I’m probably muddling the lines between non-native species, which can be anywhere from harmful to neutral to occasionally beneficial, and invasive species which are pretty universally bad when introduced to a new ecosystem. But the point stands that native species are pretty much always going to be better for their ecosystem than non-native ones. These relationships developed over very long periods of time, and the rate at which we have thrown different species into these mixes is far faster than what nature typically does. This means that those ecosystems aren’t able to adequately adapt to the newcomers, who may be overly aggressive and damaging.

Here, have some relevant links (mostly US-centric):

http://www.invasivespeciesinfo.gov/ – USDA site on invasive species

http://www.invasive.org/ – Center for Invasive Species and Ecosystem Health

https://www.rrisc.org/ – Reduce Risks from Invasive Species Coalition

http://www.bringingnaturehome.net/ – includes info on a really good book on why native species are better for an ecosystem, including your garden, than invasive

Species Portrayed: North American porcupine (Erethizon dorsatum), milk snake (Lampropeltis triangulum), American yellow warbler (Setophaga petechia), Fly agaric (Amanita muscaria), Pacific banana slug (Ariolimax columbianus), Roosevelt elk (Cervus canadensis roosevelti), Steller’s jay (Cyanocitta stelleri), bobcat (Lynx rufus), snowshoe hare (Lepus americanus), Garry oak (Quercus garryana), American robin (Turdus migratorius), American grasshopper (Schistocerca americana), Scotch broom (Cytisus scoparius), garlic mustard (Alliaria petiolata), domestic cat (Felis catus), bull thistle (Cirsium vulgare), domestic goat (Capra aegagrus hircus), dandelion (Taraxacum officinale), gypsy moth (Lymantria dispar), brown rat (Rattus norvegicus), domestic pig (Sus scrofa domesticus), broadleaf plantain (Plantago major), butterfly bush (Buddleia davidii), European starling (Sturnus vulgaris), American bullfrog (Lithobates catesbeianus), northern cardinal (Cardinalis cardinalis), Yunnan Lake newt (Cynops wolterstorffi), kāmaʻo thrush (Myadestes myadestinus), Guam broadbill (Myiagra freycineti), Stephens Island wren (Traversia lyalli), lesser bilby (Macrotis leucura), North Island snipe (Coenocorypha barrierensis), South Island snipe (Coenocorypha iredalei), Jamaican poorwill (Siphonorhis americana), Jamaica petrel (Pterodroma caribbaea), southern pig-footed bandicoot (Chaeropus ecaudatus), northern pig-footed bandicoot (Chaeropus yirratji), Hawaiian tree snail (Achatinella apexfulva), bar-winged rail (Nesoclopeus poecilopterus), American chestnut (Castanea dentata), American elm (Ulmus americana), Fraser fir (Abies fraseri), butternut (Juglans cinerea), English ivy (Hedera helix), kudzu (Pueraria sp.), Japanese honeysuckle (Lonerica japonica), Bradford pear (Pyrus calleryana), pampas grass (includes Cortaderia sp., Erianthus ravennae and Miscanthus sinensis), tree of heaven (Ailanthus altissima), Burmese python (Python bivittatus), red alder (Alnus rubra), Pacific rhododendron (Rhododendron macrophyllum), Solomon’s seal (Polygonatum biflorum), false solomon’s seal (Maianthemum racemosum), Pacific trillium (Trillium ovatum), beach strawberry (Fragaria chiloensis), western sword fern (Polystichum munitum), redwood sorrel (Oxalis oregana), western red cedar (Thuja plicata), salal (Gaultheria shallon)