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Delicious (TV series)
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Delicious
Genre
Drama
Written by
Dan Sefton
Directed by
Clare Kilner
John Hardwick
Starring
Dawn French
Emilia Fox
Tanya Reynolds
Ruairi O'Connor
Iain Glen
Sheila Hancock
Risteárd Cooper
Franco Nero
Country of origin
United Kingdom
Original language(s)
English
No. of series
2
No. of episodes
8
Production
Executive producer(s)
Phillippa Giles
Anna Ferguson
Location(s)
Cornwall, England
Production company(s)
Bandit Television[1]
Distributor
Endemol Shine International[1]
Release
Original network
Sky 1
Original release
30 December 2016 (2016-12-30) – present
External links
Website
Delicious is a British television drama series that premiered on Sky 1 on 30 December 2016.[2] Written by Dan Sefton and directed by Clare Kilner and John Hardwick,[3] the four-part first series aired on Sky 1 from December 2016 to January 2017. Sky renewed the show for a second series in February 2017.[1] The second series aired on Sky 1 from Friday, 29 December 2017. On 13 February 2018, it was announced that Delicious had been renewed for a third season.[4]
The series is predominantly filmed in South East Cornwall with Pentillie Castle[5] featuring as Leo's Penrose Hotel. While many of the exterior shots are filmed at Pentillie Castle, the interiors can be found at a number of other country houses including Port Eliot and Boconnoc.
Contents
[hide]
1 Synopsis
2 Cast and characters
3 Episodes
4 Production
5 International broadcast
6 Reception
6.1 Critical response
6.2 Ratings
7 References
8 External links
Synopsis[edit]
The series is set in Cornwall, England, where celebrity chef Leo is married to the beautiful Sam and has a successful hotel business.[2] However, he is having an affair with his first wife Gina, a talented cook from whom he stole many of his recipes and cheated on for years.[1]
Cast and characters[edit]
Dawn French as Gina Benelli, Leo's ex-wife[6]
Emilia Fox as Sam Vincent, Leo's wife[6]
Tanya Reynolds as Teresa Benelli, Leo and Gina's daughter
Ruairi O'Connor as Michael Vincent, Leo and Sam's son
Iain Glen as Leo Vincent, a celebrity chef[6]
Sheila Hancock as Mimi Vincent, Leo's mother[6]
Risteárd Cooper as James Harley, Gina's ex and Teresa's biological father
Franco Nero as Joe Benelli, Gina's estranged father
Aaron Anthony as Adam Hasketh, Gina’s protege and Leo’s biological son
Episodes[edit]
No.
overall
No. in
series
Title
Directed by
Written by
Original air date
UK viewers
(millions) [7]
1
1 "Episode 1" Clare Kilner Dan Sefton 30 December 2016 (2016-12-30) 1.22
2
2 "Episode 2" Clare Kilner Dan Sefton 6 January 2017 (2017-01-06) 1.81
3
3 "Episode 3" John Hardwick Dan Sefton 13 January 2017 (2017-01-13) 2.00
4
4 "Episode 4" John Hardwick Dan Sefton 20 January 2017 (2017-01-20) 1.79
Production[edit]
The series is filmed in Cornwall and features the Pentillie Castle as the "Penrose Hotel" run by Leo.[8]
International broadcast[edit]
In Australia, Delicious premiered on ABC Television in May 2017.[9] Sweden on SVT1 in January 2018.
Reception[edit]
Critical response[edit]
The series has garnered mixed reviews. The Sydney Morning Herald's Bridget McManus gave the first episode four stars out of four and praised French's performance.[9] The Radio Times' Ben Dowell commented positively on the series, saying that it has "offered a visual feast but it’s the sure-footed storytelling and strong central performances that has got me hooked."[10]
On the other hand, The Daily Telegraph's Ed Power gave the first episode two stars out of five, saying that: "The awkward blend of soapy escapism and dark comedy left a funny taste, with mismatched performances adding to the queasiness."[6]
Ratings[edit]
The first season of Delicious had an average audience of 1.87 million, making it the most watched Sky 1 original drama in 2016.[1]
References[edit]
^ Jump up to: a b c d e Mitchell, Robert (9 February 2017). "Sky 1 Gets More 'Delicious,' Announces New Original Productions". Variety.
^ Jump up to: a b Dowell, Ben (2 December 2016). "Ten TV shows to watch in December". BBC.
Jump up ^ "Sky 1 drama Delicious adds over a million viewers to episode one". corporate.sky.com. 11 January 2017.
Jump up ^ Dowell, Ben. "Dawn French and Emilia Fox to return for another Delicious series on Sky 1". Radio Times.
Jump up ^ "Is the Penrose Hotel really Pentillie Castle, Cornwall?". Pentillie Castle & Estate. Retrieved 2017-12-12.
^ Jump up to: a b c d e Power, Ed (30 December 2016). "Dawn French's new culinary comedy Delicious fails the taste test – review". The Telegraph.
Jump up ^ "Weekly Viewing Summary (see relevant week)". BARB.
Jump up ^ Dodd, Rachael (28 December 2016). "Dawn French's new TV show Delicious was filmed just over the water". The Herald.
^ Jump up to: a b McManus, Bridget (21 May 2017). "Barely recognisable Dawn French as forceful as ever in Delicious". The Sydney Morning Herald.
Jump up ^ Dowell, Ben (16 June 2017). "Dawn French and Iain Glen drama Delicious ends episode one with a stunning twist". Radio Times.
External links[edit]
Official website
Delicious on IMDb
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The Walking Dead (season 8)
From Wikipedia, the free encyclopedia
Jump to: navigation, search
The Walking Dead (season 8)
Promotional poster
Starring
Andrew Lincoln
Norman Reedus
Lauren Cohan
Chandler Riggs
Danai Gurira
Melissa McBride
Lennie James
Alanna Masterson
Josh McDermitt
Christian Serratos
Seth Gilliam
Ross Marquand
Jeffrey Dean Morgan
Austin Amelio
Tom Payne
Xander Berkeley
Khary Payton
Steven Ogg
Katelyn Nacon
Pollyanna McIntosh
Country of origin
United States
No. of episodes
16
Release
Original network
AMC
Original release
October 22, 2017 (2017-10-22) – April 15, 2018 (2018-04-15)
Season chronology
← Previous
Season 7
List of The Walking Dead episodes
The eighth season of The Walking Dead, an American post-apocalyptic horror television series on AMC, premiered on October 22, 2017, and concluded on April 15, 2018, consisting of 16 episodes. Developed for television by Frank Darabont, the series is based on the eponymous series of comic books by Robert Kirkman, Tony Moore, and Charlie Adlard. The executive producers are Kirkman, David Alpert, Scott M. Gimple, Greg Nicotero, Tom Luse, and Gale Anne Hurd, with Gimple as showrunner for his fifth and final season.
This season adapts the "All Out War" story arc from the comics, with the survivors of the Alexandria Safe-Zone, the Hilltop, the Kingdom, and later the Scavengers taking on Negan (Jeffrey Dean Morgan) and the Saviors.[1]
Contents
[hide]
1 Cast
1.1 Main cast
1.1.1 Starring
1.1.2 Also starring
1.2 Supporting cast
1.2.1 Alexandria Safe-Zone
1.2.2 The Hilltop
1.2.3 The Saviors
1.2.4 The Kingdom
1.2.5 Oceanside
1.2.6 The Scavengers
1.2.7 Miscellaneous
2 Production
3 Episodes
4 Release
5 Reception
5.1 Critical response
5.2 Ratings
6 References
7 External links
Cast[edit]
Main article: List of The Walking Dead (TV series) characters
Main cast[edit]
The primary characters of the eighth season include (from left to right): Rick, Carol, Morgan, Daryl, Carl, Enid, Rosita, Tara, Michonne, Gabriel, Aaron, Maggie, Jesus, Gregory, Shiva, Ezekiel, Jadis, Eugene, Simon, Dwight, and Negan
The eighth season features twenty series regulars overall. For this season, Katelyn Nacon, Khary Payton, Steven Ogg, and Pollyanna McIntosh were promoted to series regular status, after previously having recurring roles, while Seth Gilliam and Ross Marquand were added to the opening credits.
Starring[edit]
Andrew Lincoln as Rick Grimes, the series' protagonist, a former sheriff and the leader of Alexandria, who is leading a new alliance to fight Negan and the Saviors.
Norman Reedus as Daryl Dixon, Rick's right-hand man, the group's primary hunter and a recruiter for Alexandria.
Lauren Cohan as Maggie Rhee, the pregnant widow of Glenn and a leading figure of the Hilltop.
Chandler Riggs as Carl Grimes, Rick's bold and courageous teenage son.
Danai Gurira as Michonne, Rick's katana-wielding girlfriend, who acts as a mother figure to Carl and Judith.
Melissa McBride as Carol Peletier, a fierce survivor who is spurred into fighting the Saviors as revenge for the deaths of her friends.
Lennie James as Morgan Jones, the first survivor Rick had ever encountered, who now resides in the Kingdom and fights for his sanity.
Alanna Masterson as Tara Chambler, a caring, witty member of the group and supply runner for Alexandria who serves as a liaison with Oceanside.
Josh McDermitt as Eugene Porter, a timorous former member of the group whose resourcefulness leads Negan to take him under his wing.
Christian Serratos as Rosita Espinosa, an impulsive member of the group, who is motivated to avenge her ex-boyfriend Spencer and Abraham's death.
Seth Gilliam as Gabriel Stokes, a priest who has become hardened from his experiences with Rick's group.
Ross Marquand as Aaron, an Alexandrian recruiter who brought Rick's group to Alexandria and is currently in the fight against the Saviors.
Jeffrey Dean Morgan as Negan, the leader of the Saviors who serves as the season's primary antagonist.
Also starring[edit]
Austin Amelio as Dwight, an ex-subordinate of Negan who now works for Rick as a double agent against the Saviors.
Tom Payne as Paul "Jesus" Rovia, a scout for the Hilltop.
Xander Berkeley as Gregory, the selfish and hypocritical leader of the Hilltop whose influence diminished with Maggie's prominence.
Khary Payton as Ezekiel, the charismatic leader of the Kingdom who allies with Rick against the Saviors.
Steven Ogg as Simon, a former mortgage broker and Negan's second-in-command, he does not hide his intentions to overthrow Negan.[2]
Katelyn Nacon as Enid, a former member of Alexandria who moved to Hilltop to be with Maggie, and has formed a relationship with Carl.[2]
Pollyanna McIntosh as Anne "Jadis", the deceptive leader of the Scavengers who betrayed Rick's group, and maintains a neutral stance in the war.[2]
Supporting cast[edit]
Alexandria Safe-Zone[edit]
Jason Douglas as Tobin, the foreman of Alexandria's construction crew and member of Rick's militia.
Jordan Woods-Robinson as Eric Raleigh, Aaron's boyfriend and his former recruiting partner, who is now a member of Rick's militia.
Kenric Green as Scott, a supply runner in Alexandria and member of Rick's militia.
Dahlia Legault as Francine, a member of Alexandria's construction crew and member of Rick's militia.
Mandi Christine Kerr as Barbara, resident of Alexandria.
Ted Huckabee as Bruce, resident and member of Alexandria's construction.
The Hilltop[edit]
James Chen as Kal, a guard of the Hilltop.
Peter Zimmerman as Eduardo, a guard of the Hilltop and soldier of the Hilltop's militia.
Karen Ceesay as Bertie, a resident of the Hilltop and soldier of the Hilltop's militia.
Jeremy Palko as Andy, a resident of the Hilltop and soldier of the Hilltop's militia.
Brett Gentile as Freddie, a resident of the Hilltop and soldier of the Hilltop's militia.
R. Keith Harris as Harlan Carson, is the doctor of the Hilltop, who was captured by Simon in the previous season.
The Saviors[edit]
Jayson Warner Smith as Gavin, one of Negan's top lieutenants, who leads the weapons base.
Traci Dinwiddie as Regina, one of Negan's top lieutenants.
Elizabeth Ludlow as Arat, one of Negan's top lieutenants.
Mike Seal as Gary, one of Negan's top lieutenants.
Lindsley Register as Laura, a member of the Saviors.
Juan Pareja as Morales, a survivor from Rick's original Atlanta camp who joined the Saviors.
Joshua Mikel as Jared, Benjamin's killer, and a hostile member of the Saviors who antagonizes Morgan.
Callan McAuliffe as Alden, a member of the Saviors who surrenders to Jesus at the satellite station outpost.
Lindsey Garrett as Mara, a Savior who guards one of many outposts.
Lee Norris as Todd, a timid member of the Saviors who works at the same outpost as Mara.
Whitmer Thomas as Gunther, a member of the Saviors who tortures Ezekiel.
Charles Halford as Yago, a Savior who manages Gavin's weapons base.
Ciera L. Payton as Zia, a Savior whom Rosita and Michonne encounter at a supply warehouse.
Adam Cronan as Leo, a Savior whom Rosita and Michonne encounter at a supply warehouse.
Chloe Aktas as Tanya, one of Negan's wives.
Elyse Dufour as Frankie, one of Negan's wives.
Adam Fristoe as Dean, a savior who tried to kill Jesus.
The Kingdom[edit]
Cooper Andrews as Jerry, Ezekiel's loyal and good-natured bodyguard.
Kerry Cahill as Dianne, one of Ezekiel's top soldiers and a skilled archer.
Daniel Newman as Daniel, one of Ezekiel's top soldiers.
Carlos Navarro as Alvaro, one of Ezekiel's top soldiers.
Macsen Lintz as Henry, a resident of the Kingdom and younger brother of the deceased Benjamin.
Jason Burkey as Kevin, a resident of the Kingdom.
Nadine Marissa as Nabila, a resident and gardener of the Kingdom.
Oceanside[edit]
Deborah May as Natania, the vigilant leader of Oceanside.
Sydney Park as Cyndie, Natania's granddaughter.
Briana Venskus as Beatrice, one of Oceanside's top soldiers.
Nicole Barré as Kathy, one of Oceanside's top soldiers.
Mimi Kirkland as Rachel, an aggressive young member of Oceanside.
The Scavengers[edit]
Sabrina Gennarino as Tamiel, a leading member of the Scavengers.
Thomas Francis Murphy as Brion, a leading member of the Scavengers.
Miscellaneous[edit]
Avi Nash as Siddiq, a mysterious vagabond survivor who befriends Carl.
Jayne Atkinson as Georgie, the leader of a mysterious humanitarian group.
Production[edit]
The Walking Dead was renewed by AMC for a 16-episode eighth season on October 16, 2016.[3] Production began on April 25, 2017, in Atlanta, Georgia.[4] On July 12, 2017, production was shut down after stuntman John Bernecker was killed, after falling more than 20 feet onto a concrete floor.[5] Production resumed on July 17.[6]
The season premiere, which also serves as the series' milestone 100th episode, was directed by executive producer Greg Nicotero.[7]
In November 2017, it was announced that Lennie James who portrays Morgan Jones, would be leaving The Walking Dead after the conclusion of this season, and he will join the cast of the spin-off series Fear the Walking Dead.[8]
Episodes[edit]
See also: List of The Walking Dead episodes
No.
overall
No. in
season
Title
Directed by
Written by
Original air date
U.S. viewers
(millions)
100
1 "Mercy" Greg Nicotero Scott M. Gimple October 22, 2017 (2017-10-22) 11.44[9]
Rick, Maggie, and Ezekiel rally their communities together to take down Negan. Gregory attempts to have the Hilltop residents side with Negan, but they all firmly stand behind Maggie. The group attacks the Sanctuary, taking down its fences and flooding the compound with walkers. With the Sanctuary defaced, everyone leaves except Gabriel, who reluctantly stays to save Gregory, but is left behind when Gregory abandons him. Surrounded by walkers, Gabriel hides in a trailer, where he is trapped inside with Negan.
101
2 "The Damned" Rosemary Rodriguez Matthew Negrete & Channing Powell October 29, 2017 (2017-10-29) 8.92[10]
Rick's forces split into separate parties to attack several of the Saviors' outposts, during which many members of the group are killed; Eric is critically injured and rushed away by Aaron. Jesus stops Tara and Morgan from executing a group of surrendered Saviors. While clearing an outpost with Daryl, Rick is confronted and held at gunpoint by Morales, a survivor he met in the initial Atlanta camp, who is now with the Saviors.
102
3 "Monsters" Greg Nicotero Matthew Negrete & Channing Powell November 5, 2017 (2017-11-05) 8.52[11]
Daryl finds Morales threatening Rick and kills him; the duo then pursue a group of Saviors who are transporting weapons to another outpost. Gregory returns to Hilltop, and after a heated argument, Maggie ultimately allows him back in the community. Eric dies from his injuries, leaving Aaron distraught. Despite Tara and Morgan's objections, Jesus leads the group of surrendered Saviors to Hilltop. Ezekiel's group attacks another Savior compound, during which several Kingdommers are shot while protecting Ezekiel.
103
4 "Some Guy" Dan Liu David Leslie Johnson November 12, 2017 (2017-11-12) 8.69[12]
Ezekiel's group is overwhelmed by the Saviors, who kill all of them except for Ezekiel himself and Jerry. Carol clears the inside of the compound, killing all but two Saviors, who almost escape but are eventually caught by Rick and Daryl. En route to the Kingdom, Ezekiel, Jerry, and Carol are surrounded by walkers, but Shiva sacrifices herself to save them. The trio returns to the Kingdom, where Ezekiel's confidence in himself as a leader has diminished.
104
5 "The Big Scary U" Michael E. Satrazemis Story by : Scott M. Gimple & David Leslie Johnson & Angela Kang
Teleplay by : David Leslie Johnson & Angela Kang November 19, 2017 (2017-11-19) 7.85[13]
After confessing their sins to each other, Gabriel and Negan manage to escape from the trailer. Simon and the other lieutenants grow suspicious of each other, knowing that Rick’s forces must have inside information. The workers in the Sanctuary become increasingly frustrated with their living conditions, and a riot nearly ensues, until Negan returns and restores order. Gabriel is locked in a cell, where Eugene discovers him sick and suffering. Meanwhile, Rick and Daryl argue over how to take out the Saviors, leading Daryl to abandon Rick.
105
6 "The King, the Widow, and Rick" John Polson Angela Kang & Corey Reed November 26, 2017 (2017-11-26) 8.28[14]
Rick visits Jadis in hopes of convincing her to turn against Negan; Jadis refuses, and locks Rick in a shipping container. Carl encounters Siddiq in the woods and recruits him to Alexandria. Daryl and Tara plot to deviate from Rick’s plans by destroying the Sanctuary. Ezekiel isolates himself at the Kingdom, where Carol tries to encourage him to be the leader his people need. Maggie has the group of captured Saviors placed in a holding area and forces Gregory to join them as punishment for betraying Hilltop.
106
7 "Time for After" Larry Teng Matthew Negrete & Corey Reed December 3, 2017 (2017-12-03) 7.47[15]
After learning of Dwight's association with Rick's group, Eugene affirms his loyalty to Negan and outlines a plan to get rid of the walkers surrounding the Sanctuary. With help from Morgan and Tara, Daryl drives a truck through the Sanctuary’s walls, flooding its interior with walkers, killing many Saviors. Rick finally convinces Jadis and the Scavengers to align with him, and they plan to force the Saviors to surrender. However, when they arrive at the Sanctuary, Rick is horrified to see the breached walls and no sign of the walker herd.
107
8 "How It's Gotta Be" Michael E. Satrazemis David Leslie Johnson & Angela Kang December 10, 2017 (2017-12-10) 7.89[16]
Eugene's plan allows the Saviors to escape the Sanctuary, and separately, the Saviors waylay the Alexandria, Hilltop, and Kingdom forces. The Scavengers abandon Rick, after which he returns to Alexandria. Aaron and Enid are ambushed by Oceanside soldiers, leading Enid to kill Natania. Ezekiel ensures that the Kingdom residents are able to escape before locking himself in the community with the Saviors. Eugene aids Gabriel and Doctor Carson in escaping the Sanctuary in order to ease his conscience. Negan attacks Alexandria, but Carl devises a plan to allow the Alexandria residents to escape into the sewers. Carl reveals he was bitten by a walker while escorting Siddiq to Alexandria.
108
9 "Honor" Greg Nicotero Matthew Negrete & Channing Powell February 25, 2018 (2018-02-25) 8.28[17]
Realizing his time alive is limited, Carl writes several letters to his loved ones. After the Saviors leave Alexandria, the survivors make for the Hilltop while Rick and Michonne stay behind to say their final goodbyes to a dying Carl, who pleads with Rick to build a better future alongside the Saviors. Morgan and Carol launch a rescue mission for Ezekiel and successfully retake the Kingdom from the invading Saviors; their lieutenant, Gavin, is killed by Benjamin's vengeful younger brother, Henry.
109
10 "The Lost and the Plunderers" David Boyd Angela Kang & Channing Powell & Corey Reed March 4, 2018 (2018-03-04) 6.82[18]
Aaron and Enid try to convince Oceanside to join the fight against the Saviors, but they refuse; Enid returns to Hilltop while Aaron opts to stay at Oceanside until he can convince them to join. Upon learning of the Scavenger’s siding with Rick, Negan orders Simon to kill only one of Jadis’ people. Rick and Michonne travel to the junkyard to warn Jadis of the Saviors’ impending attack, but they are too late; Simon had ordered the Saviors to slaughter the entire group; Jadis, who managed to escape lures her reanimated comrades into a waste shredder to protect herself.
110
11 "Dead or Alive Or" Michael E. Satrazemis Eddie Guzelian March 11, 2018 (2018-03-11) 6.60[19]
The Saviors hunt the surviving Alexandrians as they make their way to the Hilltop; Dwight affirms his loyalty to Rick's group as he distracts the Saviors and helps lead the group to safety. Eugene leads a crew of Saviors in crafting bullets at a new outpost while Negan plans to taint the Saviors' weapons with walker blood, in order to make the others "turn" instead of killing them. Doctor Carson tries to help a feverish and nearly blind Gabriel to safety, but the Saviors eventually catch up, killing Carson and recapturing Gabriel.
111
12 "The Key" Greg Nicotero Corey Reed & Channing Powell March 18, 2018 (2018-03-18) 6.66[20]
Maggie, Enid, Michonne and Rosita encounter a seemingly benevolent woman named Georgie, who gives them food and documents in exchange for phonograph records; Georgie claims the documents to be "a key to the future". Negan leads the Saviors to the Hilltop to send a warning via their newly tainted weapons; Rick pursues the Saviors and chases Negan into a building. Negan eventually escapes, only to be captured at gunpoint by Jadis. Unable to find Negan, Simon instructs the Saviors to attack the Hilltop and "expunge" the community for good.
112
13 "Do Not Send Us Astray" Jeffrey F. January Angela Kang & Matthew Negrete March 25, 2018 (2018-03-25) 6.77[21]
The Saviors attack the Hilltop with their tainted weapons, leading to a battle in which both sides suffer heavy casualties. Tara is non-fatally shot by Dwight in an effort to prevent Simon from killing her. Overnight, the injured die from their tainted wounds and attack the sleeping survivors after reanimating. Henry tries to take revenge for the murder of his brother, leading to the breakout of the Savior prisoners and the disappearance of Henry. Having seen the Saviors' callous attitude for themselves, Alden and several other Saviors choose to remain at the Hilltop rather than return to the Saviors.
113
14 "Still Gotta Mean Something" Michael E. Satrazemis Eddie Guzelian April 1, 2018 (2018-04-01) 6.30[22]
Carol and Morgan search for Henry while Rick hunts the escaped Savior prisoners; Morgan abandons Carol and joins Rick, and together, they find and kill the prisoners. Jadis tortures Negan until he informs her that he had nothing to do with Simon massacring her people; a helicopter flies nearby, but Jadis fails to catch its attention. Daryl and Rosita plot to stop Eugene from crafting ammunition for the Saviors. Carol finds Henry alive in the woods and they return to Hilltop. Upon Rick and Morgan's return, Michonne encourages Rick to read Carl's letter to him.
114
15 "Worth" Michael Slovis David Leslie Johnson & Corey Reed April 8, 2018 (2018-04-08) 6.67[23]
Negan returns to the Sanctuary and regains control of the Saviors. Dwight secretly prepares notes to Rick about Negan's plans, and later sends Gregory to deliver the notes. Daryl and Rosita capture Eugene from his outpost, but he manages to escape and continues pushing his workers to craft bullets. Dwight lures Simon into a meeting where Negan accosts him for going against his orders with the Scavengers, and kills him in a fist fight. Negan then reveals that Laura informed him of Dwight's siding with Rick, and that his planning was a ruse upon knowing of Dwight's disloyalty. Negan is contacted by Michonne - who reads Carl's letter to him at the request of making peace; Negan remains intent on killing Rick and his allies once and for all.
115
16 "Wrath" Greg Nicotero Scott M. Gimple & Angela Kang & Matthew Negrete April 15, 2018 (2018-04-15) 7.92[24]
Rick's group follows the false plans given to them by Gregory, leading them into a trap. As the Saviors fire, their weapons backfire due to their ammo being sabotaged by Eugene. The surviving Saviors surrender, while Rick chases down Negan; the two brawl and Rick manages to slice Negan's neck, but immediately has Siddiq tend to the wound, knowing that Carl wanted Negan to survive. Meanwhile, an attack at Hilltop is stopped with help from Aaron and the Oceanside soldiers. The survivors regroup and rebuild their communities, but Rick's decision to spare Negan angers Maggie and she vows to take action against Rick in the future.
Release[edit]
The first trailer for the season was released on July 21, 2017 at the San Diego Comic-Con. The second trailer was released on February 1, 2018 for the second part of the season.[25]
On March 15, 2018, it was announced that the season finale and the fourth season premiere of Fear the Walking Dead would be screened at AMC, Regal, and Cinemark theaters across the United States on April 15, the same day as the TV airing, for "Survival Sunday: The Walking Dead & Fear the Walking Dead". The episodes marked the first crossover between the two series. The cinema screening also included an extra half-hour of exclusive bonus content.[26]
Reception[edit]
Critical response[edit]
The eighth season of The Walking Dead has received positive reviews from critics. On Rotten Tomatoes, the season holds a score of 71% with an average rating of 6.94 out of 10, based on 13 reviews, and an average episode score 72%. The site's critical consensus reads: "The Walking Dead's eighth season energizes its characters with some much-needed angst and action, though it's still occasionally choppy and lacking forward-moving plot progression."[27]
The Walking Dead (season 8): Critical reception by episode
Season 8 (2017–18): Percentage of positive reviews tracked by the website Rotten Tomatoes[27]
Ratings[edit]
No.
Title
Air date
Rating/share
(18–49)
Viewers
(millions)
DVR
(18–49)
DVR viewers
(millions)
Total
(18–49)
Total viewers
(millions)
1 "Mercy" October 22, 2017 5.0 11.44[9] 2.2 4.28 7.2 15.74[28]
2 "The Damned" October 29, 2017 4.0 8.92[10] 2.0 4.16 6.0 13.10[29]
3 "Monsters" November 5, 2017 3.8 8.52[11] 2.2 4.47 6.0 13.01[30]
4 "Some Guy" November 12, 2017 3.9 8.69[12] 1.8 3.66 5.7 12.36[31]1
5 "The Big Scary U" November 19, 2017 3.4 7.85[13] TBD TBD TBD TBD
6 "The King, the Widow, and Rick" November 26, 2017 3.6 8.28[14] 2.1 4.44 5.7 12.73[32]
7 "Time for After" December 3, 2017 3.3 7.47[15] 1.9 4.15 5.2 11.63[33]
8 "How It's Gotta Be" December 10, 2017 3.4 7.89[16] 2.0 4.23 5.4 12.13[34]
9 "Honor" February 25, 2018 3.6 8.28[17] N/A N/A N/A N/A
10 "The Lost and the Plunderers" March 4, 2018 2.9 6.82[18] 1.7 3.80 4.6 10.63[35]
11 "Dead or Alive Or" March 11, 2018 2.8 6.60[19] 1.6 3.44 4.4 10.06[36]
12 "The Key" March 18, 2018 2.8 6.66[20] 1.7 3.76 4.5 10.44[37]
13 "Do Not Send Us Astray" March 25, 2018 3.0 6.77[21] 1.7 3.82 4.7 10.62[38]
14 "Still Gotta Mean Something" April 1, 2018 2.6 6.30[22] 1.8 3.68 4.4 9.99[39]
15 "Worth" April 8, 2018 2.8 6.67[23] 1.7 3.64 4.5 10.32[40]
16 "Wrath" April 15, 2018 3.4 7.92[24] TBD TBD TBD TBD
^1 Live +7 ratings were not available, so Live +3 ratings have been used instead.
References[edit]
Jump up ^ Goldberg, Lesley (April 17, 2017). "'Walking Dead' Promotes Trio to Series Regular for Season 8". The Hollywood Reporter. Retrieved May 4, 2017.
^ Jump up to: a b c Ausiello, Michael (April 17, 2017). "The Walking Dead Promotes 3 Actors to Series Regular Ahead of Season 8". TV Line. Retrieved October 25, 2017.
Jump up ^ Hibberd, James (October 16, 2016). "Walking Dead gets early season 8 renewal". Entertainment Weekly. Retrieved October 16, 2016.
Jump up ^ Davis, Brandon (April 24, 2017). "The Walking Dead Cast And Crew Assemble For Season 8". Comicbook.com. Retrieved July 22, 2017.
Jump up ^ Otterson, Joe (July 13, 2017). "'Walking Dead' Stuntman Dies After On-Set Accident". Variety. Retrieved July 22, 2017.
Jump up ^ Pedersen, Erik (July 17, 2017). "'Walking Dead' Production Resumes After Stuntman's Death". Deadline. Retrieved July 22, 2017.
Jump up ^ Davis, Brandon (April 25, 2017). "Exclusive: Greg Nicotero To Direct The Walking Dead Episode 100, Season 8 Premiere". Comicbook.com. Retrieved July 22, 2017.
Jump up ^ Ross, Dalton (November 26, 2017). "The Walking Dead: Lennie James will cross over to Fear The Walking Dead". Entertainment Weekly. Retrieved November 27, 2017.
^ Jump up to: a b Porter, Rick (October 24, 2017). "Sunday cable ratings: 'The Walking Dead' has lowest-rated premiere since Season 2". TV by the Numbers. Retrieved October 24, 2017.
^ Jump up to: a b Porter, Rick (October 31, 2017). "Sunday cable ratings: 'The Walking Dead' stumbles to 5-year low". TV by the Numbers. Retrieved October 31, 2017.
^ Jump up to: a b Porter, Rick (November 7, 2017). "Sunday cable ratings: 'Shameless' has its best premiere in 4-plus years". TV by the Numbers. Retrieved November 7, 2017.
^ Jump up to: a b Porter, Rick (November 14, 2017). "Sunday cable ratings: 'The Walking Dead' improves, 'Shameless' dips in week 2". TV by the Numbers. Retrieved November 14, 2017.
^ Jump up to: a b Porter, Rick (November 21, 2017). "Sunday cable ratings: 6-year low for 'The Walking Dead'". TV by the Numbers. Retrieved November 21, 2017.
^ Jump up to: a b Porter, Rick (November 29, 2017). "Sunday cable ratings: Hallmark's 'Switched for Christmas' hits a high, 'Walking Dead' rebounds some". TV by the Numbers. Retrieved November 29, 2017.
^ Jump up to: a b Porter, Rick (December 5, 2017). "Sunday cable ratings: 'The Walking Dead' goes low again". TV by the Numbers. Retrieved December 5, 2017.
^ Jump up to: a b Porter, Rick (December 12, 2017). "Sunday cable ratings: 'Walking Dead' fall finale ticks up, Season 8 still way down". TV by the Numbers. Retrieved December 12, 2017.
^ Jump up to: a b Porter, Rick (February 27, 2018). "Sunday cable ratings: 'The Walking Dead' returns a little higher". TV by the Numbers. Retrieved February 27, 2018.
^ Jump up to: a b Porter, Rick (March 6, 2018). "Sunday cable ratings: 'The Walking Dead' at lowest point since Season 1". TV by the Numbers. Retrieved March 6, 2018.
^ Jump up to: a b Porter, Rick (March 13, 2018). "Sunday cable ratings: 'The Walking Dead' goes even lower". TV by the Numbers. Retrieved March 13, 2018.
^ Jump up to: a b Porter, Rick (March 20, 2018). "Sunday cable ratings: 'The Walking Dead' levels off". TV by the Numbers. Retrieved March 20, 2018.
^ Jump up to: a b Porter, Rick (March 27, 2018). "Sunday cable ratings: 'The Terror' gets decent start behind 'The Walking Dead'". TV by the Numbers. Retrieved March 27, 2018.
^ Jump up to: a b Porter, Rick (April 3, 2018). "Sunday cable ratings: 'The Walking Dead' falls, NCAA women's championship off a little". TV by the Numbers. Retrieved April 3, 2018.
^ Jump up to: a b Porter, Rick (April 10, 2018). "Sunday cable ratings: 'Walking Dead,' 'Real Housewives of Atlanta' improve". TV by the Numbers. Retrieved April 10, 2018.
^ Jump up to: a b Porter, Rick (April 17, 2018). "Sunday cable ratings: 'Fear the Walking Dead' opens higher". TV by the Numbers. Retrieved April 17, 2018.
Jump up ^ Snierson, Dan (July 21, 2017). "The Walking Dead season 8 trailer teases surprise flash-forward". Entertainment Weekly. Retrieved July 22, 2017.
Jump up ^ Nyren, Erin (March 15, 2018). "'The Walking Dead' Finale and 'Fear' Premiere to Screen in Theaters". Variety. Retrieved March 21, 2018.
^ Jump up to: a b "The Walking Dead: Season 8". Rotten Tomatoes. Retrieved April 17, 2016.
Jump up ^ Porter, Rick (November 3, 2017). "'Walking Dead' premiere grows a lot, still trails Season 7 debut by a lot: Cable Live +7 ratings for Oct. 16-22". TV by the Numbers. Retrieved November 3, 2017.
Jump up ^ Porter, Rick (November 9, 2017). "'Walking Dead,' 'AHS: Cult' way above everything else in cable Live +7 ratings for Oct. 23-29". TV by the Numbers. Retrieved November 9, 2017.
Jump up ^ Porter, Rick (November 17, 2017). "'American Horror Story: Cult' triples in cable Live +7 ratings for Oct. 30-Nov. 5". TV by the Numbers. Retrieved November 17, 2017.
Jump up ^ Porter, Rick (November 19, 2017). "'The Walking Dead' keeps pace in cable Live +3 ratings for Nov. 6-12". TV by the Numbers. Retrieved November 19, 2017.
Jump up ^ Porter, Rick (December 7, 2017). "'The Walking Dead' laps the field in cable Live +7 ratings for Nov. 20-26". TV by the Numbers. Retrieved December 7, 2017.
Jump up ^ Porter, Rick (December 15, 2017). "'The Walking Dead' outpaces everything else in cable Live +7 ratings for Nov. 27-Dec. 3". TV by the Numbers. Retrieved December 15, 2017.
Jump up ^ Porter, Rick (December 21, 2017). "'Top Chef' premiere more than doubles in cable Live +7 ratings for Dec. 4-10". TV by the Numbers. Retrieved December 21, 2017.
Jump up ^ Porter, Rick (March 15, 2018). "'Walking Dead' stays atop the cable Live +7 ratings for Feb. 26-March 4". TV by the Numbers. Retrieved March 15, 2018.
Jump up ^ Porter, Rick (March 22, 2018). "'Atlanta' and 'The Alienist' make more solid gains in cable Live +7 ratings for March 5-11". TV by the Numbers. Retrieved March 22, 2018.
Jump up ^ Porter, Rick (March 29, 2018). "'The Fosters' finale doubles in cable Live +7 ratings for March 12-18". TV by the Numbers. Retrieved March 29, 2018.
Jump up ^ Porter, Rick (April 6, 2018). "'Krypton' premiere makes solid gains in cable Live +7 ratings for March 19-25". TV by the Numbers. Retrieved April 6, 2018.
Jump up ^ Porter, Rick (April 11, 2018). "'Siren' premiere doubles in cable Live +7 ratings for March 26-April 1". TV by the Numbers. Retrieved April 11, 2018.
Jump up ^ Porter, Rick (April 19, 2018). "'Fixer Upper' finale goes out strong: Cable Live +7 ratings for April 2-8". TV by the Numbers. Retrieved April 19, 2018.
External links[edit]
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"Mercy"
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"The Big Scary U"
"The King, the Widow, and Rick"
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text:
Hardy–Weinberg principle
From Wikipedia, the free encyclopedia
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Hardy–Weinberg proportions for two alleles: the horizontal axis shows the two allele frequencies p and q and the vertical axis shows the expected genotype frequencies. Each line shows one of the three possible genotypes.
The Hardy–Weinberg principle, also known as the Hardy–Weinberg equilibrium, model, theorem, or law, states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences. These influences include mate choice, mutation, selection, genetic drift, gene flow and meiotic drive.
In the simplest case of a single locus with two alleles denoted A and a with frequencies f(A) = p and f(a) = q, respectively, the expected genotype frequencies under random mating are f(AA) = p2 for the AA homozygotes, f(aa) = q2 for the aa homozygotes, and f(Aa) = 2pq for the heterozygotes. In the absence of selection, mutation, genetic drift, or other forces, allele frequencies p and q are constant between generations, so equilibrium is reached.
The principle is named after G. H. Hardy and Wilhelm Weinberg, who first demonstrated it mathematically. Hardy's paper was focused on debunking the then-commonly held view that a dominant allele would automatically tend to increase in frequency; today, confusion between dominance and selection is less common. Today, tests for Hardy-Weinberg genotype frequencies are used primarily to test for population stratification and other forms of non-random mating.
Contents
[hide]
1 Derivation
2 Deviations from Hardy–Weinberg equilibrium
3 Sex linkage
4 Generalizations
4.1 Generalization for more than two alleles
4.2 Generalization for polyploidy
4.3 Complete generalization
5 Applications
5.1 Application to cases of complete dominance
6 Significance tests for deviation
6.1 Example χ 2 {\displaystyle \chi ^{2}} test for deviation
6.2 Fisher's exact test (probability test)
7 Inbreeding coefficient
8 History
8.1 Derivation of Hardy's equations
8.2 Numerical example
9 Graphical representation
10 See also
11 References
12 Bibliography
13 External links
Derivation[edit]
Consider a population of monoecious diploids, where each organism produces male and female gametes at equal frequency, and has two alleles at each gene locus. Organisms reproduce by random union of gametes (the “gene pool” population model). A locus in this population has two alleles, A and a, that occur with initial frequencies f0(A) = p and f0(a) = q, respectively.[1] The allele frequencies at each generation are obtained by pooling together the alleles from each genotype of the same generation according to the expected contribution from the homozygote and heterozygote genotypes, which are 1 and 1/2, respectively:
f t ( A ) = f t ( AA ) + 1 2 f t ( Aa ) {\displaystyle f_{t}({\text{A}})=f_{t}({\text{AA}})+{\tfrac {1}{2}}f_{t}({\text{Aa}})}
(1)
f t ( a ) = f t ( aa ) + 1 2 f t ( Aa ) {\displaystyle f_{t}({\text{a}})=f_{t}({\text{aa}})+{\tfrac {1}{2}}f_{t}({\text{Aa}})}
(2)
Length of p, q corresponds to allele frequencies (here p = 0.6, q = 0.4). Then area of rectangle represents genotype frequencies (thus AA : Aa : aa = 0.36 : 0.48 : 0.16).
The different ways to form genotypes for the next generation can be shown in a Punnett square, where the proportion of each genotype is equal to the product of the row and column allele frequencies from the current generation.
Table 1: Punnett square for Hardy–Weinberg
Females
A (p)
a (q)
Males
A (p)
AA (p2) Aa (pq)
a (q)
Aa (qp) aa (q2)
The sum of the entries is p2 + 2pq + q2 = 1, as the genotype frequencies must sum to one.
Note again that as p + q = 1, the binomial expansion of (p + q)2 = p2 + 2pq + q2 = 1 gives the same relationships.
Summing the elements of the Punnett square or the binomial expansion, we obtain the expected genotype proportions among the offspring after a single generation:
f 1 ( AA ) = p 2 = f 0 ( A ) 2 {\displaystyle f_{1}({\text{AA}})=p^{2}=f_{0}({\text{A}})^{2}}
(3)
f 1 ( Aa ) = p q + q p = 2 p q = 2 f 0 ( A ) f 0 ( a ) {\displaystyle f_{1}({\text{Aa}})=pq+qp=2pq=2f_{0}({\text{A}})f_{0}({\text{a}})}
(4)
f 1 ( aa ) = q 2 = f 0 ( a ) 2 {\displaystyle f_{1}({\text{aa}})=q^{2}=f_{0}({\text{a}})^{2}}
(5)
These frequencies define the Hardy–Weinberg equilibrium. It should be mentioned that the genotype frequencies after the first generation need not equal the genotype frequencies from the initial generation, e.g. f1(AA) ≠ f0(AA). However, the genotype frequencies for all future times will equal the Hardy–Weinberg frequencies, e.g. ft(AA) = f1(AA) for t > 1. This follows since the genotype frequencies of the next generation depend only on the allele frequencies of the current generation which, as calculated by equations (1) and (2), are preserved from the initial generation:
f 1 ( A ) = f 1 ( AA ) + 1 2 f 1 ( Aa ) = p 2 + p q = p ( p + q ) = p = f 0 ( A ) f 1 ( a ) = f 1 ( aa ) + 1 2 f 1 ( Aa ) = q 2 + p q = q ( p + q ) = q = f 0 ( a ) {\displaystyle {\begin{aligned}f_{1}({\text{A}})&=f_{1}({\text{AA}})+{\tfrac {1}{2}}f_{1}({\text{Aa}})=p^{2}+pq=p(p+q)=p=f_{0}({\text{A}})\\f_{1}({\text{a}})&=f_{1}({\text{aa}})+{\tfrac {1}{2}}f_{1}({\text{Aa}})=q^{2}+pq=q(p+q)=q=f_{0}({\text{a}})\end{aligned}}}
For the more general case of dioecious diploids [organisms are either male or female] that reproduce by random mating of individuals, it is necessary to calculate the genotype frequencies from the nine possible matings between each parental genotype (AA, Aa, and aa) in either sex, weighted by the expected genotype contributions of each such mating.[2] Equivalently, one considers the six unique diploid-diploid combinations:
[ ( AA , AA ) , ( AA , Aa ) , ( AA , aa ) , ( Aa , Aa ) , ( Aa , aa ) , ( aa , aa ) ] {\displaystyle \left[({\text{AA}},{\text{AA}}),({\text{AA}},{\text{Aa}}),({\text{AA}},{\text{aa}}),({\text{Aa}},{\text{Aa}}),({\text{Aa}},{\text{aa}}),({\text{aa}},{\text{aa}})\right]}
and constructs a Punnett square for each, so as to calculate its contribution to the next generation's genotypes. These contributions are weighted according to the probability of each diploid-diploid combination, which follows a multinomial distribution with k = 3. For example, the probability of the mating combination (AA,aa) is 2 ft(AA)ft(aa) and it can only result in the Aa genotype: [0,1,0]. Overall, the resulting genotype frequencies are calculated as:
[ f t + 1 ( AA ) , f t + 1 ( Aa ) , f t + 1 ( aa ) ] = = f t ( AA ) f t ( AA ) [ 1 , 0 , 0 ] + 2 f t ( AA ) f t ( Aa ) [ 1 2 , 1 2 , 0 ] + 2 f t ( AA ) f t ( aa ) [ 0 , 1 , 0 ] + f t ( Aa ) f t ( Aa ) [ 1 4 , 1 2 , 1 4 ] + 2 f t ( Aa ) f t ( aa ) [ 0 , 1 2 , 1 2 ] + f t ( aa ) f t ( aa ) [ 0 , 0 , 1 ] = [ ( f t ( AA ) + 1 2 f t ( Aa ) ) 2 , 2 ( f t ( AA ) + 1 2 f t ( Aa ) ) ( f t ( aa ) + 1 2 f t ( Aa ) ) , ( f t ( aa ) + 1 2 f t ( Aa ) ) 2 ] = [ f t ( A ) 2 , 2 f t ( A ) f t ( a ) , f t ( a ) 2 ] {\displaystyle {\begin{aligned}&\left[f_{t+1}({\text{AA}}),f_{t+1}({\text{Aa}}),f_{t+1}({\text{aa}})\right]=\\&\qquad =f_{t}({\text{AA}})f_{t}({\text{AA}})\left[1,0,0\right]+2f_{t}({\text{AA}})f_{t}({\text{Aa}})\left[{\tfrac {1}{2}},{\tfrac {1}{2}},0\right]+2f_{t}({\text{AA}})f_{t}({\text{aa}})\left[0,1,0\right]\\&\qquad \qquad +f_{t}({\text{Aa}})f_{t}({\text{Aa}})\left[{\tfrac {1}{4}},{\tfrac {1}{2}},{\tfrac {1}{4}}\right]+2f_{t}({\text{Aa}})f_{t}({\text{aa}})\left[0,{\tfrac {1}{2}},{\tfrac {1}{2}}\right]+f_{t}({\text{aa}})f_{t}({\text{aa}})\left[0,0,1\right]\\&\qquad =\left[\left(f_{t}({\text{AA}})+{\tfrac {1}{2}}f_{t}({\text{Aa}})\right)^{2},2\left(f_{t}({\text{AA}})+{\tfrac {1}{2}}f_{t}({\text{Aa}})\right)\left(f_{t}({\text{aa}})+{\tfrac {1}{2}}f_{t}({\text{Aa}})\right),\left(f_{t}({\text{aa}})+{\tfrac {1}{2}}f_{t}({\text{Aa}})\right)^{2}\right]\\&\qquad =\left[f_{t}({\text{A}})^{2},2f_{t}({\text{A}})f_{t}({\text{a}}),f_{t}({\text{a}})^{2}\right]\end{aligned}}}
As before, one can show that the allele frequencies at time t+1 equal those at time t, and so, are constant in time. Similarly, the genotype frequencies depend only on the allele frequencies, and so, after time t=1 are also constant in time.
If in either monoecious or dioecious organisms, either the allele or genotype proportions are initially unequal in either sex, it can be shown that constant proportions are obtained after one generation of random mating. If dioecious organisms are heterogametic and the gene locus is located on the X chromosome, it can be shown that if the allele frequencies are initially unequal in the two sexes [e.g., XX females and XY males, as in humans], f′(a) in the heterogametic sex ‘chases’ f(a) in the homogametic sex of the previous generation, until an equilibrium is reached at the weighted average of the two initial frequencies.
Deviations from Hardy–Weinberg equilibrium[edit]
The seven assumptions underlying Hardy–Weinberg equilibrium are as follows:[3]
organisms are diploid
only sexual reproduction occurs
generations are nonoverlapping
mating is random
population size is infinitely large
allele frequencies are equal in the sexes
there is no migration, mutation or selection
Violations of the Hardy–Weinberg assumptions can cause deviations from expectation. How this affects the population depends on the assumptions that are violated.
Random mating. The HWP states the population will have the given genotypic frequencies (called Hardy–Weinberg proportions) after a single generation of random mating within the population. When the random mating assumption is violated, the population will not have Hardy–Weinberg proportions. A common cause of non-random mating is inbreeding, which causes an increase in homozygosity for all genes.
If a population violates one of the following four assumptions, the population may continue to have Hardy–Weinberg proportions each generation, but the allele frequencies will change over time.
Selection, in general, causes allele frequencies to change, often quite rapidly. While directional selection eventually leads to the loss of all alleles except the favored one (unless one allele is dominant, in which case recessive alleles can survive at low frequencies), some forms of selection, such as balancing selection, lead to equilibrium without loss of alleles.
Mutation will have a very subtle effect on allele frequencies. Mutation rates are of the order 10−4 to 10−8, and the change in allele frequency will be, at most, the same order. Recurrent mutation will maintain alleles in the population, even if there is strong selection against them.
Migration genetically links two or more populations together. In general, allele frequencies will become more homogeneous among the populations. Some models for migration inherently include nonrandom mating (Wahlund effect, for example). For those models, the Hardy–Weinberg proportions will normally not be valid.
Small population size can cause a random change in allele frequencies. This is due to a sampling effect, and is called genetic drift. Sampling effects are most important when the allele is present in a small number of copies.
Sex linkage[edit]
Where the A gene is sex linked, the heterogametic sex (e.g., mammalian males; avian females) have only one copy of the gene (and are termed hemizygous), while the homogametic sex (e.g., human females) have two copies. The genotype frequencies at equilibrium are p and q for the heterogametic sex but p2, 2pq and q2 for the homogametic sex.
For example, in humans red–green colorblindness is an X-linked recessive trait. In western European males, the trait affects about 1 in 12, (q = 0.083) whereas it affects about 1 in 200 females (0.005, compared to q2 = 0.007), very close to Hardy–Weinberg proportions.
If a population is brought together with males and females with a different allele frequency in each subpopulation (males or females), the allele frequency of the male population in the next generation will follow that of the female population because each son receives its X chromosome from its mother. The population converges on equilibrium very quickly.
Generalizations[edit]
The simple derivation above can be generalized for more than two alleles and polyploidy.
Generalization for more than two alleles[edit]
Punnett square for three-allele case (left) and four-allele case (right). White areas are homozygotes. Colored areas are heterozygotes.
Consider an extra allele frequency, r. The two-allele case is the binomial expansion of (p + q)2, and thus the three-allele case is the trinomial expansion of (p + q + r)2.
( p + q + r ) 2 = p 2 + q 2 + r 2 + 2 p q + 2 p r + 2 q r {\displaystyle (p+q+r)^{2}=p^{2}+q^{2}+r^{2}+2pq+2pr+2qr\,}
More generally, consider the alleles A1, ..., An given by the allele frequencies p1 to pn;
( p 1 + ⋯ + p n ) 2 {\displaystyle (p_{1}+\cdots +p_{n})^{2}\,}
giving for all homozygotes:
f ( A i A i ) = p i 2 {\displaystyle f(A_{i}A_{i})=p_{i}^{2}\,}
and for all heterozygotes:
f ( A i A j ) = 2 p i p j {\displaystyle f(A_{i}A_{j})=2p_{i}p_{j}\,}
Generalization for polyploidy[edit]
The Hardy–Weinberg principle may also be generalized to polyploid systems, that is, for organisms that have more than two copies of each chromosome. Consider again only two alleles. The diploid case is the binomial expansion of:
( p + q ) 2 {\displaystyle (p+q)^{2}\,}
and therefore the polyploid case is the polynomial expansion of:
( p + q ) c {\displaystyle (p+q)^{c}\,}
where c is the ploidy, for example with tetraploid (c = 4):
Table 2: Expected genotype frequencies for tetraploidy
Genotype
Frequency
AAAA p 4 {\displaystyle p^{4}}
AAAa 4 p 3 q {\displaystyle 4p^{3}q}
AAaa 6 p 2 q 2 {\displaystyle 6p^{2}q^{2}}
Aaaa 4 p q 3 {\displaystyle 4pq^{3}}
aaaa q 4 {\displaystyle q^{4}}
Depending on whether the organism is a 'true' tetraploid or an amphidiploid will determine how long it will take for the population to reach Hardy–Weinberg equilibrium.
Complete generalization[edit]
For n {\displaystyle n} distinct alleles in c {\displaystyle c} -ploids, the genotype frequencies in the Hardy–Weinberg equilibrium are given by individual terms in the multinomial expansion of ( p 1 + ⋯ + p n ) c {\displaystyle (p_{1}+\cdots +p_{n})^{c}} :
( p 1 + ⋯ + p n ) c = ∑ k 1 , … , k n ∈ N : k 1 + ⋯ + k n = c ( c k 1 , … , k n ) p 1 k 1 ⋯ p n k n {\displaystyle (p_{1}+\cdots +p_{n})^{c}=\sum _{k_{1},\ldots ,k_{n}\ \in \mathbb {N} :k_{1}+\cdots +k_{n}=c}{c \choose k_{1},\ldots ,k_{n}}p_{1}^{k_{1}}\cdots p_{n}^{k_{n}}}
Applications[edit]
The Hardy–Weinberg principle may be applied in two ways, either a population is assumed to be in Hardy–Weinberg proportions, in which the genotype frequencies can be calculated, or if the genotype frequencies of all three genotypes are known, they can be tested for deviations that are statistically significant.
Application to cases of complete dominance[edit]
Suppose that the phenotypes of AA and Aa are indistinguishable, i.e., there is complete dominance. Assuming that the Hardy–Weinberg principle applies to the population, then q {\displaystyle q} can still be calculated from f(aa):
q = f ( aa ) {\displaystyle q={\sqrt {f({\text{aa}})}}}
and p {\displaystyle p} can be calculated from q {\displaystyle q} . And thus an estimate of f(AA) and f(Aa) derived from p 2 {\displaystyle p^{2}} and 2 p q {\displaystyle 2pq} respectively. Note however, such a population cannot be tested for equilibrium using the significance tests below because it is assumed a priori.
Significance tests for deviation[edit]
Testing deviation from the HWP is generally performed using Pearson's chi-squared test, using the observed genotype frequencies obtained from the data and the expected genotype frequencies obtained using the HWP. For systems where there are large numbers of alleles, this may result in data with many empty possible genotypes and low genotype counts, because there are often not enough individuals present in the sample to adequately represent all genotype classes. If this is the case, then the asymptotic assumption of the chi-squared distribution, will no longer hold, and it may be necessary to use a form of Fisher's exact test, which requires a computer to solve. More recently a number of MCMC methods of testing for deviations from HWP have been proposed (Guo & Thompson, 1992; Wigginton et al. 2005)
Example χ 2 {\displaystyle \chi ^{2}} test for deviation[edit]
This data is from E.B. Ford (1971) on the Scarlet tiger moth, for which the phenotypes of a sample of the population were recorded. Genotype-phenotype distinction is assumed to be negligibly small. The null hypothesis is that the population is in Hardy–Weinberg proportions, and the alternative hypothesis is that the population is not in Hardy–Weinberg proportions.
Table 3: Example Hardy–Weinberg principle calculation
Phenotype
White-spotted (AA) Intermediate (Aa) Little spotting (aa)
Total
Number
1469 138 5 1612
From this, allele frequencies can be calculated:
p = 2 × o b s ( AA ) + o b s ( Aa ) 2 × ( o b s ( AA ) + o b s ( Aa ) + o b s ( aa ) ) = 1469 × 2 + 138 2 × ( 1469 + 138 + 5 ) = 3076 3224 = 0.954 {\displaystyle {\begin{aligned}p&={2\times \mathrm {obs} ({\text{AA}})+\mathrm {obs} ({\text{Aa}}) \over 2\times (\mathrm {obs} ({\text{AA}})+\mathrm {obs} ({\text{Aa}})+\mathrm {obs} ({\text{aa}}))}\\\\&={1469\times 2+138 \over 2\times (1469+138+5)}\\\\&={3076 \over 3224}\\\\&=0.954\end{aligned}}}
and
q = 1 − p = 1 − 0.954 = 0.046 {\displaystyle {\begin{aligned}q&=1-p\\&=1-0.954\\&=0.046\end{aligned}}}
So the Hardy–Weinberg expectation is:
E x p ( AA ) = p 2 n = 0.954 2 × 1612 = 1467.4 E x p ( Aa ) = 2 p q n = 2 × 0.954 × 0.046 × 1612 = 141.2 E x p ( aa ) = q 2 n = 0.046 2 × 1612 = 3.4 {\displaystyle {\begin{aligned}\mathrm {Exp} ({\text{AA}})&=p^{2}n=0.954^{2}\times 1612=1467.4\\\mathrm {Exp} ({\text{Aa}})&=2pqn=2\times 0.954\times 0.046\times 1612=141.2\\\mathrm {Exp} ({\text{aa}})&=q^{2}n=0.046^{2}\times 1612=3.4\end{aligned}}}
Pearson's chi-squared test states:
χ 2 = ∑ ( O − E ) 2 E = ( 1469 − 1467.4 ) 2 1467.4 + ( 138 − 141.2 ) 2 141.2 + ( 5 − 3.4 ) 2 3.4 = 0.001 + 0.073 + 0.756 = 0.83 {\displaystyle {\begin{aligned}\chi ^{2}&=\sum {(O-E)^{2} \over E}\\&={(1469-1467.4)^{2} \over 1467.4}+{(138-141.2)^{2} \over 141.2}+{(5-3.4)^{2} \over 3.4}\\&=0.001+0.073+0.756\\&=0.83\end{aligned}}}
There is 1 degree of freedom (degrees of freedom for test for Hardy–Weinberg proportions are # genotypes − # alleles). The 5% significance level for 1 degree of freedom is 3.84, and since the χ2 value is less than this, the null hypothesis that the population is in Hardy–Weinberg frequencies is not rejected.
Fisher's exact test (probability test)[edit]
Fisher's exact test can be applied to testing for Hardy–Weinberg proportions. Since the test is conditional on the allele frequencies, p and q, the problem can be viewed as testing for the proper number of heterozygotes. In this way, the hypothesis of Hardy–Weinberg proportions is rejected if the number of heterozygotes is too large or too small. The conditional probabilities for the heterozygote, given the allele frequencies are given in Emigh (1980) as
prob  [ n 12 | n 1 ] = ( n n 11 , n 12 , n 22 ) ( 2 n n 1 , n 2 ) 2 n 12 , {\displaystyle \operatorname {prob} [n_{12}|n_{1}]={\frac {\binom {n}{n_{11},n_{12},n_{22}}}{\binom {2n}{n_{1},n_{2}}}}2^{n_{12}},}
where n11, n12, n22 are the observed numbers of the three genotypes, AA, Aa, and aa, respectively, and n1 is the number of A alleles, where n 1 = 2 n 11 + n 12 {\displaystyle n_{1}=2n_{11}+n_{12}} .
An example Using one of the examples from Emigh (1980),[4] we can consider the case where n = 100, and p = 0.34. The possible observed heterozygotes and their exact significance level is given in Table 4.
Table 4: Example of Fisher's exact test for n = 100, p = 0.34.[4]
Number of heterozygotes
Significance level
0 0.000
2 0.000
4 0.000
6 0.000
8 0.000
10 0.000
12 0.000
14 0.000
16 0.000
18 0.001
20 0.007
22 0.034
34 0.067
24 0.151
32 0.291
26 0.474
30 0.730
28 1.000
Using this table, one must look up the significance level of the test based on the observed number of heterozygotes. For example, if one observed 20 heterozygotes, the significance level for the test is 0.007. As is typical for Fisher's exact test for small samples, the gradation of significance levels is quite coarse.
However, a table like this has to be created for every experiment, since the tables are dependent on both n and p.
Inbreeding coefficient[edit]
The inbreeding coefficient, F (see also F-statistics), is one minus the observed frequency of heterozygotes over that expected from Hardy–Weinberg equilibrium.
F = E  ( f ( Aa ) ) − O  ( f ( Aa ) ) E  ( f ( Aa ) ) = 1 − O  ( f ( Aa ) ) E  ( f ( Aa ) ) , {\displaystyle F={\frac {\operatorname {E} {(f({\text{Aa}}))}-\operatorname {O} (f({\text{Aa}}))}{\operatorname {E} (f({\text{Aa}}))}}=1-{\frac {\operatorname {O} (f({\text{Aa}}))}{\operatorname {E} (f({\text{Aa}}))}},}
where the expected value from Hardy–Weinberg equilibrium is given by
E  ( f ( Aa ) ) = 2 p q {\displaystyle \operatorname {E} (f({\text{Aa}}))=2pq}
For example, for Ford's data above;
F = 1 − 138 141.2 = 0.023. {\displaystyle F=1-{138 \over 141.2}=0.023.}
For two alleles, the chi-squared goodness of fit test for Hardy–Weinberg proportions is equivalent to the test for inbreeding, F = 0.
The inbreeding coefficient is unstable as the expected value approaches zero, and thus not useful for rare and very common alleles. For: E = 0, O > 0, F = −∞ and E = 0, O = 0, F is undefined.
History[edit]
Mendelian genetics were rediscovered in 1900. However, it remained somewhat controversial for several years as it was not then known how it could cause continuous characteristics. Udny Yule (1902) argued against Mendelism because he thought that dominant alleles would increase in the population.[5] The American William E. Castle (1903) showed that without selection, the genotype frequencies would remain stable.[6] Karl Pearson (1903) found one equilibrium position with values of p = q = 0.5.[7] Reginald Punnett, unable to counter Yule's point, introduced the problem to G. H. Hardy, a British mathematician, with whom he played cricket. Hardy was a pure mathematician and held applied mathematics in some contempt; his view of biologists' use of mathematics comes across in his 1908 paper where he describes this as "very simple":[8]
To the Editor of Science: I am reluctant to intrude in a discussion concerning matters of which I have no expert knowledge, and I should have expected the very simple point which I wish to make to have been familiar to biologists. However, some remarks of Mr. Udny Yule, to which Mr. R. C. Punnett has called my attention, suggest that it may still be worth making...
Suppose that Aa is a pair of Mendelian characters, A being dominant, and that in any given generation the number of pure dominants (AA), heterozygotes (Aa), and pure recessives (aa) are as p:2q:r. Finally, suppose that the numbers are fairly large, so that mating may be regarded as random, that the sexes are evenly distributed among the three varieties, and that all are equally fertile. A little mathematics of the multiplication-table type is enough to show that in the next generation the numbers will be as (p + q)2:2(p + q)(q + r):(q + r)2, or as p1:2q1:r1, say.
The interesting question is: in what circumstances will this distribution be the same as that in the generation before? It is easy to see that the condition for this is q2 = pr. And since q12 = p1r1, whatever the values of p, q, and r may be, the distribution will in any case continue unchanged after the second generation
The principle was thus known as Hardy's law in the English-speaking world until 1943, when Curt Stern pointed out that it had first been formulated independently in 1908 by the German physician Wilhelm Weinberg.[9][10] William Castle in 1903 also derived the ratios for the special case of equal allele frequencies, and it is sometimes (but rarely) called the Hardy–Weinberg–Castle Law.
Derivation of Hardy's equations[edit]
Hardy's statement begins with a recurrence relation for the frequencies p, 2q, and r. These recurrence relations follow from fundamental concepts in probability, specifically independence, and conditional probability. For example, consider the probability of an offspring from the generation t {\displaystyle \textstyle t} being homozygous dominant. Alleles are inherited independently from each parent. A dominant allele can be inherited from a homozygous dominant parent with probability 1, or from a heterozygous parent with probability 0.5. To represent this reasoning in an equation, let A t {\displaystyle \textstyle A_{t}} represent inheritance of a dominant allele from a parent. Furthermore, let A A t − 1 {\displaystyle \textstyle AA_{t-1}} and A a t − 1 {\displaystyle \textstyle Aa_{t-1}} represent potential parental genotypes in the preceding generation.
p t = P ( A t , A t ) = P ( A t ) 2 = ( P ( A t | A A t − 1 ) P ( A A t − 1 ) + P ( A t | A a t − 1 ) P ( A a t − 1 ) ) 2 = ( ( 1 ) p t − 1 + ( 0.5 ) 2 q t − 1 ) 2 = ( p t − 1 + q t − 1 ) 2 {\displaystyle {\begin{aligned}p_{t}&=P(A_{t},A_{t})=P(A_{t})^{2}\\&=\left(P(A_{t}|AA_{t-1})P(AA_{t-1})+P(A_{t}|Aa_{t-1})P(Aa_{t-1})\right)^{2}\\&=\left((1)p_{t-1}+(0.5)2q_{t-1}\right)^{2}\\&=\left(p_{t-1}+q_{t-1}\right)^{2}\end{aligned}}}
The same reasoning, applied to the other genotypes yields the two remaining recurrence relations. Equilibrium occurs when each proportion is constant between subsequent generations. More formally, a population is at equilibrium at generation t {\displaystyle \textstyle t} when
0 = p t − p t − 1 {\displaystyle \textstyle 0=p_{t}-p_{t-1}} , 0 = q t − q t − 1 {\displaystyle \textstyle 0=q_{t}-q_{t-1}} , and 0 = r t − r t − 1 {\displaystyle \textstyle 0=r_{t}-r_{t-1}}
By solving these equations necessary and sufficient conditions for equilibrium to occur can be determined. Again, consider the frequency of homozygous dominant animals. Equilibrium implies
0 = p t − p t − 1 = p t − 1 2 + 2 p t − 1 q t − 1 + q t − 1 2 − p t − 1 {\displaystyle {\begin{aligned}0&=p_{t}-p_{t-1}\\&=p_{t-1}^{2}+2p_{t-1}q_{t-1}+q_{t-1}^{2}-p_{t-1}\end{aligned}}}
First consider the case, where p t − 1 = 0 {\displaystyle \textstyle p_{t-1}=0} , and note that it implies that q t − 1 = 0 {\displaystyle \textstyle q_{t-1}=0} and r t − 1 = 1 {\displaystyle \textstyle r_{t-1}=1} . Now consider the remaining case, where p t − 1 {\displaystyle \textstyle p_{t-1}} ≠ 0 {\displaystyle \textstyle 0}
0 = p t − 1 ( p t − 1 + 2 q t − 1 + q t − 1 2 / p t − 1 − 1 ) = q t − 1 2 / p t − 1 − r t − 1 {\displaystyle {\begin{aligned}0&=p_{t-1}(p_{t-1}+2q_{t-1}+q_{t-1}^{2}/p_{t-1}-1)\\&=q_{t-1}^{2}/p_{t-1}-r_{t-1}\end{aligned}}}
Where the final equality holds because the allele proportions must sum to one. In both cases, q t − 1 2 = p t − 1 r t − 1 {\displaystyle \textstyle q_{t-1}^{2}=p_{t-1}r_{t-1}} . It can be shown that the other two equilibrium conditions imply the same equation. Together, the solutions of the three equilibrium equations imply sufficiency of Hardy's condition for equilibrium. Since the condition always holds for the second generation, all succeeding generations have the same proportions.
Numerical example[edit]
An example computation of the genotype distribution given by Hardy's original equations is instructive. The phenotype distribution from Table 3 above will be used to compute Hardy's initial genotype distribution. Note that the p and q values used by Hardy are not the same as those used above.
sum = o b s ( AA ) + 2 × o b s ( Aa ) + o b s ( aa ) = 1469 + 2 × 138 + 5 = 1750 {\displaystyle {\begin{aligned}{\text{sum}}&={\mathrm {obs} ({\text{AA}})+2\times \mathrm {obs} ({\text{Aa}})+\mathrm {obs} ({\text{aa}})}={1469+2\times 138+5}\\&=1750\end{aligned}}}
p = 1469 1750 = 0.83943 2 q = 2 × 138 1750 = 0.15771 r = 5 1750 = 0.00286 {\displaystyle {\begin{aligned}p&={1469 \over 1750}=0.83943\\2q&={2\times 138 \over 1750}=0.15771\\r&={5 \over 1750}=0.00286\end{aligned}}}
As checks on the distribution, compute
p + 2 q + r = 0.83943 + 0.15771 + 0.00286 = 1.00000 {\displaystyle p+2q+r=0.83943+0.15771+0.00286=1.00000\,}
and
E 0 = q 2 − p r = 0.00382. {\displaystyle E_{0}=q^{2}-pr=0.00382.\,}
For the next generation, Hardy's equations give
q = 0.15771 2 = 0.07886 p 1 = ( p + q ) 2 = 0.84325 2 q 1 = 2 ( p + q ) ( q + r ) = 0.15007 r 1 = ( q + r ) 2 = 0.00668. {\displaystyle {\begin{aligned}q&={0.15771 \over 2}=0.07886\\\\p_{1}&=(p+q)^{2}=0.84325\\2q_{1}&=2(p+q)(q+r)=0.15007\\r_{1}&=(q+r)^{2}=0.00668.\end{aligned}}}
Again as checks on the distribution, compute
p 1 + 2 q 1 + r 1 = 0.84325 + 0.15007 + 0.00668 = 1.00000 {\displaystyle p_{1}+2q_{1}+r_{1}=0.84325+0.15007+0.00668=1.00000\,}
and
E 1 = q 1 2 − p 1 r 1 = 0.00000 {\displaystyle E_{1}=q_{1}^{2}-p_{1}r_{1}=0.00000\,}
which are the expected values. The reader may demonstrate that subsequent use of the second-generation values for a third generation will yield identical results.
Graphical representation[edit]
A de Finetti diagram representing a distribution of genotype frequencies
It is possible to represent the distribution of genotype frequencies for a bi-allelic locus within a population graphically using a de Finetti diagram. This uses a triangular plot (also known as trilinear, triaxial or ternary plot) to represent the distribution of the three genotype frequencies in relation to each other. It differs from many other such plots in that the direction of one of the axes has been reversed.[11] The curved line in the diagram is the Hardy–Weinberg parabola and represents the state where alleles are in Hardy–Weinberg equilibrium. It is possible to represent the effects of natural selection and its effect on allele frequency on such graphs.[12] The de Finetti diagram has been developed and used extensively by A. W. F. Edwards in his book Foundations of Mathematical Genetics.[13]
See also[edit]
Regression toward the mean
Multinomial distribution (Hardy–Weinberg is a trinomial distribution with probabilities ( θ 2 , 2 θ ( 1 − θ ) , ( 1 − θ ) 2 ) {\displaystyle (\theta ^{2},2\theta (1-\theta ),(1-\theta )^{2})} )
Additive disequilibrium and z statistic
References[edit]
Jump up ^ The term frequency usually refers to a number or count, but in this context, it is synonymous with probability.
Jump up ^ Carr, Dr. Steven M. "Hardy-Weinberg in dioecious organisms". www.mun.ca.
Jump up ^ Hartl DL, Clarke AG (2007) Principles of population genetics. Sunderland, MA: Sinauer
^ Jump up to: a b Emigh, Ted H. (1980). "A Comparison of Tests for Hardy–Weinberg Equilibrium". Biometrics. 36 (4): 627–642. doi:10.2307/2556115. JSTOR 2556115.
Jump up ^ Yule, 1902
Jump up ^ Castle, 1903
Jump up ^ Pearson, 1903
Jump up ^ Hardy, 1908
Jump up ^ Crow, James F. (1999). "Hardy, Weinberg and language impediments". Genetics. 152 (3): 821–825. PMC 1460671  . PMID 10388804.
Jump up ^ Stern, Curt (1962). "Wilhelm Weinberg". Genetics. 47: 1–5.
Jump up ^ Cannings, C.; Edwards, A.W.F. (1968). "Natural selection and the de Finetti diagram". Annals of Human Genetics. 31: 421–428. doi:10.1111/j.1469-1809.1968.tb00575.x.
Jump up ^ See e.g. Ineichen & Batschelet 1975
Jump up ^ Edwards, 1977
Bibliography[edit]
Castle, W. E. (1903). "The laws of Galton and Mendel and some laws governing race improvement by selection". Proceedings of the American Academy of Arts and Sciences. 35: 233–242.
Crow, Jf (Jul 1999). "Hardy, Weinberg and language impediments". Genetics. 152 (3): 821–5. ISSN 0016-6731. PMC 1460671  . PMID 10388804.
Edwards, A.W.F. 1977. Foundations of Mathematical Genetics. Cambridge University Press, Cambridge (2nd ed., 2000). ISBN 0-521-77544-2
Emigh, T.H. (1980). "A comparison of tests for Hardy–Weinberg equilibrium". Biometrics. 36 (4): 627–642. doi:10.2307/2556115. JSTOR 2556115.
Ford, E.B. (1971). Ecological Genetics, London.
Guo, Sw; Thompson, Elizabeth A. (Jun 1992). "Performing the exact test of Hardy–Weinberg proportion for multiple alleles". Biometrics. Biometrics, Vol. 48, No. 2. 48 (2): 361–72. doi:10.2307/2532296. ISSN 0006-341X. JSTOR 2532296. PMID 1637966.
Hardy, G. H. (Jul 1908). "Mendelian Proportions in a Mixed Population" (PDF). Science. 28 (706): 49–50. doi:10.1126/science.28.706.49. ISSN 0036-8075. PMID 17779291.
Ineichen, Robert; Batschelet, Eduard (1975). "Genetic selection and de Finetti diagrams". Journal of Mathematical Biology. 2: 33. doi:10.1007/BF00276014.
Masel, Joanna (2012). "Rethinking Hardy–Weinberg and genetic drift in undergraduate biology". BioEssays. 34 (8): 701–10. doi:10.1002/bies.201100178. PMID 22576789.
Pearson, K. (1903). "Mathematical contributions to the theory of evolution. XI. On the influence of natural selection on the variability and correlation of organs". Philosophical Transactions of the Royal Society A. 200 (321–330): 1–66. doi:10.1098/rsta.1903.0001.
Stern, C. (1943). "The Hardy–Weinberg law". Science. 97 (2510): 137–138. doi:10.1126/science.97.2510.137. JSTOR 1670409. PMID 17788516.
Weinberg, W. (1908). "Über den Nachweis der Vererbung beim Menschen". Jahreshefte des Vereins für vaterländische Naturkunde in Württemberg. 64: 368–382.
Wigginton, Je; Cutler, Dj; Abecasis, Gr (May 2005). "A Note on Exact Tests of Hardy–Weinberg Equilibrium". American Journal of Human Genetics. 76 (5): 887–93. doi:10.1086/429864. ISSN 0002-9297. PMC 1199378  . PMID 15789306.
Yule, G. U. (1902). "Mendel's laws and their probable relation to intra-racial heredity". New Phytol. 1 (193–207): 222–238. doi:10.1111/j.1469-8137.1902.tb07336.x.
External links[edit]
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Online de Finetti Diagram Generator and Hardy–Weinberg equilibrium tests
Online Hardy–Weinberg equilibrium tests and drawing of de Finetti diagrams
Hardy–Weinberg Equilibrium Calculator
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