You need to change:

        for my $size (@sizeOfTrees) {
            my $quant = $tree_collection{$years}{$trees}{$size} || "-"
+;
            printf "%9s", "$quant";

            # { no warnings; $total += $quant; }    # WHY DO I NEED TH
+IS?
        }
[download]

To:

        for my $size (@sizeOfTrees) {
            my $quant = $tree_collection{$years}{$trees}{$size} || 0;
            printf "%9s", $quant || '-';

            $total += $quant;
        }
[download]

my $quantity        = ();
my $total_quantity  = ();

    my $total      = ();
    my $year_total = ();
[download]

Why are you trying to assign a list to a scalar variable?    Don't do that, it makes no sense!

            printf "%9s", "$quant";
        printf "%5s", "$total";
        printf "%9s", "$total_col{$i}";
    printf "%5s", "$year_total";
[download]

Don't quote scalar variables.    Perl is not a shell!    What's wrong with always quoting "$vars"?