LENK, J.

Acting under Blackstone's wetlands by-law (1991), that town's conservation commission denied to the plaintiffs an order of conditions for construction of a house and driveway on a lot that bordered on and included a vegetative wetland. The proposed construction would violate a by-law prohibition against building within 100 feet of a wetland, and would, the commission concluded, have an adverse impact on interests protected by the by-law, including ground water supply, storm damage prevention, prevention of pollution, and protection of wildlife habitat. The plaintiffs appealed from the denial to the Superior Court in an action in the nature of certiorari, see G. L. c. 249, § 4, claiming that the commission had acted arbitrarily and capriciously in denying the order of conditions. The plaintiffs also alleged that the commission's denial was preempted by a subsequent superseding order of conditions issued by the Department of Environmental Protection (DEP) under the Wetlands Protection Act, and that the by-law was invalid as applied to the plaintiffs' land; thus, denial of the order of conditions constituted a regulatory taking in violation of the Fifth Amendment to the United States Constitution. The Superior Court affirmed, concluding that the commission's decision was not preempted by the DEP superseding order and did not constitute a taking. The plaintiffs appeal from the court's decision. We affirm.

On July 15, 1992, the plaintiff FIC Homes (FIC) purchased thirty-eight lots in the sixty-five-lot Federal Hill Estates subdivision located in Blackstone. The prior developer had defaulted, and FIC purchased the property from the Federal Deposit Insurance Corporation. Five years before FIC bought the lots, the prior developer, in March, 1987, had obtained an order of conditions from the commission, pursuant to the Wetlands Protection Act (act), G. L. c. 131, § 40, and c. 119 of the Blackstone wetlands by-law (by-law), authorizing construction of roadways, drainage, and utilities in the subdivision (1987 order). The 1987 order, which expired by its own terms in 1990, required construction of wetlands replication areas on lots 7, 8, and 47 as compensation for the loss of wetlands resulting from construction of the major road through the subdivision, Rocco Drive. After the road construction and replication work were completed, part of the replication area on lot 47 leaked onto lot 48, thereby also creating a wetland area on lot 48. On September 3, 1992, the plaintiffs, acting pursuant to the act and the by-law, filed a notice of intent (NOI) with the commission to build a house and driveway on lot 48. As proposed, a small part of the house and virtually the entire driveway would be within a 100-foot buffer zone protected by the by-law. When the plaintiffs filed the NOI, and indeed, when FIC purchased the property in July, 1992, the by-law then in effect, at § 119-2, required filing of a NOI for any work proposed within 100 feet of wetlands (the buffer zone), and, at § 119-12(B), a mandatory 100-foot setback from the wetlands for any buildings.

The commission held public hearings on the plaintiffs' proposal on September 29, 1992, October 20, 1992, November 10, 1992 (at which the plaintiffs requested a continuance, because they were revising their site plan as a result of inaccuracies noted by commission members), December 8, 1992 (where the plaintiffs requested a further continuance), and January 12, 1993. The plaintiffs revised their plan a number of times during this period, in response to concerns raised regarding impacts of the project on the wetlands values protected by the act and the by-law. However, the commission found the final submitted plan (dated November, 1992) inadequate and voted unanimously to deny the order of conditions at its January 12, 1993, meeting. The formal order of conditions denying permission for the project was issued on February 1, 1993, pursuant to both the act and the by-law. On March 3, 1993, the plaintiffs appealed from the commission's decision under the by-law to the Superior Court. While the Superior Court appeal was pending, the plaintiffs also appealed from the commission's decision under the act to the DEP. In response to concerns expressed by the DEP, the plaintiffs modified their plan once more, on June 4, 1993. DEP found the modifications adequate to safeguard wetlands interests protected by the act, and, during the pendency of the Superior Court action, issued a superseding order of conditions on July 27, 1993, granting permission for the project to proceed under the act. The commission did not appeal from the superseding order. The plaintiffs did not request the commission to reconsider its February 1, 1993, decision based upon the plaintiffs' revised June, 1993, plans.

1. Review under certiorari. The plaintiffs appealed from the commission's denial of an order of conditions under a writ of certiorari pursuant to G. L. c. 249, § 4. In a review under certiorari, the court is limited to correcting "substantial errors of law apparent on the record adversely affecting material rights." Commissioner of Rev. v. Lawrence, 379 Mass. 205, 208 (1979) (citations omitted). See also Carney v. Springfield, 403 Mass. 604, 605 (1988). The standard of review varies "according to the nature of the action for which review is sought." Forsyth Sch. for Dental Hygienists v. Board of Registration in Dentistry, 404 Mass. 211, 217 (1989), and cases cited. As the plaintiffs argue that the commission applied improper criteria in denying the order of conditions, we apply the "arbitrary and capricious" standard to our review of its decision. See Fafard v. Conservation Commn. of Reading, ante 565 (1996). "A decision is not arbitrary and capricious unless there is no ground which `reasonable [persons] might deem proper' to support it." T.D.J. Dev. Corp. v. Conservation Commn. of N. Andover, 36 Mass. App. Ct. 124, 128 (1994), quoting from Cotter v. Chelsea, 329 Mass. 314, 318 (1952).

The plaintiffs complain that in its decision under the by-law, the commission: (a) relied on a "presumption of significance" for the denial of the plaintiffs' proposal, where the by-law contains no provision for such a presumption; and (b) considered the proposed activity on lot 48 in relation to the entire subdivision, and in relation to previous impacts on lot 48 and adjacent lots, where these concerns are not explicitly articulated in the by-law.

a. Presumption of significance. The commission's February 1, 1993, written denial of the order of conditions states, "A Denial of Order of Conditions under the . . . Wetland Bylaw is issued for the proposed work. Presumption of significance was not overcome in relation to ground water supply, storm damage prevention, prevention of pollution, and protection of wildlife habitat." The plaintiffs argue that, while the act contains a presumption of significance for inland wetlands (see 310 Code Mass. Regs. § 10.55[3] [1989]), no such language appears in the town by-law. The plaintiffs acknowledge, however, that the by-law, at § 119-9, places the burden of proof on them to demonstrate that their proposed project will not harm interests protected by the by-law. We see no functional difference between placing the burden of proof on the applicant to show that activities in protected areas will not harm interests protected by the by-law, and a presumption of significance for protected areas. We note that the plaintiffs do not cite to any evidence in the administrative record demonstrating that they met their burden before the commission.

Moreover, the plaintiffs have not explained their failure to seek a variance for their acknowledged violation of § 119-12(B) of the by-law, which imposes a 100-foot wetlands setback requirement on buildings. This was another of the commission's reasons for denying their proposal, and is alone sufficient to uphold the commission's decision, as it is well established that no one is entitled to a variance. Pendergast v. Board of Appeals of Barnstable, 331 Mass. at 559. See also Gulf Oil Corp. v. Board of Appeals of Framingham, 355 Mass. 275, 277 (1969).

b. Consideration of previous impacts and context of entire subdivision. In section 3 of its order, the commission states, "The proposed activity on Lot 48 in relation to the scope of the subdivision and previous impacts to Lot 48 and adjacent lots have not been taken into consideration." The plaintiffs argue that the by-law does not explicitly allow for such considerations. While the plaintiffs' brief does not rise to the level of appellate argument on this point, see Mass.R.A.P. 16(a)(4), as amended, 367 Mass. 921 (1975), we nonetheless note that the by-law does not bar such considerations, which, as the trial court noted, appear to be highly relevant to an assessment of the potential effects of the proposed project on the interests protected by the by-law. For example, at the time of the plaintiffs' proposal, lot 48 itself contained wetlands, as a result of wetland replication work on the abutting lot 47 that had leaked onto lot 48. Such considerations are certainly not irrelevant in assessing the impacts of the plaintiffs' proposal. The commission's denial of the order of conditions was not arbitrary or capricious.

2. Preemption. The plaintiffs argue that as the Blackstone by-law is no more stringent than the Wetlands Protection Act, the act governs their proposal. The commission's denial of an order of conditions was, therefore, superseded by DEP's subsequent superseding order of conditions allowing the project to proceed. It is well established that municipalities may enact more stringent requirements than those provided in the act. Lovequist v. Conservation Commn. of Dennis, 379 Mass. at 14-15. When a local conservation commission rests its decision on a wetlands by-law that provides greater protection than the act, its decision cannot be preempted by a DEP superseding order. DeGrace v. Conservation Commn. of Harwich, 31 Mass. App. Ct. 132, 136 (1991), citing Hamilton v. Conservation Commn. of Orleans, 12 Mass. App. Ct. 359, 368 (1981).

The Blackstone wetlands by-law clearly affords greater protection than the act. The by-law requires applicants to file a notice of intent for any work within a 100-foot buffer zone of a wetland. In contrast, the act regulates activities in the buffer zone only if they will "alter" a nearby wetland. In addition, the by-law requires a 100-foot wetlands setback for any building, a requirement that has no parallel provision in the act. Thus, "the by-law's scope of control is more expansive than that of the act and eliminates the burden of proof problems associated with the State regulation." T.D.J. Dev. Corp. v. Conservation Commn. of N. Andover, 36 Mass. App. Ct. at 127. In the instant case, virtually all of the proposed work would take place in the 100-foot buffer zone; no work in the wetland was proposed. As the by-law's more expansive protection of the buffer zone served as a basis for the commission's decision, it cannot be preempted by a DEP superseding order under the act. Id. at 126-128.

3. Regulatory taking. The plaintiffs contend that, by issuing an order of conditions barring them from building a driveway and house on lot 48, the commission has effected a regulatory taking of their property under the Fifth Amendment to the United States Constitution. As provided by Lucas v. South Carolina Coastal Council, 505 U.S. 1003, 1027, 1029 (1992), if application of the wetlands by-law deprived the plaintiffs of all economically beneficial use of their property, a per se taking would have been effected, unless certain exceptions obtain. See Lopes v. Peabody, 417 Mass. 299, 303 (1994). If, however, the regulation has resulted in less than a total loss of the economic value of the plaintiffs' property, the question as to whether there has been a regulatory taking must be analyzed under pre- Lucas principles requiring the consideration of several interrelated factors; viz. (i) the validity of the by-law as applied to the plaintiffs' property; (ii) the plaintiffs' reasonable investment-backed expectations; (iii) the economic impact on the plaintiffs' property; and (iv) the character of the governmental action. Lopes v. Peabody, supra at 304. Leonard v. Brimfield, 423 Mass. 152, 154 (1996).

a. Per se taking. We turn first to the question whether the plaintiffs have been deprived of all the economic value of their property.

"Because our test for regulatory taking requires us to compare the value that has been taken from the property with the value that remains in the property, one of the critical questions is determining how to define the unit of property `whose value is to furnish the denominator of the fraction.'"

Keystone Bituminous Coal Assn. v. DeBenedictis, 480 U.S. 470, 497 (1987) (citation omitted). In determining the proper "denominator," we consider the regulation's effect on the entire parcel, rather than on individual segments of the parcel.

"`Taking' jurisprudence does not divide a single parcel into discrete segments and attempt to determine whether rights in a particular segment have been entirely abrogated. In deciding whether a particular governmental action has effected a taking, this Court focuses rather both on the character of the action and on the nature and extent of the interference with rights in the parcel as a whole . . . ." (Emphasis supplied.)

Moskow v. Commissioner of Envtl. Mgmt., 384 Mass. 530, 533 (1981), quoting from Penn Cent. Transp. Co. v. New York City, 438 U.S. 104, 130-131 (1978). Accord Fragopoulos v. Rent Control Bd. of Cambridge, 408 Mass. 302, 308 (1990).

On July 15, 1992, by one deed, FIC purchased thirty-eight lots in the Federal Hill Estates subdivision. There was evidence at trial that FIC paid $389,474 for the thirty-eight lots, including three lots (lots 7, 8, and 47) which it acknowledged at the time of purchase (and does not contest here) to be unbuildable. According to the plaintiffs' appraiser, lot 48 is worth $31,800 if buildable, and $1,200 if not buildable. This represents a loss in value of $30,600. There was further evidence that the thirty-four buildable lots in the parcel had sold (with houses on them) for an average of $115,000 each. The plaintiffs' gross proceeds from the sale of the thirty-four buildable lots on the parcel were, therefore, roughly $3,910,000. There was no evidence at trial as to the plaintiffs' costs for constructing homes on the lots, nor was there evidence indicating the plaintiffs' net profit from sale of the thirty-four buildable lots. However, it surely is reasonable to conclude that, with gross sales of close to $4 million, a loss of roughly $31,000 does not represent a 100 percent loss of economic value. There was, therefore, no per se taking of the plaintiffs' property.

b. Pre-Lucas analysis. We turn then to the pre- Lucas analysis of the plaintiffs' claims, an examination of the several interrelated factors to determine whether there has been a regulatory taking of their property. We consider first whether the wetlands by-law was valid as applied to the plaintiffs' property.

i. Validity of the by-law as applied to plaintiffs' property. The plaintiffs carry the burden of demonstrating that the by-law as applied to their property does not "substantially advance legitimate State interests." Lopes v. Peabody, 417 Mass. at 307 n. 13. See also Steinbergh v. Cambridge, 413 Mass. 736, 745 (1992), cert. denied, 508 U.S. 909 (1993). The Blackstone wetlands by-law protects a variety of "wetlands values," including, inter alia, "public and private water supply, groundwater, flood control, erosion and sedimentation control, storm damage prevention, water pollution prevention . . . [and] wildlife habitat." There is no question that these are legitimate State interests. See Turnpike Realty Co. v. Dedham, 362 Mass. 221, 227-229 (1972), cert. denied, 409 U.S. 1108 (1973); Lovequist v. Conservation Commn. of Dennis, 379 Mass. at 18-19; Moskow v. Commissioner of Envtl. Mgmt., 384 Mass. at 532; Southern New England Conference Assn. of Seventh-Day Adventists v. Burlington, 21 Mass. App. Ct. 701, 709-710 (1986), citing Fogelman v. Chatham, 15 Mass. App. Ct. 585, 588 (1983). It is also well established that, in furtherance of those interests, the town may include requirements in its wetlands by-law that are more stringent than those in the act, as Blackstone has done by requiring a notice of intent for any work in the 100-foot buffer zone, and by barring building within the buffer zone. See discussion at part 2, supra. Thus, the plaintiffs have the burden of proving that the by-law, as applied to their property, does not substantially advance the town's interest in protecting wetlands values in both the buffer zone and the wetlands resources.

The plaintiffs do not claim to have satisfied the requirements of the by-law. It is undisputed that their project would include building in the buffer zone, and that such activity is barred by the by-law. The plaintiffs argued before the commission that only eighteen percent of the buffer zone would be disturbed by the proposed driveway. However, the commission observed that, since the plaintiffs' proposed driveway runs the length of the lot, and bisects the buffer zone, it severs the upper portion of the buffer from the wetland it is intended to protect. The commission therefore concluded that the upper portion of the lot would no longer be "a functional wetland buffer zone." The plaintiffs' response was that they had not conducted a "functional value assessment" of their project and that they had addressed the protection of wetlands interests as expressed in the State act. As noted above, the by-law requires more than the State act, and thus satisfaction of the act's requirements does not necessarily satisfy the interests protected by the by-law.

The plaintiffs have argued that protection of the buffer zone is only a means to the goal of protecting the wetland resource itself. To that end, the plaintiffs introduced testimony at trial that the wetland resource would not be harmed by their proposed project. Three persons testified on behalf of the plaintiffs regarding the impact of the plaintiffs' proposed project on the wetlands. Franklin Pond, a registered civil engineer who had done the original engineering design for the entire development, testified that the original design of the drainage system accommodated the runoff from all of the lots in the subdivision and that the over-all drainage system for all of the lots was adequate. He offered no specific testimony about lot 48 and did not testify as to the change in the character of lot 48 since either the time he had designed the over-all drainage system or since the time the wetlands replication had been completed on lot 47 and had crept onto lot 48.

Scott Rabideau, a self-described wetlands biologist who had prepared the NOI for lot 48 (submitted on August 12, 1992), opined that the project adequately protects the wetland resource area. He acknowledged that the plans for lot 48 were revised a number of times after the initial NOI was filed in August, 1992. Significantly, DEP, as well as the commission, had concerns about potential negative impacts of the November, 1992, revised plan. DEP's concerns were not allayed until the plan was again revised in June, 1993.

Marielle Stone, an environmental analyst at DEP, testified that, based on the November, 1992, plan submitted to DEP in connection with the plaintiffs' request for a superseding order of conditions, DEP was concerned about the structural integrity of the driveway, and about the need to install a culvert in order to prevent water from backing up. There was evidence that in April, 1993, DEP was concerned (based on the November, 1992, plan) about flooding to adjacent property owners, the project's impact on the wetlands resource, and possible interference of the water and sewer lines with the function of the culverts. As a result of and in response to DEP's concerns, the plaintiffs submitted a plan modified in numerous respects on June 4, 1993. There is no evidence in the record that the plaintiffs ever requested the commission to review the June 4, 1993, revisions, and on that basis to reconsider its denial of an order of conditions based on the by-law.

In the final conservation commission meeting on the proposal, held January 12, 1993, concerns were raised regarding the same issues identified by DEP based on its review of the November, 1992, plan. It was further noted that the wetlands supported by the buffer zone were already marginal because of the poor quality of the replication work, and that, since all the vegetation in the subdivision, except that on lot 48, had already been clear-cut, this was the only quality buffer zone remaining in the entire subdivision. The commission found that the old growth habitat on the lot supported wildlife, which in turn supports the ecosystem that supports the wetland. Lastly, the commission indicated that, based on the results of its soil auguring on the lot, it found the plaintiffs' map to be inaccurate with respect to drainage patterns and the seep area on lot 48. This in turn brought into question the accuracy of the plaintiffs' predictions about the impact of the drainage patterns on the wetland. For all of these reasons, the commission validly applied the by-law to the plaintiffs' property when it denied the order of conditions in its February 1, 1993, order citing, inter alia, negative impacts on ground water supply, storm damage prevention, prevention of pollution, and protection of wildlife habitat.

ii. Plaintiffs' reasonable investment-backed expectations. In order to rise to the level of an unconstitutional regulatory taking, the investment-backed expectations frustrated by governmental regulation must be "reasonable and predicated on existing conditions," Leonard v. Brimfield, 423 Mass. at 155, not merely a "unilateral expectation or an abstract need." Ibid., quoting from Ruckelshaus v. Monsanto Co., 467 U.S. 986, 1005 (1984), quoting from Webb's Fabulous Pharmacies, Inc. v. Beckwith, 449 U.S. 155, 161 (1980). When FIC purchased the property in 1992, the Blackstone wetlands by-law was already in effect, including its 1991 amendment, adding § 119-12B (see note 10, supra), which requires buildings to be set back 100 feet from a wetlands resource. FIC therefore had no reasonable expectation that it could build in the buffer zone, or that its project would not be subject to the by-law. "[T]he government is not required to compensate an individual for denying him the right to use that which he has never owned." Flynn v. Cambridge, 383 Mass. 152, 160 (1981). Fragopoulos v. Rent Control Bd. of Cambridge, 408 Mass. at 308. Leonard v. Brimfield, 423 Mass. at 155. See also Steinbergh v. Cambridge, 413 Mass. at 742. Neither do the plaintiffs contradict the defendants' assertion that when FIC purchased the property, the wetlands replication on lot 47 had already been completed, and had leaked onto lot 48. The price FIC paid for the entire thirty-eight-lot parcel should have reflected the limitations imposed by the wetlands by-law. Id. at 743. The plaintiffs also could not reasonably believe that a 1987 order of conditions expiring in 1990 (before FIC purchased the property), and addressed only to the construction of the subdivision's roads (not to housing construction), would have the effect of granting them permission to build a house and driveway on lot 48 in 1992. The plaintiffs' reasonable investment-backed expectations were not frustrated by application of the wetlands by-law to their property.

iii. Economic impact. As noted above (see section 3[a] supra), the plaintiffs have not demonstrated that their economic loss was severe. Of the thirty-eight lots purchased, three were known to be unbuildable at the time of purchase. The commission's action had the effect of making just one additional lot unbuildable. "A reduction in the number of houses that an owner may build is a diminution in value and not a taking." Moskow v. Commissioner of Envtl. Mgmt., 384 Mass. at 534 n.3. Nor were the plaintiffs deprived of all beneficial use of the property. The vast majority of the thirty-eight-lot parcel (thirty-four of thirty-eight lots) has been devoted to housing. Compare Leonard v. Brimfield, 423 Mass. at 156 (economic loss not severe where owner prevented from constructing houses on more than half her acreage). Moreover, lot 48 may still be devoted to woodland, wetland, and recreational purposes, which are beneficial uses, Turnpike Realty Co. v. Dedham, 362 Mass. at 235, or as additional acreage for residential abutters' properties, a use valued at $1,200 by the plaintiffs' appraiser, and an amount which the abutters assert they can afford to pay. See S. Kemble Fischer Realty Trust v. Board of Appeals of Concord, 9 Mass. App. Ct. 477, 481-482, cert. denied, 449 U.S. 1011 (1980).

iv. Character of the governmental action. "A `taking' may more readily be found when the interference with property can be characterized as a physical invasion by government." Leonard v. Brimfield, 423 Mass. at 156, quoting from Penn Cent. Transp. Co. v. New York City, 438 U.S. at 124. Here, no physical invasion of the plaintiffs' property has been alleged.

Thus, in view of the facts before us, the application of the wetlands by-law to the plaintiffs' property does not constitute a compensable taking under Federal law.

Judgment affirmed.