You will find that gardeners have mixed feelings on eradicating insect pests in the garden. There are some areas of the garden where you spend a lot of time. In these areas you are most likely to notice any type of pest infestation right away. Such places as container plants on the patio, or frequently harvested crops, or plants in the greenhouse or conservatory.
However, in a large garden with shrubs and mature borders in a wild area, or maybe near a pond or a large hedge at the bottom of the garden, you will not be able to see problems in their early stages and therefore, will not be able to deal with every outbreak do not worry too much about pests that appear in mature areas of the garden.
Insect pests, such as aphids, will build up, particularly at certain times of the year, but will rarely become a serious ongoing problem. Generally, once pest numbers reach a certain level, natural predators will be attracted to them as a food source. This will reduce their numbers to a manageable level again.
There are various things that you can do in a garden to attract natural predators, but it is often more a case of not doing anything.
Chances are if you spray your plants you will also be spraying the predators that will eat the pests. The ladybug, lacewings, housefly larvae, parasitic wasps, and small birds such as the titmouse are all such predators that help control pests. Encouraging these species into the garden means refraining from spraying and allowing the aphid population to build up to a level that attracts the predators.
This by no means should be interpreted as doing nothing for a small garden where the infestation can be controlled. Gardens that are very large are hard to maintain and keep up with pests. Many pests will certainly go un-noticed unless it is contained by such predators, or gets to a state where it damages your plants.
Many people shy away from pesticides these days. If you can control your pests by natural means it will certainly be better for the environment as well as your plants.