If you want to be clever, you can get the filename from the LWP's HTTP::Response and use it as a filename to dump the file.

$browser->follow_link( text_regex => qr/Download as TAB/i );
print $browser->content();  # prints TAB delimited file to STDOUT
[download]

$browser->follow_link( text_regex => qr/Download as TAB/i );
if ( my $filename = $browser->res->filename )
{
    die "file already exists [$filename]" if -e $filename;
    print STDERR "Saving downloaded file to [$filename]\n";
    open my $fh, ">", $filename;
    print $fh $browser->content;
    close $fh;
}
[download]

#!env perl
use strict;
use warnings;
use autodie qw/ open close /;
use 5.012;
use WWW::Mechanize;

# create WWW::Mechanize object
# autocheck 1 checks each request to ensure it was successful
my $browser = WWW::Mechanize->new( autocheck => [1] );

# retrieve page
$browser->get('http://www.ncbi.nlm.nih.gov/Traces/wgs/');

#select form to fill based on mech-dump output
$browser->form_number(1);

# fill field 'term' with name of species
$browser->field( 'term', 'Escherichia' );
$browser->field( 'size', 'all' );


# click apply button
$browser->submit('Apply');

my $url = $browser->uri;
print "url: $url\n";

$browser->follow_link( text_regex => qr/Download as TAB/i );
#print $browser->content();  # prints TAB delimited file to STDOUT

if ( my $filename = $browser->res->filename )
{
    die "file already exists [$filename]" if -e $filename;
    print STDERR "Saving downloaded file to [$filename]\n";
    open my $fh, ">", $filename;
    print $fh $browser->content;
    close $fh;
}
[download]

Spazm, thanks much, especially for the explanations!

Question. If mech-dump doesn't output content of drop down lists, do I always need to look at the page source and, if so, then add the selection as a 'field' entry?

I was just about to suggest mech-dump, good that you are already using it!

Mechanize will only return form elements that are within <form></form> elements.

The "All" dropdown is not within a set of form tags, it directly triggers javascript to reload the page. In cases like this you just have to figure out what the script is doing and duplicate. Possibly just by inspecting the request URL submitted by the browser.

This is an area where scraping pages becomes tedious and tricky.