
687 N.W.2d 195 (2004)
268 Neb. 694
Amy C. ROBB, appellee
v.
Timothy L. ROBB, appellant.
No. S-03-970.
Supreme Court of Nebraska.
October 8, 2004.
*198 Kelly T. Shattuck, of Cohen, Vacanti, Higgins & Shattuck, Omaha, for appellant.
Jeffrey A. Silver, Omaha, for appellee.
HENDRY, C.J., WRIGHT, CONNOLLY, GERRARD, STEPHAN, McCORMACK, and MILLER-LERMAN, JJ.
STEPHAN, J.
Amy C. Robb filed a petition in the district court for Douglas County seeking dissolution of her marriage to Timothy L. Robb and sole custody of the couple's two minor children. Timothy filed an answer and cross-petition in which he sought joint custody. A temporary order provided that during the pendency of the dissolution proceedings, the parties were to have joint custody of the children, with Amy to have "primary possession." Following a trial, the district court entered a decree of dissolution which awarded sole custody of the children to Amy and specified Timothy's visitation rights. Timothy filed this timely appeal.

FACTS
The parties were married on June 26, 1993. Their daughter Courtney was born on March 30, 1998, and their daughter Alyssa was born on May 8, 2000. The children were ages five and three, respectively, when trial commenced on May 27, 2003.
Timothy left the marital home on June 30, 2002. Prior to their separation, both parties were employed outside the home during the day and both participated in the care of the children. On a typical workday, Timothy would wake the girls and prepare their breakfast, while Amy prepared herself for work, selected clothing for the children, and packed any items they would need during the day. Amy would then take the children to their daycare facility before going to her job, while Timothy prepared himself for work. Because Amy had longer work hours, Timothy brought the children home from daycare and usually prepared their dinner before Amy returned home. They shared bathing and bedtime responsibilities. Weekend parenting was also shared during the time that the parties resided together.
*199 Timothy lived with his parents for 5 weeks after leaving the marital home and before moving into his new home. During that time, the children visited Timothy on Monday and Wednesday evenings and either Saturday or Sunday of each week, with no overnight visits. In October 2002, the district court entered a temporary order of joint custody which provided for overnight visitation with Timothy on Monday and Wednesday of each week, along with one overnight every weekend alternating between Friday and Saturday nights.
Amy testified that prior to the overnight visits, the children were progressing in terms of development, but that subsequent to the temporary order, upon returning from Timothy's home, the girls exhibited signs of defiance, of being "very tired," and wanting to "cling." Amy's mother and Amy's brother each testified that the children became "clingy" after the overnight visits began. Amy also testified that the children were very tired upon return from Timothy's home, that Courtney was at times resistant to go to Timothy's home, and that Alyssa's potty training had regressed.
Timothy testified that he did not observe any of the above-described behavior when the children were with him. He testified that the children experienced some difficulty during the time between his separation from the marital residence and his moving into his new home, but that thereafter, they seemed to adapt well to the arrangement and were happy at home and at daycare. Several friends of Timothy and Amy, along with Timothy's parents, testified that they observed Timothy and his children interact, saw Timothy involved in their care and welfare (including bathing and feeding), and thought the children to be well bonded with Timothy.
Amy called Dr. Thomas Haley to testify as an expert witness. He was permitted to give opinion testimony over Timothy's objection which generally supported Amy's position with respect to custody.
Timothy called Dr. Cynthia Topf as a rebuttal witness. Topf holds a Ph.D. and is a psychologist practicing in Omaha, with emphases on individual counseling, custody evaluations, and forensic assessments. She testified that clinical opinion and observation, while relied upon by expert psychologists, would be the very minimum of something that would be reliable. She further testified that a proper custody evaluation normally involves a minimum of 4 to 8 hours of direct contact with the children, plus testing time.
In its decree, the district court found that during the parties' separation, the children had spent 57 percent of the time with Amy and 43 percent with Timothy. The court further found:
That the testimony of [Amy] that the frequent changes in houses and parents leads to inconsistency in guiding and caring for the children and a generally unstable lifestyle along with Psychologist Dr. Thomas Haley's testimony that the alternate visitation schedule now in place eliminates the sense of home and belonging necessary for a healthy up-bringing of the children are persuasive.
That it is in the best interests of the minor children that their care, custody and control be placed solely with [Amy].
The decree included a visitation schedule granting Timothy visitation rights on certain weekends, weekdays, holidays, and for a 6-week period each summer.

ASSIGNMENTS OF ERROR
Timothy assigns, renumbered and restated, that the district court erred in (1) admitting Haley's testimony and (2) failing *200 to find that joint custody was in the best interests of the minor children.

STANDARD OF REVIEW
Child custody determinations are matters initially entrusted to the discretion of the trial court, and although reviewed de novo on the record, the trial court's determination will normally be affirmed absent an abuse of discretion. Marcovitz v. Rogers, 267 Neb. 456, 675 N.W.2d 132 (2004); Heistand v. Heistand, 267 Neb. 300, 673 N.W.2d 541 (2004).
Generally, a trial court's ruling in receiving or excluding an expert's testimony which is otherwise relevant will be reversed only when there has been an abuse of discretion. Carlson v. Okerstrom, 267 Neb. 397, 675 N.W.2d 89 (2004).
A judicial abuse of discretion requires that the reasons or rulings of a trial judge be clearly untenable, unfairly depriving a litigant of a substantial right and a just result. Mathews v. Mathews, 267 Neb. 604, 676 N.W.2d 42 (2004); Marcovitz v. Rogers, supra.

ANALYSIS
The principal issue presented in this appeal is whether the district court abused its discretion in awarding sole custody of the minor children to Amy, subject to Timothy's visitation rights, instead of awarding joint custody to the parties. A secondary issue is whether the district court erred in receiving certain opinion testimony of Haley over Timothy's objection. We begin with the evidentiary issue.

EXPERT TESTIMONY OF DR. THOMAS HALEY
Haley is a psychologist licensed by the State of Nebraska. He has been engaged in a general private practice in Omaha since 1983. He holds an undergraduate degree from the University of Iowa and a master's degree and a Ph.D. from the University of Nebraska. His practice includes working with children and families, and he has testified as an expert on custody issues on more than 100 occasions since 1978. At the request of Amy's counsel, he interviewed and evaluated the parties and their children on two occasions in December 2002, but did not perform a "full custody evaluation." He recorded his observations and opinions in a written memorandum dated December 28, 2002, which was apparently furnished to counsel for both parties prior to trial. At the time Haley authored his memorandum, the alternating visitation schedule under the temporary order was in effect.
The record discloses no pretrial objection to Haley's expert testimony. At trial, during direct examination by Amy's counsel, Haley was asked to state his opinion with respect to the alternating visitation schedule in effect under the temporary order. Timothy's counsel objected and requested leave to "voir dire the witness on his qualifications." Leave was granted, and voir dire examination elicited Haley's admission that he had not seen the parties or their children since December 2002 and that his opinion had not changed since he wrote the memorandum of December 28, 2002. Haley also conceded that he did not perform a full custody evaluation, which would have required additional testing. At the close of his voir dire, Timothy's counsel objected to Haley "providing any expert evaluation," arguing that he had not performed a full custody evaluation. The court sustained the objection "as to the methodology" and suggested that additional foundation was needed. Amy's counsel then elicited Haley's testimony that his techniques were established and recognized in the profession of psychology, that they were peer reviewable, and that he had formed opinions to a reasonable degree of psychological certainty.
*201 Haley was then asked if in his opinion "it was in the best interests of the children to move them frequently" from Amy's home to Timothy's home. Timothy's counsel objected "as to foundation and to qualifications," and the court overruled the objection. Haley then testified that frequent movement of the children was not in their best interests because it eliminated "the experience of having a home base, a sense of home, a place where they belong." He further opined that with frequent movement, "there's no sense of their own room, their own friends, their own neighborhood."
Haley was then asked if he had an opinion "as to whether or not it is better to have them have extended stays at [Amy's] house?" Timothy's counsel objected on grounds that Haley had not done a custody evaluation and that the requested opinion was not set forth in his December 28, 2002, memorandum. The court overruled the objection, and Haley gave an affirmative response to the question. During recross-examination, Haley admitted that his memorandum did not state an opinion as to which parent should be awarded custody of the children and that the memorandum was directed solely to the circumstances existing under the temporary order then in effect. Timothy's counsel offered the memorandum into evidence without limitation, and it was received without objection.
An expert's opinion is ordinarily admissible under Neb.Rev.Stat. § 27-702 (Reissue 1995) if the witness (1) qualifies as an expert, (2) has an opinion that will assist the trier of fact, (3) states his or her opinion, and (4) is prepared to disclose the basis of that opinion on cross-examination. Heistand v. Heistand, 267 Neb. 300, 673 N.W.2d 541 (2004). When the opinion involves scientific or specialized knowledge, this court held in Schafersman v. Agland Coop, 262 Neb. 215, 631 N.W.2d 862 (2001), that we will apply the principles of Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993). Under our recent Daubert/Schafersman jurisprudence, the trial court acts as a gatekeeper to ensure the evidentiary relevance and reliability of an expert's opinion. Zimmerman v. Powell, ante, 268 Neb. 422, 684 N.W.2d 1 (2004); Carlson v. Okerstrom, 267 Neb. 397, 675 N.W.2d 89 (2004). This entails a preliminary assessment of whether the reasoning or methodology underlying the testimony is valid and whether that reasoning or methodology can be applied to the facts in issue. Zimmerman v. Powell, supra; Schafersman v. Agland Coop, supra. In addition, the trial court must determine if the witness has applied the methodology in a reliable manner. Carlson v. Okerstrom, supra.
In this appeal, Timothy does not challenge Haley's professional qualifications or the scientific reliability of the methodology used by psychologists like Haley in conducting child custody evaluations. Rather, he argues that Haley's opinions were inadmissible because he did not conduct a full custody evaluation or perform any of the testing that would have been included in such an evaluation. We understand this argument to be directed at the second component of the Daubert/Schafersman analysis, namely, whether the expert has reliably applied methodology which is itself reliable if properly applied. We conclude that this argument has merit with respect to Haley's opinion that it would be in the best interests of the children to award permanent custody to Amy. The record clearly reflects that Haley did not apply the accepted psychological methodology necessary to formulate this opinion. Accordingly, we disregard *202 Haley's opinion as to permanent custody in our de novo review of that issue.
To the extent that Timothy is challenging Haley's opinion regarding the children's behavior during the period when the temporary order was in effect, we find no similar infirmity. This opinion is based upon Haley's clinical observation and impression of the parties and their children at a specific point in time several months prior to trial. Haley's trial testimony in this regard reflects the content of his December 28, 2002, memorandum, which was received in evidence without limitation or objection. Accordingly, we will consider this aspect of Haley's testimony in our de novo review of the custody determination.

PERMANENT CUSTODY
In reviewing a custody determination de novo on the record, we reappraise the properly admitted evidence as presented by the record and reach our independent conclusion with respect to the issue presented. See Hajenga v. Hajenga, 257 Neb. 841, 601 N.W.2d 528 (1999). When custody of a minor child is an issue in a proceeding to dissolve the marriage of the child's parents, child custody is determined by parental fitness and the child's best interests. Mathews v. Mathews, 267 Neb. 604, 676 N.W.2d 42 (2004); Marcovitz v. Rogers, 267 Neb. 456, 675 N.W.2d 132 (2004). In determining the best interests of the child in a custody determination, a court must consider, at a minimum,
(a) [t]he relationship of the minor child to each parent prior to the commencement of the action or any subsequent hearing;
(b) [t]he desires and wishes of the minor child if of an age of comprehension regardless of chronological age, when such desires and wishes are based on sound reasoning;
(c) [t]he general health, welfare, and social behavior of the minor child; and
(d) [c]redible evidence of abuse inflicted on any family or household member.
Neb.Rev.Stat. § 42-364(2) (Reissue 1998); Marcovitz v. Rogers, supra. Other pertinent factors include the moral fitness of the child's parents, including sexual conduct; respective environments offered by each parent; the age, sex, and health of the child and parents; the effect on the child as a result of continuing or disrupting an existing relationship; the attitude and stability of each parent's character; and parental capacity to provide physical care and satisfy educational needs of the child. See, Davidson v. Davidson, 254 Neb. 357, 576 N.W.2d 779 (1998); Ritter v. Ritter, 234 Neb. 203, 450 N.W.2d 204 (1990).
Here, the record reflects that each parent is fit and had a close, positive relationship with each of the children during the marriage, as well as during the ensuing period of separation. There is no evidence of any form of abuse within the family. The record is silent as to the desires and wishes of the children on the question of permanent custody, no doubt due to their tender age. There is no indication that either child has health problems or special needs. As noted, there is conflicting evidence as to the children's social behavior during the period of joint custody under the temporary order.
The primary issue in this case is whether the district court abused its discretion by awarding sole custody to Amy instead of awarding the joint custody sought by Timothy. The statutory rules governing joint custody of minor children in dissolution proceedings are set forth in § 42-364(5):
After a hearing in open court, the court may place the custody of a minor child with both parents on a shared or joint custody basis when both parties *203 agree to such an arrangement. In that event, each parent shall have equal rights to make decisions in the best interests of the minor child in his or her custody. The court may place a minor child in joint custody after conducting a hearing in open court and specifically finding that joint custody is in the best interests of the minor child regardless of any parental agreement or consent.
Because the parties in this case did not agree to joint custody, the last sentence of the statute governs the issue. Thus, the question before us on de novo review is whether the trial court abused its discretion in not making a specific finding that joint custody is in the best interests of the children, applying the criteria set forth above.
As noted above, there was conflicting evidence regarding the behavior of the children under the joint custody arrangement specified in the temporary order. Amy and several other witnesses testified that the children became clingy and appeared more tired than usual, that Courtney was reluctant to go to school, and that Alyssa's toilet training regressed. Timothy and several other witnesses disputed that these behaviors occurred. In child custody cases, where the 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. Mathews v. Mathews, 267 Neb. 604, 676 N.W.2d 42 (2004). See, Brockman v. Brockman, 264 Neb. 106, 646 N.W.2d 594 (2002); Heald v. Heald, 259 Neb. 604, 611 N.W.2d 598 (2000). The district court found Amy's testimony credible in this regard, and we give weight to that finding. We also find persuasive and significant Haley's opinion that younger children need "a home base, a sense of home, a place where they belong," and that frequent movement can be disruptive of this need. Accordingly, based up-on our de novo review, we find no compelling reason why joint custody would be preferable to the sole custody subject to liberal visitation ordered by the district court. That arrangement, in our view, is in the best interests of these children because it results in the children's spending ample time with each parent while providing the stability of a "home base."
We find no abuse of discretion in the custody determination made by the district court and therefore affirm its judgment.
AFFIRMED.
