### CSSU: Bridging a theoretical model to real-life ecology

**I have previously challenged readers to apply the MRW-based theory to explore animal space use from this alternative methodology. For example, by studying local strength of habitat utilization as indexed by CSSU (Characteristic Scale of Space Use), as a substitute for the traditional home range size estimates. Can this theoretical approach prove itself as a more realistic and sharp-edged statistical tool in some fields of behavioural ecology? We have previously provided some empirical pilot analyses on sets of GPS fixes. The results provide good coherence between model expectations and real data with respect to the biophysical process of memory utilization and scaling of habitat selection. However, what is still missing is a thorough ecological research into the often wide distribution of respective sets of CSSU estimates, as given by the parameter c. **

While common methods to estimate home range sizes are influenced by the non-trivial effects of autocorrelation and sample size of fixes, the alternative index CSSU, "area per square root of relocations" from the model *I*(N) = *c*N^{0.5}, is basically not influenced by these factors given the methodology provided. Thus, I invite researchers to explore and apply this approach, now that we have developed its theoretical foundation and explored it by simulations from many angles (Gautestad 2021, 2022).

*c*) scores (see inset in the Figure to the right) has unfortunately fallen outside the scope of our empirical research.

*c*) from analyses of red deer

*Cervus elaphus*movements. Incidence log (

*I*) as a function of sample size of fixes log(N) supports MRW, since the slope

*z*= 0.41 <<1 and stable (implying a scale-free kind of site fidelity) over a substantial range of N. The plots show the average

*I*(N) for 18 individuals (+/− 1 standard error), where each individual’s characteristic spatial scale parameter

*c*has been normalized to

*c*≈ 1 by respective grid scale adjustments*. Hence, testing the model as such was the main task, and not drilling into the magnitude of CSSU in real terms.

*Ursus americanus*. In this result, CSSU was given directly instead of the model parameter

*c*.

Again, we had no analysis of the specific habitat for the respective individuals, since the task was to test the model as such. Thus, the distribution of CSSU only indicated that the respective individuals utilized their habitat over a wide range of the "balancing scale", CSSU.

*z*was independent of the magnitude of CSSU. The lower illustration shows that z was independent of the sample size of fixes, N. These two results provide strong additional support for the feasibility of the MRW model, and thus the CSSU concept.

**However, the follow-up application of this model is still missing: what characterizes the habitat of the small-CSSU indices relative to the large ones?**

REFERENCES

Gautestad, A. O. 2015. Animal Space Use: Memory Effects, Scaling Complexity, and Biophysical Model Coherence Dog Ear Publishing, Indianapolis.

Gautestad, A. O. 2021. Animal Space Use, Second Edition: Memory Effects, Scaling Complexity and Biophysical Model Coherence. Cambridge Scholars Publishing, Newcastle upon Tyne.

Gautestad, A. O. 2022. Individual Network Topology of Patch Selection Under Influence of Drifting Site Fidelity. Frontiers in Ecology and Evolution 10:695854.

Gautestad, A. O. and A. Mysterud. 2013. The Lévy flight foraging hypothesis: forgetting about memory may lead to false verification of Brownian motion. Movement Ecology 1:1-18.

NOTES

* The normalization of *c *does not need to be exact; it is trivial to estimate *c* = 1 [log(*c*) = 0] from a somewhat smaller or larger value given by the regression. The distribution of the actual *c*-estimates (magnitudes in m^{2}) is shown in the inset.

** At this stage I have to trust next generation of researchers to drill into the theme of the present post. My blog came about as a follow-up on my book's first edition (Gautestad 2015). Over the subsequent years new posts have appeared at irregular intervals, with low-activity periods in particular since 2019 due to personal health issues, like being struck both by brain hemorrhage and cancer treatment during my *annus horribilis* 2019, and unfortunate after-effects related to chronic fatigue. Anyway, I have managed to get Second Edition of my book published (Gautestad 2021). If you already have the first edition, there is not much novel stuff in the new edition. Thus, the latest developments you find in this blog and in Gautestad (2022).