Conservation Biology and SLOSS , Part I: Time to Challenge System Assumptions

The contrasting ideas of a single large or several small (SLOSS) habitat reserves ignited a heated debate in conservation biology (Diamond 1975; Simberloff and Abele 1982). The recent development in movement ecology – in particular the theoretical aspects of spatial memory and scale-free space use of individuals – makes time ripe to initiate a study of the SLOSS concept under this contemporary perspective. In order to produce realistic predictions community, population and individual processes need to be understood from a coherent system theory involving all levels of system abstraction. Under this premise the original SLOSS concept seems to fall apart.

A single large reserve was argued to be preferable to several smaller reserves whose total areas were equal to the larger (Diamond 1975). On the other hand, if the smaller reserves had unshared species it was possible that two smaller reserves it sum could have more species than a single large reserve of the same total area (Simberloff and Abele). Opposing the latter view, it was argued that habitat fragmentation is probably the major threat to the loss of global biological diversity (Wilcox and Murphy 1985).

However, the SLOSS concept – originating in the field of conservation biology – was understood from the perspective of dispersion of species under various landscape configurations. In my view that approach drove the debate into a dune of sand, due to over-simplification or ignorance of a community system’s lower-level dynamics.

In a traditional metapopulation system, immigration to a given local population (green area) can be concptualized as a fixed rate, representing the average number of emigrant individuals from other populations that by chance happen to reach the present population pr. unit time. In the alternative Zoomer model; the population level formulation of the individual MRW model, immigrants represent a mixture of individuals from other populations that perform exploratory moves over a wider range of scales than assumed by the classic model; i.e., scale-free movement, in addition to individuals that return in a spatially memory-dependent manner (red arrows). Such goal-oriented spatial behaviour leads to the emergence of complex population kinetics.

The original SLOSS debate was considering relative presence and absence of species in various settings of reserve designs. From this classic community system perspective the theory tended to ignore population dispersal effects explicitly. However, to the extent that dispersal was considered [primarily in the context of metapopulation theory; see, for example Robert (2009)] it was assumed that emigration was a deterministic process at the spatial scale of local populations while immigration was a stochastic process at this scale (random influx). This direction-dependent toggle between deterministic and stochastic population flow follows logically from the traditional premise of a diffusion-advection framework for metapopulation systems. I criticized this core assumption of metapopulation theory in this post, and in the Figure to the right I summarize the argument. My critique pinpointed the theoretical consequences of allowing for complex population kinetics (the Zoomer model). The basic metapopulation principle of slow rate of population mixing between subpopulations may in this system variant be additionally influenced by some degree of returning individuals; i.e., a deterministic component of population flow even of the immigration rate. This potential is facilitated by spatial memory and temporally multi-scaled displacements (parallel processing). In other words, system complexity.

Such complexity plays havoc with a classic metapopulation system. After occasional sallies to other habitat reserves/sub-populations, individuals may perform directed and potentially long distance returns to a previous reserve. And such returns could be a function of the respective individuals’ current conditions both at source and target reserves.

Consequently, individuals are – according to this paradigm-opposing assumption – occasionally able to transcend the matrix of intermediate environment between refuges in an energetically effective manner and with sufficiently low travel risk to make such coarse-scale moves statistically worthwhile and positive in fitness terms (see this post). This property of the Multi-scaled random walk (MRW) theory is now gaining additional anecdotal support, for example from studies on Fowler’s toads Anaxyrus fowleri (Marchand et al. 2017) and free-ranging bison Bison bison.

To be more precise, let’s first assume that we are considering a “several small” reserve system where the spatial scale (size) of these local reserves is reflecting – say – 50-60% of the median displacement distance of the respective population constituents at the time resolution of a reproductive season. If we consider day-to-day movement rather that the coarser time scale of a season, long displacements beyond this defined 50-60% limit accumulate a small part of the area under the displacement distribution (the scale-free dispersal kernel becomes more apparent at fine temporal scales). In this manner, due to the “thin” long-tale part of displacements under the premise of scale-free space use, the system complies with the basic metapopulation property of a low inter-season migration rate between subpopulations relative to the higher intra-population mixing rate at finer scales*. Also consider that the long-tail part of the displacement distribution extends to the scale of this  system’s spatial extent. Hence, individuals may occasionally displace themselves over the entire arena (exploratory sallies of various length and duration), and occasionally perform directed returns to previous locations within the same scale range.

This assumed property of scale-free and memory-influenced returns at the individual level violates the traditional metapopulation theory at the population level and – of course – the traditional SLOSS theory at the community level. In addition to the relatively high frequency mixing of individuals at the local scale a less frequent and partly memory-driven mixing takes place at coarser scales. The latter contributes to the emergence of an inter-connected network of complex migration.

The very interesting studies on snail kite Rostrhamus sociabilis plumbeus in Florida (Reichert et al. 2016; Valle et al. 2017) illustrates the profound potential this kind of system complexity may generate, with consequence also for community ecology in general and the SLOSS debate in particular. The results 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. I cite from my discussion of Valle et al.’s paper:

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. […] 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 particular, observe that even long distance returns could be a function of the respective individuals’ current conditions both at source and target reserves. Referring to the illustration above, the relative number of directed returns (deterministic behaviour, red arrows) may suddenly – at a finer temporal scale than the inter-season population change –  increase or decrease substantially. The cause of such events cannot be understood simply from local conditions, as under traditional mechanistic modelling. Coarser scale conditions both in time and space need to be studied in parallel. A single, more or less fixed immigration rate as applied in traditional metapopulation modelling does not suffice. Citing from above, “…some distant patches occasionally showed stronger modular connectivity than intermediate patches“. This is system complexity in a nutshell, whether we are considering single- or multi-species scenaria. Much work is needed to achieve a better understanding of multi-scaled behaviour under influence of spatial memory.

NOTE

*) As explained in other posts (for example, here), a scale-free displacement curve for individuals is expected to become more truncated if the time scale is coarsened, for example from short term displacements to longer sampling intervals. The reason is the increased influence from intermediate return events as observation intervals slide from the fine-grained time scale of population kinetics (observing fast mixing from individual movement) towards the coarser-grained dynamics of changing dispersion for example at the scale of a season (Gautestad 2012).

REFERENCES

Diamond, J.M. 1975. The Island Dilemma: Lessons of Modern Biogeographic Studies for the Design of Natural Reserves. Biological Conservation 7:129–146.

Gautestad, A. O. 2012. Brownian motion or Lévy walk? Stepping towards an extended statistical mechanics for animal locomotion. Journal of the Royal Society Interface 9:2332-2340.

Reichert, B. E., R. J. Fletcher, 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.

Robert, A. 2009. The effects of spatially correlated perturbations and habitatconfiguration on metapopulation persistence. Oikos 118:1590-1600.

Simberloff, D. S. and L. G. Abele. 1982. Refuge design and island biogeographic theory – effects of fragmentation. American Naturalist 120:41-56.

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.

Wilcox, B. A., and D. D. Murphy. 1985. Conservation strategy – effects of fragmentation on extinction. American Naturalist 125:879-887.