Chaos Theory
What is a paradoxical term for Chaos Theory?
Deterministic Chaos
Cause an unpredictably large impact given a long frame of time
What is the relationship between the uncertainty of a chaotic system and time?
It increases exponentially with respect to time
Can chaotic systems be fractal?
Yes
Define adaptationism
environmental adaptation driven by natural selection
What are dynamical systems highly sensitive to?
Initial Conditions/Change in Initial Conditions
Why does the butterfly effect ensure that no matter how much data is collected and analyzed, long-range weather forecasting will always have fundamental limitations?
chaotic systems are nonlinear and thus small variations in starting conditions grow exponentially with respect to time
A meaningful predication may only be made within how many Lyapunov times?
What is the defining trait of a fractal?
Fractals are self similar on all scales
Given the deterministic chaos nature of macroevolution are we able to predict macroevolution of the far future, or simply of the near future?
Near future
What separates a Dynamical system from a Chaotic systems?
A dynamical system changes over time with respect to a set of rules, while a chaotic system is a dynamical system, where the system is highly sensitive to initial conditions
Which scientist/meteorologist discovered that a simple model of heat convection posses a natural and intrinsic unpredictability?
Edward Norton Lorenz/Edward Lorenz/Lorenz
Angle and Velocity
Are phylogenetic trees fractal?
Yes
To show how North American tree taxa reached their respective present positions after the glaciers retreated at the end of the last ice age, what did palaeoecologist Margaret Davis use to create the map?
fossilised tree pollen from lake and peat sediments
Is the one dimensional logistic map x->4x(1-x) chaotic everywhere? not at all? or partially?
It is chaotic everywhere
What modification was made to the weather simulation that caused it to produce an entirely different simulation? (Double points if give the exact values)
Rounding a value from 0.506127 to 0.506
In a spectrum of Lyapunov exponents, what does the maximal Lyapunov exponent determine?
a notion of predictability in a dynamic system
Is the butterfly effect a fractal?
no, the lorenz attractor model that usually demonstrates the butterfly effect is
What did palaeoecologist Margaret Davis's research conclude?
species show no predictable response to climate change, and respond individually rather than as communities of species.
What three things is the amount of time for which you can determine the behavior of a chaotic system dependent on? (100 points for 1/3, 300 points for 2/3)
Tolerance of uncertainty, accuracy to which the current state can be measured to, and timescale dependent on the dynamics of the system.
Given that the butterfly effect is highly sensitivity to initial conditions, what might counteract this inherent unpredictability and create a semblance of stability over time?
Constraining mechanisms like attractors or negative feedback loops constrains chaos and guides it toward structured and stable patterns
The formula for Rate of divergence of two trajectories in a phase space? some variables you may want to use are delta (lowercased), absolute value, approximately equal to, euler's number, and lambda
|δ Z(t)| ≈ e^(λt|δ Z_0|)
Given a chaotic systems, that exhibit strange attractors, where does the evolution of the system map to?
The chaotic system has a fractal state space structure, thus the evolution of the system maps to points on the fractal
What is another proposal for the cause of Macroevolution? give one reason that proves this
The real source of Macroevolution lies in the chaotic dynamics between genotypes and phenotypes.
The relationship is chaotic/non-linear, mutation is highly sensitive to initial conditions, polygenetic trees are self-similar/fractal in nature