A jury convicted Defendant Stephen James Stapleton of several counts of mail fraud, 18 U.S.C. § 1341 , and several counts of wire fraud, 18 U.S.C. § 1343 . On appeal, he challenges an instruction that permitted the jury to find him vicariously liable for acts of other participants in the fraudulent scheme of which he was a part. We affirm.

I. THE FRAUDULENT SCHEME

Criminal charges against several people, including Defendant, arose from their involvement in a telephone-marketing company called Gecko Holdings, Inc. (Gecko), which operated from December 1997 to March 1999. Defendant was a telephone salesperson there from October 1998 until March 1999. 1

Gecko was a fraudulent organization that purported to be initiating a public stock offering for an Internet casino. It operated out of two offices in Orange County, California, under the direction of Robert Syrax. 2

Gecko’s participating telemarketers called potential investors and made false statements to induce them to send money to Gecko. The false statements included representations that Gecko’s managers were affiliated with Cryptologic, an Internet casino that had been taken public successfully; that Gecko was operating a casino on the island of St. Kitts in the Caribbean; that only a limited number of Gecko shares would be available; that there was little risk associated with the investment; that investors could expect huge returns quickly; and that Gecko was very close to going public on the NASDAQ exchange. None of the foregoing representations was accurate.

In addition, Gecko sent three different versions of its prospectus to its victims. Each version contained a different list of officers. The named individuals either were not officers (for example, one was an acquaintance from a health club who was not associated with Gecko and who had not given permission to use his name) or were entirely fictitious. The “lead sheets” containing the names and telephone numbers of potential investors were color-coded so *1114 that the telemarketers knew which version of the prospectus a particular person had received and, thus, which fictitious corporate officers could be discussed in the conversation. Gecko also sent letters to investors, allegedly signed by fictitious officers, which discussed the go-public price of the stock.

II. PROCEDURAL BACKGROUND

Defendant and six others were charged with several counts of mail fraud and several counts of wire fraud. Three of those charged pleaded guilty. The remaining four, including Defendant, were tried jointly. The district court granted Defendant’s motion for a judgment of acquittal on one charge; the jury found him guilty on the rest.

A co-defendant filed a motion for a new trial, in which Defendant joined. The court denied the motion and, thereafter, sentenced Defendant to 46 months of imprisonment, to be followed by three years of supervised release, plus restitution of $4,147,961.25 and a special assessment of $1,700. Defendant filed this timely appeal.

III. THE “CO SCHEMER” INSTRUCTION

Defendant’s only argument on appeal is that the district court erred in instructing the jury on a theory of “co-schemer” liability. He asserts that the instruction unlawfully broadened the indictment and omitted essential elements of the offense.

A. Standards of Review

We review de novo whether the district court’s instructions omitted or misstated an element of the charged offense. United States v. Knapp, 120 F.3d 928, 930 (9th Cir.1997). We review for abuse of discretion the formulation of the instructions. Id. We must consider the instructions as a whole, and in context. United States v. Warren, 25 F.3d 890, 898 (9th Cir.1994).

B. The Instructions

After providing general instructions, including instructions about the presumption of innocence and the requirement of proof beyond a reasonable doubt, the court gave the following instructions concerning the elements of mail fraud, the elements of wire fraud, and the ways in which a defendant may be held personally responsible for the commission of an act of mail fraud or wire fraud:

(Boldface highlighting added.)

The court then completed the instructions concerning aiding and abetting and concluded with some general instructions. Defendant challenges only the above-highlighted portion of the instructions.

During deliberations, the jury sent this note to the judge: “The jury requests the following: Jurors question[ ] whether one can be a co-schemer with one he has no personal knowledge of.” After a discussion with counsel, the court further instructed the jury as follows:

Defendant does not challenge this supplemental instruction directly but cites it as evidence that the above-highlighted instruction on vicarious liability, combined with the absence of a full conspiracy instruction, “played some role in the deliberation.”

C. The “Co-schemer” Theory in Our Past Cases

In United States v. Lothian, 976 F.2d 1257 (9th Cir.1992), we considered in detail the concept of vicarious liability for acts of mail fraud and wire fraud. Lothian had been convicted (along with several co-defendants) on numerous counts of mail fraud, wire fraud, and interstate transportation of property obtained by fraud. Id. at 1259 . The indictment contained no conspiracy count, but only substantive counts. Id. at 1260 . Lothian argued, among other things, that he withdrew from the operation and could not be convicted for acts that occurred after he withdrew. In response, we stated:

Id. at 1261 (citations omitted).

In that context — the presence of substantive fraud counts and the absence of conspiracy counts — we held that vicarious liability is appropriate and drew a parallel to conspiracy law:

Id. at 1262-68 (citations omitted). Applying those parallel principles, we held that withdrawal from a fraudulent scheme ends a co-schemer’s knowing participation and can, therefore, negate the element of using or causing the use of the mails or wires; but vicarious liability remains for uses of the mails or wires that are an inevitable consequence of actions taken while the defendant was a knowing participant in the scheme. Id. at 1263 .

Later cases have continued to emphasize the propriety of vicarious liability for fraudulent telemarketing schemes. For example, in United States v. Blitz, 151 F.3d 1002, 1006 (9th Cir.1998), we held that the evidence was sufficient to hold one defendant criminally hable for the acts of another.

Similarly, in United States v. Hanley, 190 F.3d 1017, 1022 (9th Cir.1999), we turned away a claim of insufficient evidence to support convictions for wire fraud, quoting Lothian and explaining “that co-schemers in a scheme to defraud may be held vicariously hable for the acts of their co-schemers.”

None of our earlier cases involved the validity of particular instructions. They do estabhsh certain principles, however, which bear on whether the instructions that the district court gave in this case were proper:

D. The Fit Between the Instructions and the Theory

When we examine the instructions in the light of our precedents, we find no error of law in the court’s description of the elements of vicarious liability and no abuse of discretion in the court’s particular formulation of those elements.

The instructions stated that a member of a scheme to defraud is criminally liable for acts of mail or wire fraud committed by *1118 co-schemers. As we have discussed, that is not a novel theory of liability in this circuit. Our precedents plainly support it. Although the instruction employed the term “member of a scheme to defraud” and did not use the phrase “knowing participant,” we find no error because the instructions required the jury to find that Defendant was a member of a scheme to defraud who personally had the intent to defraud; defined “intent to defraud” to require a finding that Defendant intended to deceive or cheat; defined “scheme to defraud” to require a finding that there was a deliberate plan of action designed to deceive or cheat another person; required the jury to find that the co-schemers’ acts were in furtherance of the unlawful scheme; and required the jury to find that Defendant personally made up or participated in the scheme. If a jury made findings in accordance with those instructions, it could not have found that Defendant failed to participate in the fraudulent scheme or that his participation was other than “knowing.”

The instructions limited vicarious liability to acts of co-schemers during the life of the scheme and acts that were reasonably foreseeable as a necessary and natural consequence of the fraudulent scheme. While that formulation differs somewhat from the discussion in Lothian , we find no abuse of discretion, particularly because Defendant was convicted for acts that occurred only during his active participation in the scheme to defraud.

Thus, before the jury imposed vicarious liability, the instructions required a finding that Defendant was a member of the scheme to defraud and personally had the intent to defraud. 3 Further, the instructions limited the imposition of vicarious liability to acts within the scope of the fraudulent scheme. The instructions were therefore consistent with the theory of vicarious liability that we articulated in Lot-hian.

The mere fact that the district court based the wording of this instruction on one of the pattern instructions for conspiracy, 9th Cir.Crim. Jury Instr. 8.20 (2000), does not necessarily make it either erroneous or incomplete. As we noted in Lothian , co-schemer liability is similar to co-conspirator liability. 976 F.2d at 1262-63 . Having recognized that the two kinds of liability are analogous, we conclude that the district court did not abuse its discretion by patterning the co-schemer liability instruction the co-conspirator liability instruction.

1. The Challenged Instruction Did Not Broaden the Indictment.

The indictment in this case expressly charged a scheme to defraud and expressly charged that Defendant was a knowing participant in the scheme. Under the heading “THE SCHEME TO DEFRAUD,” for example, the indictment charged that a number of people, including Defendant, “knowingly and with the intent to defraud, devised, participated in, and executed a scheme to defraud victims.” The indictment further charged that Defendant “knowingly engaged in and caused *1119 others to engage in” specified fraudulent practices. The indictment referred to the participants as “eo-schemer[s].”

Notwithstanding the indictment’s inclusion of the co-schemer theory, Defendant argues that he cannot be held liable for mail or wire fraud except in the context of a discrete conspiracy charge. As he puts it: “The instruction on the Pinkerton 4 liability assumes the existence of a conspiracy such that [Defendant] could be convicted on the non participator counts based on conspiracy liability. Conspiracy was not a theory set forth in the Indictment.” Thus, he reasons, the instruction on vicarious liability “created an impermissible constructive amendment to the Indictment.” Lothian and its progeny establish the principle, however, that vicarious liability for substantive counts of mail or wire fraud does not require that the indictment charge conspiracy. 976 F.2d at 1262-63 .

2. The Challenged Instruction Did Not Omit Elements of the Offense.

The mail fraud statute, 18 U.S.C. § 1341 , provides:

The wire fraud statute, 18 U.S.C. § 1343 , provides:

The quoted instructions correctly stated the elements of those crimes. The instructions given here substantially mirror those recommended for both mail and wire fraud in the Ninth Circuit Manual of Model Jury Instructions. 9th Cir.Crim. Jury Instrs. 8.101, 8.103 (2000). Indeed, Defendant does not argue that elements were missing *1120 from the instructions describing the elements of mail fraud or wire fraud.

Instead, his argument about missing instructional elements stems from the same mistaken premise as his argument about a missing charge in the indictment, that is, that this is a “conspiracy” case requiring a full “conspiracy” instruction:

As we have discussed above, the substantive law of this circuit is that co-schemer liability for mail or wire fraud does not require proof of a conspiracy. We have held that co-schemer liability is possible for knowing participants in the fraudulent scheme for which the mails or wires were used. Indeed, it would have been error for the court to have given the requested conspiracy instruction. No conspiracy (unlawful agreement) was charged, but only substantive fraud offenses; and no conspiracy had to be charged. Vicarious liability was properly instructed and imposed for the mail and wire fraud counts alone.

IV. CONCLUSION

The district court did not commit reversible error in instructing the jury on vicarious liability for mail fraud and wire fraud. Accordingly, the judgment is

AFFIRMED.

. Defendant does not argue that there is legal significance to his participation during only part of the existence of the scheme to defraud. The mailings for which he was convicted began on October 30, 1998, and the wire communications for which he was convicted began on October 15, 1998.

. In a separate case, Syrax pleaded guilty to one count each of mail fraud, wire fraud, interstate transportation of property obtained by fraud, and money laundering. We affirmed Syrax's convictions and sentence in United States v. Syrax, 235 F.3d 422 (9th Cir.2000), cert. denied, 532 U.S. 988 , 121 S.Ct. 1639 , 149 L.Ed.2d 498 (2001).

. Defendant does not challenge specifically the supplemental instruction, which told the jury that a defendant need not know the names or identities of other members of the fraudulent scheme in order to be vicariously liable, nor does he challenge specifically the part of the instruction that said a defendant can be vicariously liable without knowing what a particular co-schemer said or did. We find no plain error. See United States v. McIver, 186 F.3d 1119, 1130-31 (9th Cir.1999) (reviewing for plain error an unpre-served objection to a supplemental instruction). None of our past cases on co-schemer liability has required personal knowledge of a co-schemer’s identity or activity, and none has differentiated co-schemer liability from co-conspirator liability in this respect.

. In Pinkerton v. United States, 328 U.S. 640, 645-47 , 66 S.Ct. 1180 , 90 L.Ed. 1489 (1946), the Supreme Court held that a conspirator may properly be found vicariously liable for any substantive offense committed by a co-conspiralor, as long as the offense was committed during the course of and in furtherance of the conspiracy.