When it comes to wildlife populations, biologists and managers are interested in changes in numbers and changes in structure (sex and age ratios). How fitting that one of the first population estimation techniques is known as Change-in-Ratio.  

First described in 1940, the Change-in-Ratio method is based on differential harvest of sexes.  If the proportion of animal “types” (e.g., antlered vs non-antlered, males vs females, etc.) can be estimated before and after selective removal (e.g., only harvest the antlered type), then the population can be estimated. 

Basically, the estimator works like this: First, go out and sample the population (e.g., do a spotlight survey) and record the ratio of antlered to antlerless deer. Second, have a hunting season on antlered deer only and tally the harvest. Third, conduct another spotlight survey and record the ratio of antlered to antlerless deer. If you have estimates of the antlered:antlerlesss ratio before and after the hunting season (hence, change in ratio!) and the number of antlered deer removed from the population, then you can estimate the number of deer in the population.

If you want to see the equations and calculations that go into this method, you’ll have to google it.  This blog post is boring enough!  Suffice it to say, only people like Duane put the inner workings and minute details of models on their summer fun reading list.  

This is our first Moving the Chains installment into population estimation history and use in Pennsylvania.  It definitely doesn’t have the same excitement as watching buck movement videos.  But unlike those videos, it has way more bearing on deer management. 

The critical components of any model are assumptions.  They are kind of important.  Violation of any model assumptions affects the accuracy and applicability of its results.  We can never perfectly meet all assumptions in the real world.  A major assumption of the NFL chain gang is the accuracy of referee ball placement on the previous downs.  Does anyone think this assumption is being met?!?!?  No, but the game is played anyway. 

Change-in-Ratio assumptions include:

  • animal “types” are sampled with equal probability. For example, if you do spotlight surveys you are just as likely to see an antlered deer as an antlerless deer.
  • no births or deaths occur between the sampling periods except for known removals (such as harvest)
  • the proportion of x-type animal in harvest is different than in the pre-removal population
  • male and female fawns are equally represented in post-hunt population
  • calculation of minimum fawn population requires equal harvest rates for fawns and does
  • the adult sex ratio in the harvest accurately reflects the adult sex ratio in the population, as does the fawn:doe ratio in the harvest.

Estimating the proportion of animal “types” in the population takes a fair amount of work.  And doing that on a statewide basis is logistically impossible.  However, in 1978, a PGC deer biologist, William K. Shope, published a variation of the Change-in-Ratio technique based on harvest data. Sweet!

The Shope Change-in-Ratio method came with its own added set of assumptions:

  • 1.5-year-old males and females have the same survival rate from birth. A reasonable assumption because up until that time our field research has found no difference between males and females.

The Shope Change-in-Ratio methods evolved from an earlier Harvest Age Structure model that was developed by another PGC biologist, Lincoln Lang. Using age distribution of harvest to estimate survival rates, a life table can be created.  The only input needed is the age structure of harvested males.  Assumptions include:

  • the total antlered male harvest is known or can be estimated. In fact, this is the case for Pennsylvania (Rosenberry et al. 2004)

The Game Commission collects age and sex data from harvested deer annually.  The Harvest Age Structure technique is a viable population estimation technique given the input needed.  In fact, Shope developed his Change-in-Ratio model using Game Commission harvest data.  This was the method used to estimate deer populations for over 20 years and it performed well.  

So why was this population estimation method abandoned in 2001?  Change-in-Ratio models can be sensitive to sampling variation.  Small changes in ratios can produce large changes in population estimates resulting in erratic population trends.  If there is one thing all wildlife managers like, it’s consistency.  

Up until 2001, harvest statistics were consistent.  Season structure and antlered harvest rates varied little from year to year.  And then…APRs happened.

Antler point restrictions put an end to any Change-in-Ratio or Harvest Age Structure population estimation techniques for Pennsylvania.  Remember that assumption about equal probability of being sampled.  Well, with over half of yearling males protected, males were no longer equally vulnerable to harvest.  

Population models are driven by harvest, reproduction, and natural mortality.  But their usefulness depends on their validity.  Does the model ADEQUATELY represent reality?  No model will ever completely represent reality, but we don’t require perfection.  Wildlife managers need something that will provide a reliable indicator of population trends.  

We all recognize the limitations of population models but the questions we need to ask of all these methods are “Is the model adequate?” and “Can we improve upon our model given the constraints of time, personnel, and money?” For over 20 years, the answer was “yes” to the first question and “no” to the second. 

While the Shope Change-in-Ratio method was adequate for many years, with APRs it no longer works in Pennsylvania.  So we adapt and look for one that does.  

-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 (you are here)

Sex Age Kill



Over the River

Warm and Fuzzy

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