Question

Given the distance matrix in the table below, construct a parsimonious tree. Species 1 Species 2 Species 3 Species 4 Species 5 Species 6 Species 7 Species 1 11 18 2 19 17 3 Species 2 11 17 9 18 19 10 Species 3 18 17 18 2 4 17 Species 4 2 9 18 20 5 4 Species 5 19 18 2 20 7 17 Species 6 17 19 4 5 7 21 Species 7 3 10 17 4 17 21

Can someone please show me the solution to this problem? Thanks.

Answer 1

first, remember that this is a distance matrix showing the "distance" between the species, this distance is a difference in characters, that can be phenotypic or genetic among others.
Thas why S1 -S1 = 0, S2-S2 = 0 and so on, as they are at 0 distance between themselves. Also, remember that you only need the data on either side of the 0 diagonal so you can choose one side to work

Now to know how to pair up the species, one way to start is looking for the closest related species:

S1 - S4 = 2

S3- S5 = 2

this means:

-s1 -S3 C C S4 -S5

and now that you have paireded them yo can treat them as a single unit S1S4 and S3S5 now you check the distances to these groups, for example

S1 - S2 = 11
S4 - S2 = 2
you sum and take the average.
S1S4 - S2 = 13/2 = 6.5
and you do the same whit the rest: ( filling the rest normally)

	S1S4	S2	S3	S5	S6	S7
S1S4	0	6.5	(18+18)/2 =18	(19+20)/2=19.5	(17+5)/2=11	(3+4)/2 = 3.5
S2		0	17	18	19	10
S3			0	2	4	17
S5				0	7	17
S6					0	21
S7						0

once you are done whit S1S4, you add S3S5 in the same manner, ( in here you use the values of the previous table)
S1S4 - S6 =11
S1S4 - S3S5 = (18+19.5)/2 = 18.75

	S1S4	S3S5	S2	S6	S7
S1S4	0	18.75	6.5	11	3.5
S3S5		0	17.5	6.5	17
S2			0	19	10
S6				0	21
S7					0

Now you can start linking again, knowing that the closest to S1S4 is S7

-s1 _S4 -S7

and again a new table. again using the previus one

S1S4S7 - S3S5 = (18.75 + 17)/2 = 17.875
S1S4S7 - S6 = (11 + 21)/2 = 16

	S1S4S7	S3S5	S2	S6
S1S4S7	0	17.875	8.25	16
S3S5		0	17.5	6.5
S2			0	19
S6				0

this suggests a new link between S3S5 to S6,

-s1 S4 -S7 -S3 S5 -S6

and again a new table. again using the previous one

S3S5S6 - S3S5S6= (17.875 + 16)/2 = 16.9

	S1S4S7	S3S5S6	S2
S1S4S7	0	16.9	8.25
S3S5S6		0	18.25
S2			0

this suggests a new link between S1S4S7 to S2,

-s1 54 -S7 s2 -s3 s5 s6

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