
589 F.3d 1323 (2009)
UNITED STATES of America, Plaintiff-Appellee,
v.
Michael CALDWELL, Defendant-Appellant.
No. 08-6143.
United States Court of Appeals, Tenth Circuit.
December 29, 2009.
*1326 John T. Carlson, Assistant Federal Public Defender (Raymond P. Moore, Federal Public Defender, with him on the briefs), Denver, CO, for the Defendant-Appellant.
Sanford C. Coats, Assistant U.S. Attorney (John C. Richter, U.S. Attorney, with him on the briefs), Oklahoma City, OK, for the Plaintiff-Appellee.
Before LUCERO, ANDERSON, and EBEL, Circuit Judges.
LUCERO, Circuit Judge.
This case is before us on direct appeal of a criminal conviction and sentence. Among other dispositions,[1] Michael Caldwell was convicted by a jury of participating in a three-party conspiracy to distribute marijuana. The government alleged the conspiracy consisted of Caldwell, the defendant; David Anderson, a street dealer of marijuana; and Samuel Herrera, the drug supplier for both Anderson and Caldwell. *1327 In its verdict, the jury concluded the three men entered into a single conspiracya tripartite conspiracyto distribute at least 100 kilograms of marijuana over a two-year period. Although Caldwell admits that he conspired with Herrera, he argues that insufficient evidence supports the theory of a tripartite conspiracy. Caldwell maintains that both the jury and the sentencing judge attributed an improper quantity of marijuana to him. He also asserts that, during trial, the district court erroneously admitted evidence of his prior convictions for drug-related crimes.
On our review of the record on appeal, we conclude that the evidence presented at Caldwell's trial was indeed sufficient to establish conspiracies between Caldwell and Herrera and between Caldwell and Anderson, but that it was insufficient to establish a tripartite conspiracy among all three. Both the jury and the sentencing court erroneously attributed quantities of marijuana to Caldwell based on the existence of a tripartite conspiracy. Exercising jurisdiction under 28 U.S.C. § 1291 and 18 U.S.C. § 3742(a)(1), we affirm Caldwell's conviction, but vacate his sentence and remand the case to the district court for resentencing.

I
Beginning in 1995, the United States Drug Enforcement Administration ("DEA") began investigating a drug ring headed by the Rosales family of El Paso, Texas. The family's main contact in Oklahoma was Robert Williams, who distributed marijuana to a number of intermediary suppliers in the state. These suppliers distributed the marijuana, mostly on consignment, to street-level dealers.
Herrera was one such intermediary supplier. He sold marijuana to a number of street-level dealers in Oklahoma City, including Caldwell. The first transaction between Herrera and Caldwell took place in 2004. During that transaction, Caldwell received between two to four kilograms of marijuana on consignment. For approximately two years thereafter, Herrera distributed two to seven kilograms of marijuana once every several weeks to Caldwell. Caldwell then resold the marijuana to users.
Anderson, a friend of Caldwell's since early 2005, eventually became another one of Herrera's main customers. Early in their friendship, Anderson dealt drugs to Caldwell: On two or three occasions shortly after they met, Anderson sold Caldwell approximately one kilogram of marijuana on consignment. For roughly one year after these sales occurred, Anderson and Caldwell had no drug-related interaction. Then in early 2006, Anderson's regular supplier was "running short" on marijuana, and Anderson asked Caldwell if he knew of a reliable drug supplier. Caldwell arranged a meeting between Anderson and Herrera. Even though Caldwell was present at the initial meeting, during which Herrera sold approximately 4.5 kilograms of marijuana to Anderson on consignment, Caldwell received no economic benefit from the introduction. From that point on, Anderson and Herrera dealt with one another "one-on-one"that is, no subsequent drug transactions between Anderson and Herrera involved Caldwell. Anderson received monthly supplies of approximately four to nine kilograms of marijuana from Herrera, generally on consignment.
During the course of its investigation, the DEA intercepted several incriminating calls regarding the distribution of marijuana between Herrera and Caldwell,[2] and a *1328 number of similar calls between Herrera and Anderson. It did not intercept any drug-related telephone conversations between Caldwell and Anderson.
In October 2007, a grand jury indicted Caldwell for conspiracy to distribute 100 kilograms or more of marijuana in violation of 21 U.S.C. § 841(a)(1). The indictment listed Caldwell, Herrera, and Anderson as members of the same conspiracy. In exchange for reduced sentences, both Herrera and Anderson testified at trial. A DEA agent also testified that, during the course of the conspiracy, Herrera sold 54 to 163 kilograms of marijuana to Caldwell and 163 to 327 kilograms of marijuana to Anderson.
Over Caldwell's objection, the government also introduced evidence of Caldwell's prior drug-related convictions, several of which occurred more than fifteen years before his indictment in this matter. In instructing the jury on the limited admission, the district court stated that Caldwell's prior convictions "must not be taken by [the jury] as proof that [Caldwell] did what is charged in the indictment of this case," but could only be used to determine "whether he had a motive or opportunity to commit the acts charged in this case and what his intent was."
Caldwell was convicted of conspiracy to distribute marijuana, and the jury returned a special verdict finding that the conspiracy involved 100 kilograms or more of marijuana. During sentencing, the court relied on the special verdict and a presentence investigation report ("PSR"). The PSR attributed 188 kilograms of marijuana to Caldwell. Caldwell objected to the drug quantity determinations of the jury and the PSR, but the court overruled Caldwell's objection. Based on its finding that over 100 kilograms of marijuana was attributable to Caldwell, the court sentenced Caldwell to 130 months' imprisonment.

II

A
We must first consider whether the government produced sufficient evidence for a reasonable jury to conclude that Herrera, Caldwell, and Anderson were engaged in a tripartite conspiracy to distribute marijuana. Where "an indictment charges a single conspiracy, but the evidence presented at trial proves only the existence of multiple conspiracies," a variance occurs. United States v. Carnagie, 533 F.3d 1231, 1237 (10th Cir.2008). In considering a claimed variance, "we view the evidence and draw all reasonable inferences therefrom in the light most favorable to the government, asking whether a reasonable jury could have found [the defendant] guilty of the charged conspirac[y] beyond a reasonable doubt." Id. The existence of a variance that would support acquittal is a matter of law that we review de novo. See United States v. Avery, 295 F.3d 1158, 1177 (10th Cir.2002); see also United States v. Griffin, 493 F.3d 856, 862 (7th Cir.2007) ("We treat a conspiracy variance claim as an attack on the sufficiency of the evidence supporting the jury's finding that each defendant was a member of the same conspiracy.").
As noted, we conclude that Herrera's role as a common supplier, Caldwell's earlier purchase of marijuana from Anderson, and Caldwell's introduction of Anderson to Herrera do not constitute sufficient evidence of a single conspiracy among the three drug dealers. Instead, the evidence presented at trial demonstrates the existence *1329 of separate conspiracies between Caldwell and Anderson, and between Caldwell and Herrera. Assuredly, each of the three conspired to distribute marijuana, but a conspiracy did not exist among Herrera, Caldwell, and Anderson as a group.

1
Distinguishing between a single, large conspiracy and several smaller conspiracies is often difficult; we will generally defer to the jury's determination of the matter. See United States v. Powell, 982 F.2d 1422, 1431 (10th Cir.1992). Nonetheless, "we may not uphold a conviction obtained by piling inference upon inference.... The evidence supporting the conviction must be substantial and do more than raise a suspicion of guilt." United States v. Anderson, 189 F.3d 1201, 1205 (10th Cir.1999).
To prove a conspiracy, the government must demonstrate: "(1) that two or more persons agreed to violate the law, (2) that the defendant knew at least the essential objectives of the conspiracy, (3) that the defendant knowingly and voluntarily became a part of it, and (4) that the alleged coconspirators were interdependent." United States v. Sells, 477 F.3d 1226, 1235 (10th Cir.2007) (quotation and alteration omitted). In reviewing a jury's determination that a single conspiracy existed, "a focal point of the analysis is whether the alleged coconspirators' conduct exhibited interdependence." United States v. Edwards, 69 F.3d 419, 432 (10th Cir.1995). Interdependence exists where coconspirators "inten[d] to act together for their shared mutual benefit within the scope of the conspiracy charged." United States v. Evans, 970 F.2d 663, 671 (10th Cir.1992). Circumstantial evidence alone is often sufficient to demonstrate interdependence; indeed, it is often the only evidence available to the government. See United States v. Hutchinson, 573 F.3d 1011, 1035 (10th Cir.2009). Further, a single act can be sufficient to demonstrate interdependence. See, e.g., United States v. Hamilton, 587 F.3d 1199, 1208-09 (10th Cir. 2009) (determining that a single instance of traveling to collect another drug dealer's debts was sufficient to show defendant became a part of a large and wide-reaching conspiracy).
We are told by the government that the relationship between Caldwell, Anderson, and Herrera was a "vertical conspiracy." A vertical conspiracy, or "chain-and-link" conspiracy, involves a series of consecutive buyer-seller relationships. The classic vertical conspiracy involves Supplier A selling contraband to Supplier B, who then sells the contraband to Supplier C. See United States v. Dickey, 736 F.2d 571, 582 (10th Cir.1984). But as we indicated in Dickey, drug distribution organizations often do not fit neatly into the concept of vertical conspiracy. Id.
In the present case, Caldwell and Anderson were equal-level purchasers rather than links in a vertical chain. After Herrera became their joint supplier, neither Caldwell nor Anderson bought or sold marijuana to the other. Instead, each independently sold marijuana to third parties. Thus, their relationship does not evince the characteristics of a vertical conspiracy. Cf. United States v. Kiister, No. 99-3042, 2000 WL 228304, at *7 n. 10 (10th Cir. Feb.29, 2000) (unpublished) (indicating that evidence showing a conspiracy among "equal-level purchasers" may be "less applicable in a vertical conspiracy" context). Were we to categorize this alleged conspiracy, it would fit more neatly into the concept of a "hub-and-spoke" conspiracy, in which several separate players all interact with a common central actor, here Herrera. See, e.g., Kotteakos v. United States, 328 U.S. 750, 754-55, 66 S.Ct. 1239, 90 *1330 L.Ed. 1557 (1946). However, because any conspiracy requires a showing of interdependence, we prefer to eschew rigid labels and instead engage in the general, yet fact-specific, inquiry of whether there is evidence of interdependence among all alleged coconspirators.

2
When multiple individuals are involved in the sale of illegal drugs, they are engaged in an inherently illicit enterprise. Consequently, the degree of specificity with which the government must prove interdependence among them may be lower in the drug context than in the context of other types of conspiracies. Carnagie, 533 F.3d at 1239 n. 5; see also United States v. Small, 423 F.3d 1164, 1183 (10th Cir.2005). But even in the drug context, we must "scrupulously safeguard each defendant individually, as far as possible, from loss of identity in the mass." Kotteakos, 328 U.S. at 776, 66 S.Ct. 1239.
It is essential that the evidence demonstrate a mutual benefit before we proceed to determine that several drug dealers who interact with one another are involved in a single conspiracy:
It is not enough that a group of people separately intend to distribute drugs in a single area, nor even that their activities occasionally or sporadically place them in contact with each other. People in the same industry in the same locale (even competitors) can occasionally be expected to interact with each other without thereby becoming coconspirators. What is needed is proof that they intended to act together for their shared mutual benefit within the scope of the conspiracy charged.
Evans, 970 F.2d at 670-71. For example, we determined in Powell that several drug dealers who shared a common supplier and sold to the same customers and wholesalers in a cooperative matter could be found to have engaged in a single conspiracy. 982 F.2d at 1431. However, sharing a common supplier, without more, does not demonstrate that two drug dealers are acting together for their shared mutual benefit. See Edwards, 69 F.3d at 431. Accordingly, in the case at bar, the fact that Caldwell and Anderson both bought from Herrera is insufficient to establish interdependence among the three.

3
The government argues that Anderson's sale of a relatively small amount of marijuana to Caldwell, approximately one year before Anderson met Herrera, supports the jury's finding of a tripartite conspiracy. Undoubtedly, the government presented sufficient evidence for a jury to conclude that Caldwell and Anderson were involved in a conspiracy to distribute marijuana in early 2005: Anderson provided Caldwell with two or three kilograms of marijuana on consignment in early 2005. Our court has previously held that providing drugs on credit can be sufficient to demonstrate a conspiracy to distribute drugs. See Hamilton, 587 F.3d at *1210-11. But the question is whether Caldwell's introduction of Anderson to Herrera constituted a continuation of the earlier Caldwell-Anderson conspiracy. If Caldwell and Anderson were still involved in a conspiracy to distribute marijuana when the introduction occurred, that conspiracy (and thus Caldwell as a member) would have benefitted from Anderson being introduced to Herrera.
"[A] conspiracy, once instituted, continues to exist until it is abandoned, succeeds, or is otherwise terminated by some affirmative act, such as withdrawal by the defendant." United States v. Russell, 963 F.2d 1320, 1322 (10th Cir.1992). Although a lapse in time does not necessarily *1331 convert a single conspiracy into multiple conspiracies, time in combination with other factors can "sever the single continuous conspiracy alleged in the indictment into two separate conspiracies." United States v. Williamson, 53 F.3d 1500, 1513-14 (10th Cir.1995).
Under the totality of the circumstances present here, a reasonable jury could not have concluded that the introduction of Anderson to Herrera constituted a continuation of the earlier Caldwell-Anderson conspiracy. Approximately one year passed between Anderson's last sale of drugs to Caldwell and the introduction. A relatively small quantity of drugs passed between Anderson and Caldwell, indicating the objectives of their conspiracy were achieved through a discrete sale of marijuana. Unlike the coconspirators in Williamson, Anderson and Caldwell did not spend their year apart merely "enjoying the fruits of their proceeds," and Anderson did not stop selling drugs to Caldwell in order to cover up their crimes. See id. at 1514. To the contrary, Anderson and Caldwell used the year to build separate illicit businesses, wherein each obtained marijuana and sold it to customers. Because this arrangement demonstrates that the two were competing rather than cooperating, the government failed to meet its burden of proving that the earlier Caldwell-Anderson conspiracy "still functioned as a single ongoing entity" when Caldwell introduced Anderson to Herrera. Id.

4
We now address a question of first impression for the Tenth Circuit: Is the mere introduction of a common supplier, made by one drug dealer to another, sufficient to create a single conspiracy among all the dealers? We conclude that it is not.
The government attempts to equate this case with United States v. Ivy, 83 F.3d 1266 (10th Cir.1996), in which we held that a single conspiracy existed among three drug dealers. There, a jury convicted Kenny Taylor, a street-level drug dealer, of conspiring with Samuel Norwood and Raymond Hickman to distribute crack cocaine. Id. at 1271. Norwood sold crack cocaine to Hickman, who in turn sold it to Taylor. Id. at 1286. We upheld the jury's finding of a single conspiracy in part because Taylor referred a customer to Hickman. Id. In that situation, however, the government used the introduction to demonstrate that Taylor, Norwood, and Hickman were interdependent, not that Taylor and the man he introduced to Hickman were interdependent.[3]Id. By contrast, the government is attempting to use an introduction to show that Caldwell was interdependent with Anderson, the man Caldwell introduced to his supplier.
Having established that Ivy does not govern this case, we look to the type of evidence required to uphold a conspiracy conviction. Under our case law, "mere presence is not sufficient in and of itself [to establish a conspiracy], nor is it sufficient for the government to show only mere association with conspirators known to be involved in crime." Id. at 1285 (internal quotations and citations omitted). Likewise, "the government must do more than show there were casual transactions between the defendant and the conspirators." Id. (quotation omitted). To distinguish a "casual transaction" from an act demonstrating interdependence, we consider *1332 the circumstances surrounding the transaction.
Evidence showing that an alleged coconspirator has an economic stake in the outcome of a drug transaction can demonstrate that a transaction is not merely casual. Of course, direct economic benefit for all individuals involved is not necessarily a prerequisite for a jury to find a single conspiracy. See, e.g., Direct Sales Co. v. United States, 319 U.S. 703, 711, 63 S.Ct. 1265, 87 L.Ed. 1674 (1943); United States v. Harrison, 942 F.2d 751, 756 (10th Cir. 1991). But in the profit-driven world of illicit drugs, the fact that several individuals are in an economically symbiotic relationship may demonstrate that transactions among them are in pursuit of mutual benefit. For example, in Edwards, we determined that a reasonable jury could have found a single conspiracy existed when multiple defendants pooled their money to negotiate a lower drug price from a supplier. 69 F.3d at 431-32.
On the other hand, an act that merely facilitates the distribution of drugs may be insufficient to show that two individuals intend to act together for their mutual benefit. For example, loaning scales to a drug dealer knowing he would use them to weigh crack cocaine is, in isolation, insufficient to establish a conspiracy between the person who loans the scales and the person who uses them. Evans, 970 F.2d at 673. Without more, loaning of scales "could have been merely a gratuitous favor or isolated act among friends." Id.
United States v. Pressler, 256 F.3d 144 (3d Cir.2001), is instructive in determining whether Caldwell's introduction of Anderson to Herrera was merely a casual favor among friends, or evidence of interdependence among coconspirators. In that case, a jury convicted Scott Shreffler of conspiracy to distribute heroin. Id. at 147. Shreffler introduced two other drug dealers, Anthony and Aaron Forshey, to his heroin supplier, Pete Caban. Id. at 153. As in the present case, Shreffler did not receive a discount on his own drug purchases or any other economic benefit from Caban or the Forsheys as a result of this introduction. Id. The Third Circuit held that evidence showing "Shreffler introduced the Forsheys to another, superior source of supply from which Shreffler himself had purchased a large amount of heroin" was insufficient to establish that Shreffler had entered into any sort of agreement to distribute heroin to the Forsheys. Id. In a somewhat insouciant comparison, the court stated:
It is common for people to tell their friends about a good store or restaurant. Though the Government proved that Shreffler was a very good customer to Caban, that he had recommended Caban to others, and that Caban benefitted from Shreffler's patronage, it did not show that Shreffler and Caban ever agreed to work together on anything.

Id. at 154 (emphasis added).
Similarly, Caldwell's introduction of Anderson to Herrera undoubtedly broadened Herrera's customer base. But the facts surrounding the introduction demonstrate that it was friendly rather than conspiratorial. As in Pressler, the government offered no evidence that Caldwell received any economic benefit from the introduction, and Anderson testified that Caldwell received no such benefit. After the introduction, Caldwell was not involved with any drug transaction between Herrera and Anderson. On the facts of this case, Caldwell's introduction alone cannot demonstrate beyond a reasonable doubt that a single conspiracy existed among Caldwell, Anderson, and Herrera. Although the government established that Caldwell was involved in two separate conspiracies, it failed to prove the tripartite *1333 conspiracy alleged in the indictment. As a result, a variance occurred.

B
Not every variance, however, requires reversal. United States v. Windrix, 405 F.3d 1146, 1153 (10th Cir.2005). A variance becomes fatal, and thus reversible error, "only if it affects the substantial rights of the accused." United States v. Ailsworth, 138 F.3d 843, 848 (10th Cir. 1998). We review de novo the question of whether a particular variance constitutes reversible error. Windrix, 405 F.3d at 1153-54.
A variance is not fatal "merely because the defendant is convicted upon evidence which tends to show a narrower scheme than that contained in the indictment, provided that the narrower scheme is fully included within the indictment." Harrison, 942 F.2d at 758 (quotation omitted). The primary purpose of the prohibition against variances is "to insure notice of the charges." Williamson, 53 F.3d at 1513. When an indictment charges a conspiracy among multiple individuals, it generally provides sufficient notice to a defendant that she must defend against the smaller conspiracies. See Windrix, 405 F.3d at 1154. By comparison, a variance may be substantially prejudicial "if the evidence adduced against co-conspirators involved in separate conspiracies was more likely than not imputed to the defendant by the jury in its determination of the defendant's guilt." Id. (quotation and alteration omitted).
Caldwell contends he was substantially prejudiced because the jury must have relied on the amount of marijuana Herrera sold to Anderson in assessing drug quantity. Caldwell's argument fails, however, because "when asking what facts the jury had to find in order to convict, we look to the elements of the crime as defined by law." United States v. Nacchio, 519 F.3d 1140, 1157 (10th Cir. 2008), vacated in part on other grounds by 555 F.3d 1234 (10th Cir.2009) (en banc). Drug quantity is an essential element only "if the quantity triggers a sentence beyond the maximum allowed for violation of the base § 841(a)(1) offense." United States v. Montgomery, 468 F.3d 715, 719 (10th Cir.2006).
Caldwell received a sentence below the statutory maximum. Although the government submitted the issue of drug quantity to the jury by way of a special verdict form, drug quantity was not listed in the jury instructions as an element of conspiracy or possession with intent to distribute. Moreover, Caldwell admits that the government presented sufficient evidence to prove Caldwell was involved in two separate drug conspiracies. As a result, drug quantity did not affect the jury's determination of Caldwell's guilt. His conviction stands.

III
Even though Caldwell's conviction is valid, his sentence is not. We review a sentencing court's determination of drug quantity for clear error. United States v. Zapata, 546 F.3d 1179, 1192 (10th Cir. 2008).
In the present case, the jury's determination of drug quantity was clearly erroneous because it was based on an unsupported tripartite conspiracy. The government proved at trial that Herrera sold Caldwell between 54 and 163 kilograms of marijuana, and that Anderson sold Caldwell between 2 and 4 kilograms of marijuana. While these ranges demonstrate that Caldwell could have been responsible for over 100 kilograms of marijuana, they do not demonstrate beyond a reasonable *1334 doubt that Caldwell was responsible for that quantity.
Moreover, the PSR attributed approximately 188 kilograms to Caldwell, a quantity that could not have been reached without taking into account the marijuana Herrera sold to Anderson. The sentencing court relied both on this amount and the jury's special verdict in calculating Caldwell's sentence. Consequently, the factual basis for Caldwell's sentence was clearly erroneous, and we remand the matter to the district court for resentencing. In doing so, the district court should not consider the amount of marijuana Herrera sold to Anderson.

IV
Finally, Caldwell contends that the district court erred in applying Federal Rule of Evidence 404(b) to allow the introduction of Caldwell's five prior drug-related convictions into evidence. Assuming without deciding that the district court abused its discretion in overruling Caldwell's Rule 404(b) objection,[4] we conclude any such error was harmless.
We will not disturb a jury verdict based on a Rule 404(b) error if it was harmless. See Becker, 230 F.3d at 1232-33. "[An] error is considered harmless unless it had a substantial influence on the outcome [of the trial] or leaves one in grave doubt as to whether it had such effect." Id. (quotations omitted). When the evidence against a defendant is overwhelming, an erroneous admission of prior convictions is harmlessespecially when the trial court issues a proper limiting instruction. See, e.g., United States v. Oberle, 136 F.3d 1414, 1419 (10th Cir.1998); United States v. Sloan, 65 F.3d 861, 865 (10th Cir.1995).
In this case, the government presented overwhelming evidence that Caldwell separately conspired to distribute marijuana with Herrera and with Anderson. Further, the judge specifically instructed the jury not to use the prior convictions as evidence of guilt. Therefore, any error was harmless.

V
For the foregoing reasons, we AFFIRM Caldwell's conspiracy conviction but VACATE his sentence. We REMAND the matter to the district court for resentencing.
NOTES
[1]  Caldwell was also convicted of two counts of using a telephone in furtherance of a drug trafficking crime. Caldwell does not appeal those convictions or sentences.
[2]  Herrera and Caldwell spoke in code during these conversations, for example, by referring to marijuana as "Jordans" or "CDs." On appeal, Caldwell does not contend that these conversations concerned tennis shoes or music.
[3]  The government also presented more evidence than just the introduction: It demonstrated that Hickman sold Taylor large quantities of crack cocaine, the vast majority of which Hickman had obtained from Norwood. Id. at 1286-87.
[4]  At trial, Caldwell objected to the admission of his prior convictions on relevancy grounds, but the court overruled the objection on Rule 404(b) grounds. The government contends that we should review for plain error because Caldwell failed to object to the evidence on Rule 404(b) grounds at trial. But objections made during trial need not be perfect to preserve an issue for appeal. They need only "substantially satisf[y] the requirement of putting the court on notice" as to the grounds for the objection. Beech Aircraft Corp. v. Rainey, 488 U.S. 153, 174, 109 S.Ct. 439, 102 L.Ed.2d 445 (1988). Because the district court overruled the objection on Rule 404(b) grounds, it had notice of a Rule 404(b) objection. Thus, the issue has been properly preserved, and an abuse of discretion standard of review applies. See United States v. Becker, 230 F.3d 1224, 1232 (10th Cir.2000).
