
747 So.2d 958 (1999)
Julia TOLEDO and Connie Peterson, mother and next friend of Jason Peterson, a minor, Appellants,
v.
HILLSBOROUGH COUNTY HOSPITAL AUTHORITY, d/b/a and operating as Tampa General Hospital, Appellee.
No. 98-04296.
District Court of Appeal of Florida, Second District.
August 18, 1999.
*959 Emmett Abdoney and John W. Hoft, Jr., Tampa, for Appellants.
Richard A. Harrison and Tabatha A. Liebert of Allen, Dell, Frank & Trinkle, P.A., Tampa, for Appellee.
PARKER, Acting Chief Judge.
Julia Toledo and Connie Peterson (the Plaintiffs) seek review of an interlocutory order of the trial court denying their motion for class certification. Because we find that the trial court did not abuse its discretion in finding that the Plaintiffs failed to establish numerosity, we affirm. We also note that the trial court erred in disregarding the law of the case on the issue of adequate representation.
In 1993 Julia Toledo and Jason Peterson, Connie Peterson's son, received treatment at Tampa General Hospital (the Hospital). The Hospital subsequently served billings and filed liens against the Plaintiffs and, in 1995 the Plaintiffs filed a complaint alleging that the Hospital's billing practice interfered with their health insurance contracts and was actionable in tort. The complaint charged the Hospital with tortious interference with contract, tortious interference with advantageous business relationship, wrongful lien, civil theft, and conversion. The trial court dismissed the cause of action for conversion and eventually granted summary judgment on the civil theft claim. The Plaintiffs also filed a demand for class certification and subsequently identified the proposed class as all persons the Hospital had filed liens against to collect bills that were in excess of the discount amount charged to their insurer.
In 1996 the Plaintiffs filed a motion for class certification. At an evidentiary hearing on this motion, Brenda Mulder, the Plaintiffs' economics expert, testified that she had conducted a survey from which she concluded that the class consisted of 1607 individuals. In January 1997 the trial court signed an order granting class certification. Seventeen days later, the Plaintiffs filed a motion for clarification and correction of order noting that the order granting class certification contained a clerical mistake and that the Plaintiffs had inadvertently omitted a time for determination of notice. The trial judge entered an order of recusal before hearing the motion for clarification. The Hospital then filed a notice of appeal of the January 1997 order, and this court affirmed. See Hillsborough County Hosp. Auth. v. Toledo, *960 696 So.2d 350 (Fla. 2d DCA 1997) (per curiam).
Thereafter, the successor judge granted the Plaintiffs' motion for clarification and correction and ordered an evidentiary hearing regarding class certification. The Hospital filed an affidavit of Dr. Susan A. McManus, an expert in survey analysis and design, which concluded that Mulder's methodology failed to conform to generally-accepted principles of statistical analysis and would not be accepted by competent professional survey researchers. The Hospital also offered into evidence a certified copy of the Hillsborough County Index, which showed that Mulder had based her survey on an incorrect number of lienees. The trial court subsequently entered an order denying class certification, which is the order on appeal before this court.
Under Florida Rule of Civil Procedure 1.220(a), there are four prerequisites to class certification:
(1) the members of the class are so numerous that separate joinder of each member is impracticable, (2) the claim or defense of the representative party raises questions of law or fact common to the questions of law or fact raised by the claim or defense of each member of the class, (3) the claim or defense of the representative party is typical of the claim or defense of each member of the class, and (4) the representative party can fairly and adequately protect and represent the interests of each member of the class.
In this case, the trial court concluded that, while the Plaintiffs had met the commonality and typicality prerequisites of rule 1.220, they had not met the numerosity or adequate representation prerequisites. The trial court determined that Mulder's methodology was "flawed to the extent that the Court cannot give it any weight" and stated that Mulder's conclusions "amount to mere supposition." The trial court also found that there was no evidence that Peterson was familiar with the facts or had the requisite knowledge of essential issues required to establish adequate representation.
The Plaintiffs argue that the trial court erred in disregarding the law of the case as established when this court issued its mandate affirming the trial court's previous order granting class certification. We find merit in this argument as it pertains to the adequate representation prerequisite for class certification, but not as to the numerosity prerequisite. Once an appellate court issues a mandate in a case, the determinative issues become the law of the case and the trial court is without authority to modify, nullify, or evade that mandate. See Brunner Enters., Inc. v. Department of Revenue, 452 So.2d 550, 552 (Fla.1984); O.P. Corp. v. Village of North Palm Beach, 302 So.2d 130, 131 (Fla.1974). The doctrine of law of the case applies in subsequent proceedings as long as there has been no change in the facts on which the mandate was based. See Feigen v. Sokolsky, 65 So.2d 769, 771 (Fla.1953) (en banc); Mitzenmacher v. Mitzenmacher, 656 So.2d 178, 179 (Fla. 3d DCA 1995). Due to the trial court's broad authority to alter or amend orders determining class certification, the doctrine of law of the case "applies only sparingly in class certification proceedings." Fair Housing for Children Coalition, Inc. v. Pornchai Int'l, 890 F.2d 420, at 421 (9th Cir.1989) (unpublished disposition).[1]
In this case, the only new evidence introduced at the evidentiary hearing pertained to numerosity. Because neither party offered additional evidence relating to Peterson's ability to adequately represent the class, this court's mandate[2]*961 affirming a finding of adequate representation became the law of the case. Accordingly, the trial court erred in finding that the Plaintiffs did not meet the adequate representation prerequisite. However, the law of the case does not apply to the finding regarding numerosity because the Hospital introduced new evidence which refuted the Plaintiffs' basis for numerosity.
At issue then is whether the trial court erred in finding that the Hospital's evidence discredited Mulder's analysis to such an extent that it negated a previous finding of numerosity. This court will not reverse an order determining class certification absent an abuse of discretion. See Goldfarb v. Insurance Co. of North America, 642 So.2d 586, 587 (Fla. 3d DCA 1994). It is well-settled that, while a plaintiff is not required to plead the exact number of persons included in a proposed class, a plaintiff is precluded from relying on speculation as to class size. See Marcial v. Coronet Ins. Co., 880 F.2d 954, 956 (7th Cir.1989); Trull v. Plaza Assocs., No. 97 C 0704, 1998 WL 578173, at *3 (N.D.Ill.1998) (unpublished disposition).
In this case, the trial court found that the Hospital's evidence discredited Mulder's survey, leaving the Plaintiffs' allegation that the class consisted of 1607 individuals to be supported by mere speculation. According to Mulder, the Hospital filed 5013 hospital liens in 1993 and she selected 520 as a 10% random sample universe. She received fifty-three responses as a result of the survey and concluded that 32% or 1607 individuals were members of the class while 67.9% were not. Mulder stated that she was 85% confident that the class would be within the range stated within a 10% error. However, Dr. McManus concluded:
An 85% level of confidence is unconventionally low, a 10% margin of error is unusually high and sample size of 53 is well below the minimum sample size necessary to ensure [a] generally acceptable confidence level of 95%, even with a margin of error of 10%. The combination of such an unconventionally low level of confidence, unusually high margin of error and unacceptably small sample size renders any such survey highly unreliable and any conclusions one might attempt to draw from a survey conducted with [sic] these parameters would be equally highly unreliable.
Additionally, Mulder had based her survey on 5013 lienees, but the Hillsborough County Index showed that Hospital actually filed 3298 claims of liens in 1993.
Because Mulder's survey was the only basis for establishing numerosity, we find that the Hospital provided sufficient evidence from which to conclude that the Plaintiffs' allegation that the class consisted of 1607 individuals resulted from mere speculation. We affirm because we find that the trial court did not abuse its discretion in finding that the Plaintiffs failed to establish numerosity. We also note that, with the presentation of new evidence, the Plaintiffs again may move for class certification at any time before entry of a judgment on the merits. See Fla. R. Civ. P. 1.220(d).
Affirmed.
GREEN, J., and HAYES, HUGH D., Associate Judge, Concur.
NOTES
[1]  Since Florida Rule of Civil Procedure 1.220, which governs class certification, is based on Federal Rule of Civil Procedure 23, federal cases are persuasive authority for interpretation of rule 1.220. See Concerned Class Members v. Sailfish Point, Inc., 704 So.2d 200, 201 (Fla. 4th DCA 1998).
[2]  A per curiam mandate issued by the appellate court becomes the law of the case on all issues involved in the appeal, regardless of whether the court addresses the issues in the opinion. See Mitzenmacher v. Mitzenmacher, 656 So.2d 178, 179 (Fla. 3d DCA 1995).
