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Tree Swallow Migration using Matrices

Tree Swallow Migration using Matrices. Rachel Fovargue. Migration. Defined as… the periodic passage of groups of animals (especially birds or fishes) from one region to another for feeding or breeding. Birds. Mammals. Humans. Bird Migration.

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Tree Swallow Migration using Matrices

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  1. Tree Swallow Migration using Matrices Rachel Fovargue

  2. Migration • Defined as… • the periodic passage of groups of animals (especially birds or fishes) from one region to another for feeding or breeding

  3. Birds

  4. Mammals

  5. Humans

  6. Bird Migration • Some move to follow food source, others travel south to avoid frozen waters • Advantage: Breeding in North… days are long, food is plentiful • Disadvantage: Travel in perilous, lots of energy used, predation common • Most species travel to tropical regions for winter, although there are exceptions • Mainly a Northern Hemisphere Phenomenon

  7. Tree SwallowsTachycineta bicolor • Size: 12-15 cm (5-6 in) • Wingspan: 30-35 cm (12-14 in) • Weight: 16-25 g (0.56-0.88 ounces) • Habitat: Open areas near water and fields, especially wooded swamps and shorelines. • Food: Flying insects and some berries • Catches insects in flight.

  8. Tree Swallow Migration • Pic or info - Travel in large flocks - Roost together at night

  9. Reproduction Nest an open cup of grass or pine needles placed in tree cavity or nest box. Lined with feathers, usually of waterfowl. • Egg Description: White, ~25 mm in length, • Clutch Size: average 5-7 eggs per nest • Fledging: average of 4.6 nestlings fledge per nest

  10. Matrix Model • X1 =Population of North • X2 = Population of Birds Flying South • X3 = Population of South • X4 = Population of Birds Flying North • a = Survival rate for North • b = Survival rate for Flight South • c = Survival rate for South • d = Survival rate for Flight North • e = Dispersal rate of Northern Population • f = Dispersal rate of Population Flying South • g = Dispersal rate of Southern Population • h = Dispersal rate of Population Flying North • m = Reproduction rate

  11. MatLab Program for Two AreasNorth/South • clear all m=1.0046 x=[0; 400] y=zeros(2,1460); y(:,1)=x;  %initialize for n=1:1459 a=sin((n-91)*2*pi/365)*.004+.9959 b=-sin((n-91)*2*pi/365)*.004+.9959 d=-sin((n-91)*2*pi/365)/50+.02 e=sin((n-91)*2*pi/365)/50+.02 A=[a*(1-d)*m b*e; a*d b*(1-e)]    y(:,n+1)=A*y(:,n);   %update with matrix model end plot([1:1460],y(1,:),'*r',[1:1460],y(2,:),'xb') legend('North','South')

  12. MatLab Program with Four AreasNorth/Trip Down/South/Return Trip • clear all m=1.0093 x=[30; 4000; 4700; 20] y=zeros(4,730); y(:,1)=x;   %initialize for n=1:729 a=sin((n-(365/4))*2*pi/365)*.004+.9934  %survival rate North b=-sin((n)*2*pi/365)*.003+.997   %survival rate Trip Down c=-sin((n-(365/4))*2*pi/365)*.003+.997   %survival rate South d=sin((n)*2*pi/365)*.003+.997   %survival rate Trip Back e=-sin((n-(365/4))*2*pi/365)/50+.02   %Dispersal Rate North f=sin((n)*2*pi/365)/50+.02   %Dispersal Rate Trip Down g=sin((n-(365/4))*2*pi/365)/50+.02   %Dispersal Rate South h=-sin((n)*2*pi/365)/50+.02   %Dispersal Rate Trip Back A=[a*(1-e)*m 0 0 d*h; a*e b*(1-f) 0 0; 0 b*f c*(1-g) 0; 0 0 c*g d*(1-h);]  y(:,n+1)=A*y(:,n);    %update with matrix model end plot([1:730],y(1,:),'*b',[1:730],y(2,:),'xg',[1:730],y(3,:),'ok',[1:730],y(4,:),'*r') legend('North','Trip Down','South','Return Trip')

  13. Bird Count • http://ebird.org/go/GuideMe?source=changeLocation&speciesCodes=treswa&reportType=species&bMonth=01&bYear=1996&eMonth=12&eYear=2006&monthRadio=-1&parentState=US-NY&getLocations=states&states=US-NY&countyState=US-NY&hotspotState=US-NY&bcrState=US-NY&continue.x=0&continue.y=0 • http://ebird.org/go/GuideMe?source=changeLocation&speciesCodes=treswa&reportType=species&bMonth=01&bYear=1996&eMonth=12&eYear=2006&monthRadio=-1&parentState=US-NY&getLocations=states&states=US-AL&states=US-GA&states=US-SC&countyState=US-NY&hotspotState=US-NY&bcrState=US-NY&continue.x=0&continue.y=0 • http://ebird.org/go/GuideMe?source=changeLocation&speciesCodes=treswa&reportType=species&bMonth=01&bYear=1996&eMonth=12&eYear=2006&monthRadio=-1&parentState=US-NY&getLocations=states&states=US-FL&countyState=US-NY&hotspotState=US-NY&bcrState=US-NY&continue.x=0&continue.y=0

  14. Conclusion • Can predict population Locations throughout the year • Also predict outcome of drop in survival rate in a particular location • Lower survival in any population leads to a sink and an inevitable demise in the total population • Conservation efforts have been started in many states to ensure nesting grounds for these birds

  15. References • Cornell Lab of Ornithology. All About Birds. Tree Swallow. http://www.birds.cornell.edu/AllAboutBirds/BirdGuide/Tree_Swallow_dtl.html. 2003 • Wikipedia. Bird Migration. http://en.wikipedia.org/wiki/Bird_migration. 2006 • Ebird.org. Cornell Lab of Ornithology. 2006 • Stocker, S. and D. Weis. Bird Migration. An energy analysis. 1998. http://imammb.oxfordjournals.org/cgi/reprint/15/1/65.pdf • Butler, R. Population Dynamics and Migration Routes of Tree Swallows. Field Ornithology. 59: 1988

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