>Complex adaptive systems </b><br />
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.<br />
<br />
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. <br />
<br />
Governments exhibit<br />
-- phenotypic variation,<br />
-- heritable phenotypic variation, insofar as governments persist and self-replicate,<br />
-- fitness differences among variants.<br />
<br />
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.<br />
<br />
<b>Social Darwinism? No, not in the original sense.</b><br />
<br />
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. <br />
<br />
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.<br />
<br />
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 <i>vs</i>.
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.]<br />
<br />
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.<br />
<br />
<br />
<span style="font-size: x-small;"><b>References cited</b> </span><br />
<span style="font-size: x-small;"><br /></span><br />
<span style="font-size: x-small;">1. Endler, J. <i>Natural Selection in the Wild. Princeton monographs.</i></span><br />
<span style="font-size: x-small;">2.<i> </i>Wikipedia, 2011, http://en.wikipedia.org/w/index.php?title=Social_Darwinism&oldid=461877577</span><br />
<span style="font-size: x-small;">3. Nowak, 8 December 2006, <i>Science</i>; Nowak et al. 26 August 2010. <i>Nature.</i></span>Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-22017150942183686812011-11-09T22:40:00.000-05:002011-11-09T22:40:13.560-05:00Oops. Another poorly implemented assignmentFor 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 <a href="https://docs.google.com/document/d/1Y1SjimyI2CVAJVY602MgF6R90D_7KoFNfpGvK06LQ2k/edit" target="_blank">more guidance (see Week 12 in the linked document)</a>, but this was the gist of it.<br />
<br />
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. <br />
<br />
I need to break down the assignment into smaller, more explicit pieces. For example:<br />
"From the material that you have read for this week, <br />
1. What are the important topics in this area of this sub-discipline of ecology?<br />
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.]<br />
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>"</i><br />
<i><br /></i><br />
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....<br />
<br />
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.<br />
<br />
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....<br />
<br />
<br />Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-14386580688494456602011-11-06T10:15:00.000-05:002011-11-06T10:47:42.166-05:00Pathogen-mediated promiscuityIf 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?Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-30713213820864975762011-11-06T10:12:00.000-05:002011-11-06T10:12:23.702-05:00Can 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. :-)<br />
<br />Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-53853948300469585522011-05-16T15:05:00.000-04:002011-11-02T06:46:09.235-04:00Learning environments (more from "How Students Learn...")Donovan and Bransford (2005) describe four types of environments, "centered on" learners, content, assessment, and community.<br />
<ol>
<li>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.</li>
<li>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) <span style="font-weight: bold;">what are the core concepts we use for organization, and what are the case studies or detailed knowledge that embody those concepts?</span> (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 <span style="font-style: italic;">there are usually multiple conceptual frameworks by which we might perceive and understand a specific phenomenon.</span> 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.</li>
<li>Assessment-centered environment. <span style="font-style: italic;">Formative</span> 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.</li>
<li>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.</li>
</ol>Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-41619396329270776262011-05-16T14:26:00.000-04:002011-11-02T06:54:11.853-04:00Principles of how students learn (from Donovan and Bransford (editors). 2005. How Students Learn....)Notes to myself:<br />
<br />
The introductory chapter of this NRC book summarizes an earlier NRC report <span style="font-style: italic;">How People Learn: Brain, Mind, Experience and School.</span><br />
<br />
They describe three key principles:<br />
1. New knowledge must connect to existing knowledge already learned.<br />
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.<br />
3. Metacognition (understanding tips, tricks, and principles of learning) helps facilitate learning.<br />
<br />
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 <span style="font-style: italic;">their</span> 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:<br />
<ol>
<li>"Here is a new conceptual framework, and here is how it works and what it is good for."</li>
<li>"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."</li>
<li>"Here is another example...can you figure out how this example fits into the framework?"</li>
<li>"Here are more examples. Go for it." </li>
<li>"Can you <i>find</i> other examples?"</li>
<li>"Can you imagine other ways to investigate the natural world using this framework?"</li>
<li>"What do you like about this framework? What do you find confusing or frustrating about this framework?"</li>
<li>"How might you modify this framework?"</li>
</ol>
(I might not get around to #7)Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-52731440087947574132011-04-26T13:23:00.000-04:002011-04-27T05:52:46.306-04:00Reflections on mathematical modeling (II)<span style="font-family: courier new;">Brain data dump...</span><br /><br /><span style="font-family: courier new;">levels of formalization:</span><br /><ul style="font-family: courier new;"><li>what do previous data tell us - deterministic models (e.g., average, linear regression)</li><li>what do previous data tell us - stochastic models (e.g., range, standard dev., standard error)</li><li>increased sophistication (e.g., non-normal forms of stochasticity: null models, interesting parametric distributions).<br /></li><li>meta-analysis - combining previous empirical studies<br /></li><li>models with and without feedback or loops</li></ul><span style="font-family: courier new;">Learning a language, learning modeling concepts.</span><br /><br /><span style="font-family: courier new;">Modeling data, modeling dynamics.</span><br /><br /><span style="font-family: courier new;">Learning by,</span><br /><ol style="font-family: courier new;"><li>copying,</li><li>applying,</li><li>combining,</li><li>creating.<br /></li></ol>Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-52568278156520241592011-04-22T11:39:00.000-04:002011-04-23T07:22:33.634-04:00Discussing 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:<br />1. Is the question addressed in the paper interesting?<br />2. Do the data address the hypotheses?<br />3. Do the results support the conclusions?<br />4. What are the implications of the conclusions (or of the results)?<br /><br />In class, we might start with #2, then #3, #4, and then maybe return to #1.Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-50862979664077726212011-04-22T11:16:00.000-04:002011-04-22T15:07:13.839-04:00Pedagogical and scientific goals<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://1.bp.blogspot.com/-KnLlRvpeyqU/TbG6RhK_7NI/AAAAAAAADao/kayZWU0aP7k/s1600/2561051920_bd9150702c.jpg"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 160px; height: 140px;" src="http://1.bp.blogspot.com/-KnLlRvpeyqU/TbG6RhK_7NI/AAAAAAAADao/kayZWU0aP7k/s320/2561051920_bd9150702c.jpg" alt="" id="BLOGGER_PHOTO_ID_5598460621923282130" border="0" /></a>I posit that <span style="font-style: italic;">understanding </span>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.<br /><br />I like to think of the scientific process of knowledge creation as a <a href="http://www.laser-razor.co.za/images/spiralcoil.gif">3D spring, coil, or spiral</a>, 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.<br /><br />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.Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-85978717730714484962011-04-21T14:26:00.000-04:002011-04-22T09:53:23.932-04:00Reflection 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.<br /><br />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.<br /><br />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.<br /><br />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.<br /><br />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:<br /><ul><li>I felt sorry for them,<br /></li><li>I wasn't 100% convinced that I should push programming and math that hard,<br /></li><li>it would have been more work for me,<br /></li><li>not everyone needed that kind of practice,<br /></li><li>those that needed that kind of practice COULD have done self-study. </li></ul>The second reason for suboptimal pedagogy was that I tried to be more flexible with the modeling assignments than I was easily capable of -- I could create stuff, but some of it took longer than was convenient. In brief, we asked students to come up with a scientific question, explain what is known and unknown regarding that question and their study system, and design a conceptual model that captures the essence of their question and/or system. Students were then asked to formalize their conceptual model using mathematics or computer code or both. The students conceptual models were not all ecosystem models with merely pools and fluxes of all the same units and element(s). Rather, most were a hodge-podge of different sorts of variables that related typically in a mechanistic fashion, but were not comprised of, for instance, pools and fluxes of carbon. Therefore, the relatively low programming ability of the students (see first reason, above) and my desire to be flexible with regard to acceptable topics meant that I had to invent lots of unique code for each different student. And that, Virignia, is the second reason why my pedagogy was sub-optimal.<br /><br /><span style="font-style: italic;">However</span>, 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 <span style="font-style: italic;">hope</span> it does all that.Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-47469854336157406102010-04-16T08:06:00.000-04:002010-08-13T05:31:53.916-04:00What is your Bayesian prior on non-human animal emotion?Although humans have a strong ability to communicate with other humans, we lack the ability to communicate as well with non-human animals. As a result, we know far more about the internal emotional states of other humans than we know about the internal emotional states of non-human animals. Where do we <span style="font-style: italic;">begin</span> to make inferences about the internal states of non-human animals? <span style="font-style: italic;">What is the appropriate Bayesian prior for making inferences about the unknown internal states of non-human animals?</span><br /><br />A long time ago, Rene Descartes (1649) posited that non-human animals are akin to machines (have no soul or mind and couldn't feel pain). Since then, it has been considered "scientific" to assume non-human animals <span style="font-style: italic;">actually</span> are machines unless there is overwhelming evidence to the contrary. I propose that this is highly unscientific, and that it is an example of <span style="font-style: italic;">argumentum ad ignorantiam</span>, that the absence of evidence is the evidence of absence. That is, Descartes, and millions since then, have found it convenient to presume that an absence of evidence about non-human animal emotion constitutes evidence of absence of non-human animal emotion.<br /><br />Another approach to understanding non-human animal emotions, universally taken by infants, is to assume that "all others are like me." Indeed, this is how humans learn about each other. In the absence of a lot of knowledge, we assume that other humans (especially those that <span style="font-style: italic;">look</span> like us) think and feel as we do. This is our Bayesian prior for interactions with other humans. Like Descartes's proclamation that non-humans are machines, this could also constitute a prior for understanding non-human animal emotion.<br /><br />Is emotion likely to be a synapomorphy shared with a wide range of taxa? In my simplistic way of thinking, I propose two lines of reasoning that suggest it is. First, emotion in humans appears to be regulated in a primitive part of the central nervous system, whose structure is shared with a wide variety of taxa. If it looks like beer, smells like beer, tastes like beer, it might be beer. Second, emotions are useful. Fear and pain are widely recognized for their fitness benefit, for their adaptive value. I suggest that other emotions are likely to have similar fitness benefit. If a behavior generates joy or euphoria or happiness, organisms would be inclined to continue that behavior. Emotions could help provide mechanistic links between biochemistry and behavior.<br /><br />Bayesian inference is useful in that it requires we think hard and think carefully about our prior beliefs. In that sense, it helps us become more scientific and maybe even more moral.Anonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com0tag:blogger.com,1999:blog-3852487663798942864.post-15346657075636225222010-04-16T05:42:00.001-04:002010-08-13T05:27:42.203-04:00To P or not to P, that is the question...I think that at least part of the reason most of us have a hard time stating what a frequentist P-value is (and is not) is because we do not know the <span style="font-weight: bold;">difference between</span> statisticians' correct definition and our common but erroneous definitions. In addition, or maybe another way of looking at it, is that the ambiguity of words in general (as opposed to math) contributes substantially to the confusion.<br /><br />Here I take a stab at it.<br /><br />A frequentist P-value (say, of a t-test for a difference between means) is the probability that a difference as large or larger than the observed difference would occur if our two samples were drawn from the same distribution, and the same experiment were conducted repeatedly <span style="font-style: italic;">ad infinitum</span> (or <span style="font-style: italic;">ad nauseum</span>). "A P value is often described as the probability of seeing results as or more extreme as those actually observed if the null hypothesis were true" (<span style="font-style: italic;">2</span>).<br /><br />A frequentist P-value of such a t-test is apparently <span style="font-style: italic;">not</span> lots of things we wish it were (<span style="font-style: italic;">1</span>):<br /><ol><li>it is not the probability that our null hypothesis is true.</li><li>it is not the probability that such a difference could occur by chance alone.</li><li>it is not the probability of falsely rejecting the null hypothesis.</li></ol>Each of these leave information out. Important elements of a correct definition include<br /><ul><li>The probability of observing data as extreme <span style="font-style: italic;">or more extreme</span> in ...</li><li>repeated identical experiments and analyses, given ...</li><li>the <span style="font-style: italic;">a priori</span> belief that the null hypothesis is true (this is a Bayesian "prior").</li></ul>Thus we see that the incorrect definitions typically share something with a complete definition, and that under <span style="font-style: italic;">most</span> circumstances, analyses that fit incorrect definitions (e.g., Bayesian posteriors) will be correlated frequentist P-values (see comment by Bolker comment below).<br /><br />A <span style="font-weight: bold;">frequentist confidence interval</span> is a region calculated from our data and our selected confidence level, α, in a manner which would include the "true" population parameter (e.g., the "true" mean) 100(1-α)% of the time if the same experiment and analysis were conducted repeatedly <span style="font-style: italic;">ad infinitum</span>. It is a region which, so calculated, would include the true population parameter in 95% of all hypothetically repeated identical experiments. Thus, the population parameter of interest is fixed (i.e., a "true" value exists), and the interval is random (because it is based on a randomized experiment).<br /><br />A frequentist confidence interval is <span style="font-style: italic;">not</span> an interval which we are 100(1-α)% certain contains the true parameter. I don't even know what this statement (i.e., 95% certain) means -- what is "certainty"?<br /><br />A 95% Bayesian credible interval (a.k.a. Bayesian confidence interval) is the a continuous subset (i.e., an interval) of a <span style="font-style: italic;">posterior probability distribution</span> of a parameter of interest (e.g., a mean). A posterior probability distribution is the probability distribution which results from combining of our prior beliefs about the parameter, and a conditional probability distribution of our data, given all possible relevant data sets. It contains all possible values of our parameter of interest (given our priors and our data, and our model). The credible interval is merely an interval which contains a most likely subset. That is, we are not sure what is was while the world turned and our data were collected, but the safest bet is inside the credible interval.<br /><br />Key differences between frequentist and Bayesian statistics:<br /><ul><li><span style="font-weight: bold;">Parameter of interest</span> (e.g., a mean): fixed (the Platonic archetype exists) <span style="font-style: italic;">vs</span>. random (i.e., subject to the whims of the gods of stochasticity)</li><li><span style="font-weight: bold;">Prior beliefs</span>: implicit and sometimes hard to discern vs. explicit and plainly stated.</li><li> <span style="font-weight: bold;">Statements of probability</span>: Pr(data|null) <span style="font-style: italic;">vs</span>. Pr(h|data). That is, frequentist P-values are the probability of observing your data (or more extreme data) given that the null hypothesis is true, whereas Bayes posterior probability distributions describe the probability of your scientific hypothesis (not the null), given that your data are true.</li><li><span style="font-weight: bold;">"P-values"</span>: Exist <span style="font-style: italic;">vs</span>. not typically presented (usually misinterpreted; Fisher used it as a "weight of evidence," whereas Neyman used it as a basis to make decisions (yes/no) but not necessarily true/false - I do not understand how or why they can do all that; in the Bayesian context, it is not always clear what such a beast would be because of differences in underlying interpretations).</li></ul><br /><span style="font-style: italic;">My problem is that I do not have an intuition about how these things all differ or under what conditions they are likely to differ substantially. Therefore, I cannot keep them clearly differentiated in my head. All I can do is repeat them.</span> <span style="font-style: italic; font-weight: bold;">It would help to explore the pathological cases where frequentist and Bayesian methods result in very different outcomes differ strongly.</span><br /><br />1. http://en.wikipedia.org/wiki/P-value#Frequent_misunderstandings<br />2. http://www.jerrydallal.com/LHSP/pval.htmAnonymoushttp://www.blogger.com/profile/09945759958857785273noreply@blogger.com1