Studies of ecology and evolution are often dependent on carefully characterizing the interactions of different organisms. In a natural setting, however, such data collection often proves to be noisy at best and impossible at worst. At the same time, mathematical models in theoretical ecology and evolutionary biology are among the most sophisticated in all of the life sciences. Laboratory-scale experiments on cellular interactions could quantitatively test some of the remarkable predictions and open the way to new theory. A) Among the most elementary interactions in nature is the predator-prey interaction. The prey in this case produces the quorum sensing pathway protein LuxI, which is engineered to drive a transcriptional cascade in the predator that produces CcdA, which inhibits the DNA replication inhibitor CcdB thereby allowing the predators to replicate. Meanwhile the predator produces the quorum sensing pathway protein LasI which activates CcdB in a LasR-dependent manner in the prey. CcdB expression in the prey prevents it from replicating. The cyclic dynamic is very similar in style to genetic oscillators: high levels of prey leads to low levels of CcdB and thus high levels of predator; high levels of predator leads to high levels of CcdB and thus low levels of prey, which subsequently leads to high levels of CcdB in predators, etc. As shown in Balagadde et al.,100 predator-prey interactions can thus result in LIMIT CYCLE OSCILLATIONS about an unstable fixed point of the dynamics, most commonly studied in the framework of the Lotka-Volterra model.
B) Simpson’s paradox is a statistical phenomenon that captures the fact that even if the producer of a common good grows at a slower rate in all given subpopulations than a nonproducer, it can nevertheless make up an increasing fraction of the population as a whole. While Simpson’s paradox usually arises as a result of misinterpretation of data, natural populations can in fact display heterogeneities in sample size that often underlie the paradox. The particular implementation in Chuang et al.102 casts bacteria that generate the autoinducer Rhl as the producer. Both producer and non producers use this Rhl that is rewired to activate synthesis of a chloramphenicol resistance gene catLVA. As shown in the middle panel, in each subpopulation the fraction of producers decreases, but as the bottom panel shows in the global population the fraction of producers actually increases, thus satisfying Simpson’s paradox.
(A, lower portion) is reproduced with permission from
Balagadde FK, Song H, Ozaki J, Collins CH, Barnet M, Arnold FH, Quake SR, You L. A synthetic Escherichia coli predator-prey ecosystem. Mol Syst Biol 4: 187 (2008) © Macmillan Publishing Ltd.
Panel (B) lower subpanels are reproduced from Figure 2a and 2b[add source of top panel] of Chuang et al.
Chuang JS, Rivoire O, Leibler S. Simpson’s paradox in a synthetic microbial system. Science 323(5911): 272–275 (2009)