A member of the SNP was suspended from the party after directing foul-mouthed homophobic abuse at Davidson during the 2015 General Election campaign.
The troll responsible for the homophobic comment was named on Twitter as Marc Hughes, a 46-year-old Celtic supporting SNP member from Tranent, East Lothian, with the profile name Laird O’Callaghan and the username @SparkyBhoyHH.
His tweet began with the words, “@RuthDavidsonMSP needs a good c**k, not a lesbian battery one.”
Speaking at the time of the Tweet, Davidson replied: "Nice. Classy. Do you kiss your mother with that mouth? Bet she's really proud of you.”
Last night, the Scottish Tory leader said there had been "too many instances" of social media being used to target "invective, aggression and abuse" at politicians and campaigners.
Davidson said: “Social media can be a useful tool to keep up to date with news and information, and allows politicians and voters to interact much more directly. While this can be positive, we have seen too many instances where people have chosen to use social media to direct invective, aggression and abuse.
“This is unacceptable, and there is no place for it in modern political discourse. That’s why we need to remind people to take ownership of what they tweet, and condemn those who step over the line. Debate and disagreement can be healthy, but it should never cross over into abuse."
Meanwhile, Dugdale, also spoke about abuse directed at her since she was first elected as a Labour MSP in 2011. The Scottish Labour leader is also understood to have faced three death threats or threats of violence during her time in as an MSP, which have led to police involvement.
Dugdale last night issued a passionate plea to social media site owners to take action to end with what she said was the "aggression, intolerance and hatred" that exists online.
She said: “Social media has allowed politicians to communicate directly with more voters, and has encouraged more people to engage in political debate. It can be a force for good, but it can also be an outlet for aggression, intolerance and hatred. Since I was elected I have had death threats and threats of violence, and have involved the police on occasion.
“Social media sites have a responsibility to work harder to remove abusive accounts, and all political parties have a duty to tackle it in their own ranks as well.”
Green MSP, Alison Johnstone, echoing concerns about the abuse, said: “Twitter and other forms of social media provide a platform for politicians and campaigners to maximise their reach. Unfortunately, the internet can often be an unpoliced debating chamber where homophobic, misogynistic, racist and sectarian abuse is posted in anonymity or without fear of any legal consequences.
“We will often disagree with our political opponents on many issues, but we’ll make our case and provide criticism in a constructive way. We’ve always made clear to our members that they too have a responsibility to continue conducting themselves in a civilised manner during public debates.”
The interventions by the senior women MSPs came after Nicola Sturgeon previously warned supporters of independence not to “hurl abuse” on the internet at unionist opponents after the Harry Potter author JK Rowling was targeted by online trolls in late 2015.
Sturgeon spoke out after Scotland’s last-minute defeat by Australia in the quarter-final of the Rugby World Cup, when hostile comments were directed at Rowling after she tweeted her support for the national team.
An independence supporter tweeting as 'Wings Over Scotland' wrote that she could "f**k off", adding: “You don’t think we’re a nation at all.”
The comment attracted much criticism on Twitter, including from those who backed Yes in the referendum.
Sturgeon, in a tweet, said: “Note to my fellow independence supporters. People who disagree are not anti-Scottish. Does our cause no good to hurl abuse (& it’s wrong).”
Sturgeon also previously warned that the so-called 'cybernats' who are members of the SNP and who “cross the line” could be disciplined by the party.
Rowling, a Labour supporter, has been branded a “traitor to Scotland” and “Blairite scum”, while fellow celebrity Sir Chris Hoy was called “a traitor” and a “typical Scots Tory naysayer” after he spoke out about the lack of training facilities in Scotland.
Equally, prominent Yes supporters with a public profile have also come in for sustained abuse online from so-called 'cyberbrits' or unionist trolls.