STEWART, Justice:
J.J.N.P. Co. brought this action challenging, on equal protection groünds, the constitutionality of U.C.A., 1958, § 23-15-10,1 which prohibits the operation of private fish installations on natural waters or on reservoirs constructed on natural stream channels. The plaintiff also challenges the Division of Wildlife Resources’ denial of a permit to establish a private fish installation and the trial court’s adjudication of the State’s claim that a dirt road crossing plaintiff’s property is a public road. The State of Utah counterclaimed for a declaratory judgment that the public has recreational rights in the waters of a natural lake even though it is entirely surrounded by plaintiff’s land. The trial court ruled in favor of the State on all issues. We affirm.
J.J.N.P., a limited partnership created under the laws of Utah, owns approximately 1200 acres in Lake Canyon, Duchesne County. Lake Canyon Lake is a natural lake surrounded on all sides by property owned by J.J.N.P. The lake is approximately 800 yards long and 200 yards wide, with a mean depth of 17 feet and a maximum depth of 33 feet. The lake is fed by natural springs in its bed and a small stream approximately 24 to 36 inches wide and 3 inches deep at full course, with headwaters approximately six miles above the lake on State land. A stream of similar size flows intermittently out of the lake during high water levels for approximately 300 yards before it disappears into the ground.
Prior to 1978, the State had an agreement with J.J.N.P.’s predecessors in interest allowing public access to the lake across their land.2 The State managed the lake, eliminated trash fish, stocked trout, and set and enforced fishing seasons and limits. When this agreement expired, J.J.N.P. filed an application with the Division of Wildlife Resources for a permit for a private fish installation. The Division denied the application pursuant to § 23-15-10, which provides in part that “no such [private fish] installation shall be developed on natural waters or natural flowing streams, or reservoirs constructed on natural stream channels.”
Seven miles below Lake Canyon Lake is another natural lake known as “Lower Lake” which sustains a private fish installation. At trial, Donald Andriano, Chief of Fisheries for the Division of Wildlife Resources, testified that the initial permit authorizing this fishery was issued before the Legislature enacted § 23-15-10 in 1971 and that the Division renewed the permits yearly because the owner had made substantial investments in the lake property. Andriano testified that fewer than six such permits for private fisheries on natural lakes and streams are issued annually.
A gravel road extends from the mouth of Lake Canyon past Lake Canyon Lake to U.S. Forest Service lands. For more than ten years, Duchesne County graded and maintained the road for public use. J.J. N.P. attempted to restrict access to its [1136]*1136lands, and necessarily the government lands beyond, by placing a gate across the gravel road. County officials and others removed the obstructions within 24 hours, and J.J. N.P. abandoned the effort.
I. RIGHTS IN PUBLIC WATERS
The State in its counterclaim asserts that Lake Canyon Lake is navigable and therefore subject to a public servitude for recreational use. Although “navigability” is a standard used to determine title to waterbeds, Monroe v. State, 111 Utah 1,175 P.2d 759 (1946), it does not establish the extent of the State’s interest in the waters of the State. See Comment, Basis for the Legal Establishment of a Public Right of Recreation in Utah’s “Non-Navigable” Waters, 5 J.Contemp.L. 95 (1978). Section 73-1-1 states: “All waters in this state, whether above or under the ground are hereby declared to be the property of the public, subject to all existing rights to the use thereof.” (Emphasis added.) Thus, individuals have no ownership interest as such in natural waters, only the right to put the water to certain uses.3 “Beneficial use shall be the basis, the measure and the limit of all rights to the use of water in this state,” § 73-1-3, and the right to beneficial use may be acquired only by compliance with the legal procedures for appropriation of a given right. But appropriation does not confer an ownership interest in the water itself. Daniels Irrigation Co. v. Daniel Summit Co., Utah, 571 P.2d 1323 (1977); Salt Lake City v. Salt Lake City Water & Elec. Power Co., 24 Utah 249, 67 P. 672 (1902).
The State regulates the use of the water, in effect, as trustee for the benefit of the people. Tanner v. Bacon, 103 Utah 494, 516, 136 P.2d 957, 966-967 (1943) (Larson, J., concurring). Accord Day v. Armstrong, Wyo., 362 P.2d 137 (1961); see also Ne-Bo-Shone Association v. Hogarth, 7 F.Supp. 885 (W.D.Mich.1934), aff’d, 81 F.2d 70 (6th Cir.1936). Public ownership is founded on the principle that water, a scarce and essential resource in this area of the country, is indispensable to the welfare of all the people; and the State must therefore assume the responsibility of allocating the use of water for the benefit and welfare of the people of the State as a whole. The doctrine of public ownership is the basis upon which the State regulates the use of water for the benefit and well being of the people. Marks v. Whitney, 6 Cal.3d 251, 491 P.2d 374, 98 Cal.Rptr. 790 (1971).
A corollary of the proposition that the public owns the water is the rule that there is a public easement over the water regardless of who owns the water beds beneath the water. Therefore, public waters do not trespass in areas where they naturally appear, and the public does not trespass when upon such waters. Day v. Armstrong, Wyo., 362 P.2d 137 (1961). Furthermore, state policy recognizes an interest of the public in the use of state waters for recreational purposes by requiring that recreational uses be considered by the State Engineer before he approves an application for appropriation, § 73-3-8, or permits the relocation of a stream, § 73-3-29.
[1137]*1137Private ownership of the land underlying natural lakes and streams does not defeat the State’s power to regulate the use of the water or defeat whatever right the public has to be on the water. Irrespective of the ownership of the bed and navigability of the water, the public, if it can obtain lawful access to a body of water, has the right to float leisure craft, hunt, fish, and participate in any lawful activity when utilizing that water. Day v. Armstrong, Wyo., 362 P.2d 137 (1961); Southern Idaho Fish and Game Association v. Picabo Livestock, Inc., 96 Idaho 360, 528 P.2d 1295 (1974).4
In effect J.J.N.P. claims rights in Lake Canyon Lake based solely on its ownership of the surrounding land. It has no right of appropriation granted by the State Engineer.
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STEWART, Justice:
J.J.N.P. Co. brought this action challenging, on equal protection groünds, the constitutionality of U.C.A., 1958, § 23-15-10,1 which prohibits the operation of private fish installations on natural waters or on reservoirs constructed on natural stream channels. The plaintiff also challenges the Division of Wildlife Resources’ denial of a permit to establish a private fish installation and the trial court’s adjudication of the State’s claim that a dirt road crossing plaintiff’s property is a public road. The State of Utah counterclaimed for a declaratory judgment that the public has recreational rights in the waters of a natural lake even though it is entirely surrounded by plaintiff’s land. The trial court ruled in favor of the State on all issues. We affirm.
J.J.N.P., a limited partnership created under the laws of Utah, owns approximately 1200 acres in Lake Canyon, Duchesne County. Lake Canyon Lake is a natural lake surrounded on all sides by property owned by J.J.N.P. The lake is approximately 800 yards long and 200 yards wide, with a mean depth of 17 feet and a maximum depth of 33 feet. The lake is fed by natural springs in its bed and a small stream approximately 24 to 36 inches wide and 3 inches deep at full course, with headwaters approximately six miles above the lake on State land. A stream of similar size flows intermittently out of the lake during high water levels for approximately 300 yards before it disappears into the ground.
Prior to 1978, the State had an agreement with J.J.N.P.’s predecessors in interest allowing public access to the lake across their land.2 The State managed the lake, eliminated trash fish, stocked trout, and set and enforced fishing seasons and limits. When this agreement expired, J.J.N.P. filed an application with the Division of Wildlife Resources for a permit for a private fish installation. The Division denied the application pursuant to § 23-15-10, which provides in part that “no such [private fish] installation shall be developed on natural waters or natural flowing streams, or reservoirs constructed on natural stream channels.”
Seven miles below Lake Canyon Lake is another natural lake known as “Lower Lake” which sustains a private fish installation. At trial, Donald Andriano, Chief of Fisheries for the Division of Wildlife Resources, testified that the initial permit authorizing this fishery was issued before the Legislature enacted § 23-15-10 in 1971 and that the Division renewed the permits yearly because the owner had made substantial investments in the lake property. Andriano testified that fewer than six such permits for private fisheries on natural lakes and streams are issued annually.
A gravel road extends from the mouth of Lake Canyon past Lake Canyon Lake to U.S. Forest Service lands. For more than ten years, Duchesne County graded and maintained the road for public use. J.J. N.P. attempted to restrict access to its [1136]*1136lands, and necessarily the government lands beyond, by placing a gate across the gravel road. County officials and others removed the obstructions within 24 hours, and J.J. N.P. abandoned the effort.
I. RIGHTS IN PUBLIC WATERS
The State in its counterclaim asserts that Lake Canyon Lake is navigable and therefore subject to a public servitude for recreational use. Although “navigability” is a standard used to determine title to waterbeds, Monroe v. State, 111 Utah 1,175 P.2d 759 (1946), it does not establish the extent of the State’s interest in the waters of the State. See Comment, Basis for the Legal Establishment of a Public Right of Recreation in Utah’s “Non-Navigable” Waters, 5 J.Contemp.L. 95 (1978). Section 73-1-1 states: “All waters in this state, whether above or under the ground are hereby declared to be the property of the public, subject to all existing rights to the use thereof.” (Emphasis added.) Thus, individuals have no ownership interest as such in natural waters, only the right to put the water to certain uses.3 “Beneficial use shall be the basis, the measure and the limit of all rights to the use of water in this state,” § 73-1-3, and the right to beneficial use may be acquired only by compliance with the legal procedures for appropriation of a given right. But appropriation does not confer an ownership interest in the water itself. Daniels Irrigation Co. v. Daniel Summit Co., Utah, 571 P.2d 1323 (1977); Salt Lake City v. Salt Lake City Water & Elec. Power Co., 24 Utah 249, 67 P. 672 (1902).
The State regulates the use of the water, in effect, as trustee for the benefit of the people. Tanner v. Bacon, 103 Utah 494, 516, 136 P.2d 957, 966-967 (1943) (Larson, J., concurring). Accord Day v. Armstrong, Wyo., 362 P.2d 137 (1961); see also Ne-Bo-Shone Association v. Hogarth, 7 F.Supp. 885 (W.D.Mich.1934), aff’d, 81 F.2d 70 (6th Cir.1936). Public ownership is founded on the principle that water, a scarce and essential resource in this area of the country, is indispensable to the welfare of all the people; and the State must therefore assume the responsibility of allocating the use of water for the benefit and welfare of the people of the State as a whole. The doctrine of public ownership is the basis upon which the State regulates the use of water for the benefit and well being of the people. Marks v. Whitney, 6 Cal.3d 251, 491 P.2d 374, 98 Cal.Rptr. 790 (1971).
A corollary of the proposition that the public owns the water is the rule that there is a public easement over the water regardless of who owns the water beds beneath the water. Therefore, public waters do not trespass in areas where they naturally appear, and the public does not trespass when upon such waters. Day v. Armstrong, Wyo., 362 P.2d 137 (1961). Furthermore, state policy recognizes an interest of the public in the use of state waters for recreational purposes by requiring that recreational uses be considered by the State Engineer before he approves an application for appropriation, § 73-3-8, or permits the relocation of a stream, § 73-3-29.
[1137]*1137Private ownership of the land underlying natural lakes and streams does not defeat the State’s power to regulate the use of the water or defeat whatever right the public has to be on the water. Irrespective of the ownership of the bed and navigability of the water, the public, if it can obtain lawful access to a body of water, has the right to float leisure craft, hunt, fish, and participate in any lawful activity when utilizing that water. Day v. Armstrong, Wyo., 362 P.2d 137 (1961); Southern Idaho Fish and Game Association v. Picabo Livestock, Inc., 96 Idaho 360, 528 P.2d 1295 (1974).4
In effect J.J.N.P. claims rights in Lake Canyon Lake based solely on its ownership of the surrounding land. It has no right of appropriation granted by the State Engineer. To permit the acquisition of water rights in the manner claimed would violate the public ownership doctrine and the state statutes regulating appropriation. State water law excludes every means of appropriation except by application to the State Engineer. U.C.A., 1953, § 73-3-1.
II. EQUAL PROTECTION
J.J.N.P. attacks § 23-15-10 on equal protection grounds under the Fourteenth Amendment to the United States Constitution and Article I, § 24 of the Utah Constitution. The argument is that the statutory classification which prohibits private fish installations on natural watercourses, reservoirs on such watercourses, and lakes, but allows them on manmade watercourses, constitutes an unconstitutional discrimination. It is also contended that the State, in allowing a private fish installation on Lower Lake, a natural watercourse, discriminates against J.J.N.P. In addition, plaintiff argues that § 23-15-10, read in light of § 23-20-14, which empowers property owners to exclude hunters and fishermen from their property, is unreasonable and arbitrary.
As part of its equal protection argument, J.J.N.P. contends that the State must show a compelling state interest to justify a discrimination between natural and unnatural watercourses. The argument is without merit. A compelling state interest need be demonstrated only when the discrimination affects fundamental rights or when suspect classifications are involved. Utah Public Employees’ Association v. State, Utah, 610 P.2d 1272 (1980). The building or maintaining of a private fish installation on public water is not a fundamental right, and the restriction of such installations to manmade watercourses is not a suspect classification.
When neither a fundamental right nor a suspect classification is involved, equal protection requires that statutory classifications bear a reasonable relation to the purpose sought to be accomplished and that there be a reasonable basis for the distinction between the classes. Classifications are not unreasonable or arbitrary as long as similarly situated people are dealt with in a similar manner and people situated differently are not treated as if their circumstances were the same. Abrahamsen v. Industrial Commission, 3 Utah 2d 289, 283 P.2d 213 (1955); State v. Mason, 94 Utah 501, 78 P.2d 920 (1938). Legislative classifications need not be applied with mathematical exactness. Baker v. Matheson, Utah, 607 P.2d 233 (1979). A classification may be reasonable even though some inequality results. Crowder v. Salt Lake County, Utah, 552 P.2d 646 (1976). Thus, [1138]*1138the law holds a discrimination invalid only if there is no reasonable basis for the classification. Leetham v. McGinn, Utah, 524 P.2d 323 (1974); Justice v. Standard Gilsonite Co., 12 Utah 2d 357, 366 P.2d 974 (1961).
A presumption of constitutionality is extended to statutes not affecting fundamental rights or based on suspect classifications, and that presumption is sufficient to sustain the constitutionality of the classification created by a statute unless the classification creates an invidious discrimination or bears no rational relationship to a legitimate state purpose. Baker v. Matheson, Utah, 607 P.2d 233 (1979); Purdie v. University of Utah, Utah, 584 P.2d 831 (1978); San Antonio Independent School District v. Rodriguez, 411 U.S. 1, 93 S.Ct. 1278, 36 L.Ed.2d 16 (1973).
In prohibiting private fish installations on natural watercourses, § 23-15-10 does not impose an invidious discrimination. The State has the right, as owner of all waters in the State, to prevent private citizens from using public waters for private uses, whether commercial or otherwise. The statute in question protects that right and serves to preserve natural waters for public use and enjoyment, regardless of who owns the bed or surrounding land. Furthermore, the State may lawfully prevent the placing of foreign objects in the water, such as would be necessary for a fishery, to preserve the natural beauty of lakes and to protect whatever native wildlife may make use of the water. Fisheries on appropriated waters in manmade channels do not interfere with any of the above purposes. We conclude that § 23-15-10 promotes legitimate state interests and that the classification between natural and man-made watercourses is reasonable. It follows that the statute is constitutional.
Furthermore, J.J.N.P. is in a different position than parties who operate private fish installations on unnatural watercourses. For water to reach unnatural watercourses it must be appropriated and diverted. Appropriated water is to be used for the purposes stated in the application. J.J. N.P. has limited water rights in the water,5 but it does not own the water in the lake even though the lake is surrounded by J.J. N.P. land.
J.J.N.P.⅛ further contention that the fish installation on Lower Lake violates its right to equal protection is also unpersuasive. Section 23-15-10 was enacted in 1971, after the Lower Lake installation was built. The statute contains no express grandfather provision for fish installations on natural watercourses existing at the time of passage of the act. However, the statute does differentiate between old and new fish installations. As to the latter, the statute prohibits the development of all new installations on natural waters. As to the former, fish installations that already existed in natural water at the time the act was passed could continue to operate under certification by the Division of Wildlife Resources. The Division, congruent with the act, has annually renewed the Lower Lake permit in recognition of the owner’s financial investment in the then existing facilities.
J.J.N.P. also argues that § 23-15-10, in prohibiting private fisheries on natural watercourses, is inconsistent with a landowner’s right to exclude sportsmen from his property pursuant to § 23-20 — 14. J.J.N.P. asserts that § 23-15-10’s purpose is to provide the public with fishing areas and, because private landowners may restrict public access to natural waters, that purpose is unachievable in the instant case. That conclusion does not follow. The right to use public waters for pleasure purposes is no less a right just because some landowners, for reasons sufficient to themselves, prohibit public access over their land to reach those public waters.6 Clearly, J.J.N.P. [1139]*1139could prohibit all overland access to Lake Canyon Lake. However, access to bodies or streams of water is not necessary to the securing of certain legitimate state interests, such as the protection of wildlife. Furthermore, remote bodies of water are now accessible by air.
The contention that the State wrongfully denied J.J.N.P.’s application for a permit is not supportable.
III. THE DIRT ROAD
The trial court concluded that the dirt road through Lake Canyon was a public road. J.J.N.P. does not challenge the correctness of that conclusion, but rather contends that the trial court should not have decided the issue since it was not raised on the pleadings. Although the issue was not properly pleaded, the record plainly indicates that both parties litigated the issue of the road. “When issues not raised by the pleadings are tried by express or implied consent of the parties, they shall be treated in all respects as if they had been raised in the pleadings.... [F]ailure so to amend does not affect the result of the trial of these issues.” Rule 15(b), U.R.Civ.P. Treating actually litigated issues as if they had been properly pleaded serves the ends of justice, whether the pleadings are actually amended or not. First Security Bank of Utah v. Colonial Ford, Utah, 597 P.2d 859 (1979). Since the issue was tried by mutual consent, there was no error in deciding the issue.
Affirmed. No costs.
OAKS, and HOWE, JJ., and J. HARLAN BURNS, District Judge, concur.
DURHAM, J., does not participate herein; BURNS, District Judge, sat.