We used a dataset comprised of 90 individual 4-year-long temperature time series (six microhabitats on 15 shores from 37 °N to 55 °N latitude, Fig. 1a) to evaluate to what extent the patterns of ecologically relevant metrics of a stressor are indeed captured by that stressor’s mean. Extreme temperature is a major stressor in most ecosystems, and especially in the rocky intertidal 16, where animals and plants a few centimetres apart can be experiencing dramatic differences in body temperature 21 22. The overall mean temperature, which is often used as a reference for estimating species distributions 17, was shown to match latitude surprisingly well (R = 0.98, Fig. 1b), thus reinforcing the idea of a relatively smooth, continuous gradient from warmer to colder temperatures with increasing latitudes along the European Atlantic coastline. However, with the exception of ‘winter mean’ and ‘winter 95 ^th percentile’ ( Fig. 1h,i, blue lines), all other metrics (‘summer mean’, ‘summer 95 ^th percentile’, and winter and summer ‘7 day mean’, ‘daily range’, ‘microhabitat range’, ‘minimum’, ‘5 ^th percentile’ and ‘maximum’) exhibited patterns deviating substantially from that of the grand mean. These differences highlight the key role played by climatic, geomorphologic and oceanographic factors at the local level, and more importantly, show that such factors can change skewness or kurtosis of the distribution of temperatures (or even causing multimodality) without affecting the mean. For example, seasonality, which is strongest within the Bay of Biscay — shores H and I — appears not to drive the grand mean for these shores too far away from the expected value given their latitude, but results in remarkably high summer temperatures (in fact the highest recorded in the study area; Fig. 1i,j, red lines) and equally remarkably low temperatures during winter (again, the lowest within the study area; Fig. 1f,g, blue lines). In another example, upwelling, which is typically stronger around shores F and L during summer 23, can be seen driving ‘summer daily range’ and ‘summer microhabitat range’ ( Fig. 1d,e, red lines), likely due to the co-occurrence of low water temperatures and high air temperatures. Again, this effect does not result in any important deviation of the grand mean from the latitudinal pattern for these shores, and would be largely missed if data at the appropriate spatial scale had not been collected. Additionally, the combination of regional factors and local context can result in surprising temperature distributions, such as seen at shore N. At this shore, all metrics were found to be lower or equal to the expected value based on latitude. However, the grand mean does not reflect the magnitude of this difference, especially considering that shore N is the coldest in the study area for some of the metrics calculated. The many patterns encapsulated within the distribution of values of a single stressor clearly indicates that the grand mean may largely misrepresent many other ecologically relevant aspects of that stressor. This is in accordance with previous studies 21 24 and reinforces the notion that a-priori knowledge of the physiological requirements of a species and a detailed characterisation of the thermal extremes at the study area are fundamental to ascertain the real stress landscape imposed on organisms.

Furthermore, using a theoretical example we show that complex biogeographic responses to climate change can be interpreted by using the appropriate metrics ( Fig. 2). We assume that the distribution of a theoretical species is determined by a group of relevant metrics (in this case the thermal extremes measured as ‘winter minimum’ and ‘summer 5 ^th percentile’) and follows Liebig’s law of the minimum (i.e., at each location density is dependent on the least favourable relevant metric). In the simplest form, the distribution pattern will be determined by the least favourable of a number of relevant metrics ( Fig. 2a, light orange area). If climate change results in a favourable monotonic change of all metrics ( Fig. 2b), the extent of suitable locations increases and a range expansion can be expected — the "general perception" poleward scenario. However, studies have highlighted that climate change not only can result in increased mean, minimum and maximum temperatures but also in increased variability — and that the exact signature of climate change varies regionally 18 25 26 27. In this case, if at least one metric becomes less favourable due to the increased variability, the whole distribution can be adversely affected, and an equatorward range contraction may occur ( Fig. 2c). Using the metrics computed in this study it is possible to further expand the example. If the distribution of a species was found to be dependent on the interplay between extremes like ‘winter minimum’ and ‘summer 5 ^th percentile’ the initial distribution pattern should include a gap at shore H, and a polar range limit at shore B ( Fig. 2d). If both ‘winter minimum’ and ‘summer 5 ^th percentile’ become warmer, a poleward range expansion can be expected ( Fig. 2e), but if ‘summer 5 ^th percentile’ becomes warmer while ‘winter minimum’ becomes colder, the harshness of winter conditions prevail over the favourable summers and a equatorward range contraction should occur ( Fig. 2f). Interestingly, in a few locations suitability would actually increase because the limiting factor was ‘summer 5 ^th percentile’ and not ‘winter minimum’ (shores L and N, Fig. 2h), highlighting the consequences of different mechanisms limiting species’ densities across different locations 28. The crucial point is that if field surveys were to reveal an equatorward range contraction for this species, this range shift would not be contrary to predictions, as general perception would suggest. Instead, it would be consistent with the predicted direction of change for this biological system’s response to climate change, thus representing positive evidence towards the establishment of a link to climate change.

In addition, it is conceivable that some organisms’ physiological requirements may include more complex interactions of aspects of a stressor than those depicted here 29 30. For example, a mobile organism will be able to explore the various microhabitats available within a site for thermoregulation. If that organisms’ physiology is found to be negatively impacted by ‘summer maximum’, it is likely that the appropriate metric to study will instead be the difference between ‘summer maximum’ and ‘summer microhabitat range’, as very high temperatures can be avoided if cooler microhabitats are available. These complex interactions between aspects of a stressor can generate new stress landscape patterns that do not match that of the grand mean, ‘summer maximum’ or ‘summer microhabitat range’, further increasing the likelihood of erroneous expectations about the extent and direction of range shifts in face of climate change if the stress landscape is not properly characterized. The findings presented in this study reinforce the notion that using the appropriate metrics of a stressor and identifying the appropriate stressor 13 can provide decisive insights towards the detection, interpretation and prediction of complex distribution patterns, spatial and temporal variations of mechanisms controlling species distributions and the direction of range shifts. In addition, the conceptual framework here outlined emphasizes the paramount importance of coupling the collection of environmental data at the appropriate scales with a detailed characterization of species’ physiological requirements (see Ashcroft et al. 31 or Greenberg et al. 32 for analogous approaches using modelled data). Although focused on the thermal regimes of the European Atlantic intertidal ecosystem, the concepts here outlined can be extended to other geographical regions, ecosystems, and stressors. Taken with necessary caution (see, for example, the cautionary advice by Austin 33 regarding assumptions of linear response to temperature), these results suggest that some of the cases where species have been shown to be shifting in directions contrary to expectations, the predicted direction of change may have been wrongly established.