To farmers on Long Island, the Colorado potato beetle poses a problem as hard as a hoe handle. It's bad enough that this black-striped pest munches on the leaves of potato plants. But perhaps worse, the beetle has developed a resistance to nearly every insecticide farmers have hurled at it.

The result is that growers on Long Island, where problems in corralling the beetle are especially severe, are often forced to spray up to 10 times a season, driving up chemical costs and causing pesticide contamination of ground water. The plight of the potato farmer points up an enduring dilemma that is increasingly threatening world food supplies, public health, and the environment: the ability of pests, from flies to fungi to rodents, to develop immunities to chemicals.

Almost since the turn of the century, farmers around the world have relied on insecticides as a potent weapon in the battle against bugs. But over time many of the enemy - the tobacco budworm, diamondback moth, and cattle tick, for instance - have developed their own genetic armor to blunt man's chemical assaults.

This is contributing to the destruction of some localized crops around the world and, in some cases, to what authorities believe are renewed outbreaks of diseases such as malaria transmitted by insects.

The problem is another parable of the risks and rewards of man's attempt to harness technology to master the environment. Pesticides, to be sure, have made inestimable contributions to world agriculture, to name one benefit. But farmers' dependence on them has exacted a toll. The recent tragedy at a Union Carbide plant in India, involving the leak of a highly toxic gas used in manufacturing pesticides, was one kind of cost. Pest resistance poses a risk of another sort.

That threat to world food supplies and health has bolstered the view of environmentalists and some others that it is time to jump off the ''pesticide treadmill'' and adopt alternative techniques, such as using natural predators, to control pest populations. To others, chemical warfare will remain the best, virtually the only, hope for man in his ongoing battle with bugs for at least several decades. Between these two positions, scientists continue to grope for ways to deal with the chemical conundrum.

''The only sure way to stop resistance is not use a pesticide - but that isn't a viable option at this time,'' says Edward Glass, a professor emeritus at Cornell University.

While the problem of pesticide resistance isn't new, it is believed to be growing in magnitude - and will require more know-how and inventive solutions to cope with it. Underscoring the gravity of concern was a recent meeting in Washington, D.C., of close to 200 scientists from around the world, as well as a new report.

Between 1970 and 1980, the number of harmful insect species immune to one or more pesticides nearly doubled, from 224 to 428, according to the study written by Michael Dover of the Washington-based World Resources Institute and Brian Croft of Oregon State University. Some 200 kinds of fungi, bacteria, and weeds are also now impervious to chemical attack, as are many dangerous rodents.

The implications of this show up on several fronts - one being the damage to crops themselves. Some 25 species of insects that destroy cotton plants in 36 countries, for instance, are now resistant to pesticides. Cotton-growing in southern Texas and northern Mexico was nearly wiped out by pests in the 1960s and '70s. At least 11 kinds of rice insects in Asia resist one or more major chemical groups. In Malaysia, diamondback moths threaten cabbage crops, a local staple.

Health is another concern, particularly in some third-world countries where mice and ''superrats'' have become resistant to chemicals. On farmers' pocketbooks, the impact is felt as growers are forced to use more potent and expensive chemicals more often. One US agricultural expert puts the cost of additional pesticide use due to resistance at $2.4 billion a year worldwide.

''This is one of the most important problems facing agriculture,'' says Dr. George Georghiou, an expert in the field from the University of California-Riverside. ''We have reached the stage where there is agreement that something needs to be done - and done quickly.''

How the problem develops is generally well understood. Some pests targeted for eradication have genetic traits that enable them to survive man's poisonous arsenals. When they reproduce, their offspring retain more of the chemical-resistant traits. For years after the development of DDT and other ''miracle'' chemicals, resistance was no problem. Companies simply came up with new elixirs.

Today, however, brews are more complex to produce - and tougher to manufacture and get approved. ''The easy chemistry has been used up,'' says Mr. Dover of the World Resources Institute.

While many in the science community agree that man won't be able to rely on chemicals alone in the future, the exact paths to pursue continue to stir disagreement. One longstanding alternative sure to grow is ''integrated pest management'' - the use of multiple techniques, such as biological control and pest-resistant plants, in addition to chemicals, to control insects.

This concept will spread as new tools are developed, including genetically engineered insect-resistant crops and more effective chemicals. Another idea is for farmers to use mixtures of chemicals or rotate the use of ones they have. Yet some scientists doubt this will work for long, since insects will quickly adapt anyway.

Educating farmers is also considered crucial. This includes providing more information on such things as what chemical doses to use and when to apply them, when to rotate crops, and how to coordinate spraying programs with neighboring farmers.

Some observers, including Dover and Croft, believe the federal government should take pest resistance into account when regulating chemicals. They would also like to see more government-industry research, as well as an industry-backed foundation to further inquiry in the field.

Chemical industry officials, predictably, don't want more government meddling. They point out, for one thing, that not enough is known about how chemicals react on pests in various environments to make broad risk assessments. Although one chemical may be effective on a tick in one area, it may not work on the same insect somewhere else. Charles Delp, a senior research associate at Du Pont, argues that pesticide resistance is best managed locally, on a case-by-case basis, and that the organization (farmers, agriculture experts, pesticide distributors) to do this is in place.

Regardless of the strategies ultimately adopted, most scientists agree that urgent action is needed. Contends Dr. Georghiou: ''We need a Manhattan Project for resistance control.

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