![]() In the co-evolutionary arms race between a pathogen and a host, pathogens often replicate faster, and therefore can evolve and adapt rapidly, while a host cannot. Co-evolution occurs when close interactions between two or more species affect each other’s selective pressures. Like natural food webs, the immune-tumor community of cell types forms an immune-web of different and identifiable interactions.Įvolution is the change in a population’s heritable traits over time subject to selection pressures through population turnover. The immune system is not just predator-prey. Finally, we propose a way forward to reconcile differences between model predictions and empirical observations. Key processes include “safety in numbers”, resource availability, time delays, interference competition, and immunoediting. ![]() Here we discuss the applicability of predator-prey models in the context of cancer immunology and evaluate possible causes for discrepancies. Standard predator-prey models can show a perpetual cycling in both prey and predator population sizes, while in oncology we see increases in tumor volume and decreases in infiltrating immune cell populations. The second concerns oscillatory dynamics. In standard predator-prey models, the predator relies on the prey for nutrients, while in the tumor microenvironment the predator and prey compete for resources (e.g. The first concerns the conversion of prey killed into predator biomass. However, two aspects of predator-prey type models are not typically observed in immuno-oncology. It allows for evaluation of tumor cell populations that change over time during immunoediting and it also considers how the immune system changes in response to these alterations. This imperfect analogy describes how immune cells (the predators) hunt and kill immunogenic tumor cells (the prey). Tumor-immune interactions are often framed as predator-prey. 4Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, FL, United States.3School of Biochemistry and Immunology, Trinity College Dublin, Dublin, Ireland.Lee Moffitt Cancer Center, Tampa, FL, United States 1EMD Serono, Merck KGaA, Billerica, MA, United States.Though we will not go through the derivations here, you can try them out on your own by replacing these terms with 0 then solving for N prey and N pred, respectively.Irina Kareva 1*† Kimberly A. ![]() In other words, we want to solve for dN pred/dt = 0 and dN prey/dt = 0. For the prey population, we want to find values of predator and prey population sizes at which the prey population remains stable. We will examine these questions by seeking equilibrium solutions to the coupled predator and prey equations we introduced above. Under what conditions will predator and prey populations both persist indefinitely? What will be their population dynamics while they coexist? In other words, will one or both populations stabilize, or will they continue to change over time?.Under what conditions will the predator population die off, leaving the prey population to expand unhindered?.Under what conditions (i.e., parameter values) will the predator population drive the prey to extinction?.We can ask several questions about the interaction between predators and their prey using these equations: Specifically, these equations lead to oscillations between the populations of predators and their prey. In other words, the equation for prey includes a term for N pred and the equation for predators includes the term N prey and changes in one population will always impact the other population. It’s important to note that the prey and predator equations above are coupled equations. R prey = prey per capita rate of increase P = attack rate efficiency (a slope: the change in prey consumed per predator per time as a function of the number of prey) higher search or handling time leads to a lower p In words, the predator population grows according to the attack rate, conversion efficiency, and prey population, minus losses to starvation.ĭN prey/dt = rate of change in prey population (change in number over change in time)ĭN pred/dt = rate of change in predator population (change in number over change in time)Ĭ = rate at which prey are converted into offspring (a slope: predators produced per predator per time as a function of prey consumed per unit time)
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