# 2019 NCAA Tournament Lesson #3: Over-Population & Lotka-Volterra, cont'd.

Updated: Jun 4, 2019

by Jess Behrens

*© 2005-2019 Jess Behrens, All Rights Reserved*

Continuing from the previous post, the figures included below show the remaining species' Lotka-Volterra plots based on the 20,000 EGT simulations.

Figure 1. Dove-Owls vs. Owls, Lotka-Volterra Equations, NCAA Tournament 2005-2019

Figure 1 shows the binary isoclines for Dove-Owls & Owls. The shape, as was the case for the Hawks & Owls, corresponds to scenario 2 on the __UT__ website. The Owls are dominating the Dove-Owls &, as far as the simulations are concerned, are pushing the Dove-Owls to extinction. Three tournament years, 2012, 2013, & 2018 are all above the Owl isocline, indicating that Owls are overpopulated. Of course, all 15 years are above the Dove-Owl isocline with respect to Owls.

**When you consider the upsets that occurred in those years (two 2 seeds & a 4 seed in 2012; a 2 seed, 3 seed, & a 4 seed in 2013; & a 1 seed & two 4 seeds in 2018), it's tempting to consider that perhaps owl over-population might be part of the reason.** While none of those high seeds who lost are Owls (they're all doves & dove-owls), the way in which the indexes I use to construct these networks function suggest that this is possible. **Consider the tournament a box, with limited space for all of the teams, or in this metaphor childrens letter blocks. When too many of a given archetype are included, at least one of them is squeezed out for lack of room (overpopulation). I'm not going to show you the math behind my indexes, but that is effectively what is happening. **

There is definitely more than just Owl overpopulation involved, however, given that 2016 & 2015 also included at least two upsets of teams seeded 4 or higher, with 2016 having having three & 2015 __a stripped 3 point attempt__ from possibly 3 as well. Those two years fall between the two isoclines, however 2015 is almost right on the Hawk isocline.

Figure 2. Dove-Owls vs. Doves, Lotka-Volterra Equations, NCAA Tournament 2005-2019

Figure 2, which also corresponds to scenario 2 on the __UT__ website, again shows that the Dove-Owls are being dominated within the EGT simulations, this time by the Doves. **In fact, all of the other species are energetically dominating the Dove-Owls. Furthermore, only one tournament, 2017, falls between the two isoclines, echoing my previous point that the tournament, specifically the early rounds, is driven by the over-population of the weaker EGT species.**

Figure 3. Doves vs. Owls, Lotka-Volterra Equations, NCAA Tournament 2005-2019

Of all the plots, Figure 3 is the most unique. **Like the Hawk/Dove plot, Figure 3 is an equilibrium, but unlike the Hawks/Doves is unstable. Tournament years that fall above the point where the two isoclines cross, but between the two lines, will be pushed up and to the left (Owl dominance). Those that fall in the small corner below and between the two lines will be pushed down & to the right (Dove dominance). Thus, as far as the EGT simulations are concerned, there are some very rare scenarios in which a year with very few Owls could result in their extinction. ** None of the tournament years 2005-2019 are anywhere near that portion of the plot, however. In fact, all 15 tournaments are above both isoclines, meaning that both Owls & Doves are overpopulated with respect to each other. Of course, this adds to the ongoing narrative that the early rounds of the tournament are effectively a 'die-off' event.

I hope the last two posts have demonstrated that Lotka-Volterra can provide some clues about how the tournament functions as a community of interacting species' archetypes. They point to some clues about unique aspects of several of the tournaments. Next, I will consider the seaborn 'clustermaps' for definitive evidence of these and other patterns.

#KeyPlayer #LotkaVolterra #PredatorPrey #EvolutionaryGameTheory #basketball #NCAA #MensCollegeBasketball #NetworkAnalysis #SpeciesFitnessPlots #MonteCarloSimulations #SpeciesCompetitionPlots #Matplotlib