In 2001, the agricultural partnership Larry Reed & Sons (the partnership) and its individual partners were found by a jury to have submitted a false cotton crop insurance claim eight years earlier. The partnership's insurance claim requested coverage for the loss of 194.1 acres of cotton in 1993, but the jury found the claim violated the False Claims Act because the 194.1 acres in question were not planted during the 1993 season. After the district court* trebled the $93,686.50 in damages awarded by the jury, the partnership was liable for $281,059.50 and the partners were each liable for additional nominal amounts. The court also assessed the partnership the maximum statutory penalty of $10,000, and it assessed the partners lesser individual fines. The partnership appeals, contending (1) the damages awarded by the jury were based on insufficient evidence; (2) the district court abused its discretion in admitting the written statement of a state witness; and (3) the district court abused its discretion in allowing expert testimony about the extent of the soil preparation on the partnership's land, which was based on computer analysis of satellite images. We review each argument in turn.

First, we review damages awarded by the jury for sufficiency of the evidence, and "[w]e will not reverse a jury verdict for insufficient evidence unless no reasonable juror could have returned a verdict for the non-moving party." EFCO Corp. v. Symons Corp., 219 F.3d 734, 738 (8th Cir.2000) (standard of review). The partnership argues that because the complaint alleged just $49,720 in damages against the partnership and, at trial, the United States proved only a $56,874 loss due to the partnership's false cotton crop insurance claim, the jury's award of nearly $94,000 against the partnership was based on insufficient evidence. In turn, the United States argues the jury damage award was based on sufficient evidence because a total of $114,746 was deposited into partnership accounts directly from the partnership's and individual partners' fraudulent cotton crop insurance claims.

We disagree with the partnership's argument that the jury lacked sufficient evidence for the damages assessed against the partnership, even though the award was more than the amount specified in the initial complaint. The Federal Rules of Civil Procedure allow issues tried by express or implied consent of the parties — such as the partners' individual deposits of fraudulent cotton crop insurance proceeds into partnership accounts — to be treated as though they had been raised in the pleadings. Fed.R.Civ.P. 15(b). Thus, because we view the complaint as constructively amended to conform to the proof, see Charles Schmitt & Co. v. Barrett, 670 F.2d 802, 806 (8th Cir.1982), the United States' failure to include the partners' individual contributions of fraudulent cotton crop insurance proceeds in the original complaint against the partnership does not nullify the jury's damage award against the partnership. We hold reasonable jurors could have reached the same conclusion as the jurors in this case, who properly considered both the partnership's direct fraudulent cotton crop claim and the partners' contributions to partnership funds from their individual fraudulent cotton crop claims. The jury's award against the partnership was based on sufficient evidence and we will not disturb it.

Second, we review the district court's decision to admit the earlier statement of government witness Lyman Reynolds, a Larry Reed & Sons partner, for abuse of discretion. See Foster v. Time Warner Entertainment Co., L.P., 250 F.3d 1189, 1197 (8th Cir.2001) (standard of review). At trial, Reynolds testified he did not know if Reed had planted cotton in 1993. The court allowed the United States to introduce Reynolds' earlier statement — that Reed did not plant cotton — for impeachment purposes under Federal Rule of Evidence 613. To introduce a witness's own earlier statement for impeachment, (1) the statements must be inconsistent, (2) the inconsistency must be relevant, (3) the inconsistent statement must, on request, be disclosed to opposing counsel, the witness allowed to explain the inconsistency, and opposing counsel allowed to question the witness, and (4) the district court should instruct the jury about the limited purpose of the earlier statement. United States v. Rogers, 549 F.2d 490, 495-98 (8th Cir.1976). In Reynolds's situation, the first three prongs of the impeachment standard were satisfied, but the fourth prong was not: the district court did not give the jury a limiting instruction. When neither party requests a limiting instruction at trial, however, we review the trial court's failure to issue such an instruction for plain error. See McKnight v. Johnson Controls, Inc., 36 F.3d 1396, 1403 n. 6 (8th Cir.1994) (standard of review). Given the context in which Reynolds's statement was introduced and the rest of the evidence against the partnership, we find no plain error here.

Third, we review for abuse of discretion the court's decision that Dr. John Brown's expert testimony about the soil preparation of the partnership's farmland, which was based on the computer analysis of satellite images, was reliable evidence. See Smith v. Rasmussen, 249 F.3d 755, 758 (8th Cir.2001) (standard of review). Generally, expert testimony is admissible when it is reliable and when it will assist the trier of fact. Fed. R. Ev. 702. Trial courts have substantial latitude to determine whether specific expert testimony is reliable, and they may consider some or all of the factors listed in Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 592-95, 113 S. Ct. 2786, 125 L. Ed. 2d 469 (1993), when evaluating reliability. Kumho Tire Co. v. Carmichael, 526 U.S. 137, 149-50, 119 S. Ct. 1167, 143 L. Ed. 2d 238 (1999).

When Brown testified about his computer analysis of May 8, 1993 satellite images which led him to conclude the partnership's cotton fields were not planted, he also discussed the acceptance of his methodology. Brown referred to "hundreds and hundreds" of academic articles published about the process of computer analysis of satellite images, the use of this method by NASA and about 10 major universities for the purpose of enhancing agricultural productivity, and the application of this method in assessing crop hail damage. (Tr. 410-11). Further, when testifying, Brown clearly explained his method of analysis, presented the satellite data, and illustrated how he applied the method to the facts before him. We conclude the district court did not abuse its discretion under Daubert and Kumho Tire when admitting Brown's expert testimony as reliable evidence.

In conclusion, because the partnership's claims lack merit, we affirm the jury damage award and the decisions of the district court. We also grant the government's motions to supplement the record and to substitute a trial exhibit.