i |
Minimum number of competitive reversals separating the
competitive system from a pure hierarchy |
Competitive reversals (see
text) |
Slater, 1961 |
d |
d =
\(\left(\frac{n}{3}\right)-\sum_{i=1}^{n}a_{i}(\frac{a_{i}-1}{2})\)
|
n = the number of species in the
system
ai = row sum of species i in a
competitive outcome matrix
|
Kendall and Babington Smith,
1940 |
ν |
v =
\(\frac{1}{2}||out\left(R\right)-\ <0,1,2,\ldots n-1>||_{1}\)
|
Where
[\(||out\left(R\right)-\ <0,1,2,\ldots n-1>||_{1}\)] is
defined as the sum of absolute differences between row sums of the
n species system and an n-species hierarchy after row sums
of both lists are arranged in ascending order |
Monsuur and Storcken,
1997 |
δ’ |
δ′ = δn\(\frac{(n-1)}{2}\)
|
Where δ is the proportion of
competitive outcomes between a pair of species within a n species
intransitive relationship |
Laird and Schamp, 2018 derived from
Bezembinder, 1981 |
u or a
|
u =
unbeatability
a = always-beatability
|
A species
is unbeatable if it outcompetes every other species in the system
(u = 1) and is always-beatable if it never wins a competitive
interactions (a = 1) |
Laird and Schamp, 2018 |
Δri
|
\(r_{i}=\ \frac{\sum_{j\neq i}^{S}{r_{i}-r_{i,-j}}}{S-1}\) |
S = the number of species in the
system
ri = the growth rate of species
i during an invasion of all S resident
species
ri,-j = the growth rate of species
i during an invasion of the community after the removal of
species j
|
Gallien et al, 2017 |