sak does not work in earn-a-buck units key assumption of sak: buck harvest can index population...

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SAK Does Not Work in Earn- A-Buck Units • Key Assumption of SAK: – Buck Harvest can Index Population Trends – Buck Harvest Rates are Relatively Stable • Buck Harvest Rates Affected by: – Earn-a-buck Permit Structure

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Accounting Population Models Deterministic: checkbook accounting style models Simulates changes over time in number of deer in each sex- and age-class. Model does not directly estimate population size: –Requires input of population size in initial year –Simulate seasonal changes in population size over several years –Simulated trends sensitive to initial population size –Can estimate likely population size if independent population trend data exists Assess effects of future harvest strategies

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Page 1: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

SAK Does Not Work in Earn-A-Buck Units

• Key Assumption of SAK: – Buck Harvest can Index Population Trends– Buck Harvest Rates are Relatively Stable

• Buck Harvest Rates Affected by:– Earn-a-buck Permit Structure

Page 2: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

1996 Earn-A-Buck Units

• 16 farmland management units• Developed a accounting-style model • Patterned after POP-II

– commercially available big game population model

• Similar to bear and furbearer population model we have used for many years

Page 3: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Accounting Population Models

• Deterministic: checkbook accounting style models• Simulates changes over time in number of deer in each sex-

and age-class.• Model does not directly estimate population size:

– Requires input of population size in initial year– Simulate seasonal changes in population size over several years– Simulated trends sensitive to initial population size– Can estimate likely population size if independent population trend

data exists• Assess effects of future harvest strategies

Page 4: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Population Model Inputs

• Initial population size, sex & age composition• Harvest mortality by sex and age• Age- & year-specific pregnancy rates, litter

size• Age-specific rates of summer and winter non-

harvest mortality• Registration compliance

Page 5: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Population Model Logic1. Create pre-birth population for initial year

A. Initial number of deerB. Sex ratio of adults in initial yearC. Age composition in initial year

2. Determine fawn productionA. Age-specific pregnancy ratesB. Mean litter sizeC. Age composition of females in pre-birth populationD. Sex ratio of fawns

3. Add fawn production to pre-birth population for post-birth population and increase ages by 1 (eg. fawns become yearlings, etc.)

Page 6: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Population Model Logic 24. Subtract summer non-harvest mortality from post-birth population to

determine pre-hunt population5. Determine harvest by age and sex using:

A. Total registered harvest by antlered/antlerless (mandatory registration)B. Age structure of harvest (aging data)C. Estimate of registration compliance

6. Subtract harvest from pre-hunt population to determine post-hunt population 7. Subtract overwinter non-harvest mortality from post-hunt population to

determine pre-birth population in year 28. Repeat steps 2-7 for year 2, year 3, etc.

Page 7: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Initial Pre-birth Population Size 3,000Initial Sex Ratio (% Males) 50%

Initial Population Age Structure% Juv. % Yrlg % Adults

Females 34% 19% 47%Males 34% 19% 47%

Initial Pre-birth PopulationJuv. Yrlg Adults Total

Females 510 285 705 1,500Males 510 285 705 1,500Total 1,020 570 1,410 3,000

Example of calculations used to create pre-birth population in year 1

Page 8: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Example of calculations used to determine kit production

Age % Pregnant Litter SizeYearling 80% 2.3Adult 85% 2.6

KitsFemales in Pre-Birth Population Produced

Yearlings 285 x 0.8 x 2.3 = 524Adults 705 x 0.85 x 2.6 = 1,558Total 2,082

Sex Ratio of Kits Assumed to be Equal 1,041 Female Kits1,041 Male Kits

Page 9: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Kit production is added to pre-birth population for post-birth population

Pre-Birth Juv. ==> Yearlings and Pre-Birth Yearlings ==> Adults

Pre-birth PopulationJuv. Yrlg Adults Total

Females 510 285 705 1,500Males 510 285 705 1,500Total 1,020 570 1,410 3,000

Kits Females 1,041 Males 1,041

Post-birth PopulationJuv. Yrlg Adults Total

Females 1,041 510 990 2,541Males 1,041 510 990 2,541Total 2,082 1,020 1,980 5,082

Page 10: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Summer losses =post-birth population * summer non-harvest mortality rates

Post-birth Population Juv. Yrlg Adults TotalFemales 1,041 510 990 2,541Males 1,041 510 990 2,541Total 2,082 1,020 1,980 5,082

Summer Non-Harvest Mortality RatesJuv. Yrlg Adults

25% 12% 10%

Summer Losses Juv. Yrlg Adults TotalFemales 260 61 99 421Males 260 61 99 421Total 521 122 198 841

Page 11: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Subtract summer losses from post-birth population to determine pre-hunt population

Post-birth Population Juv. Yrlg Adults TotalFemales 1,041 510 990 2,541Males 1,041 510 990 2,541

MinusSummer Losses Juv. Yrlg Adults Total

Females 260 61 99 421Males 260 61 99 421

Pre-Hunt Population Juv. Yrlg Adults TotalFemales 781 449 891 2,121Males 781 449 891 2,121

1,562 898 1,782 4,241

Page 12: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Harvest by sex and age

Reported Harvest Females 50 Males 50Harvest Age Structure % Juv. % Yrlg % Adults

Females 43% 28% 29%Males 53% 18% 29%

Poaching/Wounding (% of Registered Harvest) 75%

Harvest Related Mortality Juv. Yrlg Adults TotalFemales 38 25 25 88Males 46 16 25 88

84 40 51 175

Page 13: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Subtract harvest related mortality from pre-hunt population to determine post-hunt population

Pre-Hunt Population Juv. Yrlg Adults TotalFemales 781 449 891 2,121Males 781 449 891 2,121

1,562 898 1,782 4,241MinusHarvest Related Mortality Juv. Yrlg Adults Total

Females 38 25 25 88Males 46 16 25 88

84 40 51 175Post-Hunt Population Juv. Yrlg Adults Total

Females 743 424 866 2,033Males 735 433 866 2,033

1,478 857 1,731 4,066

Page 14: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Winter Losses =Post-Hunt Population * Winter Non-Harvest Mortality Rates

Post-Hunt Population Juv. Yrlg Adults TotalFemales 743 424 866 2,033Males 735 433 866 2,033Total 1,478 857 1,731 4,066

Winter Non-Harvest Mortality RatesJuv. Yrlg Adults

25% 12% 10%

Winter Losses Juv. Yrlg Adults TotalFemales 186 51 87 323Males 184 52 87 322Total 369 103 173 645

Page 15: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Subtract Winter Losses From Post-Hunt Population to Determine Pre-Birth Population in Year 2

Post-Hunt Population Juv. Yrlg Adults TotalFemales 743 424 866 2,033Males 735 433 866 2,033

MinusWinter Losses Juv. Yrlg Adults Total

Females 186 51 87 323Males 184 52 87 322

Pre-Birth Population Yr. 2 Juv. Yrlg Adults TotalFemales 557 373 779 1,710Males 551 381 779 1,711

1,108 754 1,558 3,421

Repeat for Year 2, Year 3, etc.

Page 16: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Model Calculations

------ Pre-Birth Population ------ ------ ------ Post-birth Population ------ ------ Summer Non-Harvest Mortality ------ Pre-Hunt Population

=======Females==============Males ==== =======Females==============Males ==== =======Females==============Males ==== =======Females

Year Juv. Yrlgs Adults Juv. Yrlgs Adults Juv. Yrlgs Adults Juv. Yrlgs Adults Juv. Yrlgs Adults Juv. Yrlgs Adults Juv. Yrlgs

1984 527 295 729 527 295 729 1076 527 1023 1076 527 1023 269 63 102 269 63 102 807 464

1985 577 387 806 570 394 806 1246 577 1192 1246 570 1200 312 69 119 312 68 120 935 508

1986 673 425 943 666 428 949 1433 673 1368 1433 666 1377 358 81 137 358 80 138 1075 592

1987 777 499 1085 773 503 1094 1658 777 1584 1658 773 1597 414 93 158 414 93 160 1243 684

1988 841 532 1209 831 559 1227 1825 841 1741 1825 831 1785 456 101 174 456 100 179 1369 740

1989 952 594 1350 938 608 1388 2038 952 1944 2038 938 1996 509 114 194 509 113 200 1528 838

1990 1059 670 1504 1022 677 1535 2278 1059 2174 2278 1022 2212 569 127 217 569 123 221 1708 932

1991 1184 740 1722 1152 717 1726 2583 1184 2462 2583 1152 2444 646 142 246 646 138 244 1937 1042

1992 1377 867 1950 1403 860 1937 2952 1377 2817 2952 1403 2797 738 165 282 738 168 280 2214 1212

------ Harvest+Poaching Mortality ------ ------ Post-Hunt Population ------ ------ Winter Non-Harvest Mortality

=======Females==============Males ==== =======Females =======Males ==== =======Females=== =======Males ====

Year Juv. Yrlgs Adults Juv. Yrlgs Adults Juv. Yrlgs Adults Juv. Yrlgs Adults Juv. Yrlgs Adults Juv. Yrlgs Adults

1984 38 25 25 46 16 25 769 439 895 761 448 895 192 53 90 190 54 90

1985 38 25 25 46 16 25 897 483 1048 888 486 1055 224 58 105 222 58 105

1986 38 25 26 44 15 24 1037 567 1206 1031 571 1216 259 68 121 258 69 122

1987 122 79 82 135 46 74 1122 605 1343 1108 635 1363 280 73 134 277 76 136

1988 100 65 67 118 40 64 1269 675 1500 1251 691 1542 317 81 150 313 83 154

1989 117 76 79 166 56 91 1412 762 1671 1362 769 1706 353 91 167 341 92 171

1990 130 91 43 172 84 73 1578 841 1913 1536 815 1918 395 101 191 384 98 192

1991 101 56 49 67 37 47 1836 986 2166 1870 977 2153 459 118 217 468 117 215

1992 518 250 226 539 270 255 1696 962 2309 1676 964 2262 424 115 231 419 116 226

Page 17: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Simulated Population Trend for Wisconsin Fishers

0

2,000

4,000

6,000

8,000

10,000

12,000

1982 1986 1990 1994 1998 2002Year

Num

ber o

f Fis

hers

Pre-huntPost-hunt

Page 18: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Simulated trend sensitive to initial population size

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

1982 1986 1990 1994 1998 2002Year

Num

ber o

f Fis

hers

Initial population = 2,900Initial population = 3,000Initial population = 3,100

Page 19: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Fisher Tracks/Transect, Statewide, 1980-2003

0

1

2

3

4

5

6

7

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002Year

Trac

ks/T

rans

ect

Annual Tracks/Transect3-yr average

Page 20: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Calibrate simulated population to independent information on population trend

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

11,000

1982 1986 1990 1994 1998 2002Year

Num

ber o

f Fis

hers

0

1

2

3

4

5

6

7

Trac

ks/T

rans

ect

Posthunt PopulationTracks/Transect

Page 21: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Population Model Assumptions

• Does Not Assume:– Harvest age structure reflect population age structure

– Buck harvest rates are stable

• Does Assume:– Initial population size and composition can be accurately

estimated

– Nonharvest mortality rates and reproduction can be accurately estimated

Page 22: SAK Does Not Work in Earn-A-Buck Units Key Assumption of SAK: Buck Harvest can Index Population Trends Buck Harvest Rates are Relatively Stable Buck

Accounting Models Most Useful

• When long histories (10+ years) of independent estimates of population size or trend are available