A Novel, Unbiased Analysis Approach for Investigating Population Dynamics: A Case Study on Calanus finmarchicus and Its Decline in the North Sea.

Marine populations are controlled by a series of drivers, pertaining to both the physical environment and the biological environment (trophic predator-prey interactions). There is heated debate over drivers, especially when trying to understand the causes of major ecosystem events termed regime shifts. In this work, we have researched and developed a novel methodology based on Genetic Programming (GP) for distinguishing which drivers can influence species abundance. This methodology benefits of having no a priori assumptions either on the ecological parameters used or on the underlying mathematical relationships among them. We have validated this methodology applying it to the North Sea pelagic ecosystem. We use the target species Calanus finmarchicus, a key copepod in temperate and subarctic ecosystems, along with 86 biological, hydrographical and climatic time series, ranging from local water nutrients and fish predation, to large scale climate pressure patterns. The chosen study area is the central North Sea, from 1972 to 2011, during which period there was an ecological regime shift. The GP based analysis identified 3 likely drivers of C. finmarchicus abundance, which highlights the importance of considering both physical and trophic drivers: temperature, North Sea circulation (net flow into the North Atlantic), and predation (herring). No large scale climate patterns were selected, suggesting that when there is availability of both data types, local drivers are more important. The results produced by the GP based procedure are consistent with the literature published to date, and validate the use of GP for interpreting species dynamics. We propose that this methodology holds promises for the highly non-linear field of ecology

The new conceptual model of potential drivers of <i>Calanus finmarchicus</i> abundance deduced from the GP method supplemented by the relevance and gradient analyses.

<p>The new model is composed of two physical variables, North Atlantic net flow and Sea Surface Temperature, and one biological variable, Herring, which is recognised as a top-down driver.</p

Relevant variables selected by the Genetic Programming based methodology combined with the relevance analysis, the abbreviations used in this article, and the frequency of occurrence of each variable in the 104 approximating functions in the population pool.

<p>The last column indicates the type of relationship between the relevant variables and <i>C</i>. <i>finmarchicus</i>, identified with the gradient analysis.</p

Sequences of abrupt shifts in the North Sea.

<p>Time series of <i>C</i>. <i>finmarchicus</i> average annual abundance, with arrows indicating the years of the regime shifts, detected using cumulative sums analysis both on this species and in the 9 variables identified as relevant by GP. The table in the insert specifies the year of the shift and shows its direction: + meaning an increase,—meaning a decrease.</p

Time series of <i>Calanus finmarchicus</i> and the 9 relevant variables identified by the GP procedure.

<p>The time series are ordered from left to right of most frequently occurring. All time series were normalised by dividing each value by the time series maximum value before the GP process.</p

Variables identified as potential drivers of the abundance of <i>C</i>. <i>finmarchicus</i>.

<p>Potential drivers have been sectioned into physical, on the left, and biological, on the right. Biological variables have subsequently been divided into two further groups, top-down and bottom-up, which are positioned above and below <i>C</i>. <i>finmarchicus</i> respectively. The data used in this research article are listed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0158230#pone.0158230.t001" target="_blank">Table 1</a>.</p

Timeseries used in this study.

<p>The links to the data sets used are shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0158230#pone.0158230.s003" target="_blank">S3 File</a>.</p