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Key Factor Analysis
Populations in constant state of Flux
BUT…….rarely go extinct or increase unbounded
0
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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
1.0
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
Tra
pped
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
e B
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