Deeper realism is needed in modelling of population dynamics

Among vertebrates, most populations represent rare species. If this fact is not challenging enough in a survival perspective, all populations - whether rare or abundant - live in an open environment.  In some previous posts I've focused on survival-enhancing mechanisms like intraspecific cohesion from conspecific attraction. I have also pointed out the survival value of deterministic individual returns to a homestead following temporary long range excursions outside a given local population. Of course, such lifelines require individuals' cognitive capacity to relate to the environment an explicit spatio-temporal manner. In other words, to counteract the destructive effects of free dispersal beyond the local population's respective core areas, memory map utilization is key. Dispersal is an important aspect of animal space use optimization, but so is the advantage to returning home even over vast distances if this improves survival. If the memory premise becomes broadly accepted by theoretical ecologists, much modelling in the field of population dynamics - at least for vertebrates - need a novel foundation.

Three species of sea gulls resting at the Western
coast of Norway. Photo: AOG.

The reason is that the current theory of animal movement and dispersal still rests on physics of memory-less diffusion.  I have pointed this out repeatedly. Metapopulation theory in its various variants describe emigration as more or less deterministic, while immigration is modelled as a random inflow of individuals - a rate that is independent of local conditions* The underlying foundation of differential and partial differential equations is given by the premise of diffusion of particles; i.e., individuals. In short, it all can be bundled together as low order Markovian processes.

To cite from an earlier post, "Simulating Populations VI: the Lack of Realism of Standard Models (March 10, 2018)"

Consider dropping a single drop of ink into a water-filled bathtub – representing our “open environment”. The black dot will over time spread out and become uniformly dispersed. Consider that the ink molecules have a limited life span, and (hypothetically!) two molecules need to meet within their respective life span to produce additional ink molecules. Since we are considering a bathtub; a constrained space, the ink “population” may still survive. However, the larger the bathtub the smaller the rate of inter-molecular encounters. The critical space size is given by the level (bathtub size) where the given diffusion rate – after temporal rescaling to match the net reproductive rate (see above) – becomes larger than the reproduction rate pr. individual of new ink molecules! This balance between diffusion rate and reproduction rate is diminished by increasing bathtub size, invoking an Allée effect in larger bathtubs!

I should add that under normal conditions the bathtub is huge relative to the size of the drop of ink, meaning that the system may be considered "open". The larger the tub, the larger the probability of increased death rate due to Allée effects under the conditions described. Flipping the coin;, this population analogy may be enhanced by considering a memory map capacity at the individual level. Drops of ink may "mysteriously" re-assemble themselves in violation of the force of diffusion.

To explore an alternative approach to Markovian-based processing: search this blog for "The Zoomer model".

NOTES

* Two examples given: 

MRW and Ecology – Part IV: Metapopulations? (November 08, 2017).

Conservation Biology and SLOSS , Part I: Time to Challenge System Assumptions (April 06, 2019).