Habitat foraging niche of a High Arctic zooplanktivorous seabird in a changing environment

Here, we model current and future distribution of a foraging Arctic endemic species, the little auk (Alle alle), a small zooplanktivorous Arctic seabird. We characterized environmental conditions [sea depth, sea surface temperature (SST), marginal sea ice zone (MIZ)] at foraging positions of GPS-tracked individuals from three breeding colonies in Svalbard: one located at the southern rim of the Arctic zone (hereafter ‘boreo-Arctic’) and two in the high-Arctic zone on Spitsbergen (‘high-Arctic’). The birds from one ‘high-Arctic’ colony, influenced by cold Arctic water, foraged in the shallow shelf zone near the colony. The birds from remaining colonies foraged in a wider range of depths, in a higher SST zone (‘boreo-Arctic’) or in the productive but distant MIZ (second ‘high-Arctic’ colony). Given this flexible foraging behaviour, little auks may be temporarily resilient to moderate climate changes. However, our fuzzy logic models of future distribution under scenarios of 1 °C and 2 °C SST increase predict losses of suitable foraging habitat for the majority of little auk colonies studied. Over longer time scales negative consequences of global warming are inevitable. The actual response of little auks to future environmental conditions will depend on the range of their plasticity and pace of ecosystem changes.


Fuzzy logic approach
Fuzzy logic is a knowledge-based method, developed to represent imprecise or uncertain knowledge, for describing complex or ill-defined systems. It retains the uncertainty information of each class by taking into account the gradual change from membership to nonmembership 1,2 . The fuzzy logic approach is advantageous compared to conventional habitat modelling methods; it allows for the numerical processing of expert qualitative knowledge, and it can consider multivariate effects of variables without the assumption of independence of input parameters. This allows for the inclusion of numerous combinations of factors (summarized in 2 ). The fuzzy suitability maps are considered as more informative than conventional suitability maps as they provide extra information about the partial degree of suitability across space. Moreover, fuzzy suitability maps achieve better predictive accuracies than their classic map-overlay approaches (pass/fail screening, graduated screening, weighted linear combination) 3 .
Fuzzy models due to their transparency and user friendliness are widely applied in environmental modelling, especially in species distribution modelling 4 . This approach is especially useful in the cases where little systematic field investigations have been conducted.
It allows for the use of readily available expertise of specialists in the modelling process to 2 estimate habitat suitability for a study species. On the other hand, the requirement of expert knowledge, which may be subjective, is considered as the main bottleneck of this approach.
Complementing fuzzy systems by data-driven techniques can solve this knowledge acquisition bottleneck 4 . Thus, in the present study we investigated environmental factors affecting Little auk foraging using a simultaneously data-driven technique (conditional inference tree) and fuzzy logic model based on expert knowledge.
In our analyses, we followed the main steps of fuzzy logic systems 3 :

III)
Defining a fuzzy inference engine refers to the rules of association to combine the evaluation of multiple factors. We used a weighted linear combination model using a weighted averaging (ANDOR) operator. This operator, in contrast to standard fuzzy intersect (AND) and standard fuzzy union operations (OR), allows for the compensation of a low rating on one factor by a high rating on another factor 3 . We weighted the particular factors based on expert knowledge (Table 1)  above and below the given threshold. We further calculated the positive predictive power for particular thresholds for the whole data set and for "boreo-Arctic" and 'high Arctic' subgroups. Finally, we chose the following two thresholds with the highest positive predictive 5 power as the optimal defuzzification threshold to predict the distribution of little auk foraging positions: 1) 0.9 -with high accuracy for 'high-Arctic' Spitsbergen colonies (97%) but worse performance for all colonies (64%). This represents a conservative response to climate change with foraging restricted only to optimal, cold water areas reflecting current feeding habitats of populations breeding on Spitsbergen.
2) 0.7 -with a little bit lower accuracy for all colonies (92%) but higher for 'boreo-Arctic' foraging areas around Bjørnøya (87%, in contrast to 41% for 0.9 threshold). This reflects a Svalbard-wide plasticity in little auk reactions to environmental changes, meaning foraging in a wider range of temperatures reflecting the full range of current feeding niches including both 'high-Arctic' and boreo-Arctic' conditions.