WILKINS, C.J.

This case concerns a challenge to a three-acre minimum area requirement for residential lots in the RA-120 Residential/Agricultural zoning district (RA-120 district) in Edgartown on the island of Martha's Vineyard. The plaintiff landowners, trustees of the Herring Creek Farm Trust, whom we shall refer to as the trust, sought a declaratory judgment, pursuant to G. L. c. 240, § 14A, that the three-acre requirement is arbitrary and unreasonable because it does not advance any valid zoning objective.

A judge of the Land Court entered a judgment that the challenged by-law serves a permissible public purpose and does not violate any constitutional or statutory provision. We granted direct appellate review of the trust's appeal. Before us, the trust asserts that the challenged by-law bears no substantial relation to any legitimate public interest. We affirm the judgment of the Land Court.

We summarize relevant parts of the judge's decision. Edgartown adopted a revised zoning by-law in 1973, establishing zoning districts with minimum lot requirements then ranging from 5,000 square feet to three acres. The RA-120 district boundaries are consistent with a plan prepared by the engineering firm of Metcalf Eddy designating certain areas as "open space" due to the "fragile" nature of the environment. Now, about one-half the town (8,736 of 17,181 acres) is zoned for three-acre lots; about 4,900 acres are zoned for one-half acre or one acre lots; and about 3,200 acres are zoned for one and one-half acre lots. During the early 1970's, other Martha's Vineyard towns (Tisbury, West Tisbury, and Chilmark on their south shores) as well as Nantucket adopted three-acre zoning for portions of their towns.

The trust owns 215 acres in the RA-120 district abutting the Atlantic Ocean on the south and Edgartown Great Pond on the west. A farm on the locus is devoted to horticultural uses and has received a special assessment and tax rate under G. L. c. 61A, § 4. Earlier in this decade, the trust submitted to the town's planning board a fifty-four lot subdivision plan for the locus, each lot having in excess of three acres and twenty-five acres dedicated to open space. That plan was referred to the Martha's Vineyard Commission. See St. 1977, c. 831. On February 10, 1994, the commission voted to deny permission to grant the necessary development permits.

The judge considered extensive expert testimony from both sides in relation to the permissible statutory objectives of zoning and concluded that there was a substantial relation between the by-law and the permissible objectives of zoning. He stated that the by-law "facilitates the provision of open space, conserves the value of land, promotes the conservation of natural resources, prevents blight and pollution of the environment, and preserves the Island's unique natural, ecological and other values." The judge credited the testimony of the town's expert, a marine ecologist specializing in coastal areas, to conclude that the effect of nitrate loading on drinking water and on Edgartown Great Pond justified three-acre zoning in the RA-120 district to protect the public health, water, water supply, and water resources. He also concluded that the three-acre requirement allowed a reasonable margin to provide for future problems. The judge identified an independent justification in the "unique ecological integrity of the area including coastal waters, embayments, plant and animal life."

The judge considered the trust's claim that the area requirement of the RA-120 district excluded certain people from the town. He said: "Edgartown is located on a relatively small island with limited accessibility and with inherent resulting economic issues including those of supply and demand. In addition, it is apparent that the setting, topography, weather and natural resources make the entire island highly desirable as a vacation and retirement area. One would reasonably expect such factors to exert an increasingly upward pressure on the price of real estate. Zoning most likely makes some contribution to such pressures, but there is herein a lack of credible evidence as to how and to what extent if any, zoning factors contribute to the availability (or unavailability) of real estate, and more importantly, whether or not the determinative factor of the equation is large lot zoning. I note further the lack of evidence of any person being denied housing because of, or largely because of, such zoning constraints."

We turn first to general principles that guide our decision. In a sense, insular thinking is appropriate here. The values that the town seeks to protect are not simply local ones. The Legislature has recognized "a regional and statewide interest in preserving and enhancing" Martha's Vineyard's "unique natural, historical, ecological, scientific, cultural, and other values," values that may be irreversibly damaged by inappropriate uses of land. St. 1977, c. 831, § 1. In a challenge to an Edgartown zoning by-law, the Legislature's expression of public interest in the preservation of the qualities of Martha's Vineyard is a relevant factor. See Sturges v. Chilmark, 380 Mass. 246, 256 (1980). The Legislature's proclamation also blunts any claim that, in purporting to act to protect its environment, Edgartown is doing so only in support of its parochial interests.

The fact that Edgartown is on an island is important in another respect. Edgartown is not a rural or suburban municipality lying in the path of suburban growth. The trust's claim that large lot zoning is exclusionary, and thus particularly suspect, lacks the force it might have in many other situations. The trust did not establish, nor indeed did it seek to prove by direct evidence, that people were excluded from settling in Edgartown because of three-acre zoning in approximately half the town. In discussing a challenge to a zoning provision of another Martha's Vineyard town, we said that "in a rural, as opposed to a suburban, setting, where no showing has been made of regional demand for primary housing, the public interest in preserving the environment and protecting a way of life may outweigh whatever undesirable economic and social consequences inhere in partly `closing the doors' to affluent outsiders primarily seeking vacation homes" (citation omitted). Sturges v. Chilmark, supra at 255. We reject any suggestion that Edgartown's three-acre zoning is presumptively exclusionary and that, therefore, the town should have the burden of proving the reasonableness of the zoning regulation.

Apart from its argument that the burden falls on a municipality to justify its large lot zoning because it is exclusionary, the trust argues, in any event, that the traditional, heavy burden on one challenging the constitutionality of a zoning law should not be imposed in a challenge to large lot zoning. We do not agree. The general rule is that a zoning by-law whose reasonableness is fairly debatable will be sustained. See Sturges v. Chilmark, supra at 256; Aronson v. Sharon, 346 Mass. 598, 602 (1964). On occasion the court has adopted the criminal law concept of proof "beyond reasonable doubt" to describe the burden that is placed on one challenging the validity of a zoning provision. See, e.g., Crall v. Leominster, 362 Mass. 95, 102 (1972); Caires v. Building Comm'r of Hingham, 323 Mass. 589, 594 (1949). The characterization of a challenger's burden as one of proof beyond reasonable doubt may not be instructive. A better characterization is that the challenger must prove by a preponderance of the evidence that the zoning regulation is arbitrary and unreasonable, or substantially unrelated to the public health, safety, morals, or general welfare. See Sturges v. Chilmark, supra at 256; Massachusetts Broken Stone Co. v. Weston, 346 Mass. 657, 659-660 (1964); Simon v. Needham, 311 Mass. 560, 564 (1942).

As residential lot size requirements increase, it becomes more difficult to justify the requirements. See Aronson v. Sharon, supra at 604 (in such situations, "the law of diminishing returns will set in at some point"). In Simon v. Needham, supra, although skeptical of the town's position, this court rejected a challenge to a zoning requirement of one acre for each house lot, concluding that the town could fairly decide that such a requirement would enhance the public interest. Id. at 564. The case appears to have been decided on the classical standard of what the town's legislative body could rationally have concluded. Id. The court intimated that the result would have been different if a landowner had proved that the one-acre requirement created "a barrier against the influx of thrifty and respectable citizens who desire to live there and who are able and willing to erect homes upon lots upon which fair and reasonable restrictions have been imposed." Id. at 565.

Twenty-two years later, in Aronson v. Sharon, supra at 604, this court held invalid a town zoning by-law requiring house lots of 100,000 square feet. The court decided that the zoning provision exceeded the town's statutory authority and suggested that the operation of the by-law was confiscatory. Id. The town sought to justify the large lot requirement on the ground that it would encourage the retention of land in its natural state for the benefit of the community. Id. at 603-604. The court concluded that the permissible and judicially assumed advantages that justified one-acre zoning in Simon v. Needham, supra, would not justify 100,000 square foot house lots. Aronson v. Sharon, supra at 604.

Although an objecting landowner has the burden of proving that large lot zoning is unjustified, the Aronson opinion indicates that a municipality's reliance on generalities concerning the public benefit of large lot zoning will not carry the day. In such a case, the municipality has the burden of coming forward with something tangible to justify its action. Thus, in 1975, in deciding a challenge to two-acre zoning in a portion of Sherborn, the Appeals Court stated that the record must show that there is a reasonable basis for concluding "that there are special needs that are met by two-acre zoning." Wilson v. Sherborn, 3 Mass. App. Ct. 237, 240 (1975). The town successfully justified its two-acre zoning as an appropriate health protection measure based on an established and reasonable relationship between two-acre zoning and sewage and water conditions in the two-acre zone. Id. at 242-243, 245.

We are now in a position to move from general considerations to the specifics of the record in this case to see whether the judge was warranted in finding that the evidence justified his conclusion that the three-acre zoning requirement served a permissible public purpose authorized by The Zoning Act (G. L. c. 40A). See St. 1975, c. 808, § 2A. Not every beneficial effect of the three-acre zoning requirement in the RA-120 district that the judge noted would, standing alone, justify the restriction. Neither the provision of open space nor the protection of plant and animal life, for example, would singly justify large lot zoning. That benefits of this character incidentally may flow from large lot zoning does not, however, detract from those justifications that do support large lot zoning. We, therefore, need not dwell on the trust's persuasive argument that the record does not support any claim that three-acre zoning in the RA-120 district is partially justified by a need to preserve animal and plant life. We turn, therefore, to other reasons advanced by the town in support of the area requirements of the RA-120 district.

The parties substantially agree that a lot of two acres in the RA-120 district would be sufficient to provide a safe on-site source of water on a lot having its own septic system. We need not decide whether there is any justification for adding an acre as a margin of safety for on-site drinking water, a concept whose reasonableness was not explained in the record. Nor need we reach the trust's doubtful argument that the State's requirements for septic systems somehow make inappropriate zoning requirements founded on considerations of safe drinking water and pollution from sewage. We need not decide these points because there is an independent ground for concluding that the town has come forward with sufficient proof of a reasonable basis for the need of three-acre zoning in the RA-120 district.

The town produced evidence, credited by the judge, that house lots of three acres or more were required in order to protect the ecology of Edgartown Great Pond. The pond, which consists of 890 acres, is a coastal and marine water formed in the sandy soil of the outwash plain of the melting glacier that created Martha's Vineyard. The pond, which the town opens to the ocean periodically and which opens naturally as well from time to time, is brackish (its water being between saline and fresh). It is vulnerable to nutrient pollution from excess nitrogen which would encourage plant growth that periodically deprives the water of oxygen. This anoxia kills shellfish and other organisms on the bottom of the pond and kills finfish. Without oxygen, sulfates in the water will produce hydrogen sulfide gas, "a sewer gas smell." The pond is on the brink of, and sometimes crosses the line of, becoming unhealthy.

The town's evidence concerning the need to protect the ecology of Edgartown Great Pond, evidence of the need for pollution control that the judge accepted, was sufficient to meet its burden of going forward with a demonstration of why three-acre zoning in the RA-120 district is rational and related to the public welfare. The town's expert testified that the nitrogen carrying capacity of the pond was five grams per square meter each year and that the appropriate average minimum lot size in the RA-120 district, to limit properly the nitrogen entering the pond, was three to three and one-half acres. An expert presented by the trust had testified before the Martha's Vineyard Commission that his nutrient loading study validated "the density allowed by current zoning of one unit at three acres."

The judge's ruling is bolstered by the need to protect the amenities and character of a rural resort, such as the Vineyard, in order to assist its economic stability, including its shellfish industry and tourism. As one of the trust's experts testified, the quality of the Vineyard's landscape is important to the quality of life and the promotion of tourism. As we noted earlier, there are regional and Statewide interests in the preservation of the unique quality of Martha's Vineyard. Those interests justify the making of conservative assumptions about the consequences of land uses, even if standing alone protection of those interests might not support the imposition of three-acre zoning.

The trust makes much of the fact that part of its land is not within the watershed of Edgartown Great Pond. The burden was on the trust to prove that the zoning restriction was unlawful, and not on the town to prove its validity. The trust's land not within the watershed of the great pond is generally in the watershed of another coastal pond, and the trust did not prove that the circumstances of any other watershed were significantly different from the conditions in the watershed of Edgartown Great Pond.

This opinion should not be read as an endorsement of three-acre zoning. We have upheld the challenged zoning provision because of the special circumstances of this case, particularly the proximity of the restricted land to a coastal great pond. We are confident in the special circumstances of this case that the three-acre zoning provision has not been shown to be arbitrary and unreasonable or substantially unrelated to the public health, safety, and general welfare.

Judgment affirmed.