When I arrive at my daughter and son-in-law’s Brooklyn apartment in New York on Thursdays, my 18-month-old granddaughter hurtles toward me, happy for our weekly date.

While her parents work, we spend the day doing toddler stuff — reading favorite books six times in a row, singing about spiders and stars, placing objects into containers and dumping them out again, going to the park, napping (baby, not Bubbe, alas). If we’re lucky, I spend half an hour with the whole family, once my daughter gets home, then head back to my place in New Jersey.

The routine I call Bubbe Day (for the Yiddish word for grandmother) has come to feel so natural that I never considered whether it would have unfolded differently if my granddaughter had been a son’s child, not a daughter’s. But it might well have.

You hear this often: Paternal grandparents tread very carefully, mindful that a daughter-in-law might not appreciate their overtures or their frequent presence, anxious that she could limit access to their grandkids. I thought it an old stereotype, possibly never accurate and certainly now outmoded.

But researchers exploring family affiliations point out that a so-called “matrilineal advantage” does exist. That is, daughters generally have closer ties to their own parents than to their in-laws, which leads to warmer relationships between their children and the maternal grandparents.

“The mother-daughter dyads engage in more frequent phone contact, more emotional support and advice — more than mothers do with sons or fathers with daughters,” said Karen Fingerman, who teaches human development and family sciences at the University of Texas, Austin, and has published studies on this topic.

One possible explanation is that women still shoulder more of what researchers call “kinkeeping” — arranging for calls and visits, planning holiday gatherings.

“Women are more active in maintaining those relationships,” said Jan Mutchler, a sociologist and gerontologist at the University of Massachusetts, Boston. “When you have mothers and daughters, then you have two women working on it.”

What happens with sons and their children? “It’s about your relationship to the person they married,” Fingerman said. She has found that parents’ rapport with a daughter-in-law — “a key figure” — significantly influences their bond with her children. The connection with this gatekeeper (more than with a son-in-law, for unexplained reasons) can cement or thwart grandparental closeness.

Let’s acknowledge how many variables can affect generational ties, such as simple geography, health and whether the grandparents are working or retired. Finances matter, because disposable income makes it easier to visit from afar.

Then, consider the complexities of family dynamics. Despite the supposed matrilineal advantage, I know several hardworking new grandmas providing regular care for their sons’ children, and all seems amicable.

Further, we all know women stiff-arming their own mothers. Social science examines trends in groups of people, but can’t predict what happens in an individual family.

Still, a nurse on Long Island named Susan (she asked me to omit her surname, lest she contribute to familial strain) provides a kind of test case: She has a son and daughter, each living about 15 minutes away.

She has seen her daughter’s 2-year-old boy at least twice weekly since his birth. “He comes to our house and runs right to the toy box,” Susan said. Her daughter seeks her advice and may take it or not, but their relationship remains “very relaxed.”

But she can go a month without seeing her son’s two kids. “We have said, ‘You don’t need an invitation, just come over.’ We have said, ‘We need to see you more often,’” Susan said. It doesn’t seem to help; contact must be carefully orchestrated.

“My husband says, if you say anything to her” — meaning, their son’s wife — “we might not see them for two months,” Susan said. “It’s eggshells all the way.”

Wouldn’t you think this pattern would have shifted since researchers began identifying it decades ago?

Lots of boomer parents tried to raise kids with fewer gender restrictions and expectations, so aren’t those engaged dads taking on more of the kinkeeping by now? Are contemporary working mothers still under the influence of tired mother-in-law jokes and stereotypes? Or are we grandparents being pushier, and thus less welcomed by children-in-law, than we realize?

When I called Dr. Arthur Kornhaber, a child psychiatrist in California and author of “The Grandparent Guide,” he said he thought these differences were basically immutable. “The bond between a woman and her mother is unique,” he said. “This is the way humans are.”

But some societies function patrilineally, so perhaps this difference, where it exists, is more cultural than biological. Over time, with sensitivity and a desire to bolster families, it might change.