article
Computational complexity of ecological and evolutionary spatial dynamics
published
yes
Rasmus
Ibsen-Jensen
author 3B699956-F248-11E8-B48F-1D18A9856A87
Krishnendu
Chatterjee
author 2E5DCA20-F248-11E8-B48F-1D18A9856A870000-0002-4561-241X
Martin
Nowak
author
KrCh
department
There are deep, yet largely unexplored, connections between computer science and biology. Both disciplines examine how information proliferates in time and space. Central results in computer science describe the complexity of algorithms that solve certain classes of problems. An algorithm is deemed efficient if it can solve a problem in polynomial time, which means the running time of the algorithm is a polynomial function of the length of the input. There are classes of harder problems for which the fastest possible algorithm requires exponential time. Another criterion is the space requirement of the algorithm. There is a crucial distinction between algorithms that can find a solution, verify a solution, or list several distinct solutions in given time and space. The complexity hierarchy that is generated in this way is the foundation of theoretical computer science. Precise complexity results can be notoriously difficult. The famous question whether polynomial time equals nondeterministic polynomial time (i.e., P = NP) is one of the hardest open problems in computer science and all of mathematics. Here, we consider simple processes of ecological and evolutionary spatial dynamics. The basic question is: What is the probability that a new invader (or a new mutant)will take over a resident population?We derive precise complexity results for a variety of scenarios. We therefore show that some fundamental questions in this area cannot be answered by simple equations (assuming that P is not equal to NP).
National Academy of Sciences2015
eng
PNAS
2664456910.1073/pnas.1511366112
1125115636 - 15641
Ibsen-Jensen R, Chatterjee K, Nowak M. 2015. Computational complexity of ecological and evolutionary spatial dynamics. PNAS. 112(51), 15636–15641.
Ibsen-Jensen, Rasmus, Krishnendu Chatterjee, and Martin Nowak. “Computational Complexity of Ecological and Evolutionary Spatial Dynamics.” <i>PNAS</i> 112, no. 51 (2015): 15636–41. <a href="https://doi.org/10.1073/pnas.1511366112">https://doi.org/10.1073/pnas.1511366112</a>.
Ibsen-Jensen, Rasmus, et al. “Computational Complexity of Ecological and Evolutionary Spatial Dynamics.” <i>PNAS</i>, vol. 112, no. 51, National Academy of Sciences, 2015, pp. 15636–41, doi:<a href="https://doi.org/10.1073/pnas.1511366112">10.1073/pnas.1511366112</a>.
R. Ibsen-Jensen, K. Chatterjee, and M. Nowak, “Computational complexity of ecological and evolutionary spatial dynamics,” <i>PNAS</i>, vol. 112, no. 51, pp. 15636–15641, 2015.
Ibsen-Jensen R, Chatterjee K, Nowak M. Computational complexity of ecological and evolutionary spatial dynamics. <i>PNAS</i>. 2015;112(51):15636-15641. doi:<a href="https://doi.org/10.1073/pnas.1511366112">10.1073/pnas.1511366112</a>
R. Ibsen-Jensen, K. Chatterjee, M. Nowak, PNAS 112 (2015) 15636–15641.
Ibsen-Jensen, R., Chatterjee, K., & Nowak, M. (2015). Computational complexity of ecological and evolutionary spatial dynamics. <i>PNAS</i>, <i>112</i>(51), 15636–15641. <a href="https://doi.org/10.1073/pnas.1511366112">https://doi.org/10.1073/pnas.1511366112</a>
15592018-12-11T11:52:43Z2020-08-11T10:09:17Z