Application of the METAL Theory at the community level
1. Creation of a hypothetical pool of pseudo-species
Assuming that the thermal niche determines a large part of the spatial and temporal responses to species to changes in the climatic regime (e.g. seasonality, year-to-year and decadal changes; see application of the METAL theory at the species level), we can create a global pool of species by using the following equation:
With Ei,j,s the expected abundance of a pseudospecies s at location i and time j; cs the maximum value of abundance for species s (here this was fixed to one); xi,j the value of temperature at location i and time j; us the thermal optimum and ts the thermal amplitude for species s. The thermal tolerance is an estimation of the breadth (or thermal amplitude) of the species thermal niche (or bioclimatic envelope) (Ter Braak 1996). Please note that in the examples below we use mean surface temperature either at a monthly or an annual resolution.
A large number of pseudo-species can be created with us varying between -1.8°C and 40°C by 0.1°C increments and ts varying between 1.1°C and 10°C by increments of 0.05°C. This represented a total of 39,218 potential species; this amount of species can be divided by 2 without altering the ecogeographic biodiversity patterns (Beaugrand et al. 2015). At the end of the procedure, the global pool of pseudo-species equal to 19,609.
2. Predicted spatial patterns of biodiversity from METAL
In each geographical cell of the ocean, we can create pseudo-community composed of a given number of pseudo-species (Figure 1). Each pseudo-species has an index of abundance varying between 0 and 1. Here, the expected abundance of such pseudo-species is assessed by linear interpolation from the pseudo-species’ thermal niche and monthly SSTs in a given geographical cell from 1960 to 2015 (Figure 1). The sum of all species that can occur in a given oceanic area gives pseudo-species richness, or in other word, the expected biodiversity at equilibrium or at saturation (see next sections).
Figure 1. Schematics that illustrate how the METAL model generates pseudo-species and associated ecological niches to provide expected ecogeographic patterns in biodiversity *: herea pseudo-species is considered to be present in a geographical cell when its annual abundance (between 0 and 1) is > 0.1.
The use of other niche shapes leads to a similar map. For example, Beaugrand and colleagues used rectangular niches to investigate ecogeographic biodiversity patterns (Beaugrand et al 2013, Global Ecology and Biogeography). We summarise this study below.
The latitudinal biodiversity gradient reflects the tendency of many taxonomic groups to show an increase in biodiversity from the poles to the equator. In the marine domain, groups such as foraminifers, pteropods, euphausiids and fish exhibit this pattern. However, its cause has been vigorously debated for decades and more than 25 hypotheses have been proposed. Using the METAL theory (and rectangular niche; see section applying the METAL theory at the species level), we showed how temperature (mean and variability), modulated by climate, can create gradients in species richness by interacting with the species thermal niche (Beaugrand et al. 2013b). In this work, we also used a one-dimensional thermal niche. This simplification was acceptable for the marine domain. In the terrestrial realm, a measure of water availability to plants or precipitation would have been as necessary as temperature to recreate the ecogeographical pattern. The thermal niches were rectangular to relax the constraints due to the niche shape. Within the model, each pseudo-species, from strict stenotherms to universal eurytherms, was allowed to inhabit a given oceanic region so long as it could endure weekly SST changes. To potentially occupy a vacant geographical cell, a pseudo-species had to remain inside its thermal niche. Some species could temporarily occur outside their thermal tolerance. For example, some pelagic species such as copepods exhibit a dormancy stage in their life cycle and are able to survive far below their thermal optimum for short time periods. Finally, in order for the pseudospecies to survive after colonisation, a minimum of geographical cells must be occupied by the species to conform with the size of minimum viable population (Shaffer 1981). Niche nonsaturation often occurs (Rohde 2005) and to consider this fact, some of the potential niches could also be removed either randomly or by increasing the rate of random elimination polewards to consider the hypothesis that repeated glaciations of the Pleistocene might have removed a larger proportion of species polewards (Fisher 1960; Rohde 2005). The theory reconstructed well the latitudinal gradient in species richness and explained more than 90% of latitudinal biodiversity patterns of foraminifers and copepods (Figure 2).
Figure 2. Modelled biodiversity patterns from the METAL theory and observed biodiversity patterns in foraminifers and copepods. (A) Modelled spatial diversity patterns from the METAL theory. (B) Relationships between latitudinal changes predicted by the theory (blue line) and observed biodiversity patterns for foraminifers (orange line) and calanoid copepods (black line). Normalised SST (red line) is superimposed. Horizontal dashed lines indicate the equator (E) and the latitude 30°N and 30°S. Modified, from Beaugrand and co-workers (Beaugrand et al. 2013b).
Interestingly, the latitudinal variation was not a constant cline but displayed a hump-shaped relationship, a pattern often observed for foraminifers and copepods (Rombouts et al. 2009; Rutherford et al. 1999). These theoretical results also suggest that the latitudinal gradient can set up rapidly, as was observed recently among invasive species (Sax 2001). Sax (Sax 2001) showed that the establishment of the latitudinal gradient in species diversity occurred in a few decades for European and North American exotic species. Our findings suggest that hypotheses based on past glaciation events or speciation rate do not represent the primary cause of the biodiversity pattern although our results were improved when direct effects for (1) higher niche vacancies polewards due to the repeated Pleistocene glaciations (Crame 2004) and (2) indirect effects of higher speciation rates in the tropics (Rohde 1992) were included in the model. A strong Mid-Domain Effect (MDE) arose from the generation of all thermal niches in the Euclidean space but climate ultimately selected pseudo-species that could establish in a section of the thermal gradient. This effect was probably not negligible but it is important to note that it did not take place in the geographical space.
Theoretical spatial biodiversity patterns were examined according to the degree of pseudo-species stenothermy/eurythermy. The dissection of the patterns explained discrepancies observed between biodiversity patterns of some taxonomic groups such as pinnipeds (Tittensor et al. 2010). Expected species richness of strict stenotherms was high in polar regions and to a lesser extent over the tropics where both seasonal and year-to-year fluctuations in weekly SST are lower (Figure 3).
Figure 3. Modelled spatial biodiversity patterns from highly stenotherm to highly eurytherm species. (A) species with a thermal niche breadth ≤ 6°C; (B) species with a thermal niche breadth between 7° and 16°C; (C) species with a thermal niche breadth between 17° and 26°C; (D) species with a thermal niche breadth between 27° and 36°C; (E) species with a thermal niche breadth > 36°C. Biodiversity is here expressed as a percentage of the total species richness per geographical cell. Modified, from Beaugrand and co-workers (Beaugrand et al. 2013b).
This pattern has been found for some marine fish (Brett 1970) and it is well-known that many polar animals occurring in the Arctic Ocean are stenothermic (Menzies et al. 1973). When the degree of eurythermy increased, expected biodiversity was higher in subpolar regions and over the tropics (Figure 3B). Biodiversity peaked in all regions but polar biomes with a maximum diversity detected over mid-latitude oceanic regions (Figure 3C). Modelled richness of eurytherms exhibits a maximum in temperate regions (Figure 3D) and as expected for high eurytherms a maximum was detected towards polar regions (Figure 3E). This dissection of the global biodiversity pattern shows that according to the degree of stenothermy/eurythermy, related to the phylogenetic origin and to some extent to the degree of evolution or speciation of a group, taxa can exhibit different diversity patterns. Therefore, the METAL theory explains why some taxonomic groups should exhibit different latitudinal biodiversity patterns.
Expectedly, we observed that the breadth of the modelled thermal niches was positively correlated to the latitudinal range amplitude of pseudo-species and with the number of geographical cells inhabited by pseudospecies. The Rapoport's pattern states that the mean latitudinal range of a species increases with latitude (Stevens 1989), which led Stevens to conjecture that the ecogeographical biodiversity pattern may be the result of this rule. Although the Rapoport's pattern was not formally tested (Gaston et al. 1998), as niche breath positively correlated to both the latitudinal range amplitude and the number of geographical cells occupied by a species, results from the METAL theory suggest that it cannot be general. If this was the case, a progressive increase in pseudo-species richness would be detected polewards when the breadth of the thermal niche increases (and so the latitudinal range amplitude). This was not observed for strict stenotherms, which exhibited an inverse pattern (Figure 3A) and for stenotherms that showed a bimodal pattern (Figure 3B). However, from medium to high eurytherms, a Rapoport's effect was detected, although intermediate maxima were observed (Figure 3C-D). The METAL theory therefore shows the lack of generality of the Rapoport's effect (Gaston et al. 1998). As with exception of the latitudinal gradient in species richness, inconsistencies (other than methodological) should be related to the breadth of the thermal niches. The METAL theory applied to global biodiversity patterns shows that a large part of these patterns results from the interaction of species thermal tolerance with both seasonal and year-to-year fluctuations in climate. Some aspects of the theory were earlier hypothesized by authors such as Stevens, although not formally described (the climate variability hypothesis). The METAL theory explains the primary cause of the latitudinal biodiversity gradient although it is clear that other factors are also influential. For example, genetic differentiation and speciation are central to establish new niches. The theory holds true at a global scale but it is also patent from field observations that interspecific relationships (e.g. competition and mutualism) inflates locally biodiversity. All these factors have synergistically contributed to shape the present biodiversity and have a strong influence at more local scales.
3. Long-term biological shifts
How climate change may trigger long-term community changes including Abrupt Community Shifts (ACSs) remains unresolved in many systems. An ecosystem regime shift is often defined as a substantial and relatively rapid shift between two contrasting stable states (De Young et al. 2008). A common explanation to the origin of some shifts refers to the theory of alternative stable states (Holling 1973; Scheffer 2009; Scheffer and Carpenter 2003). The theory stipulates that, for a given system, some alternative stable states or attractors are possible and that the shift from one system to another depends on the size of the attraction basin and the strength of both positive or negative feedbacks. The transition from one state to another is difficult to predict, and the return to initial environmental conditions is not sufficient for the system to switch back in the case of hysteresis (Scheffer and Van Nes 2004). Although some stepwise ecosystem changes may well be caused by the existence of several attractors, their existence remains difficult to prove (Seekell et al. 2013). Some processes and alternative stable states leading to such a phenomenon have been identified in lakes and in some marine ecosystems (Nystrom et al. 2000; Scheffer 2009; Scheffer and Van Nes 2004). When the system is controlled by engineer species, such as in coral-dominated ecosystems (Nystrom et al. 2000) or a keystone species, such as in seaweed-structured marine ecosystems (Carpenter 1990), alternative stable states (coral/macroalgae and seaweed/deforested states) and their causes can be well explained (Scheffer 2009). Algal overgrowth in Caribbean coral reefs is mainly attributed to (1) nutrient loading, which stimulates algal growth, and (2) overfishing that reduces the number of herbivorous fish that controls algal proliferation (Nystrom et al. 2000); similar mechanisms have also been invoked to explain regime shifts in kelp forest ecosystems. In contrast to these local benthic ecosystems, the processes and mechanisms leading to abrupt community shifts in pelagic ecosystems remain difficult to both identify and understand (Casini et al. 2009; De Young et al. 2008) and scientists have mainly progressed on the detection of patterns (Beaugrand et al. 2012; Hare and Mantua 2000; Luczak et al. 2011; Reid et al. 2001).
While climate and temperature have repeatedly been assumed to be at the origin of regime shifts in pelagic ecosystems such as those of the Pacific Ocean (Hare and Mantua 2000) and the North Sea (Reid et al. 2001; Weijerman et al. 2005), or more recently in the north-east Atlantic and its adjacent seas (Beaugrand et al. 2012; Luczak et al. 2011), the mechanisms by which a climate signal may bring about these ecosystem responses (Mackas et al. 2012; Perry et al. 2005), are unclear. Even the existence of relatively stable states has also been questioned for some systems (e.g. North Sea), which led some authors to prefer the term of abrupt community/ecosystem shift (ACS or AES) (Beaugrand et al. 2008). Investigating long-term changes in the state of calanoid assemblages in the North Sea, Beaugrand & Ibañez (Beaugrand and Ibanez 2004) revealed an abrupt shift in the 1980s between two apparent stable states. As the length of the time series increased however, the existence of stable states became less apparent (Beaugrand et al. 2008) and long-term changes in the community state were more comparable to climatic vacillations (Hufty 2005). This led Beaugrand and colleagues (2008) to propose to base the detection of these shifts by the change in the multi-scale multivariate (multispecies) temporal variance of the community, the approach removing the necessity of having a stable state; the highest the variance signature, the greater the magnitude of the shift (Carpenter and Brock 2006). The METAL theory proposes that the interaction between the species ecological niche and the environment (including climate) should propagate from the species to the community level. To show how this should occur, we generated a number of hypothetical thermal niches for both eurytherms and stenotherms (Figure 4; see the Equation above)(Beaugrand et al. 2014a). We estimated hypothetical changes in the abundance of each species according to their niches.
Figure 4. theoretical examples showing how the thermal niche of eurytherms and stenotherms may interact with climate-induced temperature changes to produce community shifts. A. Thermal niche of six eurytherms (thermal optimum us=14°C,16°C,18°C,20°C,24°C,28°C and a thermal tolerance ts=5°C). B. Expected changes associated with an increase of 1°C. C. Expected changes based on a hypothetical time series in SSTs (mean of 20°C and year-to-year variability corresponding to measured North Sea SSTs between 1958 to 2010). D. Thermal niche of six stenotherms (us=14°C,16°C,18°C,20°C,24°C,28°C and ts=2°C). E. Expected changes associated with an increase of 1°C. F. Expected changes based on a hypothetical time series in SSTs (mean of 20°C and year-to-year variability corresponding to measured North Sea SSTs between 1958 to 2010). G. Theoretical long-term ecosystem changes as indicated by the first principal component after using a standardized PCA on the table years (1958-2010) x 12 pseudo-species (six eurytherms and six stenotherms). From Beaugrand and co-workers (Beaugrand et al. 2014a).
If the METAL theory applies at the community level, community shifts may be detected when substantial temperature shifts occur. For example, a 1°C increase in temperature may trigger substantial changes in the abundance of some eurytherms, especially those for which the initial thermal regime is close to THV (Figure 4A-B; see the figure in the section). In the fictive example, note that no change is observed for one pseudospecies (blue sky; Figure 4A-B) because the initial thermal regime corresponds to its thermal optimum Topt, and the region of the niche between the two points Ts are stable. The magnitude of the change is expected to be larger for some stenotherms (Figure 4D-E)(Beaugrand 2014). Note that some stenotherms for which the initial thermal regime was close to the edge of their thermal niche (outside TD) and for which the initial thermal regime was close to their thermal optimum (Topt) exhibit small changes in abundance (Figure 4D-E). The same expectations emerge when pseudo-species abundance (eurytherms and stenotherms) are assessed from a time series of temperature (mean average=20°C) having the same variability than long-term changes in temperatures observed in the North Sea for the period 1958-2010 (Figure 4C and Figure 4F). When the 12 pseudo-species (6 eurytherms and 6 stenotherms) are combined and their long-term changes analysed by standardized Principal Components Analysis (PCA), the first principal component (80.05% of the total variance) reveals major changes in this pseudo-community, including a stepwise and rapid shift the late-1980s (Figure 4G). Note that this corresponds to the time of a major shift observed in North Sea pelagic ecosystems.
This theoretical example illustrates how the nonlinear interaction between the thermal niche of each species in a community and temperature may lead to long-term changes and abrupt community shifts (ACSs). Rapid changes in regional temperatures may originate from a rapid change in atmospheric circulation (Hare and Mantua 2000) or climate change (Beaugrand et al. 2008) and are more frequent at thermal frontal zones, often located at the boundaries between systems, e.g. transitional regions between the temperate and the polar biomes (Beaugrand et al. 2008). In such ecosystems, the METAL theory predicts that the response of the community is directly a function of the magnitude of the thermal shift (Figure 4C and Figure 4F).
The application of the METAL theory at the community level leads to several predictions: (1) a stepwise shift in temperature leads to an ACS; (2) Long-term shift in temperature will be amplified at the community scale by the nonlinear interaction between the species thermal niche and the thermal regime, this being more prominent when the number of stenotherms is higher in the community or when the thermal regime of the region is close to the point THV of eurytherms (Beaugrand 2014). This prediction may explain the amplification of small climate-induced environmental changes by the community (Taylor et al. 2002); (3) Some species do not exhibit a stepwise response to change in temperature during an ACS (e.g. species close to their optimum and species at the edge of their thermal niche beyond TD). This prediction may explicate why a large number of species do not show any substantial shifts during an ACS (Beaugrand 2004; Beaugrand et al. 2014b). We tested these predictions using data on copepods in the North Sea where substantial community changes took place in the 1980s (Beaugrand et al. 2008). A total of 90 pseudo-species each characterised by different thermal niches from stenotherms to eurytherms (Figure 5A-B) was created and their expected abundance (as annual mean) was estimated as a function of monthly SSTs.
Figure 5. The community shift in the North Sea (4°W-10°E; 51°N-60°N) reconstructed from the application of the METAL theory. Examples of some simulated niches based on (A) different thermal optimums us and a constant thermal tolerance ts and (B) a constant average us and different thermal tolerances ts. Only pseudo-species that could establish in the North Sea were used in the analyses. (C) First principal components (10,000 first principal components; black) from standardized PCAs applied on each simulated table 52 years x 27 pseudospecies and the first principal component (red) from a standardized PCA performed on the table 52 years x 27 copepods. Modified, from Beaugrand and colleagues (Beaugrand et al. 2014a).
The niche was modelled exclusively as a function of monthly SSTs because i) bathymetry does not change on a year-to-year basis and ii) both PAR and chlorophyll-a concentration were mostly important to reconstruct the seasonal and the distributional range of C. finmarchicus. None of the species had the same thermal niche following the principle of competitive exclusion of Gause (Gause 1934). The goal was to show how, by creating a pool of species with niches differing by their optimum and amplitude, the sum of the temporal changes occurring for each species could create long-term community shifts similar to those observed in the North Sea. As the number of pseudo-species generated for the model exceeded the actual number of copepods occurring in the North Sea, 27 pseudo-species were sampled at random to correspond to the number of observed copepods (27 species or taxa). We performed a standardised PCA on the table years (1958-2009) x annual expected abundance (27 pseudo-species), and repeated this procedure 10,000 times, examining the correlations between long-term (first principal components) expected and observed changes for copepods (Figure 5C). These components were compared to the first principal component originating from a standardised PCA applied on a table years (1958-2009) x annual observed abundance (27 species or taxa). Significant positive relationships (p<0.05) between expected and observed changes in the North Sea copepods were found. The correlations between expected and observed long-term changes were in general (88.90% of the 10,000 simulations) greater than the correlation calculated between annual SSTs and observed changes. The METAL theory therefore explains 56.25% of long-term changes in copepods in the North Sea and provides a mechanism to understand how climate-caused changes in temperatures may influence long-term community shifts.
Abrupt community shifts are often explained by referring to the theory of alternative stable states (Holling 1973; Scheffer 2009; Scheffer and Carpenter 2003). The theory states that the shift from one alternative stable state (or attractor) to another depends upon the size of the attraction basin and the strength of both positive and negative feedbacks. The transition is difficult to anticipate and return to initial environmental conditions is insufficient for the system to switch back in the case of hysteresis (Scheffer and Van Nes 2004). Although some rapid ecosystem shifts may well originate from the presence of attractors, their existence remains hard to establish (Seekell et al. 2013). Some processes and alternative stable states leading to ACSs have been recognised in lakes and in some marine ecosystems (Nystrom et al. 2000; Scheffer 2009; Scheffer and Van Nes 2004). For example, algal overgrowth in Caribbean coral reefs is mainly attributed to (1) nutrient loading, which stimulates algal growth, and (2) overfishing that reduces the number of herbivorous fish that controls algal proliferation (Nystrom et al. 2000); similar mechanisms have also been invoked to explain regime shifts in kelp forest ecosystems.
The first theorem states that “providing that the niche has a Gaussian shape and that there is no species interaction, a substantial increase (e.g. a 1°C of mean annual temperature) in the thermal regime of an ecosystem triggers an abrupt community shift. The magnitude of the community shift depends on the extent of the temperature change and the degree of eurythermy (stenothermy) of the species composing a community. A higher degree of stenothermy increases the sensitivity of the community to temperature change”. Therefore at the community level, a substantial changes in temperature triggers rapid community shifts. In practice, the first theorem is robust from departure to the condition on the niche shape (Ter Braak 1996). The only condition is that the niche must be unimodal. The magnitude of the observed shift is likely to strongly depend on the noise/signal ratio, which is influenced by data quality (e.g. sampling and species identification). The noise/signal ratio influences the location of the point TD along the thermal niche. This phenomenon may also be at the origin of substantial changes in the timing of a shift. This problem is probably observed when changes in the thermal regime are relatively small. I will talk about the effect of species interaction in the next sections.
The second theorem states that “during a climate-driven abrupt community shift, the response of species is individualistic, depending upon the characteristics of their thermal niche, the initial thermal regime and the magnitude of the thermal shift. It follows that not all species are expected to show a shift (e.g. species located around Topt or outside TD) and that some may react earlier (stenotherms for an initial thermal regime close to THV) than others (eurytherms or species with an initial thermal regime close to Topt or outside TD)”. This second theorem has strong practical implications. According to species or taxonomic groups, the magnitude and the timing of the shift may vary, independently of the type of statistical procedures that also influences the timing (Beaugrand 2004). In the North Sea, it has been suggested that the timing of the shift varies according to the selection of species, taxonomic group and species assemblage (Beaugrand et al. 2008; Beaugrand and Ibanez 2004; Reid et al. 2001; Weijerman et al. 2005). It is also possible that some studies focusing on the same ecosystem find a shift whereas others do not, independently of other issues related to statistical technics or sampling programmes. Since temperatures are projected to rise rapidly with anthropogenic climate change, ACSs are likely to increase in both frequency and intensity. The term regime shift has often been used in the past to describe stepwise changes in the ecosystem/community state. Because time series were relatively short (i.e. a few decades), two full dynamic regimes (apparently stable states) and a shift were frequently observed (Beaugrand and Ibanez 2004; Hare and Mantua 2000; Reid et al. 2001). Since then, time series have increased in length and have started to reveal more complex temporal patterns (Beaugrand et al. 2008). The METAL theory explains why such complex patterns forms. It may be soon become apparent that we are observing ecosystem/community state vacillations, where ACSs alternate with period of more relative stability. These periods of relative stability may not be confounded with stable states. The theory METAL offers a way to predict future climate-induced ACSs that may be at the origin of trophic cascades and amplifications.