The expected value of the squared path-difference distance under the Yule model

(By G. Cardona, A. Mir, F. Rosselló)

Supplementary Material

• Computations for all trees with number of leaves up to 7:
  • Python script used to compute all pairs of trees and find the exact value for the expected value of the squared path-difference distance. It uses the package phylonetwork.
  • Results given by the script:

    .	n	Exact Value	Experiments	Error
    .	3	1.33333333333	1.33333333333	0%
    .	4	7.40740740741	7.40740740741	0%
    .	5	21.5333333333	21.5333333333	0%
    .	6	46.6346666666	46.6346666666	0%
    .	7	85.2546031746	85.2546031746	0%

• Computations for random trees with number of leaves 10,20,...,100:
  • Python script used to compute random pairs of trees under the Yule model and find approximations to the expected value of the squared path-difference distance. It uses the package phylonetwork.
  • Results given by the script:

    .	n	Exact Value	Experiments	Error
    .	10	303.132	303.20875	0.03%
    .	20	2567.04	2567.01	0.00%
    .	30	7882.72	7785.4033	-1.23%
    .	40	16804.5	16682.484	-0.73%
    .	50	29694.5	30003.07	1.04%
    .	60	46818.3	46432.803	-0.82%
    .	70	68384.3	67993.1025	-0.57%
    .	80	94562.8	94191.035	-0.39%
    .	90	125498	123574.185	-1.53%
    .	100	161314	159282.4167	-1.26%