Computing Eigenvalues and Eigenvectors for Squamish River Wintering Bald Eagles. Jorma Jyrkkanen, jjyrkkanen76@outlook.com

Computing Eigenvalues and Eigenvectors for Squamish River Wintering Bald Eagles. Jorma Jyrkkanen, jjyrkkanen76@outlook.com 3 Dec 2018 Background I fiddled with my 4 years of Squamish Wintering Eagles demographic data and fudged a bit of the model to add males in the Reproduction and got an interesting growth rate, lambda1 and a great Eigenvector or stable age distribution. Here it is. Will play with it until I am happy with data fit and may extend it out to 15-20 years age classes. It’s a dynamic model amenable to gaming based on thousands of field observations.

Discussion What I saw from year to year though were what looked like compensatory density dependent adjustments in age specific survival so it flip flopped p due to competition from yr to yr.

This fact is not amenable to deterministic Markov models like Leslie UNLESS you ‘game it’ or program in ‘if Sxi > or < Sxi critical-then-change-Sxi+ or-n’ ie compensatory survival feedbacks to other age classes. I urge population biology students to try it and watch amazing responses to population and age structure. I used an online Calculator bandicoot.maths.adelaide page written by Mathew Roughan.

Figure 1. Sample Leslie Matrix and Start Population Vector with test age specific reproductive rates for a Female Population based on Hypothetical Statistics to Observe Deterministic Model Responses in Total Population, Age Classes and Growth Rates (Primary Eigenvalue) and proportional age class structure (Eigenvectors).December 3, 2018Created by Jorma A. Jyrkkanen Note. The last three age classes are all adults and there is some presumption of productivity from four year class Bald Eagles ie R4=0.1

Eagles Run 2 with a Working Survivorship Population Vector but discrepancy in observed and model that works.

This latter run has a high crash potential (CP) in 8 yrs and a lot of fluctuation. For a more realistic model I have to incorporate my field data.

The bottom box has the stable age structure eigenvector and age specific eigenvalues. The latter more realistic run works but stability hangs on a few percentage survivorships of juveniles age classes and only includes 8 Age classes total. Conclusion I concluded that the dynamic nature of feedbacks assures high survival of recruits to replace low adult mortality. Note how with even static Survivorships (Sij diagonals in L) there is an innate generation of wild fluctuations in age-class abundance in the curves at the bottom but I caution that in the field this is difficult to tease apart from random effects of migration linked as it is to weather and food availability. This phenomenon no doubt leads a lot of people to think a population is in trouble when only short-term observations are made and it is not true. Time lags are working to smooth out the age class distributions and real population. You only come to know these statistics as probably true after years of observation. I did 4 with thousands of observations and it was just starting to sink in. Keep in mind that these parameters apply only to the female side of the population. If you add the males it will approximately double.