Biology, like any other specialized profession, has its own language.  For us, sex and drugs have no connection to rock and roll. Killing does not elicit panic or calls to 911.  And having a double-digit age is exceedingly rare (many rodent species barely make it to one!).

All those fabulous words, however, would make an interesting and steamy plot for a David Lynch film.  In fact, there is a Twitter hashtag #scientistorserialkiller.  It’s pretty cool.  You should check it out.  

But for population modelers, string together “sex” and “age” and “kill” and you’ve got yourself a pretty useful population estimator.  First developed in 1960 in Michigan, the Sex-Age-Kill model has been used for years to estimate deer populations by states like Wisconsin.  Keith McCaffery, who’s career was dedicated to whitetails in Wisconsin, described this method best:

Like boys and girls, male and female deer are born in approximately equal numbers. By aging harvested deer, we find that adult bucks die about twice as fast as does. Thus, the prehunt adult sex ratio is about 2 does per buck. Typically, net fawn recruitment in fall averages about 1 fawn per doe. Therefore, for every adult buck in the fall herd we typically have 2 adult does, 1 buck fawn, and 1 doe fawn. At the start of the fall hunt, 1 deer out of 5 will carry antlers.

“If all of the adult bucks were harvested and registered, one could multiply the buck harvest by 5 (proportion of the prehunt population of deer represented by the registered buck kill = 0.2) to estimate the prehunt population. Obviously not all bucks are harvested each fall and some eventually die from a variety of [non-hunting] causes. If only half of the bucks are harvested, you would multiply the buck kill by 10 (proportion of the prehunt population of deer represented by the registered buck kill = 0.1). Sex, age, and production information obtained each year enables us to calculate this multiplier. SAK is merely the method used to determine this multiplier for each [management] unit each year.”

Basically, the population is built off one segment of the population – antlered deer.  Shocking, I know.  Because of that, one of the key assumptions of this model is that the annual buck harvest rate is relatively consistent from year to year.  

The assumptions that add mystery and intrigue our model noir are:

  • Constant male harvest rate across age classes, space, and time
  • Constant female harvest rate across age classes, space, and time
  • Constant yearling survival rate outside of hunting season across sex, space, and time

As I noted, Wisconsin has been using this method for years.  Like every state with deer hunters, none of those hunters like the population estimates from this method (or in reality any method really).  Wisconsin’s deer program has undergone much scrutiny other the years.  An expert panel was even convened to review its method of estimating deer populations.  Guess who was on that panel?  Our own resident model geek, Duane. 

The panel’s conclusion: the Sex-Age-Kill model as used in Wisconsin adequately represents reality.  Ok, the 124-page report is slightly more detailed, but the usefulness of any model depends on its validity.  And the question we ask of every model is “does it adequately represent reality?”  The answer for Wisconsin is yes. 

Turns out the Sex-Age-Kill model is adequate for Pennsylvania as well but with some adjustments.  Those pesky antler point restrictions violate the assumption that male harvest rates are the same across all age classes.  However, a super smart model geek squad, led by you-know-who, figured out how to account for those violations.  

So concludes our voyage into population model noir.  Somehow, it doesn’t seem quite as interesting and steamy as its name implies. 

-Duane Diefenbach and Jeannine Fleegle

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This post is part of a series on Population Estimation

Moving the Chains

Change and Structure 

Sex Age Kill (you are here)



Over the River

Warm and Fuzzy

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