Seedlings of each of the species were grown at six sites across the country, differing in climate and suitability, to see if they would behave as predicted by the models.
The seedling growth and survival were monitored over two summers and winters, with temperature and precipitation monitored hourly at each site.
Their growth was compared with three closely related native species - the nikau palm, ramarama, or bubble leaf, and seven-finger.
Half of the pest plants were also sprayed with pesticide to find whether its release could influence performance.
As Mrs Sheppard suspected, the field trials backed her modelling, showing that higher minimum temperatures and reduced frosts would provide the alien species with suitable habitats and enable their spread.
"We did expect that, with climate change, such species would benefit - but thanks to the results of the field trials, we can now have higher confidence in such model predictions."
She was further concerned to find how the weeds performed better under a wide range of climate conditions - including the severe drought last summer - than their native counterparts.
"The bangalow palm grows in similar habitats to our native palm, the nikau, and I found in my trials that everywhere it grew, it grew faster and survived better.
"Therefore it is likely to outperform the native species and may displace it in the long term."
Globally, the field trial findings were significant as this was one of the first studies directly testing such models, and put weight behind predictive modelling of such effects of climate change.
"It was all very hypothetical, but now with the studies, we have very clear evidence that they are very likely to become a problem, and it should hopefully translate into management action."
She has provided a report to Auckland Council, which is reviewing its pest management strategy.
Climate scientist Dr Jim Salinger, author of Living in a Warmer World, was not surprised by the results.
He said: "A warmer climate means we have to be much more vigilant about pests and diseases."
Read a recent full report from Niwa on the climate situation here.