Natural selection among tumor cell clones is thought to produce hallmark properties of malignancy. Efforts to understand evolution of one such hallmark—the angiogenic switch—has suggested that selection for angiogenesis can “run away” and generate a hypertumor, a form of evolutionary suicide by extreme vascular hypo- or hyperplasia. This phenomenon is predicted by models of tumor angiogenesis studied with the techniques of adaptive dynamics. These techniques also predict that selection drives tumor proliferative potential towards an evolutionarily stable strategy (ESS) that is also convergence-stable. However, adaptive dynamics are predicated on two key assumptions: (i) no more than two distinct clones or evolutionary strategies can exist in the tumor at any given time; and (ii) mutations cause small phenotypic changes. Here we show, using a stochastic simulation, that relaxation of these assumptions has no effect on the predictions of adaptive dynamics in this case. In particular, selection drives proliferative potential towards, and angiogenic potential away from, their respective ESSs. However, these simulations also show that tumor behavior is highly contingent on mutational history, particularly for angiogenesis. Individual tumors frequently grow to lethal size before the evolutionary endpoint is approached. In fact, most tumor dynamics are predicted to be in the evolutionarily transient regime throughout their natural history, so that clinically, the ESS is often largely irrelevant. In addition, we show that clonal diversity as measured by the Shannon Information Index correlates with the speed of approach to the evolutionary endpoint. This observation dovetails with results showing that clonal diversity in Barrett's esophagus predicts progression to malignancy.

Signaling cascades proliferate signals received on the cell membrane to the nucleus. While noise filtering, ultra-sensitive switches, and signal amplification have all been shown to be features of such signaling cascades, it is not understood why cascades typically show three or four layers. Using singular perturbation theory, Michaelis-Menten type equations are derived for open enzymatic systems. Cascading these equations we demonstrate that the output signal as a function of time becomes sigmoidal with the addition of more layers. Furthermore, it is shown that the activation time will speed up to a point, after which more layers become superfluous. It is shown that three layers create a reliable sigmoidal response progress curve from a wide variety of time-dependent signaling inputs arriving at the cell membrane, suggesting the evolutionary benefit of the observed cascades.

Background: Long-lived marine megavertebrates (e.g. sharks, turtles, mammals, and seabirds) are inherently vulnerable to anthropogenic mortality. Although some mathematical models have been applied successfully to manage these animals, more detailed treatments are often needed to assess potential drivers of population dynamics. In particular, factors such as age-structure, density-dependent feedbacks on reproduction, and demographic stochasticity are important for understanding population trends, but are often difficult to assess. Lemon sharks (Negaprion brevirostris) have a pelagic adult phase that makes them logistically difficult to study. However, juveniles use coastal nursery areas where their densities can be high.

Results: We use a stage-structured, Markov-chain stochastic model to describe lemon shark population dynamics from a 17-year longitudinal dataset at a coastal nursery area at Bimini, Bahamas. We found that the interaction between delayed breeding, density-dependence, and demographic stochasticity accounts for 33 to 49% of the variance in population size.

Conclusions: Demographic stochasticity contributed all random effects in this model, suggesting that the existence of unmodeled environmental factors may be driving the majority of interannual population fluctuations. In addition, we are able to use our model to estimate the natural mortality rate of older age classes of lemon sharks that are difficult to study. Further, we use our model to examine what effect the length of a time series plays on deciphering ecological patterns. We find that—even with a relatively long time series—our sampling still misses important rare events. Our approach can be used more broadly to infer population dynamics of other large vertebrates in which age structure and demographic stochasticity are important.