Meeting 5 (November 29, 2007)

Discussion facilitator -- Dr. Gabriel Huerta

At the next meeting, Professor Huerta in the stat program is leading the discussion! Here is the paper he selected: Hierarchical spatiotemporal matrix models for characterizing invasions. Biometrics 63: 558-567. He also suggested this paper to give you some background in the statistics terminologies and more: Hierarchical Spatial Models. In: Encyclopedia of Geographical Information Science. Springer. In Press.

I hope to see you all there!

Meeting 4 (November 15, 2007)

Discussion Facilitator -- Adam Ringler

Here is the link to the paper Adam selected: Can Biology lead to new theorems? by Sturmfels, published in Clay Biology.
Hope to see you all there!

For anyone wanting some background on phylogenies, here's the link to a pdf file of
Phylogenies: An Overview. (1999).
Holmes S.
IMA series, Statistics and Genetics, 112:81-119 (ed. Halloran and Geisser), Springer Verlag, NY.

Nice slogan from Joel Cohen

I thought this phrase is very nice to have as our group's conceptual goal:

"Mathematics is biology's next microscope, only better; Biology is mathematics' next physics, only better" By Joel Cohen 2004. PLoS Biology 12(12): 2017-2023.

Biologists are interested in using math to advance understanding of biological systems, and mathematicians are interested in using biological problems to advance mathematical techniques. I thought this is a nice slogan to keep in mind for our discussion. I hope that, by discussing math ecology papers, we both gain knowledge to achieve our (different) goals.

Meeting 3 (November 1, 2007)

Discussion Facilitator -- Flor Espinoza

Here is the link to the paper Flor selected: Eames and Keeling. 2002. Modeling dynamic and network heterogeneities in spread of sexually transmitted diseases. PNAS 99: 13330-
Hope to see you all there!

Comments on Kot et al. paper from Dr. Steinberg

Hello all,
Dr. Steinberg was not able to attend our first meeting, but here are his comments on the paper, especially on the mathematics the authors used. Dr. Steinberg's comments

Meeting 2 (October 18, 2007)

Discussion facilitator -- Dr. Helen Wearing

Here is the link to the paper selected by Helen: Eskola and Parvinen 2007. On the mechanistic underpinning of discrete-time population models with Allee effect. Theoretical Population Biology 72: 41-51.
Hope to see you all there!

Post-meeting note: Thanks for people who showed up today! The authors improved an existing model to mechanistically incorporate Allee effects. As opposed to phenomenologically modeling Allee effects, mechanistic parameters have physical meanings and can be measured in the field. They concluded that some sort of mating is necessary to have an Allee effect in their models. Another interesting part of this paper was that the model is a hybrid of continuous and discrete equations (although this paper is not the first one). We had mixed opinions about this paper; the math was not so interesting, and the biology is too simplified?! But the paper was good in the sense that it motivated an interesting discussion!

Meeting 1 (September 27, 2007)

Discussion facilitator -- Etsuko Nonaka
Use of integrodifference equations in modeling spread of organisms; main paper Kot et al. 1996 Ecology (77(7): 2027-2042).
Supplemental readings:

1. Veit and Lewis. 1996. American Naturalist (148(2): 255-274). -- an example of the application of integrodifference equations to invasion of house finch in USA.
   
2. Clark. 1998. American Naturalist (152(2): 204-224). -- another example. Application to migration of trees after glaciation.
   
3. Holmes et al. 1996. Ecology (75(1): 17-29). -- This is not about integrodifference equations, but about partial differential equations in ecology. However, many theories of spatial spread in ecology were developed using PDEs. Integrodifference equations are more recent techniques.
   

Post-meeting notes: We had a good turnout. We discussed the Kot paper for an hour and all felt that the discussion was fruitful (I hope). We left Adam's interesting question about the ecological meaning of the higher order conservation law regarding equation 16 to another opportunity. Also, we were not able to figure out the meaning of Figures 7 and 9 in the paper. If you need things to think about while you are taking a shower or lining up for food, maybe you can think about these things!!!
I forgot to mention this: Clark (1998) simulated tree migration using a truncated kernel, and he observed accelerating spreading rates. Kot et al, in the Discussion, stated that truncated kernels will NOT generate accelerating rate. Discrepancy....