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Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.
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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm
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Computational complexity of ecological and evolutionary spatial dynamics.

Rasmus Ibsen-Jensen1, Krishnendu Chatterjee2, Martin A Nowak3

  • 1Institute of Science and Technology Austria, A-3400 Klosterneuburg, Austria; ribsen@ist.ac.at.

Proceedings of the National Academy of Sciences of the United States of America
|December 9, 2015
PubMed
Summary
This summary is machine-generated.

Computer science complexity theory meets ecological dynamics. We show that fundamental questions in population dynamics, like invasion probability, are computationally complex, potentially unanswerable by simple equations if P is not equal to NP.

Keywords:
complexity classesevolutionary gamesfixation probability

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Area of Science:

  • Interdisciplinary research bridging theoretical computer science and ecological/evolutionary dynamics.

Background:

  • Computer science classifies problem difficulty using algorithm efficiency (time/space complexity).
  • Key concepts include polynomial time, exponential time, and the P versus NP problem.
  • Ecological and evolutionary dynamics involve spatial processes and population changes.

Purpose of the Study:

  • To explore the computational complexity of fundamental questions in ecological and evolutionary spatial dynamics.
  • To determine the probability of a new invader or mutant taking over a resident population.
  • To investigate if these ecological questions can be answered with simple equations.

Main Methods:

  • Analysis of simple spatial dynamics processes in ecology and evolution.
  • Derivation of precise computational complexity results for various scenarios.
  • Application of theoretical computer science concepts to biological problems.

Main Results:

  • Precise complexity results were derived for invasion dynamics in ecological and evolutionary scenarios.
  • Certain fundamental questions in this area were shown to be computationally hard.
  • These questions may not be solvable by simple equations, contingent on the P vs. NP problem.

Conclusions:

  • There are deep, unexplored connections between computer science complexity and biological dynamics.
  • Computational complexity provides a framework for understanding the limits of predictability in ecological systems.
  • The study highlights the potential intractability of certain biological questions, similar to unsolved problems in computer science.