Key Factor Analysis

Populations in constant state of Flux

BUT…….rarely go extinct or increase unbounded

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From: Begon, M., Harper, J.L. and Townsend, C.R. (1990). Ecology: Individuals, Populations and Communities. Blackwell Scientific, 945pp

Nicholson (1933): Density-dependent biotic interactions play main role in

determining population size, and serve as a regulating mechanism to

stabilize the population. Density-independent factors cause a temporary

relaxation of density dependent processes

Andrewartha & Birch (1954): Number of individuals in animal populations

limited by a) the shortage of material resources, b) the inaccessibility of

material resources relative to the individuals ability to search, disperse etc, c)

shortage of time when r is positive. Density-independent processes more

important than density-dependent ones.

Population Regulation

Population Size Determination

Raw

Eggs 2655Eggs Infertile 2361Eggs Disease 2241Eggs Predation 1898

Chicks Squashed 1703Chicks Predation 1354Chicks Starvation 934Chicks Fell from Nest 855Adult Emigration 765Adult Predation 644Adult Disease 568

1850Stage Mortality Factor

Raw Log

Eggs 2655 3.4241Eggs Infertile 2361 3.3730Eggs Disease 2241 3.3504Eggs Predation 1898 3.2782

Chicks Squashed 1703 3.2313Chicks Predation 1354 3.1315Chicks Starvation 934 2.9702Chicks Fell from Nest 855 2.9322Adult Emigration 765 2.8837Adult Predation 644 2.8085Adult Disease 568 2.7543

Stage Mortality Factor1850

Raw Log k

Eggs 2655 3.4241 0.0510Eggs Infertile 2361 3.3730 0.0227Eggs Disease 2241 3.3504 0.0721Eggs Predation 1898 3.2782 0.0469

Chicks Squashed 1703 3.2313 0.0998Chicks Predation 1354 3.1315 0.1613Chicks Starvation 934 2.9702 0.0380Chicks Fell from Nest 855 2.9322 0.0485Adult Emigration 765 2.8837 0.0751Adult Predation 644 2.8085 0.0543Adult Disease 568 2.7543

0.6698Total

Stage Mortality Factor1850

Magnitude of k reflects significance of the different mortality sources in

1850….

Calculate k values…

How do you go about determining the factors responsible for driving inter-annual fluctuations in population size?

1850 1851 1852 1853 1854

Eggs 2655 3021 2037 2374 1046Eggs Infertile 2361 2748 1807 2143 947Eggs Disease 2241 2552 1725 2012 893Eggs Predation 1898 2085 1494 1714 746

Chicks Squashed 1703 1830 1294 1512 652Chicks Predation 1354 1343 919 1387 533Chicks Starvation 934 857 679 1015 411Chicks Fell from Nest 855 812 671 919 367Adult Emigration 765 469 664 341 349Adult Predation 644 418 487 206 172Adult Disease 568 371 438 174 162

RAWStage Mortality Factor

1850 1851 1852 1853 1854

Eggs 3.4241 3.4801 3.3089 3.3755 3.0194Eggs Infertile 3.3730 3.4390 3.2570 3.3311 2.9765Eggs Disease 3.3504 3.4069 3.2368 3.3037 2.9510Eggs Predation 3.2782 3.3192 3.1744 3.2340 2.8728

Chicks Squashed 3.2313 3.2625 3.1120 3.1794 2.8140Chicks Predation 3.1315 3.1280 2.9633 3.1422 2.7266Chicks Starvation 2.9702 2.9329 2.8316 3.0064 2.6142Chicks Fell from Nest 2.9322 2.9097 2.8264 2.9633 2.5644Adult Emigration 2.8837 2.6715 2.8220 2.5329 2.5431Adult Predation 2.8085 2.6212 2.6874 2.3141 2.2364Adult Disease 2.7543 2.5691 2.6418 2.2398 2.2083

LOGStage Mortality Factor

1850 1851 1852 1853 1854 Average K labelEggs Infertile 0.0510 0.0411 0.0519 0.0444 0.0430 0.0463 1Eggs Disease 0.0227 0.0321 0.0203 0.0274 0.0255 0.0256 2Eggs Predation 0.0721 0.0878 0.0624 0.0697 0.0782 0.0740 3

Chicks Squashed 0.0469 0.0567 0.0623 0.0546 0.0588 0.0559 4Chicks Predation 0.0998 0.1345 0.1487 0.0372 0.0874 0.1015 5Chicks Starvation 0.1613 0.1951 0.1317 0.1358 0.1124 0.1473 6Chicks Fell from Nest 0.0380 0.0232 0.0052 0.0431 0.0498 0.0319 7Adult Emigration 0.0485 0.2382 0.0044 0.4304 0.0213 0.1486 8Adult Predation 0.0751 0.0503 0.1346 0.2188 0.3067 0.1571 9Adult Disease 0.0543 0.0521 0.0457 0.0743 0.0281 0.0509 10

0.6698 0.9110 0.6672 1.1357 0.8111 0.8390Total

kStage Mortality Factor

Similar data from different years provide an indication of whether once-off observations consistent

BUT the k values, in themselves

provide no indication of

which mortality source/s play/s a

role in determining interannual variations in

population size

K label 1850 1851 1852 1853 1854

Eggs Infertile 1 0.0510 0.0411 0.0519 0.0444 0.0430Eggs Disease 2 0.0227 0.0321 0.0203 0.0274 0.0255Eggs Predation 3 0.0721 0.0878 0.0624 0.0697 0.0782

Chicks Squashed 4 0.0469 0.0567 0.0623 0.0546 0.0588Chicks Predation 5 0.0998 0.1345 0.1487 0.0372 0.0874Chicks Starvation 6 0.1613 0.1951 0.1317 0.1358 0.1124Chicks Fell from Nest 7 0.0380 0.0232 0.0052 0.0431 0.0498Adult Emigration 8 0.0485 0.2382 0.0044 0.4304 0.0213Adult Predation 9 0.0751 0.0503 0.1346 0.2188 0.3067Adult Disease 10 0.0543 0.0521 0.0457 0.0743 0.0281

Total T 0.6698 0.9110 0.6672 1.1357 0.8111

K

Look at the relationship between each k value

and ktotal

0.0

0.1

0.2

0.3

0.4

0.5

1850 1851 1852 1853 1854

Year

K

0.0

0.2

0.4

0.6

0.8

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1.2

K1 K2 K3 K4 K5 K6

K7 K8 K9 K10 KT

Method 1

Plot various k values over time, on

the same graph.

Interannual patterns in ktotal reflect those of k8, but not those

of (e.g.) k4

Line Graph

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.50 0.70 0.90 1.10 1.30

K Total

K 8

y = 0.8893x - 0.5975

R2 = 0.8951

-0.1000

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.50 0.70 0.90 1.10 1.30

K Total

K 8

y = 0.0125x + 0.0635

R2 = 0.0656

0.0000

0.0200

0.0400

0.0600

0.0800

0.1000

0.50 0.70 0.90 1.10 1.30

K Total

K 3

K on K T

K label 1850 1851 1852 1853 1854 r 2

Eggs Infertile 1 0.0510 0.0411 0.0519 0.0444 0.0430 -0.4664Eggs Disease 2 0.0227 0.0321 0.0203 0.0274 0.0255 0.4633Eggs Predation 3 0.0721 0.0878 0.0624 0.0697 0.0782 0.0656

Chicks Squashed 4 0.0469 0.0567 0.0623 0.0546 0.0588 2.00E-07Chicks Predation 5 0.0998 0.1345 0.1487 0.0372 0.0874 -0.5002Chicks Starvation 6 0.1613 0.1951 0.1317 0.1358 0.1124 0.0029Chicks Fell from Nest 7 0.0380 0.0232 0.0052 0.0431 0.0498 0.1205Adult Emigration 8 0.0485 0.2382 0.0044 0.4304 0.0213 0.8951Adult Predation 9 0.0751 0.0503 0.1346 0.2188 0.3067 0.0859Adult Disease 10 0.0543 0.0521 0.0457 0.0743 0.0281 0.3787

Total T 0.6698 0.9110 0.6672 1.1357 0.8111

K Method 2

Regression Analysis

Generate an X-Y scatter-plot between each k value and ktotal, and look at correlation coefficient (R). R values close to one imply relationship between the two variables is very good, R values far from one are poor. Sign of R indicates if

relationship is positive or negative.

K on K T

K label 1850 1851 1852 1853 1854 r 2 r2 m c

Eggs Infertile 1 0.0510 0.0411 0.0519 0.0444 0.0430 -0.4664 0.0191 0.0037 0.0338Eggs Disease 2 0.0227 0.0321 0.0203 0.0274 0.0255 0.4633 0.0955 0.0078 0.00002Eggs Predation 3 0.0721 0.0878 0.0624 0.0697 0.0782 0.0656 0.0094 0.0051 0.0574

Chicks Squashed 4 0.0469 0.0567 0.0623 0.0546 0.0588 2.00E-07 -0.1879 -0.0141 0.1005Chicks Predation 5 0.0998 0.1345 0.1487 0.0372 0.0874 -0.5002 0.0215 0.0356 -0.0094Chicks Starvation 6 0.1613 0.1951 0.1317 0.1358 0.1124 0.0029 0.5171 0.1282 -0.2396Chicks Fell from Nest 7 0.0380 0.0232 0.0052 0.0431 0.0498 0.1205 -0.0303 -0.0197 0.0884Adult Emigration 8 0.0485 0.2382 0.0044 0.4304 0.0213 0.8951 0.3363 0.6571 -1.717Adult Predation 9 0.0751 0.0503 0.1346 0.2188 0.3067 0.0859 -0.5178 -0.4781 1.4434Adult Disease 10 0.0543 0.0521 0.0457 0.0743 0.0281 0.3787 0.013 0.0077 0.0314

Total T 0.6698 0.9110 0.6672 1.1357 0.8111

K on N B4K

K-factor analysis identifies factors responsible for driving inter-annual fluctuations in population size, BUT….density-dependent or density-independent?

Plot k against log10 numbers before and look at slope of significant relationships: > 1, over-compensating; < 1, under-compensating; = 1, exactly compensating.

Relationships where slope = 0 (all non-significant relationships) are density-independent

Num

ber

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Year

190018200

7 000

Hudson Bay Trading Company From: Begon, M., Harper, J.L. and Townsend, C.R. (1990). Ecology: Individuals, Populations and Communities. Blackwell Scientific, 945pp

0 5 9 12

Years

Rel

ativ

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iom

ass

in A

utum

n

Ruffled Grouse

Predators

Snowshoe Hares

Woody Browse(winter food)

From: Begon, M., Harper, J.L. and Townsend, C.R. (1990). Ecology: Individuals, Populations and Communities. Blackwell Scientific, 945pp