Modeling the effects of opening the great dismal swamp to black bear hunting
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Modeling the Effects of Opening the Great Dismal Swamp to Black Bear Hunting. Tristan Tronic. The Problem. Great Dismal Swamp National Wildlife Refuge is home to an estimated 300 black bears

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The problem
The Problem Black Bear Hunting

  • 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


Modeling the effects of a limited hunt what s known
Modeling the Effects of a Limited Hunt: Black Bear HuntingWhat’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


Bear population model
Bear Population Model Black Bear Hunting

Cn+1 = αSSn + αAAn

Nn+1 = βCCn

Sn+1 = βNNn

An+1 = βSSn + βAAn

α = reproduction rate

β = survival rate


Linear model for open season

0 0 .28 .58 Black Bear Hunting

.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.


Results of linear model
Results of Linear Model Black Bear Hunting

  • 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


Non linear model for fixed quota hunt
Non-Linear Model for Fixed Quota Hunt Black Bear Hunting

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


Non linear model for fixed quota hunt1

1 Black Bear Hunting

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)


Matlab program
Matlab Program Black Bear Hunting

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');


Results proposed 20 bears year
Results: Black Bear HuntingProposed 20 bears/year


Results 100 bears year
Results: Black Bear Hunting100 bears/year


Results 110 bears year
Results: Black Bear Hunting110 bears/year


Results 20 bears year 25 of normal reproduction rate for adults and subadults
Results: Black Bear Hunting20 bears/year, 25% of normal reproduction rate for adults and subadults


Problems with the model
Problems with the Model Black Bear Hunting

  • 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


Conclusions
Conclusions Black Bear Hunting

  • 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


Sources
Sources Black Bear Hunting

“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


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