This looks like a Lotka-Volterra competition model with weak, symmetric interspecific competition.  If I understand correctly, you want to build up a community by introducing new species every `T=50` time steps, where the new species has initial density of 0.01 times one of the existing species.

Call me old-fashioned, but I think this is easiest to understand when handled in an iterative `Do` loop:

    nmax = 5; (* max number of species *)
    T = 50; (* period *)
    nu = 0.05; (* interspecific competition coefficient *)

    (* set up unknown vars and differential equations, for n species *)

    vars := Table[Subscript[x, j], {j, n}];
    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, n}]))
    , {j, n}];

    (* initial ICs *)
    ics = {Subscript[x, 1][0] == 0.7};

    (* main loop *)
    Do[
      (* solve for n species *)
      sol[n] = NDSolve[{eqns, ics}, vars, {t, 0, T}][[1]];
      (* plot dynamics *)
      Print[Plot[Evaluate[Table[Subscript[x, j][t], {j, n}] /. sol[n]], {t, 0, T}, PlotRange -> {0, All}]];

      (* set up ICs for n=n+1 species *)
      ics = Join[
        Table[Subscript[x, j][0] == Evaluate[Subscript[x, j][T] /. sol[n]], {j, n}],
        {Subscript[x, n + 1][0] == Evaluate[0.01 Subscript[x, RandomInteger[{1, n}]][T] /. sol[n]]}
       ];
    , {n, nmax}]

![Mathematica graphics](https://i.sstatic.net/qS3Zl.png)
![Mathematica graphics](https://i.sstatic.net/YI1yS.png)
![Mathematica graphics](https://i.sstatic.net/9OiJ3.png)
![Mathematica graphics](https://i.sstatic.net/6nvyR.png)
![Mathematica graphics](https://i.sstatic.net/bc4bc.png)

Not sure how interesting this is, since I believe this symmetric LV system has a globally stable equilibrium at $x_i=1/(1-(n-1)nu)$ as long as $0<nu<1$, but you could use this as a basis for more interesting explorations of community assembly.