### The Florida Snail Kite: Linking Individual MRW to Population Kinetics?

The theoretical framework of the traditional space use models (“the Paradigm”) shows strong mathematical coherence between individual movement and its population level representation. Basically (in its simplest and most parsimonious form), standard random walk representing individual statistics is compliant with standard diffusion representing population statistics. Further, the trunk of the toolbox of statistical methods in space use ecology is also resting on assumptions from the Paradigm. However, the Paradigm and its large family of sophisticated sub-models is now under increasing attack from many directions – directly or indirectly – due to the growing pool of empirical results that cast doubt on its common, core assumptions. For example, recent analyses of the snail kite Rostrhamus sociabilis plumbeus in Florida indicate that individuals of this dietary specialist show a surprising capacity to rapidly adapting to changing conditions over a large range of spatial scales from localized home ranges to state-wide network of snail-rich wetland patches (Valle et al. 2017) . In this post I allow myself to speculate on a potential for space use compliance between snail kite in Florida and a specific Paradigm challenger – the dual MRW model and Zoomer model (the parallel processing framework for the individual and population level, respectively) – that is advocated in my book and here on my blog.

The picture shows  snail kite, adult male. Photo by Andreas Trepte (www.photo-natur.net).

What in my view is particularly thrilling about the snail kite analyses is the authors’ quite nontraditional approach to apply network analysis to study intra-population flow of individuals from the perspective of clustering individuals based on the locations they visit instead of clustering locations based on their connectivity to other locations (Fletcher et al. 2013, 2015; Reichert et al. 2016; Valle et al. 2017). As shown in one of their papers, network theoretical methods applied in this manner may lead to surprising results (Valle et al. 2017). What would you say if the population you are monitoring shows a relatively sudden directional drift of many individuals towards areas far away (hundreds of kilometres) relative to the apparently still suitable locations (local wetlands) where these individuals for years have shown strong site fidelity and thus spend most of their time? Adult snail kites from this sub-species rarely depart from their local wetland during the breeding season (ca 13% probability), and annual departure rate is not larger than ca 40-60%. Still, changing conditions appearing many wetland patches away (e.g., the distance between southern and northern Florida) was observed to influence local emigration rate quite suddenly; to be described below. Something like ecology’s analogy to quantum entanglement; i.e, spooky action over large distances (yes, joking)?

In a previous post I described animal space use as a combination of push and pull; mixture of tactics and strategy, under a postulate of parallel processing. The latter – a simultaneous utilization of the environment over a range of resolutions – was described as spatio-temporally multi-scaled memory utilization. Under this assumption, individuals could gradually accumulate environmental overview quite effectively, and thus build an intrinsic potential to react more swiftly to environmental change over large distances in comparison to groups that behave in accordance to more classic assumptions; i.e., the Paradigm. For example; under multi-scaled space use, if distant patches show improvement with respect to key resources, a functional response driven by spatial memory and parallel processing may represent a net pull effect; i.e., expressed as a net directed emigration rate relative to the local habitat with more constant conditions.

Consequently, the actual “force” driving long-distance pull in a population could be explained as the coarse-scale experience that emerges from a low frequency of “occasional sallies” by an individual outside its normal day of life of habitat explorations.

Under the Paradigm; i.e., the classical home range theory, such occasional sallies have historically been treated as a statistical nuisance, creating all kinds of challenges and creative workarounds for “proper” (Paradigm-compliant) home range demarcations at the local scale where the individual spends 90-99% of its time. Technically, while the Paradigm predicts compliance with a negative exponential distribution of step lengths of an individual (consequently, swiftly running out of steam for longer displacements during a given period), a scale-free kind of space use assumes compliance with a power law distribution (more short and – crucially – more superlong displacements than expected under the Paradigm).

Valle et al. (2017) studied the Florida snail kite within its total distributional range over the years 1997-2013. Then, in 2005 a natural experiment unintentionally appeared. This year an exotic snail species Pomacea maculata appeared in Lake Tohopekaliga in the north of Florida, and subsequently began spreading throughout many of the northern wetlands. These exotic snails have become an important novel food resource for the snail kite population, as a supplement to the kite’s traditional and previously almost exclusive food source, the native Florida apple snail Pomacea paludosa.

With respect to snail kite, a meso-scale functional response then commenced in 2005. Even relatively sedentary adults in the south reacted by showing a rapid increase in net migration towards the northern wetlands, some 260 km apart!

When comparing the frequency with which different groups visited each site (i.e., visitation rate) before the exotic snail invasion (1997–2004) to the next time period when the only invaded site was TOHO (2005–2009), we find a substantial increase for TOHO and a significant decline for WCA3A. This is particularly noteworthy because WCA3A is one of our southernmost sites while TOHO is one of the northernmost sites, revealing a substantial geographic shift in how the landscape is used by these individuals. Valle et al. 2017, p5

In my view it is not the distance as such that is that main point here (the snail kite can easily traverse long distances in s short period of time), but the fact that the natural experiment provided by the exotic snail showed how some distant patches occasionally showed stronger modular connectivity than intermediate patches. This property of space use is in direct violation of key assumptions of – for example – metapopulation theory (one of the branches of the Paradigm), where spatially close subpopulations cannot be more weakly connected than more distant subpopulations that are separated by intermediate ones.

In Levins’ (1969) original model it is implicitly assumed that all patches are equally connected with respect to migration rate; i.e., regardless of distance, but even this design does not embed a potential for distant patches to be dynamically stronger connected than closer ones.

Thus, strong network modularity over the meso-scale range in Florida may be indicative of a true multi-scaled space use process, involving complex spatio-temporal memory utilization with respect to patch choice by the individual kites. Hence, the Paradigm is challenged by the snail kite results.

… the lack of spatial structure identified in seasonal movements (distance related or otherwise) and results from the partial Mantel tests support previous findings that distance alone is not an adequate predictor of structure in annual dispersal of snail kites (Fletcher et al. 2015). Rather, our findings emphasize the importance of accounting for self-organized population structure, which can arise for several reasons, such as intraspecific cohesion (Gautestad & Mysterud 2006) [e.g. conspecific attraction (Fletcher 2009)], matrix resistance, or natal habitat preference. Network modularity may be a reliable approach for identifying the spatial scales relevant for understanding these processes.
Reichert et al. 2016, p1569

By the way, a glimpse into my own application of network analysis in another context can be found in a previous post (search Archive: ...).

REFERENCES

Fletcher, R.J. 2009. Does attraction to conspecifics explain the patch-size effect? An experimental test. Oikos 118:1139–1147.

Fletcher R. J. Jr, A. Revell, B. E. Reichert, W. M. Kitchens, J. D. Dixon and J. D. Austin. 2013. Network modularity reveals critical scales for connectivity in ecology and evolution. Nature Communications 4 (2572):1-7.

Fletcher R. J. Jr, E. P. Robertson, R. C. Wilcox, B. E. Reichert, J. D. Austin and W. M. Kitchens. 2015. Affinity for natal environments by dispersers impacts reproduction and explains geographical structure of a highly mobile bird. Proc. R. Soc. B 282 (2015.1545):1-7.

Gautestad, A.O. and I. Mysterud. 2006. Complex animal distribution and abundance from memory-dependent kinetics. Ecological Complexity 3:44–55.

Levins R. 1969. Some Demographic and Genetic Consequences of Environmental Heterogeneity for Biological Control. Bulletin of the Entomological Society of America 15: 237-240.

Reichert, B. E., R. J. Fletcher Jr, C. E. Cattau and W. M. Kitchens. 2016. Consistent scaling of population structure across landscapes despite intraspecific variation in movement and connectivity. Journal of Animal Ecology 85:1563–1573.

Valle, D., S. Cvetojevic, E. P. Robertson, B. E. Reichert, H. H. Hochmair and R. J. Fletcher. 2017. Individual Movement Strategies Revealed through Novel Clustering of Emergent Movement Patterns. Scientific Reports 7 (44052):1-12.