
548 F.3d 155 (2008)
ESTATE OF Daniel BENNETT, II, Arlene Bedard, Isabel Bedard, and Laurie Hart, Plaintiffs, Appellants,
v.
Christopher WAINWRIGHT, Matthew Baker, Timothy Turner, James Miclon, James Davis, Lloyd Herrick, and County of Oxford, Maine, Defendants, Appellees.
No. 07-2169.
United States Court of Appeals, First Circuit.
Heard April 7, 2008.
Decided November 26, 2008.
*158 Thomas J. Connolly, for appellants.
Peter T. Marchesi, with whom Cassandra S. Shaffer and Wheeler & Arey, P.A., were on brief, for appellees Christopher Wainwright, Matthew Baker, James Miclon, James Davis, Lloyd Herrick, and County of Oxford.
Ronald W. Lupton, Assistant Attorney General, with whom G. Steven Rowe, Attorney General, and Paul Stern, Deputy Attorney General, was on brief, for appellee Timothy Turner.
Before LYNCH, Chief Judge, CUDAHY,[*] and TORRUELLA, Circuit Judges.
TORRUELLA, Circuit Judge.
This appeal involves the tragic death of Daniel Bennett II ("Bennett"), a mentally ill young man, when he opened fire against Maine law enforcement officers who had been called to his home. The officers responded with gunfire and Bennett was killed. Bennett's estate ("the Estate")  his mother, Arlene Bedard ("Arlene"); his grandmother, Isabel Bedard ("Isabel"); and his sister, Laurie Hart ("Laurie")  brought suit against the officers asserting numerous violations of both the Estate's and Bennett's constitutional rights, as well as state law claims. The district court rejected all of the Estate's causes of action by granting the defendants' motions to dismiss, for judgment on the pleadings, and for summary judgment. The Estate now appeals. We affirm the judgment of *159 the district court for the reasons explained herein.

I. Background


A. Facts
As this appeal arises from dismissals pursuant to Federal Rules of Civil Procedure 12(b)(6), 12(c), and 56, we recite the facts in the light most favorable to the Estate as non-movant, drawing all reasonably supported inferences in its favor. See Prescott v. Higgins, 538 F.3d 32, 39 (1st Cir.2008) (addressing Rule 56 summary judgment); Pérez-Acevedo v. Rivero-Cubano, 520 F.3d 26, 29 (1st Cir.2008)(addressing Rule 12(c) judgment on the pleadings); Young v. Lepone, 305 F.3d 1, 8 (1st Cir.2002) (addressing Rule 12(b)(6) motion to dismiss).[1]
Between 1996 and 2000 Bennett suffered various psychological problems for which he was taking prescribed medication. In November 1999, Bennett stopped taking his medication. During the course of Bennett's illness, Maine state law enforcement officials had been summoned to his home on various occasions. Those police interventions resulted in Bennett being safely transported to a mental care facility each time.
The events giving rise to the present appeal took place on January 21, 2000. On that morning Bennett walked from Bucksfield, Maine, to his grandmother's house in Sumner, Maine ("Bedard residence"), a distance of between ten and fifteen miles, in the snow wearing only slippers. Upon his arrival, he beat a stray dog to death. Though the Estate asserts that his family did not perceive Bennett to be a threat, Bennett's grandmother Isabel became concerned and attempted to call his mother, Arlene. When Arlene could not be reached, Isabel called Bennett's sister, Laurie. Laurie eventually contacted Arlene, who said she would go to the Bedard residence. Laurie nonetheless remained concerned and called her cousin Derrick Laughton ("Laughton"), to request that he go to the Bedard residence immediately; he agreed to do so. Laurie then called her husband at work and told his employer that there was a real emergency. Laurie's husband also went to the Bedard residence.
Upon Arlene's arrival at the house, she found Isabel, Laughton, and Laughton's father there. Arlene tried speaking to Bennett, but he replied "leave me the fuck alone, I don't want to kill you, too." Arlene then called 9-1-1 and stated "[Bennett] just told me to get out of there, he's going to kill me, so I came out here to call you." Arlene also told the dispatcher that Bennett had killed a dog with a bat; that he was not taking his prescribed medication; that there were firearms inside the Bedard residence which were either non-functional or the location of which was unknown to Bennett; and that they "need somebody right away." The Estate asserts that Arlene specifically indicated she did not want police assistance, just a mental health transport.
The 9-1-1 operator contacted the Oxford County Sheriff's Department ("OCSD") at approximately 2:00 p.m. Deputy Sheriff Christopher Wainwright was the first officer to arrive at the scene. Wainwright had been told that Bennett had beaten a dog to death with a baseball bat, had threatened family members and *160 that there was a rifle and a shotgun present in the Bedard residence. He thereupon requested that a perimeter be established around the residence and that a Maine state police unit, as well as Deputy Sheriff Matthew Baker and the State Warden, also respond. The Estate asserts that Wainwright was known in the community as "Deputy Death" and that he had a "proclivity for confrontational escalation of police-citizen encounters" because he was responsible for the only other police shooting death in the history of Oxford County. The victim in that instance was also a mentally ill person.
Wainwright and Maine State Police Officer Timothy Turner entered the Bedard residence almost simultaneously. They spoke to the family members gathered in the kitchen and were shown the door leading through the living room to the back of the house where Bennett was located. Wainwright and Turner then notified the family that they had to evacuate. The family did so against their wishes. Isabel insisted that they keep the wood fires going inside the house lest the water pipes freeze and burst in the extremely cold weather. Wainwright and Turner accompanied the family to Laurie's residence nearby. As they were leaving, Bennett momentarily emerged from the back of the house and yelled "get the fuck out!"
OCSD Captain James Miclon arrived on the scene shortly thereafter and became the ranking officer. He ordered Turner and Wainwright to return to the house and assume a defensive position until the Maine state police tactical ("SWAT") team arrived. Chief Deputy James Davis subsequently arrived on the scene, became the ranking officer, and confirmed these orders. Wainwright and Turner, along with Deputy Sheriff Matthew Baker, re-entered the Bedard residence at approximately 3:10 p.m. and took positions in the kitchen. Baker brought with him a department-issue shotgun which he later exchanged for a lighter "long gun," an AR-15 belonging to Wainwright. As the SWAT team assembled outside, Wainwright, Turner, and Baker took turns monitoring the doorway that led through the living room to where Bennett was located. At that point, all of the defendants believed that Bennett had to be taken into protective custody and transferred to a psychiatric facility.
Shortly thereafter, Miclon contacted the District Attorney's office and sought a warrant, but was refused for lack of probable cause. In an effort to secure additional information, Miclon visited Laurie's house to speak to the assembled Bedard family members. While there, both he and Laurie tried to contact Bennett by phone but were unsuccessful. The family members then prepared two diagrams of the Bedard residence indicating the location of the firearms, and Arlene again informed Miclon that Bennett did not know where the guns were and that the only functional firearm was a single-shot breach-loader. The Estate asserts that Miclon was "shocked and despondent" about what was happening back at the Bedard residence to the point that he vomited in Laurie's restroom. Miclon also allegedly told the assembled family members that the officers at the house "were out of control," were "too gung ho," were going "way too fast," and had prevented him and available mental health workers from contacting Bennett.
Back at the Bedard residence, Wainwright identified himself from the kitchen and tried communicating with Bennett but was unsuccessful. Thereafter, Bennett emerged from the back of the house and entered the living room briefly on two occasions. On one of those occasions, Bennett surprised Baker by saying "oh shit" and Baker responded by pointing the AR-15 *161 at him and ordering him to put his hands up. When Bennett did so, he was clutching a roll of toilet paper. The estate believes that Bennett was headed towards the restroom located beyond the kitchen. After both such instances, Bennett retreated peacefully towards the back part of the house.
On his third foray, however, Bennett entered the living room without warning and aimed a single-shot breach-loader shotgun at Baker, to which Baker responded by yelling "Danny, drop the gun, drop the gun." Bennett nonetheless fired and Baker responded with five rounds from the AR-15. Wainwright also fired a full thirteen-shot magazine from his 40-caliber handgun and then reloaded. Turner did not fire because he was behind a wall that obstructed his view. After reloading, Wainwright walked into the living room and fired two or three more shots at Bennett, who had fallen behind the sofa. The Estate characterizes these shots as a "coup de grace" because one shot was to Bennett's head and the other to his chest "straight down."
After the shooting ended, Wainwright called a "signal 2000" and members of the OCSD and Maine state police rushed the Bedard residence. A sergeant with the Maine state police performed CPR on Bennett, and Bennett was transported to a hospital at 4:20 p.m. He was pronounced dead at 5:20 p.m. Bennett had been hit by the AR-15 five times, resulting in two through-and-through wounds in the left arm, a wound to the left shoulder, and Bennett's left pinky finger being shot off. The 40-caliber handgun produced two wounds, one to the head and the other to the chest.

B. Procedural History
On January 19, 2006, the Estate brought suit against Wainwright, Baker, Miclon, Davis, Lloyd Herrick (the Sheriff of Oxford County), the County of Oxford ("County") (collectively, "County defendants"), and Turner (collectively, "defendants") in Maine state court. The defendants removed the case to federal court on February 3, 2006, where the estate asserted 42 U.S.C. § 1983 claims premised on a panoply of constitutional violations, along with one supplementary claim of breach of state law. Specifically, and as concerns this appeal, the Estate alleged that the defendants had violated Bennett's substantive due process, equal protection, and Fourth Amendment rights; had violated the Estate's rights against uncompensated takings under the Fifth Amendment and unlawful seizures under the Fourth Amendment; had engaged in a § 1983 conspiracy; and had violated the Maine Civil Rights Act, Me.Rev.Stat. Ann. tit. 5, § 4652. The Estate also asserted that Herrick and the County were subject to supervisory liability under § 1983, and asked for punitive damages to be levied against all defendants. The parties conducted discovery and sixteen depositions were taken.
Thereafter, Turner moved to dismiss the complaint for failure to state a claim for which relief could be granted, and the defendants moved for judgment on the pleadings and summary judgment. Objections to these motions were filed on both sides, and the motions were referred to a magistrate judge who issued his report and recommendation on May 30, 2007. The district court adopted the recommendation in its totality on July 9, 2007. Regarding the issues on appeal, the district court (1) granted Turner's motion to dismiss the substantive due process claim; (2) granted the County defendants' motion for judgment on the pleadings regarding the substantive due process and Fifth Amendment claims; and (3) granted the defendants' *162 motions for summary judgment as to all Fourth Amendment, equal protection, supervisory liability, § 1983 conspiracy, punitive damages, and state law claims. The Estate now appeals.

II. Discussion


A. Motion to Dismiss

1. Standard of Review
We review a district court's grant of a Federal Rule of Civil Procedure 12(b)(6) motion to dismiss de novo. Gagliardi v. Sullivan, 513 F.3d 301, 305 (1st Cir.2008). In doing so, we "accept[ ] the [appellants'] well-pleaded facts as true . . . indulging all reasonable inferences therefrom." Ramos-Piñero v. Puerto Rico, 453 F.3d 48, 51 (1st Cir.2006). Nevertheless, we reject "unsupported conclusions or interpretations of law." Stein v. Royal Bank of Canada, 239 F.3d 389, 392 (1st Cir.2001) (quoting Wash. Legal Found. v. Mass. Bar Found., 993 F.2d 962, 971 (1st Cir.1993)(internal quotation mark omitted)). To survive Rule 12(b)(6) dismissal, the Estate's well-pleaded facts "must `possess enough heft' to set forth `a plausible entitlement to relief.'" Gagliardi, 513 F.3d at 305 (quoting Bell Atl. Corp. v. Twombly, 550 U.S. 544, 127 S.Ct. 1955, 1959, 167 L.Ed.2d 929 (2007)).

2. Substantive Due Process
Regarding the district court's grant of Turner's motion to dismiss, the Estate appeals only the dismissal of its substantive due process cause of action, which consists of a direct claim for the violation of the Estate members' rights and a consortium claim for the violation of Bennett's rights. At the motion to dismiss stage, we must determine "whether, using all of the well-pleaded facts stated in the complaint and viewing them in the light most favorable to the plaintiff, the plaintiff has stated a claim for a violation of a constitutional right." Riverdale Mills Corp. v. Pimpare, 392 F.3d 55, 61 (1st Cir.2004). To meet this burden on a substantive due process cause of action, the Estate must present a well-pleaded claim that a state actor deprived it of a recognized life, liberty, or property interest, and that he did so through conscience-shocking behavior. Clark v. Boscher, 514 F.3d 107, 112 (1st Cir.2008); see also Ramos-Piñero, 453 F.3d at 53 (stating that the "shock the conscience" standard implicates behavior "so egregious, so outrageous, that it may fairly be said to shock the contemporary conscience" (quoting County of Sacramento v. Lewis, 523 U.S. 833, 848 n. 8, 118 S.Ct. 1708, 140 L.Ed.2d 1043 (1998))). "Behavior `intended to injure in some way unjustifiable by any government interest'  is the sort of official action most likely to `shock the conscience.'" Ramos-Piñero, 453 F.3d at 53 (quoting Lewis, 523 U.S. at 849, 118 S.Ct. 1708). The Estate asserts that it has shown that the defendants engaged in conscience-shocking behavior, and that it may also recover under a state-created danger theory because the defendants caused Bennett to become vulnerable by forcing his family to leave the Bedard residence, thus placing Bennett in the care of Wainwright, who was also known as "Deputy Death."
Under either theory of liability, however, the Estate "must first show a deprivation of a protected interest in life, liberty, or property." Rivera v. Rhode Island, 402 F.3d 27, 33-34 (1st Cir.2005). The Estate, without more, asserts that the defendants carried out deprivations of all three such interests. Given the direct and consortium nature of the Estate's claim, we read this statement as asserting deprivations of Bennett's life, liberty, and property interests as well as those of the individual Estate members. This is not enough to meet the Estate's burden.
*163 Aside from the deprivation of Bennett's life interest, which is self-evident, the Estate does not identify what specific deprivations it allegedly suffered or even if they were of Bennett's or the Estate members' interests. Neither does the Estate identify any legal authority entitling it to the interests of which it claims to have been deprived. See Dávila-Lópes v. Zapata, 111 F.3d 192, 195 (1st Cir.1997) (stating that a recognized interest that entitles its holder to due process must be "defined by an existing rule or understanding that stems from an independent source such as state law . . .") (quoting Bd. of Regents of State Colleges v. Roth, 408 U.S. 564, 577, 92 S.Ct. 2701, 33 L.Ed.2d 548 (1972)) (internal quotation marks omitted). Accordingly, the Estate has waived its consortium claim premised on the deprivation of Bennett's liberty and property interests, as well as all of its direct substantive due process claims. See Casillas-Díaz v. Palau, 463 F.3d 77, 83 (1st Cir.2006) (repeating the well-known adage that issues not substantially developed on appeal are deemed waived); cf. Centro Médico del Turabo, Inc. v. Feliciano de Melecio, 406 F.3d 1, 8 (1st Cir.2005).
The remaining substantive due process claim premised on the deprivation of Bennett's life interest also fails because this is in essence an excessive force claim that should be  and is  brought under the Fourth Amendment. See Graham v. Connor, 490 U.S. 386, 395, 109 S.Ct. 1865, 104 L.Ed.2d 443 (1989) ("[A]ll claims that law enforcement officers have used excessive force  deadly or not  in the course of . . . [the] `seizure' of a free citizen should be analyzed under the Fourth Amendment and its `reasonableness' standard, rather than under a `substantive due process' approach." (emphasis in original)). As an alternative constitutional claim is available here, the Estate's substantive due process claim cannot advance. See Coyne v. Cronin, 386 F.3d 280, 287 (1st Cir.2004) (stating that substantive due process "may itself be invoked to challenge executive conduct where no other constitutional provision more directly applies"); see also Pagán v. Calderón, 448 F.3d 16, 34 (1st Cir.2006).[2] The district court thus properly granted Turner's motion to dismiss.

B. Judgment on the Pleadings

1. Standard of Review
We review a trial court's entry of judgment on the pleadings de novo. Feliciano v. Rhode Island, 160 F.3d 780, 788 (1st Cir.1998). A motion for judgment on the pleadings under Federal Rule of Civil Procedure 12(c) is treated much like a Rule 12(b)(6) motion to dismiss. Pérez-Acevedo, 520 F.3d at 29. Hence such judgment will issue upon a timely motion if the non-movant's factual allegations "`raise a right to relief above the speculative level, on the assumption that all the allegations in the complaint are true.'" Id. (quoting Twombly, 127 S.Ct. at 1965). This inquiry extends only to the pleadings, and we read the facts in the light most favorable to the Estate as non-movant, granting all reasonable inferences in its favor. See Zipperer v. Raytheon Co., Inc., 493 F.3d 50, 53 (1st Cir.2007); Gulf Coast Bank & Trust Co. v. Reder, 355 F.3d 35, 38 (1st Cir.2004).

2. Substantive Due Process
On appeal, the Estate challenges the district court's dismissal by judgment on the pleadings of its substantive due process *164 claim against the County defendants; it asserts the same arguments it made against Turner on the motion to dismiss. As the Rule 12(c) and 12(b)(6) standards of review are so similar, however, our prior analysis of the Estate's substantive due process claim  which is based solely on issues of law  is fully applicable to the claim asserted against the County defendants. This claim therefore fails because the Estate has not met its pleading requirement of identifying the deprivation of a recognized life, liberty, or property interest that is cognizable under the Fourteenth Amendment. See supra, section B.2.

3. Equal Protection
In its original complaint, the Estate asserted an equal protection claim against all defendants that the district court dismissed at different procedural junctures; by judgment on the pleadings for Wainwright and Baker, and on summary judgment for the remaining defendants. On appeal, however, the Estate challenges only the district court's grant of summary judgment on this claim. It does not mention the grant of judgment on the pleadings for Wainwright and Baker, nor does it argue that it has stated a valid equal protection claim based solely on the pleadings. See Gulf Coast, 355 F.3d at 38 (stating that a motion for judgment on the pleadings is decided solely on the information contained in the pleadings; if evidence outside the record is considered the motion becomes one for summary judgment). As such, the Estate has waived its equal protection claim against Wainwright and Baker. Casillas-Díaz, 463 F.3d at 83.

4. Taking
The Estate also challenges the district court's dismissal by judgment on the pleadings of its Fifth Amendment takings claim. According to the Estate, the defendants' actions in driving the Estate members from the Bedard residence, damaging the home with bullet holes and blood stains, and allowing the water pipes within the residence to freeze and burst, constitute a taking carried out under color of state law.
The takings clause applies to the individual states by virtue of the Fourteenth Amendment. Torromeo v. Town of Fremont, 438 F.3d 113, 114 n. 1 (1st Cir. 2006). Nonetheless, a threshold requirement for establishing this cause of action is that the plaintiff identify a recognized property interest that has been the subject of an illegal taking. P.R. Tel. Co. v. Telecomms. Regulatory Bd., 189 F.3d 1, 16 (1st Cir.1999) (citing Parella v. Ret. Bd. of the R.I. Employees' Ret. Sys., 173 F.3d 46, 58 (1st Cir.1999)). Estate member Laurie is unable to satisfy this requirement because she does not allege to have been a resident or an owner of the Bedard residence at the time of this tragic incident. Thus she has no property interest that was allegedly taken and her claim was properly dismissed.
Isabel as owner and Arlene as a resident of the Bedard residence argue that they were subject to a temporary physical taking. The temporary nature of a physical invasion of private property does not itself take it outside the purview of the Fifth Amendment. See Asociación De Subscripción Conjunta Del Seguro De Responsabilidad Obligatorio v. Flores-Galarza, 484 F.3d 1, 28 (1st Cir.2007) (citing First English Evangelical Lutheran Church v. County of Los Angeles, 482 U.S. 304, 318, 107 S.Ct. 2378, 96 L.Ed.2d 250 (1987)). However, it is unclear whether a seizure made in the course of police activity such as that involved in this case is cognizable as a Fifth Amendment taking. See 1 LaFave, Search and Seizure *165 § 1.10(e) (4th ed.2004). But regardless, a physical taking does not violate the Constitution unless just compensation is denied. See Deniz v. Municipality of Guaynabo, 285 F.3d 142, 146 (1st Cir.2002) (quoting Williamson County Reg'l Planning Comm'n v. Hamilton Bank, 473 U.S. 172, 194, 105 S.Ct. 3108, 87 L.Ed.2d 126 (1985)). In order to state a valid takings claim then, Isabel and Arlene were required to have sought compensation through state law mechanisms, or to prove that such mechanisms were unavailable or inadequate. Id. They have made no such pleading, and as such the district court properly dismissed their takings claim by judgment on the pleadings. See Tower v. Leslie-Brown, 326 F.3d 290, 297-98 (1st Cir.2003) (finding a takings claim properly dismissed because the plaintiff-appellant did not go through Maine state procedures to seek reimbursement for $1.60 in long distance calls that a state trooper made from her home).

C. Summary Judgment

1. Standard of Review
We review a district court's grant of summary judgment de novo. Rodríguez-Rivera v. Federico Trilla Reg'l Hosp., 532 F.3d 28, 30 (1st Cir.2008). In doing so, we read the facts in the light most favorable to the Estate as non-movant, granting all reasonable inferences in its favor. Fiacco v. Sigma Alpha Epsilon Fraternity, 528 F.3d 94, 98 (1st Cir.2008) (citing Griggs-Ryan v. Smith, 904 F.2d 112, 115 (1st Cir.1990)). Nonetheless, we are not required to contemplate conclusory allegations, improbable inferences, or unsupported speculation. Id. (citing Suárez v. Pueblo Int'l, Inc., 229 F.3d 49, 53 (1st Cir. 2000)). Reversal is warranted if "the evidence on the record is sufficiently open-ended to permit a rational factfinder to resolve the issue in favor of either side." Rodríguez-Rivera, 532 F.3d at 30 (quoting Maymí v. P.R. Ports Auth., 515 F.3d 20, 25 (1st Cir.2008) (internal quotation mark omitted)).

a. Local Rule 56
District of Maine Local Rule 56 requires a party moving for summary judgment to submit a statement, set forth in separately numbered paragraphs, detailing the material facts it alleges are undisputed. D. Me. R. 56(b). The party opposing summary judgment must then respond with its own opposing statement admitting, denying, or qualifying each numbered paragraph, and supporting each qualification or denial with a record citation. Id. 56(c). Failure to follow this procedure will result in the disputed fact being deemed admitted. Id. 56(f). We have previously lauded the purpose behind local rules such as this one, which is to relieve overworked district courts by placing the burden on litigants to identify the truly disputed material facts in the record. See Calvi v. Knox County, 470 F.3d 422, 427 (1st Cir.2006) (stating that such rules "have the capacity to dispel the smokescreen behind which litigants with marginal or unwinnable cases often seek to hide [and] greatly reduce the possibility that the district court will fall victim to an ambush"). Moreover, we have repeatedly indicated our willingness to enforce these rules nd have warned parties to "`ignore them at their peril.'" Ríos-Jiménez v. Principi, 520 F.3d 31, 38 (1st Cir.2008) (quoting Cabán-Hernández v. Philip Morris USA, Inc., 486 F.3d 1, 7 (1st Cir.2007)).
Despite these admonishments, the district court found that the Estate had not complied with the requirements of Local Rule 56. Accordingly, it struck from the record a number of the Estate's factual averments. Because the Estate did not challenge the district court's actions on appeal, we are limited to reviewing the *166 grant of summary judgment considering the facts only as they were found by the district court.
This means that we may not consider, among other things, the Estate's averments 1) that Wainwright was known as "Deputy Death" and had been involved in the previous shooting of a mentally ill person; 2) that Bennett was not a threat to his family, and his family did not perceive him as one; 3) that Arlene expressly told the 9-1-1 dispatcher that she did not want police assistance; 4) that Bennett's family members did not want to leave the Bedard residence; 5) that Miclon was upset about the goings-on inside the Bedard residence, vomited, and criticized the actions of the other defendants to the family members gathered at Laurie's house; 6) that when Bennett entered the Bedard residence's living room on one of the two times prior to when he was shot, Baker pointed his firearm at him and Bennett held up a roll of toilet paper in his hand; 8) that on his third and final foray into the living room, when Bennett pointed the shotgun at Baker, Baker responded by yelling "Danny, drop the gun, drop the gun"; 9) that Wainwright fired a full 13-shot magazine at Bennett before he reloaded; and 10) that Wainwright walked into the living room and fired a second volley of shots straight into Bennett as he lay on the ground, in the fashion of a "coup de grace."
We take all other facts as described in the "Background" section, supra.

2. Equal Protection
As we previously mentioned, the Estate challenges the district court's grant of summary judgment to defendants Turner, Miclon, Davis, Herrick, and the County, on its equal protection claim. It contends that this claim is sufficiently robust to survive summary judgment because the Estate's pleadings establish Bennett as a member of the "AMHI class for consent decree purposes"[3] and a member of the "class of Maine citizens who [have] guns in their homes and [have] a right not to be categorized as dangerous merely because of this status." The Estate cites some statistics comparing the number of mentally ill versus non-mentally ill persons shot by Maine law enforcement between 1985 and 2000, and it asserts that "the Oxford County Sheriffs[sic] Office and the County and the individual defendants have a pattern and practice of using force disproportionately against the mentally ill as a strategy of suppressing them by the use of illegal arrest." We read these allegations as asserting a claim of disparate treatment.
A requirement for stating a valid disparate treatment claim under the Fourteenth Amendment is that the plaintiff make a plausible showing that he or she was treated differently from others similarly situated. Clark, 514 F.3d at 114; see also In re Subpoena to Witzel, 531 F.3d 113, 118 (1st Cir.2008) (stating that the Equal Protection Clause guarantees that similarly situated people will be treated alike). A similarly situated person is one that is "roughly equivalent" to the plaintiff "`in all relevant respects.'" Barrington Cove Ltd. P'ship v. R.I. Hous. & Mortgage Fin. Corp., 246 F.3d 1, 8 (1st Cir.2001) (quoting Dartmouth Review v. Dartmouth Coll., 889 F.2d 13, 19 (1st Cir.1989)). The Estate, however, has failed to make this *167 showing. Its pleadings, as detailed above, make no effort to compare the treatment Bennett received at the hands of the defendants with the treatment of any person similarly situated to Bennett. Since the Estate has failed to meet this threshold requirement, summary judgment was properly granted on its equal protection claim.

3. Fourth Amendment
The Estate challenges the district court's grant of summary judgment on its multiple Fourth Amendment claims. It argues that both its members and Bennett had their Fourth Amendment rights violated by the defendants. In response, the defendants contend that no constitutional violation took place, and in the alternative, that they are entitled to qualified immunity.
The Fourth Amendment prohibits unreasonable searches and seizures. See U.S. Const. amend. IV; United States v. López, 989 F.2d 24, 26 (1st Cir.1993). The Amendment applies equally to seizures of persons and to seizures of property. Payton v. New York, 445 U.S. 573, 585, 100 S.Ct. 1371, 63 L.Ed.2d 639 (1980). A "seizure" of property occurs when a state agent meaningfully interferes with a private citizen's possessory interest in that property. Tower, 326 F.3d at 297 (citing United States v. Jacobsen, 466 U.S. 109, 113, 104 S.Ct. 1652, 80 L.Ed.2d 85 (1984)). The seizure of a person occurs when, by means of physical force or a show of authority, an officer restrains the liberty of a person and such person submits to the restriction feeling that he or she is not free to leave. United States v. Holloway, 499 F.3d 114, 117 (1st Cir.2007) (quoting United States v. Sealey, 30 F.3d 7, 9 (1st Cir. 1994)). A seizure, however, does not amount to a constitutional violation unless it is unreasonable. Reasonableness is a highly situational determination, Wood v. Clemons, 89 F.3d 922, 928 (1st Cir.1996), which generally depends "on a balance between the public interest and the individual's right to personal security free from arbitrary interference by law officers." Pennsylvania v. Mimms, 434 U.S. 106, 109, 98 S.Ct. 330, 54 L.Ed.2d 331 (1977) (quoting United States v. Brignoni-Ponce, 422 U.S. 873, 878, 95 S.Ct. 2574, 45 L.Ed.2d 607 (1975)).
Qualified immunity is a doctrine that shields government officials performing discretionary functions from liability for civil damages "insofar as their conduct does not violate clearly established statutory or constitutional rights of which a reasonable person would have known." Harlow v. Fitzgerald, 457 U.S. 800, 818, 102 S.Ct. 2727, 73 L.Ed.2d 396 (1982) (citations omitted). Under Saucier v. Katz, 533 U.S. 194, 121 S.Ct. 2151, 150 L.Ed.2d 272 (2001), this Circuit uses a three-part test when evaluating a question of whether an officer in a § 1983 suit is entitled to qualified immunity. Buchanan, 469 F.3d at 167; see also Saucier, 533 U.S. at 205, 121 S.Ct. 2151 ("If the officer's mistake as to what the law requires is reasonable . . . the officer is entitled to the immunity defense"). The court must ask:
[1] whether at some abstract level the plaintiffs have asserted a violation of constitutional rights, [2] whether those rights are clearly established, and [3] whether a reasonable officer could have concluded that his actions did not violate plaintiffs' constitutional rights.
Buchanan, 469 F.3d at 167 (quoting Tremblay v. McClellan, 350 F.3d 195, 199 (1st Cir.2003)) (internal quotation marks omitted). Generally, courts are encouraged to address the requisites of a qualified immunity defense in "proper sequence," i.e., determining first whether a constitutional violation has been asserted. See Saucier, *168 533 U.S. at 200, 121 S.Ct. 2151. The initial inquiry is whether a constitutional right would have been violated on the facts alleged, for if no right would have been violated, there is no need for further inquiry into immunity. See id. at 201, 121 S.Ct. 2151. Thus, under Saucier, only if the first prong is satisfied should courts go on to address the other two. See id. at 200, 121 S.Ct. 2151.
The reason to favor addressing the first prong at the outset is that "doing so assists in the development of the law on what constitutes meritorious constitutional claims." Tremblay, 350 F.3d at 199 (citations omitted). However, we have noted that "Saucier itself suggested that the law elaboration function of the first prong would be well served only in `appropriate cases.'" Buchanan, 469 F.3d at 168 (quoting Saucier, 533 U.S. at 207, 121 S.Ct. 2151). This law elaboration purpose is not furthered "where [a] Fourth Amendment inquiry involves a reasonableness question which is highly idiosyncratic and heavily dependant on the facts." Id. In such cases, we may avoid definitive determinations of the substantive constitutional claims and turn directly to the second and third prongs of the Saucier test. Id.; see, e.g., Brosseau v. Haugen, 543 U.S. 194, 198, 125 S.Ct. 596, 160 L.Ed.2d 583 (2004) (expressing no view on correctness of Court of Appeals decision on constitutional question, but reaching remaining prongs of immunity analysis); Riverdale Mills Corp. v. Pimpare, 392 F.3d 55, 62 (1st Cir.2004)(emphasizing that "the rule stating that the first prong must be performed before the rest of the qualified immunity analysis is not completely inflexible"). This approach is especially prudent when it is clear that the officers are entitled to immunity based on the other prongs. See Buchanan, 469 F.3d at 168; Tremblay, 350 F.3d at 200. Because we find this approach prudent on the facts before us, our analysis of the Estate's various Fourth Amendment claims will generally proceed directly to the third prong.
"The third prong of the qualified immunity analysis recognizes that `law enforcement officials will in some cases reasonably but mistakenly conclude that [their conduct] is . . . lawful'; `in such cases those officials  like other officials who act in ways they reasonably believe to be lawful  should not be held personally liable.'" Buchanan, 469 F.3d at 169 (quoting Anderson v. Creighton, 483 U.S. 635, 641, 107 S.Ct. 3034, 97 L.Ed.2d 523 (1987)). Thus, "police officers are entitled to qualified immunity if reasonably well-trained officers confronted with similar circumstances could reasonably believe their actions were lawful under clearly established law." Napier v. Windham, 187 F.3d 177, 183 (1st Cir.1999); see also Saucier, 533 U.S. at 205, 121 S.Ct. 2151 ("If the officer's mistake as to what the law requires is reasonable . . . the officer is entitled to the immunity defense"). Applying this standard on review of summary judgment, our ultimate inquiry becomes whether a reasonable factfinder could conclude that the defendants' conduct was "so deficient that no reasonable officer could have made the same choices under the circumstances." Napier, 187 F.3d at 184.
We apply this analysis to each of the Estate's Fourth Amendment claims.

a. Initial Entry
The Estate argues that Wainwright and Turner's initial entry into the Bedard residence constituted a Fourth Amendment violation because, at the time of entry, the officers had not been invited into the house and did not have a warrant. The defendants dispute that the entry amounted to a Fourth Amendment violation, as it was justified by exigent circumstances and *169 probable cause, but that in any event, they are entitled to qualified immunity because they reasonably believed that their entry into the house was lawful.
A warrantless entry into a home without consent is considered a presumptively unreasonable seizure. McCabe v. Life-Line Ambulance Serv., Inc., 77 F.3d 540, 544 (1st Cir.1996). However, such entry may not be unreasonable where the government can demonstrate, in addition to probable cause, the existence of exigent circumstances. The exigent circumstances exception attaches where police officers reasonably believe that there is a compelling need for immediate action that "will not brook the delay of obtaining a warrant." Samboy, 433 F.3d at 158 (quoting Fletcher v. Town of Clinton, 196 F.3d 41, 49 (1st Cir.1999) (internal quotation mark omitted)). Such circumstances exist, for example, where law enforcement officers enter a home without a warrant under a reasonable belief that doing so is necessary to render emergency assistance to a person inside. See Mincey v. Arizona, 437 U.S. 385, 392, 98 S.Ct. 2408, 57 L.Ed.2d 290 (1978). An "imminent threat to the life or safety of members of the public, the police officers, or a person located within the residence," may qualify as an exigent circumstance that renders a warrantless entry reasonable. Buchanan, 469 F.3d at 168 (quoting McCabe, 77 F.3d at 545); see also United States v. Martins, 413 F.3d 139, 146-47 (1st Cir.2005). Maine's protective custody statute, Me. Rev.Stat. Ann. Tit. 34-B, § 3862(1), authorizes law enforcement to seize a person whom they reasonably believe to be mentally ill if that person presents a threat to himself or others.
Based on the objective facts known to them at the time, it is clear that Wainwright and Turner had reasonable grounds to believe that Bennett was a mentally ill person who "presented a threat of imminent and substantial physical harm to himself or others, including the [officers] themselves." Buchanan, 469 F.3d at 169; see also Tremblay, 350 F.3d at 200-01 (finding qualified immunity on third prong for officer who took youth into protective custody when it was reasonable to suspect youth's person or welfare was endangered). Before arriving on the scene, Wainwright and Turner were informed by the 911 dispatcher that Bennett had a mental illness, was off his medications, had savagely beat a stray dog, and had verbally threatened his mother. Wainwright and Turner were also told that Bennett was inside a residence that contained firearms. Particularly in light of Maine's protective custody statute, a reasonable officer confronted with similar circumstances could have believed there was sufficient threat of dangerous behavior to justify entering the house and taking Bennett into protective custody. Cf. Ziegler v. Aukerman, 512 F.3d 777, 783 (6th Cir. 2008) (finding that "probable cause in the mental health seizure context requires only a probability or substantial chance of dangerous behavior, not an actual showing of such behavior.")(internal quotation omitted)). Moreover, a reasonable officer under the circumstances could have reasonably believed that "waiting was not a good idea," Buchanan, 469 F.3d at 170, and that entering the house without first obtaining a warrant or express consent was necessary to prevent injury to Bennett himself, and to the family members present inside. Ultimately, "[t]hese circumstances . . . disclose substantial grounds for the officer[s] to have concluded [they] had legitimate justification under the law for acting as [they] did." Saucier, 533 U.S. at 208, 121 S.Ct. 2151; see also Buchanan, 469 F.3d at 170 (finding police officers who entered home of mentally ill man in Maine without *170 warrant or consent were entitled to qualified immunity because officers could have reasonably believed they had authority under state law). Thus, even if the officers were mistaken in their belief  that is, even if their entry was unreasonable as a matter of substantive Fourth Amendment law, they are nevertheless entitled to immunity under the third prong of the qualified immunity inquiry. Buchanan 469 F.3d at 170; see also Hegarty v. Somerset County, 53 F.3d 1367, 1374-79 (1st Cir.1995). Summary judgment was therefore properly granted on this claim.

b. Re-Entry
The Estate rephrases its previous claim by arguing that the defendants violated its Fourth Amendment rights when Wainwright, Turner, and Baker re-entered the Bedard residence after the family members had been evacuated. They allegedly did so, for a second time, without permission or a warrant. However, at the time of re-entry, the defendants still believed that Bennett was a mentally unstable individual who was inside a house containing firearms. Based on undisputed facts known to them, the officers could have reasonably believed that their prompt re-entry was necessary to respond to the imminent threat Bennett continued to pose to the officers and to himself, and therefore, that such re-entry did not violate the Fourth Amendment. Summary judgment on qualified immunity grounds was therefore proper.

c. Temporarily Seizing the Residence
The Estate further argues that, in ordering the family members to evacuate and then re-entering the house and remaining there without their consent, the defendants temporarily "seized" the Estate's property, the Bedard residence, in violation of the Fourth Amendment. The threshold question here is whether there was a seizure at all for Fourth Amendment purposes. As we explained in discussing the Estate's Fifth Amendment Takings claim, Estate member Laurie does not allege to have had a possessory interest in the Bedard residence at the time of this incident. See Tower, 326 F.3d at 297. Accordingly, she has failed to assert a Fourth Amendment violation and her claim fails at the outset. Id.
With regard to Arlene and Isabel's claims, we agree with the Estate that the defendants carried out a seizure of the Bedard residence because the officers' actions meaningfully interfered with Arlene and Isabel's possessory interests in that property. Id. (citing Jacobsen, 466 U.S. at 113, 104 S.Ct. 1652 (1984)). "In circumstances such as this, we balance the privacy-related and law enforcement related concerns to determine if the intrusion was reasonable." Id. (citing Illinois v. McArthur, 531 U.S. 326, 331, 121 S.Ct. 946, 148 L.Ed.2d 838 (2001)). Arlene's and Isabel's right to freely possess their home is certainly a weighty interest. Nevertheless, a reasonable officer could have concluded that intrusion onto that interest, by temporarily seizing the Bedard residence, was outweighed by the legitimate government interest in protecting human life and avoiding injuries to the family while performing a potentially dangerous psychiatric transfer. See id. at 297 (finding no Fourth Amendment violation where government officials remained in home in order to ensure the safety of the children who lived there after their father's arrest). Even if the officers were mistaken as a matter of substantive law as to the legality of the seizure, "a jury could not find that [the defendants'] conduct was so deficient that no reasonable officer could have made the same choice." Napier, 187 F.3d at 183 (quoting Roy v. Inhabitants of the City of *171 Lewiston, 42 F.3d 691, 695 (1st Cir.1994))(internal quotation marks omitted). Therefore, qualified immunity applies and summary judgment was proper.

d. Establishment of a Perimeter
The Estate further claims that the defendants "seized" Bennett in violation of his Fourth Amendment rights by establishing a perimeter around the Bedard residence. "A `seizure' triggering the Fourth Amendment's protections occurs only when government actors have, `by means of physical force or show of authority, . . . in some way restrained the liberty of a citizen.'" Graham, 490 U.S. at 395 n. 10, 109 S.Ct. 1865 (omission in original)(quoting Terry v. Ohio, 392 U.S. 1, 19 n. 16, 88 S.Ct. 1868, 20 L.Ed.2d 889 (1968)); see also Holloway, 499 F.3d at 117 (describing a seizure as occurring when an officer restrains an individual's liberty and the individual submits to the restriction because he feels he is not free to leave). In the case before us, no showing has been made on the summary judgment record that Bennett submitted to the restriction imposed by the police perimeter, or that he felt he was not free to leave. Indeed, the Estate neglects to assert that Bennett had seen the police perimeter from his position in the back of the house, or that he even knew that the Bedard residence had been cordoned off. Given the Estate's failure to establish Bennett's knowledge of the perimeter, no reasonable factfinder could find that a person in Bennett's circumstances would have thought that the perimeter restricted his liberty to leave the Bedard residence. See United States v. Espinoza, 490 F.3d 41, 49 (1st Cir.2007). As the existence of the perimeter cannot reasonably be characterized as a Fourth Amendment "seizure," the plaintiffs have failed to establish a constitutional violation. Thus, we "need not reach the other two prongs of the qualified immunity analysis" to conclude that there is no genuine issue as to whether the officers are entitled to qualified immunity. See Riverdale Mills Corp., 392 F.3d at 65 (finding qualified immunity on the first prong, not on the question of Fourth Amendment reasonableness, but on the antecedent question of law as to whether there had been a "search"). Summary judgment for defendants was therefore proper on this claim.

e. Calling in the SWAT Team
The Estate argues that involving the SWAT team during the standoff at the Bedard residence caused Bennett to be unlawfully seized in violation of the Fourth Amendment. As with its previous claim, however, the Estate fails to plead that Bennett was aware that the SWAT team was assembled outside the Bedard residence. Indeed, according to the district court's accepted factual account, Bennett's only interaction with the SWAT team occurred after he had been fatally shot. Thus, based on the Estate's pleadings, no reasonable factfinder could have concluded that a person in Bennett's circumstances would have thought that he was not free to leave the Bedard residence due to the SWAT team's presence. See Espinoza, 490 F.3d at 49. As the facts "[t]aken in the light most favorable to the party asserting the injury" do not show that Bennett was "seized" for purposes of the Fourth Amendment, plaintiffs have failed to show that "the officer's conduct violated a constitutional right." Saucier, 533 U.S. at 201, 121 S.Ct. 2151 (discussing first prong of qualified immunity inquiry). We thus need not get past the first prong to conclude that defendants are entitled to qualified immunity, and therefore, summary judgment was proper on this claim as well.

f. Removing Family Members from Residence
The Estate argues that the defendants accomplished an unreasonable seizure in *172 violation of the Fourth Amendment when defendants ordered them out of the Bedard residence.[4] Specifically, plaintiffs argue that they were seized when they were ordered to evacuate the Bedard residence because they submitted when the defendants, through a show of authority, placed a restraint on their freedom. In response, defendants assert that the request to evacuate was not a seizure, but that in any event, they are entitled to qualified immunity.
As a threshold matter, we note that Estate member Laurie does not allege to have been inside the Bedard residence at any point during the day at issue. As a result, Laurie could not have been ordered to leave the Bedard residence by the defendants, and her Fourth Amendment claim premised on these actions fails. With regard to Isabel's and Arlene's claims, an order to evacuate through a show of authority may be regarded as a "seizure." See Thames Shipyard & Repair Co. v. United States, 350 F.3d 247, 259 (1st Cir.2003) (holding that the Coast Guard's forcible evacuation of a sinking sea vessel constituted a seizure of the persons therein). It is irrelevant that Arlene and Isabel were free to leave the Bedard residence because, due to the coercive effect of Wainwright and Turner's show of authority, they were not free to stay and thus, their liberty interest was impinged upon.
However, a seizure does not violate the Fourth Amendment unless it is unreasonable under the circumstances. Skinner v. Ry. Labor Executives' Ass'n, 489 U.S. 602, 619, 109 S.Ct. 1402, 103 L.Ed.2d 639 (1989); Ahern v. O'Donnell, 109 F.3d 809, 816 (1st Cir.1997). To determine the reasonableness of the seizure we must balance "its intrusion" on Arlene and Isabel's substantial liberty interests in remaining in their home, against the defendants "legitimate governmental interests" in minimizing the risk of harm to Bennett, the family members, and themselves, while carrying out their duty of transporting a potentially dangerous mentally ill individual for psychiatric care. Skinner, 489 U.S. at 619, 109 S.Ct. 1402. In any event, the officers could have reasonably concluded based on the objective facts known to them at the time that the temporary and minimal restraint placed on Arlene and Isabel (who were free to go anywhere but past the police perimeter and into the Bedard residence), was outweighed by the officers' legitimate interest in minimizing the number of persons present in the zone of danger, while conducting a potentially perilous intervention inside the home. Even if the officers were mistaken in their judgment  that is, even if their seizure of the Bedard residence was unreasonable as a matter of substantive Fourth Amendment law  they are nevertheless entitled to immunity under the third prong of the qualified immunity inquiry. Therefore, summary judgment was properly granted on this claim.

g. Denying Bennett Access to the Restroom
The Estate argues that the defendants violated Bennett's Fourth Amendment rights when they blocked his access to the restroom in the Bedard residence. The Estate infers that Bennett intended to use the restroom because, during one of his initial forays into the living room, the officers in the kitchen pointed their firearms at him and Bennett responded by raising *173 his hands, one of which was holding a roll of toilet paper.
However, as we explained at the beginning of this summary judgment section, the Estate had several of its factual averments struck from the record because the district court found that it had not complied with the requirements of Local Rule 56. Among the averments struck was one stating that when Bennett entered the Bedard residence's living room at a time prior to when he was shot, he did so carrying a roll of toilet paper in his hand. In keeping with our established practice, we will not consider the struck factual averment. See Ríos-Jiménez, 520 F.3d at 38. The factual basis upon which this claim rests having been struck from the record, any reasonable factfinder would be compelled to find that the Estate has failed to show a constitutional violation. Summary judgment was therefore proper on this claim.

h. Pointing Firearms at Bennett
The Estate contends that the defendants violated Bennett's Fourth Amendment rights by pointing their firearms at Bennett when he twice ventured into the Bedard residence's living room prior to being shot. It asserts that such pointing of a weapon, which they characterize as "threatening," constitutes a seizure of Bennett's person through the use of excessive force. In response, defendants assert that deadly force was a reasonable response to the threat of deadly force they faced, and that in any event, they are entitled to qualified immunity.
A violation of the Fourth Amendment premised on excessive force is established if an officer exerts force against a plaintiff that is unreasonable under the circumstances. Jennings v. Jones, 499 F.3d 2, 11 (1st Cir.2007) (citing Graham, 490 U.S. at 397, 109 S.Ct. 1865). Reasonableness in this context is an objective inquiry based, not on the officer's underlying motivation, but on facts and circumstances that "must be judged from the perspective of a reasonable officer on the scene." Graham, 490 U.S. at 396, 109 S.Ct. 1865.
The Estate argues that the pointing of firearms at Bennett was a restraint on Bennett's liberty to which Bennett complied by moving away from the kitchen where the officers with guns drawn were located, and towards the back of the Bedard residence. Assuming that the pointing of firearms at Bennett amounted to a seizure of his person, see U.S. v. Mendenhall, 446 U.S. 544, 554, 100 S.Ct. 1870, 64 L.Ed.2d 497 (1980) (listing "the display of a weapon by an officer" as an example of a circumstance that may indicate a seizure by means of a "show of authority"), we need not decide whether such seizure was carried out with a reasonable amount of force for purposes of the Fourth Amendment because we find that the officers are entitled to qualified immunity under the third prong of the Saucier analysis. See Saucier, 533 U.S. at 206, 121 S.Ct. 2151 (holding that inquiry as to whether officers are entitled to qualified immunity for use of excessive force is distinct from inquiry on the merits of the excessive force claim).
Based on "those objective facts known to (or discernible by) the officers at the time of the event," a reasonable officer could decide that pointing a firearm at Bennett would not amount to excessive force under the circumstances. Buchanan, 469 F.3d at 169 (citing U.S. v. Tibolt, 72 F.3d 965, 969 (1st Cir.1995)). Prior to the pointing of the firearm, Officers Wainwright, Baker, and Turner had been ordered into the Bedard residence to maintain a defensive position while the SWAT team arrived and assembled outside. All of the defendants understood that Bennett had to be taken *174 into protective custody and transferred to a psychiatric facility. They knew Bennett suffered from a mental illness, was acting erratically, had been physically violent against a stray dog, and had threatened his mother with the same treatment. Most alarmingly, Bennett was known to be inside a house containing firearms where he largely remained outside the officers' line of vision, but would sporadically reappear. Given these perilous circumstances, a reasonable officer on the scene would have thought it wise to have a firearm ready, and to hold such firearm in a shooting position if Bennett's sudden appearance caused him to feel threatened. Such conduct cannot be regarded as inconsistent with the officers' need to protect themselves and others, while carrying out the extraction of a potentially dangerous individual from the inside of a home. See Flowers v. Fiore, 359 F.3d 24, 33-34 (1st Cir.2004) (finding that police officers did not use excessive force in displaying their firearms, including a shotgun, during a traffic stop, where the detained motorist fit the description of a person known to be armed and the officers perceived a threat to their safety). A reasonable officer could have believed that pointing a firearm at a mentally unstable individual with access to weapons did not amount to excessive force under the circumstances. Even if the officers were mistaken in their judgment,  that is, even if the display of firearms was unreasonable as a matter of substantive Fourth Amendment law, they are nevertheless entitled to immunity under the third prong of the qualified immunity inquiry.

i. Shooting Bennett
In its final Fourth Amendment claim, the Estate argues that Bennett's shooting was a constitutional violation because excessive force was used. In § 1983 actions alleging the use of excessive force, the qualified immunity test is based on an objective standard: "`whether an objectively reasonable officer would have believed the conduct was unreasonable.'" Asociación de Periodistas de Puerto Rico v. Mueller, 529 F.3d 52, 61 (1st Cir.2008)(quoting Jennings, 499 F.3d at 19). "[Q]ualified immunity affords protection to officers who reasonably, yet mistakenly, employ excessive force in violation of the Fourth Amendment." Jennings, 499 F.3d at 19; see also Saucier, 533 U.S. at 206, 121 S.Ct. 2151 (stating that "immunity operates . . . to protect officers from the sometimes hazy border between excessive and acceptable force") (internal quotations omitted). As we have stated, summary judgment is proper if "`a jury could not find that [the defendants' conduct] was so deficient that no reasonable officer could have made the same choice.'" Napier, 187 F.3d at 183 (quoting Roy, 42 F.3d at 694) (alteration in original).
Our analysis of this issue is based on the district court's straightforward factual account of the tragic shooting.[5] In this version, Bennett, suddenly and without warning, entered the living room of the *175 Bedard residence armed with a shotgun which he aimed at Baker. Baker yelled to Bennett, "Danny, drop the shotgun," but Bennett refused to do so, and instead fired the shotgun. Baker and Wainwright both believed that Bennett was firing at them. After Bennett had fired the shotgun, Wainwright believed that Bennett was reloading his gun, and in response, both Wainwright and Baker responded with their own gunfire, Wainwright pausing once to reload. When the shooting was over, Bennett was given immediate first aid before being pronounced dead at a nearby hospital. These facts are essentially uncontested.[6]
While the result is tragic, we cannot conclude that the officers' actions were so deficient that no reasonable officer in their position would have made the same choices under these circumstances. In the Fourth Amendment context, the use of deadly force is not excessive if an objectively reasonable officer in the same circumstances would have believed that an individual "posed a `threat of serious physical harm either to the officer or others.'" Young v. City of Providence ex rel. Napolitano, 404 F.3d 4, 23 (1st Cir.2005) (quoting Tennessee v. Garner, 471 U.S. 1, 12, 105 S.Ct. 1694, 85 L.Ed.2d 1 (1985)). Moreover, "[w]e must remember that the reasonableness of an officer's use of force must be judged from the perspective of a reasonable officer on the scene, rather than with the 20/20 vision of hindsight." Napier, 187 F.3d at 188; see also Anderson v. Russell, 247 F.3d 125, 131 (4th Cir.2001) (holding that an officer did not employ excessive force in shooting a suspect who turned out to be unarmed because, at the time of the shooting, the officer had a reasonable belief that the suspect posed a threat and was armed). In this case, reasonable officers in Wainwright and Baker's position, faced with an armed mentally ill man, who had already shot at them once, could reasonably believe that they were faced with imminent and grave physical harm that justified resort to deadly force.
The fact that officers Wainwright and Baker fired multiple shots at Bennett, and might even have reloaded their weapons, does not change our assessment. In Berube we found that the actions of an officer who continued to fire at a suspect after he fell to the ground could not be found "unreasonable" because the officer failed to "perfectly calibrate the amount of force required to protect herself." Berube v. Conley, 506 F.3d 79, 85 (1st Cir.2007). Rather, we found that the officer made "a split-second judgment in responding to an imminent threat," and while we "might regret [the officer's] failure to stop shooting as soon as Berube went down, immunity *176 encompasses `mistaken judgments'." Id. (quoting Malley v. Briggs, 475 U.S. 335, 343, 106 S.Ct. 1092, 89 L.Ed.2d 271 (1986)). Like the officer in Berube, Wainwright, in the context of this tense and dangerous situation, could have reasonably believed that Bennett posed a continuing threat, and that his own safety and the safety of the other officers required him to keep firing.
Neither are we persuaded by the Estate's argument that Bennett was effectively unarmed at the time of the fatal shooting because he had discharged the only round chambered in his single-shot breach-loader shotgun, and had been unable to reload. Whether or not Bennett was actually reloading, or capable of doing so, is not relevant if the officer's belief that he was doing so was reasonable. Though Estate member Arlene does allege to have told Captain Miclon that the only functional firearm in the Bedard residence was a single-shot breach-loader, the Estate makes no allegation that the officers in the kitchen  Wainwright, Baker, and Turner  were privy to this information. Moreover, even if the officers had been so notified, it is unreasonable to expect that having suddenly come under fire during a tense protective custody situation, officers Wainwright and Baker would have taken the time to get a good look at the type of gun Bennett was using. Nor were the officers required to do so. See Graham, 490 U.S. at 396-97, 109 S.Ct. 1865 ("The calculus of reasonableness must embody allowance for the fact that police officers are often forced to make split-second judgments  in circumstances that are tense, uncertain, and rapidly evolving  about the amount of force that is necessary in a particular situation"). An objectively reasonable officer in their situation could have felt at risk of serious bodily harm and believed deadly force to be necessary and lawful, and that is sufficient to legitimize the officers' use of deadly force. See Berube, 506 F.3d at 83-86; Napier, 187 F.3d at 187. Since a reasonable factfinder must conclude that Bennett's shooting, while unfortunate, was not the result of plain incompetence or knowing violation of law on the part of the officers, the officers are entitled to qualified immunity under the third prong of the Saucier analysis. See Asociación de Periodistas de Puerto Rico, 529 F.3d at 61 (quoting Malley, 475 U.S. at 341, 106 S.Ct. 1092), for proposition that the scope of qualified immunity protection is "intended to include `all but the plainly incompetent or those who knowingly violate the law'".
Summary judgment was thus proper on this and every one of the Estate's Fourth Amendment claims.

4. Supervisory Liability
Leaving behind the Estate's Fourth Amendment claims, we now address the Estate's challenge to the district court's grant of summary judgment on its supervisory liability claims against defendants Herrick and Oxford County. The Estate alleges that Herrick and the County are subject to supervisory liability under § 1983 because they deliberately or consciously failed to adequately train their subordinates, in deliberate indifference to Bennett's constitutional rights. The Estate further asserts that Herrick and the County had a pattern and practice of applying excessive force in the context of mental health extractions.
This Circuit recently reiterated in the case of Pineda v. Toomey that a supervisory official may be held liable under § 1983 as a secondary violator for the behavior of his subordinates only if:
(1) the behavior of [his] subordinates results in a constitutional violation, and (2) the [supervisor]'s action or inaction *177 was affirmative[ly] 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.
533 F.3d 50, 54 (1st Cir.2008) (quoting Lipsett v. Univ. of P.R., 864 F.2d 881, 902 (1st Cir.1988)); see also Camilo-Robles v. Zapata, 175 F.3d 41, 44 (1st Cir.1999) (holding that where plaintiff brings § 1983 claim against a defendant-supervisor, liability attaches if the responsible official "supervises, trains, or hires a subordinate with deliberate indifference toward the possibility that deficient performance of the task eventually may contribute to a civil rights deprivation."). Moreover, "[t]o succeed on a supervisory liability claim, a plaintiff not only must show deliberate indifference or its equivalent, but also must affirmatively connect the supervisor's conduct to the subordinate's violative act or omission." Maldonado-Denis v. Castillo-Rodríguez, 23 F.3d 576, 582 (1st Cir.1994).
With respect to the County, it is worth noting as a threshold matter that "it is not impossible for a municipality to be held liable for the actions of lower-level officers who are themselves entitled to qualified immunity." Joyce v. Town of Tewksbury, 112 F.3d 19, 23 (1st Cir.1997) (en banc) (citing Walker v. Waltham Hous. Auth., 44 F.3d 1042, 1047 (1st Cir.1995)). However, like supervisory liability, municipal liability is not vicarious. Municipalities can be held liable only if municipal employees commit unconstitutional acts and those actions are shown to have been caused by a "policy or custom" of the government. Martínez-Vélez v. Rey-Hernández, 506 F.3d 32, 41 (1st Cir.2007) (citing Monell v. Dep't of Soc. Servs., 436 U.S. 658, 694, 98 S.Ct. 2018, 56 L.Ed.2d 611 (1978)). Such custom "must be so well settled and widespread that the policymaking officials of the municipality can be said to have either actual or constructive knowledge of it yet did nothing to end the practice." Bordanaro v. McLeod, 871 F.2d 1151, 1156 (1st Cir.1989). With respect to a failure to train claim, only if the "municipality's failure to train its employees in a relevant respect evidences a `deliberate indifference' to the rights of its inhabitants can such a shortcoming be properly thought of as a city `policy or custom' that is actionable under § 1983." City of Canton v. Harris, 489 U.S. 378, 389, 109 S.Ct. 1197, 103 L.Ed.2d 412 (1989).
The establishment of § 1983 liability against either Herrick or the County would ultimately depend on plaintiff proving the commission of an underlying constitutional violation by the subordinate officers. See Pineda, 533 F.3d at 54. Because we hold that the subordinate officers are entitled to qualified immunity under the third prong of the Saucier analysis, we did not reach, in our foregoing analysis, the merits of whether actions taken during the attempt to place Bennett in protective custody amounted to a constitutional violation. We need not reach this question here either. Even if an underlying substantive constitutional violation by subordinate officers were stated by plaintiffs, we nevertheless agree with the district court that plaintiffs offer insufficient evidence to allow a reasonable factfinder to find a policy, custom, practice or any deliberate indifference on the part of either Herrick or the County that bears the requisite causal relationship to the alleged constitutional deprivation to establish liability under a supervisory theory. See Pineda, 533 F.3d at 53 (citing Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 246, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986))(stating that in reviewing district court's grant of summary judgment, we are not required to credit "conclusory *178 allegations, improbable inferences, or unsupported speculation" by the non-moving party). The estate can point to no proper record evidence that suggests deficient training or supervision. This is particularly true given that the few facts proffered by plaintiffs in support of these claims were properly struck from the record.[7] Summary judgment was therefore proper on this claim.

5. Section 1983 Conspiracy
The Estate challenge the district court's grant of summary judgment on its § 1983 conspiracy claim. A civil rights conspiracy as commonly defined is "a combination of two or more persons acting in concert to commit an unlawful act, or to commit a lawful act by unlawful means, the principal element of which is an agreement between the parties to inflict a wrong against or injury upon another, and an overt act that results in damages." Earle v. Benoit, 850 F.2d 836, 844 (1st Cir.1988)(quoting Hampton v. Hanrahan, 600 F.2d 600, 620-21 (7th Cir.1979)) (internal quotations omitted). While plaintiffs are correct that "conspiracy is a matter of inference," summary judgment may still be appropriate on a conspiracy claim where the nonmoving party rests merely on conclusory allegations. Here plaintiffs have presented no evidence, either direct or circumstantial of an agreement among defendants from which a reasonable jury could have inferred a conspiracy among them to inflict harm upon the plaintiffs. Earle, 850 F.2d at 845; see also Slotnick v. Staviskey, 560 F.2d 31, 33 (1st Cir.1977)(holding that complaint alleging a conspiracy to deprive plaintiff of his civil rights cannot survive motion to dismiss based on conclusory allegations of conspiracy which are not supported by references to material facts). Summary judgment was thus proper on this claim.

6. State Law Claim
Leaving behind the Estate's federal causes of action, we now review its challenge to the district court's grant of summary judgment on its state law claim pursuant to our pendent jurisdiction. See 28 U.S.C. § 1367(a). The Estate asserts that the defendants acted in contravention of the Maine Civil Rights Act, Me.Rev.Stat. Ann. tit. 5, § 4682(1-A), by damaging or threatening to damage the Estate's property, as well as by their interference  through the use of physical force  with Bennett's rights under Maine state and federal law.[8] Nonetheless, because the *179 protections provided by the Maine Civil Rights Act, including immunities, are coextensive with those afforded by 42 U.S.C. § 1983, the dismissal of all of the Estate's § 1983 claims mandates that this claim receive similar treatment. Berube, 506 F.3d at 85-86 (citing Dimmitt v. Ockenfels, 220 F.R.D. 116, 123 (D.Me.2004)). A reasonable factfinder would thus conclude that summary judgment was proper.

III. Conclusion

For all of the foregoing reasons, the district court's judgment is affirmed. Costs to be borne by the parties respectively.
NOTES
[*]  Of the Seventh Circuit, sitting by designation.
[1]  Nonetheless, because the lower court found that the Estate had failed to comply with the requirements of Maine District Court Local Rule 56, some unsupported factual averments have been stricken from the record and cannot be considered with regard to the motion for summary judgment. See D. Me. R. 56(d). We identify these stricken averments in our section addressing summary judgment.
[2]  Since the Estate failed to meet the threshold pleading requirement of identifying the deprivation of a recognized interest, we need not reach the question of whether this circuit recognizes a state-created danger theory of liability. See Rivera, 402 F.3d at 35.
[3]  Members of the "AMHI class" are present and former patients of the Augusta Mental Health Institute ("AMHI") who brought suit against the state of Maine over the treatment and services they received at AMHI. This lawsuit was settled by a consent decree whereby class members are entitled to receive certain continuing care after being discharged from AMHI. See Buchanan v. Maine, 469 F.3d 158, 162-63 (1st Cir.2006).
[4]  The Estate alleges that its members did not voluntarily leave the Bedard residence. Though we may not consider this factual averment due to the Estate's non-compliance with Local Rule 56, our analysis is unaltered because it is apparent from the record that the family members left the Bedard residence at Wainwright and Turner's orders.
[5]  In stating its claim on appeal the Estate relied on its own version of the events that transpired inside the Bedard residence, including averments that officer Wainwright fired a full 13-shot ammunition magazine at Bennett, reloaded, walked into the living room, and then fired several shots straight into Bennett's body in what the Estate characterizes as a "coup de grace." As we have explained, the court below found that the Estate had failed to comply with Local Rule 56 and, as a result, it struck a number of the Estate's factual averments from the record. See D. Me. R. 56(f). Those averments include the Estate's "coup de grace" version of the events surrounding Bennett's fatal shooting. As previously indicated, since the Estate does not challenge the district court's evidentiary strike we will not consider these factual averments. See Ríos-Jiménez, 520 F.3d at 38.
[6]  The Estate also makes the argument that summary judgment was precluded by the existence of several evidentiary inconsistencies which call into question the defendants' version of the events, thus creating issues of fact that must be resolved by a jury. See Fed. R.Civ.P. 56(c) (stating that summary judgment shall be granted if the record shows that "there is no genuine issue as to any material fact and that the movant is entitled to judgment as a matter of law"). These alleged inconsistencies,  the presence of blood in the Bedard residence's kitchen; a bullet hole in the bathroom wall; the location where several shotgun shells were found; the absence of a large amount of blood behind the sofa where Bennett's body allegedly fell; and an alleged discrepancy in the timing of the fatal shooting  are marshaled by the Estate to advance its theory that Bennett's death did not occur as the defendants described it and was instead covered up. No proof of these evidentiary inconsistencies appears on the record. Further, the district court does not include any of the enumerated inconsistencies in the factual account that emerged from its Local Rule 56 analysis. Thus, we are precluded from considering these inconsistencies and reject this argument outright. See id.
[7]  As explained in part II.C.1.a, supra, the court below struck a number of the Estate's factual averments as not compliant with Local Rule 56. See D. Me. R. 56(f). Those averments include the Estate's assertion that Wainwright was known as "Deputy Death" and had been involved in the previous shooting of a mentally ill person. However, because "isolated instances of unconstitutional activity ordinarily are insufficient to establish a supervisor's policy or custom, or otherwise to show deliberate indifference," Maldonado-Denis, 23 F.3d at 582, relying on the plaintiff's version of the facts would not alter our holding.
[8]  Me.Rev.Stat. Ann. tit. 5, § 4682(1-A) reads:

Whenever any person, whether or not acting under color of law, intentionally interferes or attempts to intentionally interfere by physical force or violence against a person, damage or destruction of property or trespass on property or by the threat of physical force or violence against a person, damage or destruction of property or trespass on property with the exercise or enjoyment by any other person of rights secured by the United States Constitution or the laws of the United States or of rights secured by the Constitution of Maine or laws of the State . . . the person whose exercise or enjoyment of these rights has been interfered with, or attempted to be interfered with, may institute and prosecute in that person's own name and on that person's own behalf a civil action for legal or equitable relief.
