I have an ODE system that increases in size according to the rules

n = 5;
T = 50;
nu = 0.05;
vars = Table[Subscript[x, j][t], {i, n}, {j, i}];
eqns = Table[{Subscript[x, j]'[t] == 
    Subscript[x, j][
      t] (1 - Subscript[x, j][t] - 
       nu (Sum[ Subscript[x, k][t] Boole[k != j], {k, i}]) ), 
   Subscript[x, j][0] == 
    If[j == 1 && i == 1, 0.7, 
     If[j == i, 
      0.01 Subscript[x, RandomInteger[{1, j - 1}]][t] /. t -> T, 
      Subscript[x, j][t] /. t -> T]]}, {i, n}, {j, i}]

This code solve the system of according with interpolation structure

{{x1},{x1,x2},{x1,x2,x3},{x1,x2,x3,x4,},{x1,x2,x3,x4,x5}}

I'm having trouble building the initial conditions, present in the code above

 Subscript[x, j][0] == 
        If[j == 1 && i == 1, 0.7, 
         If[j == i, 
          0.01 Subscript[x, RandomInteger[{1, j - 1}]][t] /. t -> T, 
          Subscript[x, j][t] /. t -> T]]

Where the first initial condition {x1[0]=0.7}

The next {x1[0]=x1[Last time in j past],x2[0]=[Last time in j past]}

.

.

.

{{x1[0]=[Last time in j past],x2[0]=x2[Last time in j past],x3[0]==x3[Last time in j past],x4[0]=x4[Last time in j past],x5=0.01xSubscript[RandomInteger[1,j-1]][Last time in j past]}

can anybody help me?