Plaintiffs/appellants, Carlos Pineda (“Pineda”) and Alexandra Perez (“Perez”), appeal from the district court’s entry of summary judgment in favor of the defendants/appellees, Joseph Toomey (“Too-mey”) and Joseph Watts (“Watts”), in this action for false arrest, unlawful search, and excessive force. We affirm.

I.

On April 28, 2003, a person was shot and killed at a Mobil gas station in Boston. Suspects were seen leaving the scene in a white minivan. Hearing a report of the incident over their patrol car radio, District 4 (“D-4”) Boston Police Officers William J. Gallagher (“Gallagher”) and Patrick Foley (“Foley”) headed to the gas station. While on their way, the officers were stopped by a motorist who asked if they were looking for a white minivan. The motorist reported that the white van was with a white Honda down on Cass Boulevard. When, minutes later, the officers saw a white Honda traveling on Cass Boulevard, they began following the Honda. There was no white minivan with the Honda. Foley could see and was able to identify the driver of the Honda as Norberto Serrano (“Serrano”).

After Serrano turned from Cass Boulevard onto a street in police District 2 (“B-2”), he parked the Honda in a curbside parking place and exited the vehicle. The officers then activated their overhead lights, stopped their cruiser, and approached Serrano on foot. Seeing the officers, Serrano jumped back in the Honda and sped away. The officers immediately initiated a chase. While Foley was driving, Gallagher informed the dispatcher that they were chasing a car that may have been involved in the D-4 homicide at the Mobil gas station. The officers were soon after joined in the chase by units from the state police and from various Boston Police districts C-ll, B-2, B-3, C-6, and D-4.

Serrano ultimately turned into the Franklin Hill housing project, which was in the B-3 police district, and stopped. Immediately behind the Honda and leading the procession of police cars was a cruiser driven by B-2 Boston Police Officer James Coyne (“Coyne”). Coyne saw two females exit the Honda; Coyne apprehended one and the other fled. Coyne also saw a black man run from the Honda into one of the apartments, specifically unit #81. Coyne described the man’s attire as black boots, gray pants, and a gray long-sleeved shirt with a design on the front.

B-2 Boston Police Officer Andrew Fay (“Fay”) pulled into the housing project soon after Coyne. Hearing from Coyne that two suspects had fled, Fay and a number of other officers spread out to search the outdoor premises. Other officers knocked on the door of apartment # 81. Within minutes, Fay joined the four to six officers who were already in the apartment. As Fay entered, he noticed that some officers were talking with a man clad only in boxer shorts standing in the doorway. Directed to the back of the apartment, Fay rushed past the boxer-clad man to a back bedroom, where he found a black man dressed in underwear hiding in a closet. The man was sweating profusely and was trying to hide his clothing. Foley, who was also present in the apartment, identified the man as Serrano, the driver of the Honda. Fay handcuffed Ser[*52] rano, took him out of the apartment, and placed him in the back of a police car. According to Fay, Serrano was placed in custody not only because he was a possible suspect in a homicide case but also because he had violated the law by fleeing from the police, driving erratically, running red lights, and operating a vehicle in a dangerous manner. Fay estimated that two to four minutes elapsed, at most, between the time he entered the apartment and the time he escorted Serrano out of the apartment. Serrano’s clothing, which matched the description given by Coyne, was retrieved from the closet and placed in evidence bags.

Before Fay left the apartment with Serrano in tow, he talked with one of the three B-2 supervisors present at the scene. Sergeants from other districts, some in uniform and some in plain clothes, were also present. During those minutes when he was securing Serrano, Fay was unsure whether any particular officers were “in charge,” although typically B-3 sergeants would be “in charge” at a B-3 site. Fay said that where, as here, there were multiple sergeants from multiple districts, he would take orders from all of the sergeants but would “probably seek some kind of clarification” if the sergeants’ orders were contradictory.

By the time Fay exited the apartment with Serrano, the man who was earlier standing in the doorway had been handcuffed and removed from the apartment. That man, Pineda, was sleeping in the apartment with his wife, Perez, and two children when officers knocked on his door and announced themselves as Boston Police officers. After Fay rushed into a back room, an unidentified Boston Police officer grabbed Pineda, twice pushed him up against a wall, and handcuffed him. Pine-da was then taken outside in his underwear, where he was filmed by television cameras as he was placed in the back of a Boston Police cruiser. Pineda estimates that 45 to 70 seconds may have elapsed between the time when he opened the door and the time when he was handcuffed and removed from the apartment. Pineda was taken to B-3 headquarters, fingerprinted, placed in a cell for a few hours, interviewed by D-4 homicide officers, and then returned to his home. Pineda cannot identify the officer(s) who threw him against a wall, handcuffed him, and took him to B-3 headquarters, except to say that he saw a Boston Police Department badge or patch and he was placed in a Boston Police cruiser.

As events were unfolding at the Franklin Hill housing project, Detective Dennis Harris (“Harris”), a homicide investigator, was told to go to the housing project to see if there was any link between the people arrested there and the D^l homicide that occurred earlier in the evening. When he arrived at the project, Harris learned that two individuals had been taken to B-3 headquarters for questioning. Harris proceeded to B-3, where he interviewed first Serrano and then Pineda. Harris quickly determined that Pineda had nothing to do with either the homicide or the high-speed chase. Indeed, Harris determined that neither Pineda nor Serrano was involved in the homicide.

When he was finished with the interviews, Harris drove Pineda back to his apartment. Two D^t officers, Gallagher and Foley, were still in the apartment. They had been ordered by a superior officer to keep the apartment secure until they were otherwise notified. According to Pineda, his apartment had been turned upside down while he was gone. Perez explained that, after Pineda and Serrano were taken out of the apartment, the many officers who remained in the apartment asked Perez where the gun was. When[*53] she denied knowing anything about a gun, the officers began looking in closets, opening drawers, flipping mattresses, emptying boxes, removing cushions from the furniture, and looking in the hamper. Perez admitted that she told the officers: “Go ahead. Do what you want. There’s no gun here.” She did not remember at what point she made those statements to the officers.

Watts and Toomey, both B-3 supervising sergeants, were on duty when the D-4 homicide was reported. After they heard over the radio that a white Honda was being chased, possibly into their B-3 district, Watts and Toomey took a marked cruiser and joined the chase, becoming the last car in a line of police vehicles. As they pulled into the housing project and exited their vehicle, Watts and Toomey saw “a lot of police officers running,” most of whom they did not know or could not name. When Watts and Toomey ultimately went into apartment # 81, there were numerous police officers present as well as a non-English-speaking Hispanic man (Perez’s father) and a woman (Perez). Serrano and Pineda had already been removed from the apartment. Neither Watts nor Toomey witnessed anyone being placed in handcuffs, removed from the apartment, or placed in a patrol car. Watts and Toomey left the apartment after just a few minutes, concluding that the situation was under the control of another supervisor, perhaps the D-4 supervisor who monitored the earlier chase. Toomey remembers hearing the supervisor say: “We’re freezing the apartment. Everyone out of here.” Before leaving himself, Too-mey helped two B-2 sergeants clear the apartment of all but two officers, the two D-4 officers who were left to secure the place.

Watts and Toomey were ultimately disciplined for failing to supervise the events that occurred in and outside Pineda’s apartment on the evening of April 28, 2003. Although they learned, as a result of an Internal Affairs investigation, that they were the “officers in charge” on the night in question, Watts and Toomey believed at the time that they were merely “assisting other supervisors from other districts because it ... didn’t happen in [B-3] district.”

Pineda and Perez filed a civil rights complaint against Watts and Toomey on February 3, 2005, alleging that Watts and Toomey failed to supervise adequately the events of April 28, 2003, resulting in the arrest of Pineda without probable cause, an illegal warrantless search of Pineda’s and Perez’s apartment, and the use of excessive force against Pineda during his arrest. The district court entered summary judgment in favor of Watts and Too-mey, stating that Pineda and Perez had failed to present facts that established an “affirmative link” between the defendants’ supervisory conduct and the subordinate police officers’ alleged constitutional violations. In the district court’s words:

The uncontroverted record shows that Defendants Toomey and Watts did not order, participate in, or even see the arrest of Plaintiff Pineda. Nor did Defendants Toomey or Watts order or participate in the search of his apartment.

This timely appeal followed.

II.

We review a district court’s grant of summary judgment de novo, looking at the record in the light most favorable to the non-moving parties and drawing all reasonable inferences in their favor. Rodriguez v. Smithkline Beecham, 224 F.3d 1, 5 (1st Cir.2000). The non-moving parties may not rely on conclusory allegations, improbable inferences, or unsupported speculation but must, instead, “set forth[*54] specific facts showing that there is a genuine issue for trial.” Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 256, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986).

Under 42 U.S.C. § 1983, a supervisory official may be held liable for the behavior of his subordinates only if “(1) the behavior of [his] subordinates results in a constitutional violation, and (2) the [supervisor]^ action or inaction was affirmatively] link[ed] to that behavior in the sense that it could be characterized as supervisory encouragement, condonation or acquiescence or gross negligence amounting to deliberate indifference.” Lipsett v. University of Puerto Rico, 864 F.2d 881, 902 (1st Cir.1988) (internal citations and quotation marks omitted). The requirement of an “affirmative link” between the behavior of a subordinate and the action or inaction of his supervisor “contemplates proof that the supervisor’s conduct led inexorably to the constitutional violation.” Hegarty v. Somerset County, 53 F.3d 1367, 1380 (1st Cir.1995). Deliberate indifference, moreover, “will be found only if it would be manifest to any reasonable official that his conduct was very likely to violate an individual’s constitutional rights.” Id. (internal citation and quotation marks omitted).

In this case, the district court determined that summary judgment in the defendants’ favor was appropriate because the record failed to suggest, much less establish, that the actions of Watts and Toomey amounted to “supervisory encouragement, condonation or acquiescence or gross negligence amounting to deliberate indifference.” We agree with the district court’s assessment of the record.

The evidence establishes that Watts and Toomey were among the last of many officers from multiple districts who converged at the Franklin Hill housing project on the night of April 28, 2003. Before stopping at the housing project in the B-3 district, the officers had been chasing a vehicle whose occupants were suspected of being involved in a D-4 homicide. The chase took the officers through multiple districts, including B-2 and B-3. Several sergeants from different districts were among the many officers who responded to reports of the homicide and the high-speed chase. Rightly or wrongly, Watts and Toomey assumed that they were present at the housing project to assist other supervisors and patrol officers regarding a crime that occurred not in their B-3 district but in a different district.

The record reveals that neither Watts nor Toomey was in the apartment when Pineda was slammed against the wall, placed in handcuffs, and escorted from the building. Indeed, throughout their stay at the housing project, Watts and Toomey were unaware of Pineda’s existence. Moreover, in the absence of Watts and Toomey, it is unlikely that the unidentified officer who nabbed Pineda acted in response to anything Watts and Toomey did or did not do. It cannot be said, in other words, that Watts and/or Toomey encouraged, condoned, or acquiesced in the actions of the officer who nabbed Pineda; nor can it be said that it should have been manifest to Watts and Toomey that their actions or inactions were very likely to violate Pineda’s right to be free from unlawful arrest and/or excessive force.

The record also reveals that Watts and Toomey stayed in apartment # 81 for mere minutes. When they entered the premises, they saw many other officers— most of whom were from districts other than B-3-already taking direction from a supervisor whose identity is unclear. Mistakenly or not, Watts and Toomey assumed that they were not in charge. They accordingly bowed out of the apartment, believing the situation to be under the[*55] control of another supervisor. Neither Watts nor Toomey authorized or witnessed a search during their brief stay in the apartment. Under the circumstances, we cannot say that the conduct of Watts and/or Toomey led “inexorably” to an unconstitutional search of the apartment — a search to which Perez may in all events have consented when she said: “Go ahead. Do what you want. There’s no gun here.”

III.

To trigger liability on the part of Watts and Toomey in this case, Pineda and Perez must establish not only that their constitutional rights were violated, but also that Watts and Toomey were affirmatively linked to the violations. As explained above, it is the second prong of this test that Pineda and Perez failed to meet. Because the district court correctly determined that Pineda and Perez failed to present evidence establishing that the actions of Watts and Toomey amounted to “supervisory encouragement, condonation or acquiescence or gross negligence amounting to deliberate indifference,” we AFFIRM.