In this deterministic cellular automata model, interactions between neighboring automata are described using a prisoner's dilemma. Limiting dispersal of seeds of annual plants can permit heterogeneous co-existence, whereas thorough mixing instead allows one subpopulation to dominate quickly.

In the five parts of this video, we define the derivative and then build a cribsheet of rules for expressing the slopes of simple functions and combinations of functions. These include the power rule, the chain rule, the product and quotient rules, and the rules for differentiating sinusoidal functions.

In the first video segment, we analyze the population dynamics for a test-tube of cells that affect each others' likelihoods of replication when they collide. The particular example we use is a prisoner's dilemma, which has the almost paradoxical property that survival of the relatively most fit leads overall fitness to decrease. In the second video segment, we suggest that the population dynamics from the first segment can be related to an analysis that uses payoff matrices found in traditional game theory.

In the first video segment, we present a cartoon model of a weighted chain, which can be regarded as an approximation for a polymer under tension (e.g. a strand of DNA being stretched out using optical tweezers). The Hamiltonian and partition function for this system are described in the second segment. Finally, in the third segment, we calculate the average energy and elongation of the chain.

We use eigenvector-eigenvalue analysis to walk through a simple quasispecies model described in Bull, Meyers, and Lachmann, "Quasispecies made simple," PLoS Comp Biol, 1(6):e61 (2005). The dominance of a genotype depends, not merely on its ability to breed quickly (i.e. the rudimentary concept of survival of the fittest), but also on its ability to breed "true."

In a toy model of a cell, protein X is produced according to a translation rate coefficient and eliminated according to a degradation rate coefficient. The protein copy number at which the rates for these processes balance is called the steady-state level, and the time it takes for a cell initially containing zero copies of protein X to accumulate half the steady-state level is called the _ŃŇrise time._ѝ Surprisingly, the "rise time" depends on the degradation rate coefficient only. The classic textbook presentation of this topic is found in Alon, An Introduction to Systems Biology: Design Principles of Biological Circuits, Boca Raton: Chapman & Hall/CRC, 2007 (p. 18-22).

In the first video segment, we describe the fundamental postulate of statistical mechanics. The direct product notation we introduce in the second segment helps us to discuss the states available to a collection of many parts, which helps us, in turn, to derive the Boltzmann factor in the third segment. The fourth video segment explains how the Boltzmann factor helps us to calculate average properties for systems in thermal contact with large baths and introduces entropy (Greek letter sigma), free energy (F), and the partition function (Z).