
606 N.W.2d 817 (2000)
258 Neb. 891
Jeffrey S. ANDERSON, appellant and cross-appellee,
v.
Dennis A. CUMPSTON et al., appellees and cross-appellants,
Phyllis E. Hastings and Paulsen, Inc., a Nebraska corporation, appellees, and Robert Behrens, intervenor-appellee.
No. S-97-863.
Supreme Court of Nebraska.
March 3, 2000.
*819 Patrick J. Nelson, of Jacobsen, Orr, Nelson, Wright, Harder & Lindstrom, P.C., Kearney, for appellant.
*820 Gregory C. Lauby and Donald J. Pepperl, of Pepperl & McMahon Law Offices, Lincoln, for appellees Dennis A. Cumpston, Richard L. Cumpston, Robert L. Vitera, Karen S. Vitera, and Lori S. Cumpston.
Larry R. Baumann, of Kelley, Scritsmier & Byrne, P.C., North Platte, for appellees Phyllis E. Hastings and Paulsen, Inc., and intervenor-appellee Robert Behrens.
HENDRY, C.J., WRIGHT, CONNOLLY, GERRARD, STEPHAN, McCORMACK, and MILLER-LERMAN, JJ.
PER CURIAM.

NATURE OF CASE
Jeffrey S. Anderson filed an equitable action to establish the corners and boundaries between his land and the land of the defendants pursuant to Neb.Rev.Stat. § 34-301 (Reissue 1998). Anderson owns land accretive to the south bank of the Platte River, while the defendants own land across the Platte River from Anderson, including land accretive to the north bank. After a bench trial, the district court established the boundary between Anderson's property and that of the defendants at the geographical centerline of the Platte River. Anderson timely appealed, alleging that the court erred by not establishing the boundary at the thread of the stream, which he asserts is currently in the north channel of the Platte River. Defendants Dennis A. Cumpston, Richard L. Cumpston, Lori S. Cumpston, Robert L. Vitera, and Karen S. Vitera cross-appealed (collectively defendants Cumpstons and Viteras), claiming that the district court erred by not establishing the boundary at the thread of the stream, which they allege is currently in the south channel of the Platte River. For the reasons that follow, we affirm.

FACTUAL BACKGROUND
Anderson owns land along the south meander line, or bank, of the Platte River generally described as all Platte River accretion lands deriving from and adjacent to government Lots 1, 2, and 3, Section 16, and deriving from and adjacent to government Lot 2, Section 9, all in Township 9 North, Range 22 West of the 6th P.M., Dawson County, Nebraska. Defendants Cumpstons and Viteras; Paulsen, Inc.; and intervenor, Robert Behrens, own adjacent parcels of property along the north meander line, or bank, of the Platte River; the property is located directly north from and has a south boundary contiguous with the north boundary of Anderson's property. Anderson filed the instant action to have certain corners and boundaries of his land ascertained and permanently established under § 34-301. Shortly thereafter, Behrens intervened as a defendant because he had recently entered a contract to purchase land involved in this controversy from defendant Phyllis E. Hastings.
In his petition, Anderson requested that the north boundary of his property be established at the thread of the stream of the Platte River, which he asserts is in the north channel. Defendants Cumpstons and Viteras filed an answer; in paragraph 3 thereof, it was alleged that when the United States of America conveyed the land described in Anderson's petition to the parties' predecessors in title,
the Platte River flowed seasonally bank to bank and the geographical center line roughly corresponded to the thread of the stream; that thereafter artificial structures and diversions led to sudden reductions and shifts in the flow of the stream resulting in the Platte River becoming a braided stream with many small channels.
In the same pleading, defendants Cumpstons and Viteras counterclaimed, asserting that if the court were to conclude that the thread of the stream no longer corresponded to the geographical centerline, the boundary to Anderson's property should be established at the thread of the Platte *821 River, which they claim is presently located in the south channel. Anderson filed a reply to defendants Cumpstons and Viteras' answer and counterclaim, denying certain claims and admitting the aforementioned allegations contained in paragraph 3 of their answer.
As the case progressed, but prior to trial, several landowners who were initially named as defendants in Anderson's petition either settled or were dismissed from the lawsuit by order of the district court. At the time of trial, those defendants still involved in the dispute were the Cumpstons; the Viteras; Paulsen, Inc.; Hastings; and intervenor Behrens (collectively the defendants).
At trial, the deposition of James L. Brown, state surveyor for the State of Nebraska, was admitted into evidence. Brown testified therein that the Platte River is a braided stream, which is a river or stream that does not flow in one confined channel but actually has numerous channels. A braided river or stream does not have one deep thread, but covers a very large area and contains many channels which move around in its normal bed; such interoperative channels cross one another and are subject to rapid change. Brown explained that the "thread" of the stream is that portion of the river or stream which would be the last portion to dry up. Having observed such characteristics in the Platte River, Brown's office instructed county surveyors to treat the Platte River as a braided stream.
The record amply demonstrates that the Platte River is a "braided stream," as two streams of water flow in the Platte River near the property involved in this appeal. These streams are commonly referred to as the "north channel" and the "south channel." At trial, Anderson maintained that the north boundary of his land should be established at the thread of the Platte River, which he claimed was in the north channel. The defendants requested that Anderson's north boundary be set at the geographical centerline of the Platte River or, in the alternative, at the thread of the stream, which they allege is currently located in the south channel. The present location of the thread of the Platte River was the main issue at trial.
The bed of the Platte River is composed of sand; flowing water may recede below the sand and resurface downstream, causing the Platte River to dry up in a manner different from most streams. This characteristic of the Platte River makes it very difficult, if not impossible, to determine the present location of the thread of the river. Brown testified that for tax assessment purposes, taxes on accretion land may be assessed to the geographical centerline of the Platte River in lieu of actually locating the thread of the stream. Brown acknowledged that assessment of taxes on accretion land to the geographical centerline contradicts an instruction by his office that taxes on accretion land were to be assessed to the thread of the contiguous stream. Brown explained, however, that the geographical centerline is utilized as a line of convenience and is allowed, in great part, because of the difficulty of locating the thread of the Platte River, which would ideally serve as the boundary for accretion lands were it able to be located.
Gary Donnelson, the Dawson County surveyor, testified that the determination of the banks of the main channel of the Platte River, other than from an 1869 U.S. Government survey, would be difficult because the Platte River contains many channels, any of which could appear to be the main channel at any given time. John Phillip Moore, the Dawson County assessor, testified that real estate taxes on accretion land in Dawson County are assessed to the geographical centerline. Accretion land in the area was first taxed in 1962 or 1963, at which time it was taxed to the geographical centerline. Tax assessments *822 are based in part on cadastral maps transmitted from the Dawson County surveyor, on which the geographical centerline is determined from the original meander line as determined in the 1869 U.S. Government survey.
Landowners in the area testified that they have become accustomed to having their land taxed to the geographical centerline and, for many years, have acknowledged the geographical centerline as the shared boundary at issue in this appeal. In 1971 or 1972, a fence was built along what is roughly the geographical centerline on Behrens' property. The Viteras' property is also fenced, on the eastern border, to the centerline. Although the Cumpstons have never constructed a fence on their south boundary, they have lived there since 1968with the exception of 4 yearsand have paid property taxes on the accretion land to the geographical centerline.
The district court found that it could not ascertain the location of the current thread of the Platte River. In its memorandum opinion and judgment, the district court concluded that prior to Anderson's acquiring interest in the property, his predecessor in title and the defendants or their predecessors in title had accepted the geographical centerline as the boundary between the accretion lands for a period of more than 10 years. In addition to concluding that this agreement was voluntary, the district court also determined that the defendants or their predecessors in title had met the requirements for adversely possessing the property to the geographical centerline. The district court subsequently established the north boundary of Anderson's property at the geographical centerline of the Platte River. It is from this judgment that Anderson appeals, and defendants Cumpstons and Viteras cross-appeal.

ASSIGNMENTS OF ERROR
Andersen alleges, summarized and restated, that the district court erred in (1) determining the thread of the Platte River to be at or near the geographical centerline of the Platte River, (2) determining the geographical centerline of the Platte River to be the south boundary of the defendants' properties and the north boundary of Anderson's property under the doctrine of adverse possession, (3) determining the location of a fence line along the south side of land claimed by Behrens, and (4) determining the geographical centerline of the Platte River to be the south boundary of the defendants' properties and the north boundary of Anderson's property under the doctrine of either adverse possession or recognition and acquiescence.
On cross-appeal, defendants Cumpstons and Viteras assert that the district court erred in failing to find the thread of the stream of the Platte River to be in the south channel thereof.

STANDARD OF REVIEW
An action to ascertain and permanently establish corners and boundaries of land under § 34-301 is an equity action. Cofer v. Kuhlmann, 214 Neb. 341, 333 N.W.2d 905 (1983). In an appeal from an equity action, an appellate court tries factual questions de novo on the record and reaches a conclusion independent of the findings of the trial court, provided that where credible evidence is in conflict on a material issue of fact, the appellate court considers and may give weight to the fact that the trial judge heard and observed the witnesses and accepted one version of the facts rather than another. Franksen v. Crossroads Joint Venture, 257 Neb. 597, 599 N.W.2d 603 (1999).

ANALYSIS
All of Anderson's assignments of error presuppose that it was error for the district court to establish the geographical centerline of the Platte River as the north boundary of Anderson's property. *823 Anderson urges this court to establish the boundary at the thread of the Platte River, which he contends is currently located in the north channel of the Platte River. We conclude, for reasons different than the district court's, that the court correctly established the north boundary of Anderson's property at the geographical centerline of the Platte River; thus, based upon our de novo review of the record, we affirm the judgment of the district court.
We begin our analysis by reviewing the pleadings and noting that Anderson, in his reply to the answer and counterclaim of defendants Cumpstons and Viteras, admitted that when the land at issue in this appeal was conveyed by the United States of America to Anderson's and the defendants' predecessors in title, "the Platte River flowed seasonally bank to bank and the geographical center line roughly corresponded to the thread of the stream." Admissions contained in pleadings, answers, and replies are judicial in nature and waive all controversy concerning the matter admitted. See Schmid v. Malcolm Sch. Dist., 233 Neb. 580, 447 N.W.2d 20 (1989). We have stated that a judicial admission, as a formal act done in the course of judicial proceedings, is a substitute for evidence and thereby waives and dispenses with the production of evidence by conceding for the purpose of litigation that the proposition of fact alleged by an opponent is true. See U S West Communications v. Taborski, 253 Neb. 770, 572 N.W.2d 81 (1998). By admitting that the thread of the Platte River roughly corresponded with the geographical centerline at the time of the initial conveyance to his predecessors in interest, Anderson has conceded for the purposes of this litigation that such a proposition is true. Once the thread of the Platte River is initially established, we apply the law of avulsion to determine whether the north boundary of Anderson's property was correctly established at the geographical centerline of the Platte River.
Under Nebraska law, title to riparian lands runs to the thread of the contiguous stream. Cofer v. Kuhlmann, 214 Neb. 341, 333 N.W.2d 905 (1983). The thread, or center, of a channel is the line which would give the landowners on either side access to the water, whatever its stage might be, and particularly at its lowest flow. See State v. Ecklund, 147 Neb. 508, 23 N.W.2d 782 (1946). As explained at trial, the thread of the stream is that portion of a waterway which would be the last to dry up. Where the thread of the main channel of a river is the boundary line between two estates and it changes by the slow and natural processes of accretion and reliction, the boundary follows the channel. Ziemba v. Zeller, 165 Neb. 419, 86 N.W.2d 190 (1957). The processes of accretion and reliction are not, however, to be confused with avulsion; avulsion has been defined by this court as a "`"sudden and perceptible loss or addition to land by the action of water, or a sudden change in the bed or course of a stream."'" Valder v. Wallis, 196 Neb. 222, 224, 242 N.W.2d 112, 114 (1976). In the instant case, Anderson's boundary should have been established by applying the law of avulsion.
The doctrine of avulsion is well-settled law in Nebraska. See, e.g., Cofer v. Kuhlmann, supra; Valder v. Wallis, supra; Ziemba v. Zeller, supra; State v. Ecklund, supra; Iowa Railroad Land Co. v. Coulthard, 96 Neb. 607, 148 N.W. 328 (1914). We have previously held that when a stream which forms the boundary between two parties suddenly abandons its old bed and seeks a new one, such change of channel works no change of boundary; the boundary remains as it was in the center of the old channel, although no water may be flowing therein. Ziemba v. Zeller, supra. See, also, Nebraska v. Iowa, 143 U.S. 359, 12 S.Ct. 396, 36 L.Ed. 186 (1892), enforced 145 U.S. 519, 12 S.Ct. 976, 36 L.Ed. 798. The applicability of the law of avulsion is not dependent upon the *824 navigability of the waterway. Compare Valder v. Wallis, supra (applying rule of avulsion in case concerning navigable stream), with State v. Ecklund, supra (applying rule of avulsion in case involving nonnavigable stream). With the foregoing legal principles in mind, we proceed to resolve the instant boundary dispute.
Anderson's reply to defendants Cumpstons and Viteras' answer and counterclaim not only admitted that the geographical centerline initially corresponded with the thread of the Platte River, but also admitted that "artificial structures and diversions led to sudden reductions and shifts in the flow of the stream resulting in the Platte River becoming a braided stream with many small channels." Further, the evidence establishes that, for all practical purposes, it is impossible to ascertain the present location of the thread of the Platte River. We need not make such a determination in this case, however, because Anderson has admitted that the change in the thread of the Platte River was brought about suddenly by artificial structures and diversions. In view of Anderson's foregoing admissions, the doctrine of avulsion provides that the boundary of Anderson's property should remain "`as it was[,] in the center of the old channel.'" See Ziemba v. Zeller, 165 Neb. at 422, 86 N.W.2d at 193. Applying the well-settled law of avulsion to the instant case, we conclude that the north boundary of Anderson's property is the geographical centerline of the Platte River.
Our de novo review of the record leads us to the same conclusion, based on both equitable principles and the doctrine of avulsion. The evidence establishes that in 1869, the thread of the Platte River was at or very near the geographical centerline of the Platte River. In approximately 1903, again in the 1930's, and finally in the 1970's, a series of bridges known as the Darr bridges were built across the Platte River, after which the flow of the river shifted and began to flow in two channels, the south channel initially being the wider channel. In 1941, the flow of the river was once again affected by the Kingsley Dam, the construction of which caused the north channel to carry more water than its southern counterpart. In addition to such artificial diversions, the nature of the bed of the Platte River is such that there is no way to predict which channel will be the last to dry up. Moreover, there is absolutely no evidence of either channel completely drying up after the construction of the third Darr bridge in the 1970's.
Finally, except for Anderson, each of the landowners in the area who testified at trial expressed a long-held belief that the boundary between accretion lands on the north bank and the south bank was the geographical centerline. Although Anderson testified at trial that he was unaware that he was being taxed on accretion land extending north to the geographical centerline, his failure to investigate the boundary of the property upon which he has been taxed does not justify basing our conclusion on his alleged lack of knowledge. Equity would not be done by taking land away from those who have paid taxes thereon, and regarded and treated it as their own for so long, and granting the land to another who has absolutely no reason, on the record before us, to believe that the land was his property.
Our review of the record reveals that the district court correctly determined the thread of the Platte River to be the geographical centerline thereof and accordingly established the north boundary of Anderson's property along that geographical centerline. Simply put, the establishment of the thread of the stream at anywhere but the geographical centerline would be, on the record before us, nothing but pure speculation and conjecture. This conclusion should have been reached, however, via application of the law of avulsion, *825 rather than reliance upon the theories of adverse possession or recognition and acquiescence invoked by the district court. Nonetheless, Anderson's assignments of error are without merit.
Having determined that the boundary between the property of Anderson and that of the defendants was properly established at the geographical centerline of the Platte River, we need not address defendants Cumpstons and Viteras' cross-appeal.

CONCLUSION
The law of avulsion applies to the instant case, and upon our application of that doctrine, we conclude that the north boundary of Anderson's property and the south boundary of the defendants' properties is properly established at the geographical centerline of the Platte River as measured from the original meander line of the Platte River according to the original government plat of Township 9 North, Range 22 West of the 6th P.M., in Dawson County, Nebraska, dated January 25, 1869, and filed in the Nebraska State Surveyor's office. The decision of the district court is therefore affirmed.
AFFIRMED.
WRIGHT and CONNOLLY, JJ., concur in the result.
