Key Factor Analysis Populations in constant state of Flux BUT…….rarely go extinct or increase unbounded 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

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?

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

Look at the relationship between each k value and k total Method 1 Plot various k values over time, on the same graph. Interannual patterns in k total reflect those of k 8, but not those of (e.g.) k 4 Line Graph

Method 2 Regression Analysis Generate an X-Y scatter-plot between each k value and k total, 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-factor analysis identifies factors responsible for driving inter- annual fluctuations in population size, BUT….density-dependent or density-independent? Plot k against log 10 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

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

05912 Years Relative Biomass in Autumn 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