Contributions to nonstationary community theory

Figures & data

Table

Notation	Explanation
$N_{s,t}$	Nt for species 1 in the lottery model started at time s, generally with Ns, s fixed as s changes.
$N_{j,s,t}$	As for $N_{s,t}$ but now not necessarily species 1, with j identifying the species.
rt(n)	$Z_{t+1}-Z_t=r_{1,t}\left(n\right),\text{ for }{N}_{1,t}=n$.
{τs,n}	Finite sequence in n. Times τ at which Ns(τ) ≥ c for s ≤ τ ≤ t.
	Formal definition:
	${{\tau }_{s,}}_0=s.(\text{Assume throughout that}{N}_s\in [c,1-c\left]\right).$	(A16)
	${\tau }_{s,n+1}=min\left\{\tau \right|{\tau }_{s,n}<\tau \le t,N_{s,\tau }\ge c\}.$	(A17)
	Leave τs,n+1 undefined if the set on the RHS is empty.
	Notational variations: add a subscript for species if wanting to deal with both species simultaneously. Drop the subscript s if s is understood.
$\left\{{\tau }_{j,s,n}^{\ast }\right\}$	Finite sequence in n. Defines successive intervals of time, starting at s, where cumulative low density growth is at least ψ.
	Formal definition
	${\tau }_{i,s,0}^{\ast }=s.$	(A18)
	${\tau }_{j,s,n+1}^{\ast }=min\left\{\tau |{\tau }_{j,s,n}^{\ast }<\tau \le t,\sum _{u={\tau }_{j,s,n}^{\ast }}^{\tau -1}{r}_{j,u}\left(c\right)\ge \psi \right\}.$	(A19)
	Leave undefined if the set on the RHS is empty.
	Notational variations: as for {τs,n}.