Late last year, my girlfriend and I adopted a middle-aged beagle mix named Cleo. She is an unusually beautiful creature with a long snout that grades from brown to white, ears that flap like a cartoon swan’s wings as she walks and the muscular shoulders of a boxer — heavyweight human, not the German breed. She is also both obstinate and cantankerous, fixated on food and frequently aggressive toward other dogs, especially the adorable puppy that lives on the first floor of our building. When Cleo came to live with us, I was unthinkingly convinced that we had to be firm with her if we wanted to correct these behavioral issues, sure that she wouldn’t respect us if we didn’t prove that we were in charge — that we were, to use a word I thought I understood: dominant.

As I would learn, that idea has little to no basis in the actual science of canine behavior. Most of the available research indicates that dogs do engage in behaviors of dominance and submission, but not that they try to compete with us for control over the domestic environments in which they live. Important questions still remain, however, especially about whether dogs recognize our putative dominion over them.

Somewhere to the side of these scientific debates, the conviction that we have to dominate our dogs is still widely established in dog-rearing circles: A document on the SPCA of Texas’s website instructs pet owners: “In order for your home to be a safe and happy place for pets and people, it’s best that the humans in the household assume the highest positions in the dominance hierarchy.” Some animal trainers, especially those influenced by Cesar Millan and the monks of New Skete, take such ideas to extremes, advocating physically aggressive techniques such as the “alpha roll” — in which a disobedient dog is forced onto its back — supposedly drawn from observation of wolves. Even the mild form of the belief that dogs compete with humans for dominance tends to elicit all sorts of contortions from owners eager to prove themselves pack leader: insisting on passing through doors before their dogs do, for example, or always eating first.

Much of that, as it happens, is regarded as nonsense by ethologists — scientists of animal behavior — who focus on dogs. Indeed, they contend that attempts to dominate our dogs can range from the merely unhelpful to the actively harmful. “All you’re doing with that is confusing the dog,” said James Serpell, professor of ethics and animal welfare at the University of Pennsylvania. “And what you end up with is frightening the dog and making it more aggressive.”

With such observations in mind, some dog trainers and advocates have argued that there’s simply no such thing as dominance in dogs. Serpell and other scientists tend to characterize this position as an overcorrection, but those who espouse it often begin by questioning the homology between dogs and wolves. It’s true, they acknowledge, that dogs evolved from wolves, but almost certainly from a species that is no longer extant, which means that comparisons with animals living today aren’t directly useful here. Further, they point out that many of the ideas about dominance and aggression that have been espoused by trainers such as Millan are based on observation of captive timber wolves, not wild ones.

Of course, wolves in wild packs do exhibit dominance hierarchies, but that doesn’t necessarily mean domestic dogs do. In his book “Dog Sense,” behaviorist John Bradshaw describes a study that he and his colleagues conducted at a British sanctuary, which found that dogs showed no “inclination to form anything like a wolf pack, especially when they are left to their own devices” — that is, no hierarchy that determines who gets access to what and when they get it. Although Bradshaw acknowledges that dogs can be competitive, he rejects the premise — central to Millan-style thinking — that “the dog is driven to set up a dominance hierarchy wherever it finds itself,” holding instead that “the use of ‘dominance’ and ‘hierarchy’ to account for the behavior of pet dogs can no longer be justified.”

Although that sounds definitive, many other prominent dog researchers disagree, even if they also reject the premise that responsible stewardship over dogs means showing them who’s boss. Marc Bekoff, professor emeritus of ecology and evolutionary biology at the University of Colorado at Boulder and the author of numerous books, including “A Dog’s World,” has been arguing for years that, yes, dogs engage in dominance-based behavior. As he writes in one essay, “No one who’s actually studied the social behavior of dogs in detail could possibly claim that they don’t display dominance or that dominance hierarchies don’t exist.”

That doesn’t, as he stressed to me over the phone, mean that dogs view humans as dominant over them. As Jessica Pierce, a bioethicist at the University of Colorado and Bekoff’s “A Dog’s World” co-author, put it, “What happens when they’re interacting with each other is very different from what happens when they’re interacting with us.”

In a recent paper for the journal Frontiers in Psychology, Clive Wynne, a psychology professor and director of the Canine Science Collaboratory at Arizona State University, goes further. He, too, starts from the premise that dog trainers — especially those who advocate “painful and regressive forms of animal training” — tend to misunderstand what dominance is. But in reviewing much of the scientific evidence, Wynne comes around to the conclusion that dogs almost certainly do perceive the humans in their lives as dominant. That doesn’t mean, as he makes clear, that we need to police or otherwise maintain our dominance over them. Instead, he suggests, dominance-based relations may be the inevitable consequence of the way dogs live with humans in even the most serene domestic settings.

To understand why, you have to go to the scientific meaning of “dominance.” Ask an ethologist to define the word and they’ll often slip into a description of specific behaviors in specific animals through which dominance is asserted and submission confirmed. Anindita Bhadra, an assistant professor at the Indian Institute of Science Education and Research Kolkata, who primarily studies free-roaming dogs, told me: “Typically in behavior, when we are talking about ‘dominance,’ it is either a posture or some kind of interaction. It could be a vocalization or a physical act, where one individual is trying to somehow assert its power or position over another individual.”

Although such behavior can sometimes look aggressive, it would, as Pierce stressed, be a mistake to conflate dominance with aggression. To the contrary, dominance behaviors are typically best understood as communicative strategies that help animals avoid truly violent conflict, not as ways to show that they’re the best at wreaking havoc.

Wynne offered a more direct definition, one that he summed up by telling me that “dominance is defined simply as preferential access to resources.” This has real consequences for the ways we study and identify dominance in dogs. Wynne noted, for example, that in Bradshaw’s study of sanctuary dogs, the animals under observation were mostly sterilized and had plenty of food, meaning that they had little cause to compete with one another — and hence few reasons to exhibit dominance or submission.

Whatever their disagreements about the particulars of these issues, none of the researchers I spoke to said that any of this should be taken to mean that dogs, as a species, want to dominate humans. Serpell suggested that this idea derives from a “semantic problem to do with confusing ‘dominance,’ which is about relationships, with ‘dominant,’ which is a behavior — in other words, behaving in a dominant way.” He said, “The notion that you should behave in a dominant way toward your dog, for example, to avoid it trying to assert itself and push you further down the hierarchy, really doesn’t seem to be an issue with dogs.”

The question, and it’s here that Wynne’s paper may prove most controversial, is whether, as he asserts, dogs recognize humans as dominant over them. Many of the studies Wynne reviews demonstrate how quickly dogs can attach themselves to humans, with at least one suggesting that they may do so more readily with our species than with their own. This is not, he argues, because dogs see us as fundamentally different from dogs, but because we interact with them differently, regularly providing them with food and hovering over them as we offer affection.

Simply put, our relationship to dogs may be inherently dominant; indeed, according to this line of thinking, we dominate them in a way that no other dog could, often without realizing it. Wynne coins the term “super-dominance” to describe the situation, by which he means that it “exaggerates the features of naturally occurring” dominance, because of our total resource control. Whether or not we realize it, Wynne argues, “when people stroke dogs’ heads, accept licks near the mouth and make themselves taller than dogs, they are unconsciously expressing formal dominance.” Pushing at this idea, he argues that even “positive reinforcement” — in which an animal is rewarded for desirable behaviors instead of being punished for undesirable ones — might be understood as an expression of dominance from the dog’s perspective.

When I asked Serpell about this last point, he called it “an interesting idea,” although he declined to endorse it directly. He did, however, tell me that he thinks “dogs recognize their owners as being the senior members of the group, so they defer to them naturally.” Bekoff, by contrast, rejected any such uniform interpretation of dog-human relations. “A human could say that it’s dominance, but I don’t view it that way,” he told me. As for using food to reward positive behavior, he said, “I never would think of that as dominance.”

With restrictions lifting and schedules changing, both pets and humans are experiencing separation anxiety. (Monica Rodman, Sarah Hashemi/The Washington Post)

It’s possible that the biggest challenge here may simply be the word dominance itself. Pierce, for one, prefers to use less troublesome terms. “I like using the language of freedom, control over access to basic needs,” she said. Bhadra, likewise, suggested that we might be better off discussing the “social understanding” of dogs more generally, pointing to research that has found that “people who show dominance to stray dogs, they are the ones that the dogs will avoid.”

Wynne is cognizant of such concerns, acknowledging that, yes, the word “dominance” itself may be too loaded, especially where the nonscientific public is concerned. Nevertheless, he holds that it’s still valuable to talk about dog-human relationships as they are, both because it can help us research the ways we live with them and because it’s worth being honest about what “living with them” really entails. “I think it wouldn’t do any harm to recognize that that is a form of dominance. It’s not as bad, sure. It’s preferable to the shock collars and this stupid alpha-roll nonsense,” he said. People should recognize that they are asserting their will over their dogs, “and that’s called dominance.”

Is it? Bekoff questioned the value of much of the research Wynne relies on, taking the position that laboratory studies of dogs may still tell us little about dogs as a species, and instead offer us a snapshot of those dogs under those circumstances at those times. “People have to stop normalizing dog behavior and saying, ‘Dogs do this and dogs don’t do this,’ ” he told me after reading Wynne’s paper, about which he subsequently wrote his own critical essay.

Something about that will surely resonate with ordinary dog lovers — those of us who thrill at the specific way they dance when we come through the door or the rhythms with which their chests rise and fall as they sleep. Whether or not our relationships with them are characterized by dominance, it is inevitably our responsibility to help them thrive in environments that are, as Bekoff puts it, “human dominated.” At a bare minimum, that surely means getting to know them as individuals, which is to say meeting them where they are — even if where they are is where we have asked them to sit and stay.