Southern-Summer School on Mathematical Biology

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====== Single species - additional resources ======

===== Lecture =====

  * {{http://200.145.112.249/webcast/20160104a|Video}}
  * {{http://www.ictp-saifr.org/wp-content/uploads/2015/05/lecture_1_16.pdf|Handouts}}

===== Sites =====

  * NIMBioS: National Institute for Mathematical and Biological Synthesis [[http://www.nimbios.org/]]

===== Read More =====

  * Rules of thumb for judging ecological theories, by Ginzburg & Jensen: [[http://www.sciencedirect.com/science/article/pii/S0169534703003495]]
  * The ecological literature, an idea-free distribution, by S. Scheimer: [[http://onlinelibrary.wiley.com/doi/10.1111/ele.12196/full]]. A great editorial on the current state of theory in ecology.
  * My career in Mathematical Biology Profiles from the SMB Newsletter: [[http://www.smb.org/publications/newsletter/bios.shtml]]
  * Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better , Joel Cohen: [[http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.0020439]]
  * Modeling Population Dynamics, lecture notes by Andre de Ross: [[http://staff.science.uva.nl/~aroos/downloads/pdf_readers/syllabus.pdf]]
  * Single-species models for many-species food webs: [[http://www.nature.com/nature/journal/v417/n6888/full/417541a.html]]
  * Edelstein-Keshet, L. Mathematical models in biology. Vol. 46. Siam, 1987. //(a general source, with a good review on Allee effect))//.

==== History and epistemology ====

  * Population dynamics from first principles. Chapter 2 from [[http://press.princeton.edu/titles/7436.html|Complex Population Dynamics]]. Peter Turchin, Princeton Univ Press,  2003.
  * [[http://www.press.uchicago.edu/ucp/books/book/chicago/M/bo3630803.html|Modelling Nature]], Sharon Kingsland, Chicago Univ Press.
==== Second-order ODEs====

Differential equations used to described population dynamics are in general of first order. In the book [[http://books.google.com.br/books?id=9pZfyyRP0ccC&printsec=frontcover&hl=pt-BR&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false|Ecological Orbits]] [[http://life.bio.sunysb.edu/ee/ginzburglab|Lev Ginzburg]] and [[http://www.colyvan.com/|Mark Colyvan]] make a strong point that second-order equations bring out important insights on population dynamics. In a nutshell, they stress that acceleration should be modelled instead of velocities to fully understand how populations growth and decline.

==== Counting individuals ====

Classical models of population dynamics assumes that the size of populations at different times are measurable. Two important issues here are:

==What is an individual?== 
As odd as it may sound, this is a difficult question for a huge proportion of organisms. Therefore defining birth and death is far from trivial. The two best known cases, not mutually exclusive are:

  * Modular organisms, like corals and plants: [[http://www.gbv.de/dms/bs/toc/013555383.pdf|Population Biology and Evolution of clonal organisms]]
  * Clonal organisms, like bacteria and protozoa: [[http://books.google.com.br/books/about/Sex_and_Death_in_Protozoa.html?id=0lCengzqXfsC&redir_esc=y| Sex and Death in Protozoa: the History of an Obsession]], by  [[http://biology.mcgill.ca/faculty/bell/|Graham Bell]].

==What is the size a population?==

In general we do not know the exact size of populations in field or even in lab conditions. The same is true for other demographic parameters, like survival or fecundity. So we have to rely on //estimates// of population parameters. This is a very active topic in ecological statistics. See Chapter I of the book [[https://www.elsevier.com/books/occupancy-estimation-and-modeling/mackenzie/978-0-12-088766-8|Occupancy Estimation and Modeling]] for a nice overview.