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The Jacobian tells how the system changes along different state variables (which can be, for instance, the concentrations of the predator and the prey). The Jacobian matrix by itself doesn't give you a lot of intuitive information. However, the eigenvalues of the Jacobian matrix at the equilibrium point tell you the nature of the steady state. For example ...


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Largely an informed guess based on properties of distributions rather than specific knowledge of statistical genetics: a beta distribution is useful for modeling the frequencies of two alleles at one locus. A Dirichelet distribution, which is a multivariate generalization of a beta distribution, would thus be useful for modeling a set of loci. The flip side ...


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I'll throw one more application into the pot. Population dynamics also forms the foundations of population genetics, population ecology, and more recently plays an important role in frameworks such as evolutionary game theory and eco-evolutionary dynamics. Here the models are also used as a type of theoretical exercise or thought experiment (as a previous ...


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There are three seminal works that will give you an excellent grounding in the study of dynamical systems in population biology. The first details the foundations of population genetics: Crow, James F., and Motoo Kimura. An introduction to population genetics theory. (1970). The second deals with population ecology: Maynard-Smith, John. Models in ...


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Unless I am not getting the example you give, it seems to me that there is a classic experiment that does just what you said: the fluctuation test or the luria-delbruck experiment Also, this recent paper from R. Lenski's lab is a good example too. but I am sure there must be others.


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Considering your assumption: I'm just looking at the exponential part, where the simple exponential equation works. If we assume there's sufficient nutrients for bacteria to grow unchecked for a number of hours (more-or-less true in a real culture) In your original model you are using discrete states and fixed time steps. So, if 30 min is one ...


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Real bacteria population will likely reach some carrying capacity that will prevent them to grow exponentially. As a consequence, the exponential model will be a good fit for early growth only but after a while, one will need to use some other model (typically a logistic model). Logistic model Here, I quickly present one standard model of logistic growth ...



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