How closely do real biological systems fit How closely do real biological systems fit these ideal fractal networks of West, these ideal fractal networks of West,

Brown, and Enquist?Brown, and Enquist?

or… great moments in or… great moments in scientific discourse as read by scientific discourse as read by

childrenchildren

Self similar

Slap fight

What is the subject of “size invariant?” (capillaries or service volume?)

What is the definition of “service volume?”

How do they affect the derivation?

Yes.

WBE TheoryWBE TheoryAccording to W, B & EAccording to W, B & E

Assumes:

(1) a space-filling network that branches hierarchically to supply all parts of the 3-dimensional body

(2) body-size invariant terminal units (capillaries/petioles)

(3) Minimization of the energy and time required to distribute resources

WBE Theory AssumptionsWBE Theory Assumptions

• Βk = rk+1/γk = lk+1/lk

• Βk; scale factor for vessel radius• γk; scale factor for vessel length

• Assumption; neither Β nor γ depend on k.

(1)

(2)

K&K ProblemsK&K ProblemsBWEBWE

K&KK&K

K&KK&K

BWEBWE

K&KK&K

K&KK&K