Materials
We collected from the literature and available databases a dataset of radiocarbon dates from Europe (West of 60°E and North of 37°N) either obtained from remains of the four analyzed species or from archaeological layers where they have been observed. However, we only considered observations dated between 7500 and 47,000 cal BP: their scarcity before this period may bias the GAMs, and after it, domesticated cattle, pigs and (later) horses arrived in Europe, making it difficult to differentiate them from their wild forms.
We excluded any record fitting one or more of the following conditions: unreliable; not in accord with the expected chronology of their archaeological layer; without a reported standard error; available only as terminus ante/post quem.
All dates were calibrated with OxCal5 version 4.4 using the IntCal20 curve51, and we further excluded any record for which calibration resulted in an error, resulting in the number of points presented in Table 1 as “Original dataset” (available at the link https://doi.org/10.6084/m9.figshare.20510364).
SDMs based on GAMs need presence/background data, not frequencies; moreover, multiple observations (i.e., presence in different archaeological layers) from the same site and time slice are likely to introduce stronger sample biases linked to chrono-geographically differential sampling efforts. For this reason, we collapsed our observations by keeping only one point per grid cell per time slice for each species, leaving the number of observations reported in Table 1 as “Collapsed datasets”, used for all the analyses presented in this work.
To perform all analyses, we used the R package pastclim v. 1.042 to couple each observation from the collapsed datasets to paleoclimatic reconstructions published in8 by setting dataset = “Beyer2020”. These are based on the Hadley CM3 model, include 14 different bioclimatic variables at a spatial resolution of 0.5°, and are available for the whole world every 1000 years until 22 kya and every 2000 years before that date (referred to in the manuscript as “time slices”). Specifically, each observation was associated with the relevant bioclimatic reconstruction based on its average age and spatial coordinates.
As already mentioned, the four species analyzed show different preferences regarding temperature, habitat, and altitude. Therefore, for the Species Distribution Modelling, we choose five environmental variables that should be able to capture such differences: two measures of temperature (BIO5, maximum temperature of the warmest month, and BIO6, minimum temperature of the coldest month); two variables to help capture habitat differentiation (BIO12, total annual precipitation, and Net Primary Productivity, NPP), and one measure of topography (rugosity42).
High collinearity can be problematic in SDMs; we confirmed that all our variables had a correlation below 0.7, a threshold commonly adopted for this kind of analysis52,53.
Whilst the GAMs predicted all time points; we visualized our results by creating an average estimate for the following periods: pre-LGM (from the beginning of the time range analyzed, i.e., 47 kya to 27 kya), LGM (from 27 to 18 kya), Late Glacial (from 18 to 11.7 kya), Holocene (from 11.7 kya to the end of the time range analyzed, i.e., 7.5 kya).
Methods
We generated 25 sets of background points for each species to adequately represent the existing climatic space in our SDMs. Each set was generated by sampling, for each observation, 50 random locations matched by time. This resulted in n = 25 datasets (“repetitions”) of background points and presences (observations) for each species, which we used to repeat our analyses to account for the stochastic sampling of the background. For each dataset, we used GAMs to fit two possible models: a “constant niche” model, which included only the environmental variables as covariates, and a “changing niche” model, that also included interactions of each environmental variable with time (fitted as tensor products).
In GAMs, the effect of a given continuous predictor on the response variable (in our case, the logit transformed probability of a presence) is represented by a smooth function; this smooth function can be linear or non-linear and can become highly complex in shape depending on the number of knots selected by the GAM fitting algorithm. The interaction between two covariates is modelled by tensor products54; this approach is equivalent to an interaction term in a linear model but with the added complexity of the smooth function. In our models, we confine tensor products to the interaction between an environmental variable and time; a simple way to think about such a tensor product is that it allows the smooth representation of the relationship between the variable and the probability of a presence to change progressively over time.
GAMs were fitted using the mgcv package in R54 using thin plate regression splines (TPNR; bs = “tp”, default in mgcv) for environmental variables and their tensor products with time in the “niche changing” models. The GAM algorithm automatically selects the complexity of the smooth most appropriate to the data that are being fitted; as GAM can have issues with overfitting, we added an additional penalty against overly complex smooths (gamma = 1.4) and used Restricted Maximum Likelihood (REML = TRUE), as recommended by54. It is possible that even with these settings, the complexity of the smooth is not sufficient; we used mgcv::gam.check() to check this, and increased the basis dimension of the smooth, k, to make sure that k-1 was larger than the estimated degrees of freedom (edf). We found the best maximum thresholds for k to be 16 for bio06 and 10 for all other variables.
We checked for non-linear correlation among variables using the mgcv::collinearity function and checked the values of estimated concurvity. All estimates were below the threshold of 0.8 in all models, runs and variables except for a few instances for time (Supplementary Figs. 5–8). We consider this not to be worrying: this is most likely a result of sample bias, and GAM is known to be robust to correlation/concurvity55,56.
We verified the model assumptions by inspecting the residuals using the R package DHARMa57. Standard tests for deviations from the expected distribution and dispersion were non-significant for all repetitions for all species, as were the tests for outliers. Furthermore, we tested for spatial autocorrelation among residuals by computing Moran’s I; all tests were either non-significant or, when significance was detected, the estimate of Moran’s I was very close to zero, revealing a trivial deviation from the assumptions which should not impact the results (Supplementary Tables 1–4).
We performed model choice (Supplementary Tables 5–8) by comparing the constant- and changing-niche models for each combination of species and repetition using the Akaike Information Criterion (AIC). AIC strongly supported the changing-niche model in all species and repetitions, an inference supported by the higher Nagelkerke R2 and expected deviance for those models than for the constant-niche ones (Supplementary Tables 5–8).
The model fit for each of the changing niche GAMs was evaluated with the Boyce Continuous Index25,26, designed to be used with presence-only data58,59. We set a threshold of Pearson’s correlation coefficient > 0.8 to define acceptable models25 (Supplementary Table 9).
The relative importance of each environmental variable was quantified for all the models above the BCI threshold of 0.8 in two different ways. Firstly, we computed the total deviance explained by each variable by simply fitting a GAM with only that variable. We then estimated the unique deviance explained by each variable by comparing the full model with one for which that variable was excluded (i.e., we computed the explained deviance lost by dropping that predictor). The difference between the two values represents the deviance explained by a variable which can also be accounted for by other variables (i.e., the deviance in common with other variables).
To achieve more robust predictions60, we averaged in two different ensembles the repetitions for the changing niche GAMs with BCI > 0.8: by mean and median. This step is intended to reduce the weight of models that are highly sensitive to the random sampling of the background60. Then, for each species, we selected the ensemble (either based on mean or median) with the higher BCI as the most supported and used it to perform all further analyses.
The effect of different variables through time was visualized by plotting the interactions of the GAMs. For each model with a BCI > 0.8, we used the R package gratia27 to generate a surface with time as the x-axis, the environmental variable as the y-axis, and the effect size as the z-axis (visualized as colour shades). We then plotted the mean surface for each species, which captures the signal consistent across all randomized background sets.
To visualize the prediction for each species, we then transformed the predicted probabilities of occurrence from the ensemble into binary presence/absences by using the threshold needed to get a minimum predicted area encompassing 99% of our presences (function ecospat.mpa() from the ecospat R package61). The binary predictions were then visualized using the mean over the time steps within each major climatic period.
Reporting summary
Further information on research design is available in the Nature Research Reporting Summary linked to this article.
Source: Ecology - nature.com
