Modeling the Effects of Opening the Great Dismal Swamp to Black Bear Hunting

1. Modeling the Effects of Opening the Great Dismal Swamp to Black Bear Hunting Tristan Tronic

2. The Problem • Great Dismal Swamp National Wildlife Refuge is home to an estimated 300 black bears • The Virginia Department of Game and Inland Fisheries opened the GDSNWR to a limited bear hunt December 1st and 2nd of 20 bears total • Several animal rights and environmental groups protested the VDGIF decision, saying the hunt would damage the fragile bear population • The VDGIF responded by saying the hunt would have a negligible impact

3. Modeling the Effects of a Limited Hunt:What’s Known • Bear population dynamics have been shown to depend only on the female population • Bears can be divided into four subgroups, each separated by about one year of development: Cubs, Nonreproductive subadults, Subadults, and Adults

4. Bear Population Model Cn+1 = αSSn + αAAn Nn+1 = βCCn Sn+1 = βNNn An+1 = βSSn + βAAn α = reproduction rate β = survival rate

5. 0 0 .28 .58 .8 0 0 0 0 .71 0 0 0 0 .76 .91 1 1 30 120 Linear Model for Open Season • Based on survivability and reproduction observed in hunted bears in western Virginia Initial distribution of subpopulations not well known, except that half of the population will be female, and there will be about four times as many adults as subadults.

6. Results of Linear Model • Population seems to grow despite hunting • But the linear model for an open season assumes a hunting pressure that is unrealistically low for Southeastern Virginia Female Bears Years

7. Non-Linear Model for Fixed Quota Hunt Cn+1 = αSSn + αAAn Nn+1 = βCCn Sn+1 = βNNn An+1 = βSSn + βAAn Natural bear survival up to 25 – 30 years is very high, assumed to be 1 for this experiment It is observed in Virginia that hunters kill female bears 40% of the time, and of those 60% are nonreproductive subadults, 10% are subadults, and 30% are adults H = Number of bears allowed to be killed per year βN = 1 – H*.4*.6/Nn βS = 1 – H*.4*.1/Sn βA = 1 – H*.4*.3/An - 1/25

8. 1 1 30 120 Non-Linear Model for Fixed Quota Hunt 0 0 .28 .58 1 0 0 0 0 (1 – H*.24/Nn)0 0 0 0 (1 – H*.04/Sn) (1 – H*.12/An - .04)

9. Matlab Program clear all h=20; y=zeros(4,20); y(:,1)=[1;1;30;120;] t=zeros(4,20); t(1,1)=sum(y(:,1)); for n=1:19 A=[0 0 .28 .58; 1 0 0 0; 0 1-(h*.4*.6)/y(2,n) 0 0; 0 0 1-(h*.1*.4/y(3,n)) 1-1/25-(h*.3*.4)/y(4,n);] y(:,n+1)=A*y(:,n); t(1,n+1)=sum(y(:,n+1)); end plot([1:20],y(1,:),'*r',[1:20],y(2,:),'xb',[1:20],y(3,:),'og',[1:20],y(4,:),'xr',[1:20],t(1,:),'or'); legend('cubs','nonreproductive subadults','reproductive subadults', 'adults', 'total');

10. Results:Proposed 20 bears/year

11. Results:100 bears/year

12. Results:110 bears/year

13. Results:20 bears/year, 25% of normal reproduction rate for adults and subadults

14. Problems with the Model • Assumes that all bears born in refuge stay in refuge, and no new bears migrate in • Assumes perfect nonhunting survivability, not realistic for high human density area • Initial bear population uncertain • Assumes hunting patterns and bear reproduction will be the same as in western Virginia, which is geographically distinct

15. Conclusions • A limited hunt of 20 bears per year doesn’t seem to negatively affect the bear population • Given the uncertainty in the actual size and reproductive ability of the bear population, expanding the hunt further may cause extinction

16. Sources “Bears on the Move.” Virginia Dept. of Game and Inland Fisheries. 2004. http://www.dgif.virginia.gov/hunting/va_game_wildlife/bears_on_the_move.html “Great Dismal Swamp National Wildlife Refuge and Nansemond National Wildlife Refuge Final Comprehensive Conservation Plan July 2006” http://www.chesapeake.va.us/services/citizen_info/pdf/GDSNWRfinalCCP8-2-06.pdf Klenzendorf, Sybille. “Population Dynamics of Virginia’s hunted black bear population.”   Dissertation. Virginia Polytechnic Institute, 2002.  http://scholar.lib.vt.edu/theses/available/etd-02122002-160752/unrestricted/Klenzendorf.pdf “Lottery will choose hunters for refuge's first bear hunt.” Applegate, Aaron.  Virginian- Pilot, October 7, 2006. http://content.hamptonroads.com/story.cfm?story=112263&ran=39762