Gambler's Ruin
Gambler's Ruin is a Monte Carlo software simulation based on the theoretical outline for the evolutionary Gambler's Ruin problem presented in Chapter 3 of David Raup's (1992) Extinction: Bad Genes or Bad Luck?*. The simulation follows the fate of a set of initial species through a predetermined number of discrete epochs. The simulation begins with the setting of just four parameters: the number of starting species, the number of discrete epochs (length of the simulation), the constant probability of extinction for each species at each step, and the constant probability of speciation for each species at each step. At each subsequent epoch (step), each independent species may persist, speciate into two descendant species, or terminate in extinction. Because the behavior of each simulation run is stochastic and not determinate, it is most meaningful to examine the median or modal behavior of multiple simulation runs for each parametric set.
This simulation is useful in demonstrating that a purely probabilistic model (with no selection/adaptation) evidences:
1) the inevitability of extinction of any species or descendant clade over an indefinitely large number of epochs,
2) the strong tendency for all surviving species to be the cladal descendants of a single initial species, and
3) the occurrence of patterns resembling relatively abrupt mass extinctions and radiations.
The simulation is particularly useful as a demonstration that common descent does not require selection. This is NOT an argument against the ubiquity or centrality of natural selection as an evolutionary mechanism. Although common descent does not require natural selection, adaptation certainly does.
Gambler's Ruin is currently written in VisualBasic. A Java version is under development for free distribution.
* Raup, Davd M. 1992. Extinction: Bad Genes or Bad Luck? New York. W.W. Norton & Co.
A Gambler's Ruin Laboratory Exercise for Introductory Biology
In today's second exercise, we are going to make use of a computer simulation called "Gambler's Ruin". The expression "gambler's ruin" refers to the fact that, in any game of chance, even if your chances of winning and losing are exactly even, if you participate long enough, you will eventually go broke. This may seem counterintuitive, but it is true. For a species, going broke means becoming extinct, and a gambler's ruin model correctly predicts that every species eventually goes extinct. The best long-term estimate from the fossil record suggest that about 10 million years is the average lifespan for a species.
This particular simulation traces the fates of up to 100 initial species and their descendants. A starting species and its descendants are collectively referred to as a clade. These clades are traced through up to 500 evolutionary "epochs" or discrete steps. At each step a species may speciate (turn into two descendant species), become extinct (turn into no descendant species), or simply persist (remain a single species). If at any point all of the species within a clade become extinct, then the clade itself is extinct and is eliminated from subsequent evolutionary epochs. Extinction and speciation are modeled as purely random events, wth fixed probabilities specified at the start of the simulation. This simulation is very minimalist in that it makes no provisions whatsoever for fitness or natural selection; it in fact provides the "null case" for selection. The interesting thing about this simulation is the number of general phenomena from the history of life on earth that it successfully mimics through purely random processes.
Because the output of this simulation is largely governed by probabilities, no two executions of the simulation will produce exactly the same result, even if the starting conditions are the same. One run may start with ten clades, proceed through 100 epochs, and end with five surviving clades. The very next run may start with ten clades under exactly the same specified conditions, and end with no surviving clades after only 10 epochs. For this reason the best way to use this simulation is to run the simulation repeatedly under identical starting conditions and look at the most common (modal) or central (median) outcome. Probabilistic simulations which have to be run many times to assess their behavior are called "Monte Carlo" simulations, named after the famous casinos of Monte Carlo.
Simulation 1 - Probability of survival of a single clade
1) Find the Gambler's Ruin icon on the desktop and double-click on it to start the simulation. This simulation is "line-driven" meaning you have to type in choices rather that just clicking on them. To proceed with hit the "s" key followed by the return key.
2) From the next menu choose P for "parameters". The computer will then prompt you for the conditions or parameters of the simulation, in each case providing you with the range of acceptable values. Enter the following values:
number of original species (clades): 1
number of epochs for simulation: 5
probability of speciation each epoch: .1
probability of extinction each epoch: .1
If the values printed out are correct enter y, otherwise enter n, then reenter the values.
3) What do you think the probability is that your staring clade will survive the five evolutionary steps under these conditions? Remember that probabilities are numbers between 1 (sure thing) and 0 (no way). Enter this number in the table below.
4) Hit return to get back to the main menu. On the main menu enter e for execute. The computer will rapidly plot an unside-down evolutionary "tree" representing the results of the simulation. Branch points are speciations, and dead ends are extinctions. Hitting the return key once produces a page which sumarizes and your results so far in terms of how many clades survived the 5 epochs of evolution (1 or 0). Hit return several more times. The screen will cycle between the "main menu", the results of a single new "run" of the simulation and the cumulative results of all of the runs so far.
5) Accumulate 10 runs by this method. Now when the "main menu" page comes up, enter m for multiple runs. to the prompt for the number of runs enter 40. The program will now rapidly cycle through the simulation 40 more times and stop on the cumulative results page.
6) Look closely at this final plot. For what proportion of the 50 runs did your starting clade survive? This corresponds to your measured probability of survival for any single run. Record this number in the table below.
7) Hit the return key once. then choose p from main menu. Enter the following values:
number of original species (clades): 1
number of epochs for simulation: 20
probability of speciation each epoch: .1
probability of extinction each epoch: .1
Notice that these are the same as before except that you are extending each simulation out to 20 epochs or steps. Again, make a preliminary guess as to the probability of survival of your clade and enter it in the table below. Now hit return, choose m, specify 50 runs, then hit return again and let the computer cycle through the simulation 50 times.
Did extending each simulation to 20 steps increase or reduce the probability of survival of the original clade? Enter this value in the table below.
8) Repeat step 7 three more times, changing "number of epochs" to 80, then 320, after each set of runs, enter the probability of survival in the table below.
Questions:
1) How is the probability of survival of your starting clade related to the length
(number of epochs or steps) of your simulation?
2) What is the long-term probability of survival of a single clade in this "fair" game
of speciation and extinction? In other words, what is the probability of the clade
surviving an infinite number of steps?
3) How good a guesser were you? Did you tend to underestimate or overestimate the
probability of survival of the clade?
probability of survival for a single clade 5 epochs 20 epochs 80 epochs 320 epochs your guess simulation result
Simulation 2 - Common descent as a chance phenomenon
1) On the main menu page choose p , then enter the following values:
number of original species (clades): 10
number of epochs for simulation: 5
probability of speciation each epoch: .1
probability of extinction each epoch: .1
Confirm your values the hit return to get back to the main menu.
2) Before running the simulation, make a guess as to how many of the starting clades are likely to survive. Now enter m, specify 50 runs, and let the computer cycle through the simulation 50 times. Determine the median number of surviving clades. The median is the middle value of the distribution. Enter this value in the table below.
3) Repeat step 2 for simulation lengths of 20, 80, and 320 steps or epochs and enter your guesses and results in the table below.
Questions:
1) How is the median number of surviving clades related to the length (number of epochs
or steps) of your simulation?
2) What is the long-term probability that all species at the end of a simulation will be
the descendants of just one of the starting species?
3) How good a guesser were you? Did you tend to underestimate or overestimate the
median number of surviving clades?
median number of surviving clades 5 epochs 20 epochs 80 epochs 320 epochs your guess simulation result
Punchlines
One of the central aspects of Darwinian evolution is the notion of common descent; that all modern organisms are the surviving descendants of a single common ancestral type of organism. The "man from monkey" corollary of this idea is so disturbing to many people that they reject the Theory of Natural Selection simply because it predicts or implies the unwelcome conclusion of common descent. However, as your Gambler's Ruin simulations revealed, common descent does not require natural selection at all. Common descent is the inevitable result of virtually any long-term process involving speciation and extinction, even if both speciation and extinction are governed entirely by chance.
A mass extinction is the relatively sudden disappearance of all but a few species and a radiation is the rapid fanning out of a few surviving species into many descendants. The mass extinction episodes known from the fossil record are generally assumed to have had precipitating causes, such as really big asteroid impacts. Similarly, radiations are generally assumed to be adaptive radiations where the radiating clade is expressing some traits which make them particularly fit. As the simulations for 320 epochs slowly plotted out, did you see patterns which resembled mass extinctions and radiations, generated by the purely random processes governing this simulation? Are insects, mammals, and flowering plants especially fit or particularly lucky? Where the non-avian dinosaurs sadly unfit or tragically unlucky?