
760 N.W.2d 520 (2008)
279 Mich. App. 455
SINICROPI
v.
MAZUREK.
Powers
v.
Mazurek.
Docket Nos. 281726, 281770.
Court of Appeals of Michigan.
Submitted May 7, 2008, at Lansing.
Decided July 1, 2008, at 9:10 a.m.
*521 Melissa G. Leckie, Lansing, for Gregory G. Sinicropi.
Anne Argiroff, Farmington Hills, for Holly V. Mazurek.
Elizabeth Warner for Martin A. Powers.
Before: GLEICHER, P.J., and FITZGERALD and HOEKSTRA, JJ.
GLEICHER, P.J.
In Sinicropi v. Mazurek, 273 Mich.App. 149, 729 N.W.2d 256 (2006), we instructed the trial court to determine on remand whether clear and convincing evidence supported the revocation of an acknowledgment of parentage, considering the "equities of the case." Id. at 185, 729 N.W.2d 256. After conducting an evidentiary hearing, the trial court refused to revoke the acknowledgment of parentage signed by Holly Mazurek shortly after the birth of her son, Noah Powers. Mazurek and Gregory Sinicropi, Noah's biological father, now appeal as of right. We affirm.

I. UNDERLYING FACTS AND PROCEEDINGS
This Court's prior opinion succinctly states the pertinent facts as follows:
This case concerns a child [Noah] who was born out of wedlock in 1999 to Mazurek while she was in a relationship with Powers, but Sinicropi is the biological father of the child as established by DNA (deoxyribonucleic acid) testing. Mazurek had dated Powers, then briefly dated Sinicropi, before subsequently resuming her relationship with Powers, during which time the child was born. Powers, along with Mazurek, executed an acknowledgment of parentage on the child's birth. None of the parties was aware that Sinicropi was the biological father until 2004, when the DNA testing was conducted following Mazurek's suspicion that Sinicropi might be the father given the child's developing physical characteristics and appearance. Meanwhile, Powers raised the child as his own with Mazurek.
Powers and Mazurek again split up in 2001, and Powers filed a custody action against Mazurek when the relationship ended. They immediately stipulated the entry of a consent order giving them joint legal and physical custody. In 2004, Powers sought sole custody after Mazurek moved out of Jackson, Michigan, where Powers, Mazurek, and the child had resided since the child's birth, to live with her new fiancé in Shepherd, Michigan. An ex parte order was entered granting Powers sole custody pending an evidentiary hearing. The trial court refused to dismiss Powers's custody action and to revoke the acknowledgment *522 of parentage as requested by Mazurek on multiple occasions, not because of a failure to show that Sinicropi was the biological father, but because it would be inequitable and because res judicata and collateral estoppel arising out of the consent order of joint custody would not allow it.
The trial court eventually converted the ex parte custody order into a temporary order, scheduling a full evidentiary hearing on issues of custody and parenting time. Thereafter, Sinicropi filed a paternity action under the Paternity Act. Subsequently, the trial court, after consolidating the paternity and custody cases, entered an order of filiation that recognized Sinicropi as the child's father, yet the acknowledgment of parentage was not revoked. At this stage in the proceedings, the young boy was five years old. The trial court had rejected Powers's argument that Sinicropi lacked standing to file a paternity action, and it similarly rejected renewed efforts to have Powers's custody action dismissed for lack of standing and to have the acknowledgement [sic] of parentage revoked. The trial court effectively ruled that the child had two legal fathers under the Acknowledgment of Parentage Act and the Paternity Act.
Following a best-interests evidentiary hearing on custody, the trial court awarded sole physical custody of the child to Powers, awarded Powers and Mazurek joint legal custody, and awarded Mazurek parenting time. The trial court reserved ruling on parenting time for Sinicropi and on the issue of child support. In response to postjudgment motions filed by Mazurek and Sinicropi, the trial court concluded that it should have conducted a best-interests analysis with respect to Sinicropi and custody, but the court otherwise rejected Mazurek's and Sinicropi's attack on the judgment. The trial court reviewed the child custody factors and in a separate opinion decided that it would not be in the child's best interests to award shared custody to Sinicropi. Subsequently, Mazurek and Sinicropi were both ordered to pay child support. [Sinicropi, supra at 153-155, 729 N.W.2d 256.]
In the prior decision in this case, this Court held that the trial court erred by ruling that Noah had two legally recognized fathers because an order of filiation in favor of Sinicropi could not enter until the acknowledgment of Powers's parentage had been revoked. Id. at 152, 729 N.W.2d 256. This Court remanded the case to the trial court
for further reflection on the issue of revocation of the acknowledgment of parentage. The trial court is directed to address revocation solely under MCL 722.1011(3), which requires, in part, that Mazurek prove by clear and convincing evidence that revocation of the acknowledgment of parentage is proper considering the equities of the case. Should the trial court again rule to reject revocation, the court shall pronounce Powers as the child's legal father, vacate the order of filiation and any orders based thereon, including the child support orders relative to Sinicropi, and let stand the custody determination as between Powers and Mazurek because we find no errors warranting reversal with respect to that determination. Should the trial court decide to revoke the acknowledgment of parentage on remand, the court shall pronounce Sinicropi the child's legal father consistent with the order of filiation, vacate any orders based on Powers's status as the father, including the order granting him joint legal and sole physical custody, and enter any appropriate orders, upon hearing if necessary, in regard to custody and support as those matters relate to Sinicropi and *523 Mazurek. [Id. at 185-186, 729 N.W.2d 256.]
The trial court commenced the evidentiary hearing on September 20, 2007, and continued it on October 3, 2007. In support of Mazurek's motion to revoke the acknowledgment of paternity, she presented evidence that two of Powers's former students consumed alcohol at his home on at least one occasion, and that Noah had established a good relationship with Sinicropi's parents.[1] Mazurek conceded, however, that Noah and Powers have "a significant and long-enduring bond," and that the removal of Powers from the child's life would not benefit Noah.
Sinicropi testified that he spent time with Noah on four occasions before the trial court entered a no-contact order. According to Sinicropi, Noah "knew" that Sinicropi was his father. In Sinicropi's view, Noah's best interests demanded the maintenance of a relationship with his biological father "[b]ecause he knows about me, because he's 8, and because it's the right thing."
Powers presented the testimony of Dr. Janice Lazar, a psychologist who served as a court-appointed expert pursuant to the parties' stipulation. Dr. Lazar interviewed and evaluated Mazurek, Sinicropi, Powers, and Noah. She concluded that Noah had a strong bond with both Mazurek and Powers, and opined that the termination of Noah's relationship with Powers "would be quite harmful to that child." Dr. Lazar explained:
Noah has been raised believing that Martin is his father in every sense of the word. To remove Martin from his life would be the same as removing any child's parent that they are strongly bonded and attached to. That would be extremely harmful to any child.
According to Dr. Lazar, Noah referred to Sinicropi as a "helper dad," and was unsure of Sinicropi's actual status. Dr. Lazar opined that the removal of Sinicropi from Noah's life would not harm Noah.
In its bench opinion, the trial court observed that if it granted Mazurek's motion, "Noah would lose the only father he's ever known, and I don't think that that represents the proper balancing of the equities in the case." Relying primarily on Dr. Lazar's testimony, the court denied Mazurek's request to revoke the acknowledgment of parentage, finding that Noah would endure harm from either the termination of his relationship with Powers or the introduction of another father. Mazurek and Sinicropi now appeal that decision.

II. ISSUES PRESENTED AND ANALYSIS
Mazurek and Sinicropi raise identical issues on appeal. Initially, they contend that the trial court clearly erred when it balanced the equities against revocation of the acknowledgment of parentage. According to both briefs on appeal, "the equities show that Noah has an ongoing relationship with Mr. Sinicropi, his biological father and his extended family. In contrast, Mr. Powers has demonstrated particularly poor judgment (at best) which has a direct impact on his ability to act as a responsible parent to Noah."
When reviewing a dispositional ruling in an equitable matter, "an appellate court will set aside a trial court's factual findings only if they are clearly erroneous, but whether equitable relief is proper under those facts is a question of law that an appellate court reviews de novo." McDonald v. Farm Bureau Ins. Co., 480 Mich. 191, 197, 747 N.W.2d 811 (2008). *524 Clear error exists when some evidence supports a finding, but a review of the entire record leaves the reviewing court with the definite and firm conviction that a mistake has been made. In re Conley, 216 Mich.App. 41, 42, 549 N.W.2d 353 (1996).
This Court previously stated that the sole issue to be determined on remand was whether, under MCL 722.1011(3), clear and convincing evidence of "the equities of the case" supported revocation of Mazurek's acknowledgment of Powers's parentage. The record reveals that throughout the eight years of his life, Noah knew no father besides Powers. Indeed, the trial court awarded Powers sole physical custody of Noah in September 2005, finding that Powers had "shown an enormous [parenting] capacity for a single man" and consistently "put Noah first." In contrast, Noah had only a short-lived, peripheral relationship with Sinicropi, despite some possible awareness that Sinicropi was his biological father.[2]
Dr. Lazar observed that Noah presented as a happy and "extremely enthusiastic" child, and that he expressed an inability to think of "anything that he would change in his life at this time." The evidence demonstrated that Noah enjoyed a strong and positive bond with both Powers and Mazurek, performed well in school, and, in the words of Dr. Lazar, seemed "an extremely engaging, happy and contented child who enjoys a strong relationship with all of the adults in his life, particularly his mother, Holly Mazurak [sic], and the man he is bonded to as his father, Martin Powers."
Mazurek and Sinicropi argue that the trial court erred by failing to place stronger emphasis on the testimony that several minors consumed alcohol while visiting Powers. Because this appears to have been an isolated event that may have reflected poor judgment in limited circumstances, it does not, in our view, constitute evidence that Powers is either unsuited or unfit to parent Noah. Mazurek and Sinicropi additionally contend that the trial court relied exclusively on the testimony of Dr. Lazar, and thereby "abdicated" its role as the finder of fact. This argument ignores the trial court's considerable knowledge regarding the dynamics of Noah's custodial environment, acquired during the proceedings that occurred in 2005 and intensified in 2006. At the conclusion of the October 2007 hearing, the trial court expressed its heartfelt sympathy and respect for Sinicropi, and specifically referenced its previous findings under the "best interest" factors.
Furthermore, the trial court afforded Mazurek and Sinicropi a virtually limitless opportunity to present evidence regarding any issue relevant to the equities of revocation. Mazurek and Sinicropi took full advantage of that opportunity by offering evidence that included the observations of a private detective who investigated Powers, and testimony from Sinicropi's mother describing Noah's relationship with his biological grandparents and other members of the Sinicropi family. We find no clear error in the trial court's conclusion that Mazurek and Sinicropi had failed to present clear and convincing evidence supporting revocation of the acknowledgment of parentage.
Mazurek and Sinicropi also argue that the trial court's decision conflicts with Van v. Zahorik, 460 Mich. 320, 597 N.W.2d 15 (1999), because it "essentially makes Mr. Powers an `equitable father.'" As this Court previously explained, however, Van "is not implicated here because, in contrast to the factual circumstances in Van, Powers *525 executed an acknowledgment of parentage," and at that point "is . . . deemed the natural and legal father" of Noah, and not an equitable parent. Sinicropi, supra at 162, 729 N.W.2d 256. Further, this Court's determination that Van does govern here constitutes the law of the case. Under the "law of the case" doctrine, "if an appellate court has passed on a legal question and remanded the case for further proceedings, the legal questions thus determined by the appellate court will not be differently determined on a subsequent appeal in the same case where the facts remain materially the same." CAF Investment Co. v. Saginaw Twp., 410 Mich. 428, 454, 302 N.W.2d 164 (1981).
Mazurek and Sinicropi next assert that the trial court erred by refusing to enter an order of filiation under MCL 722.717(1). However, this Court considered and decided that issue in Sinicropi, holding that "an order of filiation cannot be entered under the Paternity Act, MCL 722.711 et seq., if, under the Acknowledgment of Parentage Act, MCL 722.1001 et seq., a proper acknowledgment of parentage was previously executed and has not been revoked." Sinicropi, supra at 152, 729 N.W.2d 256. Again, the "law of the case" doctrine prohibits reconsideration of this issue because there has been no intervening change in the law.
The law of the case doctrine holds that a ruling by an appellate court on a particular issue binds the appellate court and all lower tribunals with respect to that issue. Thus, a question of law decided by an appellate court will not be decided differently on remand or in a subsequent appeal in the same case. . . . However, the doctrine does not preclude reconsideration of a question if there has been an intervening change of law. [Ashker v. Ford Motor Co., 245 Mich. App. 9, 13, 627 N.W.2d 1 (2001).]
Finally, Mazurek and Sinicropi argue that the trial court should have taken into account the "Constitutional considerations in this case [that] go directly to the issue of [the] equities." Initially, we observe that in Sinicropi, we addressed essentially the same constitutional issues as those now raised on appeal. Id. at 168-171, 729 N.W.2d 256. Because the "law of the case" doctrine governs the outcome of these constitutional questions, as well, we decline to revisit that constitutional analysis here. See also MCR 7.215(J)(1).
During oral argument, appellants' counsel contended that the absence of standards or guidelines defining "the equities" a trial court should apply when considering the potential revocation of an acknowledgment of parentage violated Mazurek's and Sinicropi's due-process rights. We reject this argument for several reasons. First, although neither caselaw nor the statute defines "the equities" as that term appears in MCL 722.1011(3), the equitable functions of a court are well-established in our jurisprudence. For example, MCL 600.601 "contains a broad grant of all equity powers traditionally exercised in chancery to the circuit courts." Lester v. Oakland Co. Sheriff, 84 Mich.App. 689, 695, 270 N.W.2d 493 (1978). Trial courts are accustomed to fashioning equitable resolutions because "[i]t is the historic function of equity to give such relief as justice and good conscience require." Levant v. Kowal, 350 Mich. 232, 241, 86 N.W.2d 336 (1957). Here, the trial court drew on virtually all the traditional equitable principles applicable in family-law cases: the best interest of the child, the fitness of the competing parents, and the past relationships of the parties. Additionally, the trial court entertained testimony from Sinicropi concerning Noah's interest in and awareness of his genetic heritage, and expert opinion regarding the existing emotional bonds and family dynamics. In *526 our view, highly charged and intimate circumstances such as these require the flexibility and practicality of a traditional equitable approach. Equity aims to "do complete justice by embracing the whole subject, deciding upon and settling the rights of all persons interested in the subject-matter, to make performance of the orders perfectly safe to those who have to obey it, and to prevent further litigation." Ladas v. Psiharis, 241 Mich. 101, 106, 216 N.W. 458 (1927). Had the Legislature intended to impose a rigid template on this decision-making process, it would have done so. Sparks v. Sparks, 440 Mich. 141, 158-159, 485 N.W.2d 893 (1992).
Lastly, we observe that this case is not equivalent to a proceeding for the termination of parental rights, in which the state must establish by at least clear and convincing evidence constitutionally sufficient grounds for termination before it may sever parental rights. Santosky v. Kramer, 455 U.S. 745, 768-770, 102 S.Ct. 1388, 71 L.Ed.2d 599 (1982). The due-process principles discussed in Santosky derive from the liberty interests inherent in a parent's already established custodial relationship with a child. The United States Supreme Court has specifically rejected the notion that biological parenthood standing alone, or even in conjunction with some additional relationship, suffices to establish a liberty interest. Michael H. v. Gerald D., 491 U.S. 110, 123, 109 S.Ct. 2333, 105 L.Ed.2d 91 (1989). Because Sinicropi's relationship to Noah is biological, rather than parental, and otherwise wholly undeveloped, he has no constitutionally protected rights in the substance or procedures of the hearing conducted pursuant to MCL 722.1011(3).
Affirmed.
NOTES
[1]  Mazurek admitted that she permitted Noah to develop a relationship with Sinicropi's parents and his other family members despite the existence of an October 2005 court order prohibiting contact between Sinicropi and the child.
[2]  In her written report admitted as an exhibit during the evidentiary hearing, Dr. Lazar stated, "Noah does not appear to have knowledge of the issue of paternity in this case. Furthermore, I do not believe he understands or has knowledge of the biological issue involved."
