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The effect of relative sea level change on the

gastropod richness in European lakes.

Student: Leonie Bouma (10898050) University of Amsterdam

Amsterdam, 2-7-2018 Supervisor: Kenneth Rijsdijk

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Abstract

Areas covered by ice during a glaciation experience isostatic uplift during the interglaciation. This, in combination with changing eustatic sea levels might influence the gastropod richness in European lakes. The two concepts are summarized in the term: relative sea level (RSL) change. This study aims to discover whether, and to what extent, the RSL change of lakes influences gastropod richness. First, it is determined when the land in which a lake formed – 467 lakes in total with a glaciation history - became ice-free. Using DEMs in time steps of 1000 years from 21 – 0 ka it is then determined what the RSL change is for each of the 658 lakes within the research area. 8 GLMs were created and the preferred GLM has an AIC value of 3731.2. With this GLM it is concluded that RSL change is a significant predictor for gastropod richness. Its coefficient estimate is -0.09 and therefore species richness is negatively influenced by the RSL change of a lake. The mean value of richness (7.25) is multiplied by 0.91 for an increase in RSL change by 1 unit.

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3 Index 1. Introduction………4 1.1 Relevance………..4 1.2 Background………...5 1.2.1 Species diversity……….5

1.2.2 Relative sea level change………5

1.2.3 The statistical model………5

1.3 Aim and research questions………6

2. Methods………6

2.1 Datasets ………..7

2.2 Data utilization………7

2.3 The generalized linear models………9

3. Results………...10

3.1 Lakes ice-free………..10

3.2 The RSL change per lake………12

3.3 The generalized linear models………12

4. Discussion……….13

4.1 Lakes ice-free………..13

4.2 The RSL change per lake………14

4.3 The generalized linear models………15

5. Conclusion………15

6. Bibliography ………19

7. Appendix………..20

7A: The final GLM data………20

7B: The ice sheet models………..20

7C: Lakes ice-free shapefiles………20

7D: Final shapefiles with all 658 lakes……….20

7E: Intersection shapefiles ………...20

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1. Introduction

A subject of many studies is how flora and fauna biodiversity in present-day Europe have been affected by glaciations, especially the last glaciation, during the Pleistocene epoch (Hewitt, 1999; Taberlet & Cheddadi, 2002; Georgopoulou et al., 2016a). The Pleistocene is characterised by global cyclic glaciations which covered large parts of Northern Europe under thick ice sheets (Lambeck & Chappell, 2001; Denton et al., 2010). The recurrence interval of these glaciations is on average 100,000 years and include a relatively short warming period (Denton et al., 2010). As a result thereof the iced over area is subjected to various degrees of lithostatic downwarping, during glaciation, and subsequent isostatic uplift throughout the interglaciations (Andrén et al., 2011). Furthermore, during glaciations ice sheets grow at the expense of the eustatic sea level; which rises again as the ice melts during the interglacations (Hebbeln et al., 1994; Andrén et al., 2011).

During the last glaciation the Eurasian ice sheets encompassed the British-Irish Ice Sheet (BIIS), the Svalbard-Barents-Kara Ice Sheet (SBKIS) and its largest segment; the Scandinavian Ice Sheet (SIS) (Hughes et al., 2016). These ice sheets reached their maximum extent before 25 ka, at 24-20 ka and at 21-20 ka respectively (ibid). Globally, and for Eurasia, the ice caps reached their maximum volume 21-19 ka which is labeled as the Last Glacial Maximum (LGM) (Clark et al., 2009; Hughes et al., 2016). Since then all ice sheets decreased in size; at 11 ka, the retreating SIS had uncovered most of the current Baltic Sea (Andrén et al., 2011; Hughes et al., 2016).

As the SIS receded northward, lakes formed in the newly exposed land. A number of geological young lakes with a glaciation history, along the Southern border of the Baltic Sea, appear to be a current diversity hotspot for lacustrine gastropods (Neubauer et al., 2015; Georgopoulou et al., 2016b). A (bio)diversity hotspot at a latitude of approximately 52° - 64° is an anomaly as the general rule is that biodiversity increases from the poles towards the equator (Allen & Gillooly, 2006; Neubauer et al., 2015). Therefore, understanding the existence of such an anomaly could further the understanding of (bio)diversity predictors.

Already adding to this knowledge is a study by Georgopoulou et al. (2016a) which divided 898 European lakes into four groups based on glaciation history (§2.1). The study presents several statistical correlations between abiotic predictors and gastropod diversity in these four lake groups. Glaciation history is ultimately classified as a significant predictor with a moderate explanatory power. But the possible disunity in historic lithostatic downwarping and isostatic uplift for the lakes with a glaciation history is not taken into consideration.

The possible variation in lithostatic downwarping and isostatic uplift for these lakes could have influenced the diversity in gastropods. This hypothesis is mainly based on the 2011 paper by Andrén et al. which studied the hydrology changes in the Baltic Sea. These hydrological changes, from fresh- to brackish- to salt water conditions and reverse, were partly due to isostatic uplift. However, the changing sea level is another main factor which determines the lake conditions (Andrén et al., 2011).

1.1 Relevance

Since different gastropod species prosper in different hydrological conditions and isostatic uplift in addition to the sea level changes may cause such hydrological differences; it may be insightful to further explore this possibility. And as 44.9% of gastropod species variance in the LG2 (explanation: §2.1) remains unexplained (Georgopoulou et al., 2016a), the gastropod species variance still represents a knowledge gap to be explored. Further understanding of how the combination of isostatic uplift and sea level change may have influenced gastropod diversity could create a better general understanding of shifts in species diversity. In addition, creating insight into the factors shaping lake diversity is important for local policymakers in their

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5 struggle against eutrophication. Eutrophication threatens a multitude of lakes surrounding the Baltic sea and the sea itself (Bergstöm, Blomqvist & Jansson, 2005; Conley et al., 2009). Insight into the aspects that shape a waterbody and its diversity; more effectively determines the impact of eutrophication on that waterbody (Humborg et al., 2000).

1.2 Background

In this study multiple concepts are mentioned that need to be thoroughly defined to avoid misconceptions and misinterpretations. Therefore, the referred to notions of species diversity and isostatic uplift in combination with sea level change will be discussed. In addition, necessary background information on the choice for the utilized statistical model is provided.

1.2.1 Species diversity

Species diversity is an important concept within present-day ecology but what the concept of species diversity encompasses is highly discussed and still open for debate (Hurlbert, 1971; Huston 1979; Tóthmérész, 1995; Tuomisto, 2010a). Three main components of species diversity are indexed as alpha, bèta and total, or gamma, diversity (Tuomisto, 2010a). However, these components are often contradictorily defined and place emphasis on different data aspects which are used to compute them (ibid). Therefore, reaching a consensus on how the alpha and beta components form the gamma diversity is an important decision but out of scope for this research (Tuomisto, 2010b).

For this study, the focus is on gastropod species richness within the lakes. Species richness is - here - defined as the number of gastropod species present within a lake for the present-day (Georgeopoulou, 2016b). The focus on species richness is based on the fact that Georeopoulou et al. (2016a) used this parameter, amongst others, in their study as well. The species richness was also included in the obtained dataset and therefore straightforward to use as the response variable (section 2.1, app. 7A)

1.2.2 Relative sea level change

The combination of isostatic uplift and a changing sea level is encapsulated in the term: relative sea level (RSL) change. It is the net effect of a change in either of those variables (Mörner, 1984). For this study, RSL change is defined as the ‘the evolution of the solid earth in combination with the geoid’ (Koene, 2017). Thus taking the changing topography and sea level into account. As the geoid is the theoretical shape of the oceans if exclusively influenced by earth's gravity and rotation; it lies at 0 m height (Mörner, 1976; Erik Koene, 2017). According to Mörner (1976) geoid changes are represented by the more general term of eustasy changes (ie. global sea level changes).

For lakes with a glaciation history or near the borders of the SIS during the last glaciation, isostatic uplift is the main driver behind a changing topography. Isostatic uplift or rebound is the vertical movement of earth’s crust in an upward direction (Uscinowicz, 2003). It is essentially the result of lifting the weight of extensive glaciers (Uscinowicz, 2003; Andrén et al., 2011). Crustal uplift starts once ice sheets are melting and increases as the glacier becomes thinner and finally retreats (Uscinowicz, 2003). The uplift rate reaches its peak right after the ice sheet melted away and then starts to slowly decline (ibid). But ice thickness has varied within the SIS, thus the subsequent isostatic uplift varies as well (Andrén et al., 2011). In fact, areas near the Southern border of the Baltic sea are subsiding (partly) due to the uplift in the Northern Baltics (Vink et a., 2007).

1.2.3 The statistical model

To estimate the response variable ‘gastropod richness’, this research employs a generalized linear model (GLM). The choice for a GLM is based on the fact that ecological data (eg.

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6 temperature or isolation) is often non-normally structured (Guisan, Edwards & Hastie, 2002). Count data, such as gastropod richness, often violate the assumptions of ordinary least squares regression (Mittelback et al., 2001). Therefore, GLMs are preferred to outline relationships between spatially distributed species and their explanatory variables (Nicholls, 1989; Mittelback et al., 2001) Using a GLM, the link between the response variable and the predictors is based on the distribution of the response variable (Guisan, Edwards & Hastie, 2002). As will be explained in §2.3, a Poisson distribution is assumed.

1.3 Aim and research questions

The aim of this study is to understand if and to what extent RSL change has an influence on the gastropod richness in European lakes between 4 – 38 degrees longitude and 44 – 71 degrees in latitude (research area). Especially with an eye on the diversity hotspot near the Baltic Sea and the unexplained variance in gastropod diversity in the study by Georgopoulou et al., (2016a). If RSL change is significantly influencing gastropod richness, a step further would be to research its effect in creating a biodiversity hotspot.

The main research question of this study is: To what extent is the gastropod richness in

lakes, within the research area, influenced by the RSL change of those lakes? In order answer

this main question, the following sub questions will be addressed: (1) When did the land in which a lake formed become ice-free?

(2) What is the RSL change of the land, in which a lake formed, since it became ice-free? (3) Is RSL change a significant predictor for gastropod richness in lakes within the research area?

2. Methods

This section refers to ArcGIS and R. ArcGIS is a program by Esri with a multitude of tools to complete GIS tasks. For this research the ArcGIS 10.6 version was used. R is a programming language mainly used for statistical computing. Rstudio, version 3.4.3, is the environment in which the calculations for and by the GLM were achieved. Also, this study often mentions ‘lakes becoming ice-free’ and ‘the RSL change of lakes’. What is meant by these statement is ‘the land in which a lake formed becoming ice-free and the RSL change for that specific area’. To complete this study multiple data sources were needed. The first section explains which dataset from what source was obtained. The second part further describes how the data was utilized. Lastly, the statistical model and the choices that were made are clarified and justified.

Figure 1: a snippet of the final dataset which is the input for the GLM. This dataset has the added columns free_mc and rsl_change which were calculated in this study.

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2.1 Datasets

The data needed for this research was obtained from Georgopoulou et al. (2016a), Hughes et al. (2016) and Erik Koene (2017). As explained, the basis for this research was the 2016 study by Georgopoulou which studied the gastropod diversity of 898 lakes in Europe. These lakes were divided into four age groups based on glaciation history; the first group (LG1) consisted of 205 lakes younger than 11 ka, the second group (LG2) included 334 lakes surrounding the Baltics with an age of 18-11 ka, the third group (LG3), 58 lakes in total, have an age of 18-11 ka as well but are located in the Alpine region and the last group (LG4) consisting of the remaining 301 lakes in Europe without a glaciation history. All 898 lakes were combined into an excel file which included per lake: the age group, gastropod species richness, latitude, longitude, altitude, area, perimeter, temperature, precipitation and isolation. This Excel file laid the groundwork for the final GLM input in this study (fig. 1, app. 7A). In addition, a shapefile with polygons representing each lake (fig. 2) was provided by the study of Georgopoulou et al. (2016a) and loaded into ArcGIS for RSL change calculations per lake.

To calculate the RSL change per lake it was necessary to determine when the land in which these lakes formed became ice-free. To determine this, ice sheet models by Hughes et al., (2016) were used. They modeled the minimum (Min), maximum (Max) and most credible (MC) extent of the ice sheets in time steps of 1000 years from 25 ka until 10 ka. Which resulted in three separate polygon shapefiles representing the extent (Min, Max or MC) of the ice sheets per time step (app. 7B). For this study it is assumed that a lake (ie. the land in which the lake formed) was free of ice since the time step its polygon, from the Georgopoulou et al. (2016a) shapefile, no longer intersected with the MC SIS model (app. 7F)

To then actually calculate the RSL change per lake, the digital elevation models (DEMs) by Erik Koene were used. These DEMs had an extent of 4 to 38 degrees in longitude and 44 to 71 degrees in latitude. The DEMs by Koene represented the topography of the area per time step of 1000 years, starting from 21 ka until 0 ka. In the accompanying reader for these DEMs, which included some background information, the following formula for calculating the RSL change was specified: T((x),t0) - T(x,t). This formula describes that to calculate the RSL change since a certain time step, the topography (ie. DEM) from that past time step needs to be subtracted from the present topography.

2.2 Data utilization

The necessary files were loaded into ArcGIS to calculate the RSL change per lake. Lakes located outside the extent of the DEMs were not included in further calculations below. In addition, lakes from LG3 which are located in the Alpine region were excluded from this study

Figure 2: this maps displays all 898 lakes in the polygon shapefile provided by Georgopoulou et al. (2016a).

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8 (app. 7D). For these lakes it was not possible to determine when they became ice-free since the Alpine glaciers were not included in the models by Hughes et al. (2016). Due to time constraints it was unattainable to complete an in-depth literature study to determine when the glacier receded from each of the 58 lakes. Hence, solely the 658 lakes from LG1, LG2 and LG4 within the extent of the DEMs were included in this study.

Using the ‘Intersect’ tool in ArcGIS it was determined when a lake, for LG1 and LG2, last intersected with the SIS according to the MC model by Hughes et al. (2016) (app. 7E). Six lakes, which were determined to have a glaciation history by Georgopoulou et al. (2016a), never intersected with the MC model of the SIS. To determine when these lakes became ice-free the Max model of the SIS was used. This data was added to the attribute table, the mc_free field, of the final shapefile which includes all 658 lakes (app. 7D). Lakes from LG4 were arbitrarily given the value 26 for mc_free as they are at least 26 ka free of ice since they do not have a glaciation history.

Through the use of the ArcGIS tool ‘Raster Calculator’ the RSL change for the entire extent of the DEMs was calculated for each time step (figure 3). To then determine the RSL change for each lakes the following steps were taken. First, using the ‘Feature to Point’ tool, 12 point feature shapefiles were created. Each containing the lakes that became ice-free during the same time step (app. 7C). Thereafter, the RSL change per lake was determined with the ‘Extract Values to Points’ tool in ArcGIS. With, for each time step, the corresponding lake points and RSL change raster as inputs (figure 3). This new data for the 658 lakes was added to the RSL_change field in the attribute table of the final shapefile which includes all lakes.

Figure 3: This figure visualizes the process to calculate the RSL change for a lake. The upper left figure is the DEM for 0 ka, the upper right figure is the DEM of 20 ka. With the raster calculator the 20 ka was subtracted from 0 ka which resulted in the

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raster output displayed in the lower figure. The lakes that became ice-free at 20 ka are also presented in that figure. These were the inputs for the ‘Extract by Point’ tool.

2.3 The generalized linear models

Four lake names in the shapefile did not correspond to a lake name in the Excel file. Therefore, these lakes had to be excluded and thus the final GLM input was 654 lakes. The Excel file, with the 654 lakes and their gastropod richness value, their predictor values and their coordinates, was exported to a csv file and loaded into R. A script, provided by Sietze Norder & Emiel van Loon, was adjusted to fit this study. For the GLM each predictor is first scaled (ie. standardized) by subtracting the mean and dividing by the standard deviation.

In the GLM, species richness is the response variable. There were seven possible predictors that could be included in the GLM: altitude, area, perimeter, temperature, precipitation, isolation and RSL change. Species richness as a function of these predictors was the input for the GLM. Species richness is count data thus cannot have had a negative value for a lake and its distribution is right skewed as well (fig. 4). Therefore, the family for the GLM was set to ‘Poisson’.

As explained, this study analyzed the influence of RSL change on the Gastropod richness per lake which are spatially distributed. Therefore, it was required to correct for spatial autocorrelation by adding the autocovariate as an explanatory

variable to a second GLM (Dormann, 2006). The autocovariate captured the similarity between the values of response variable (richness) at one location and its neighbouring locations in the first GLM (Crase, Liedloff & Wintle, 2012). It was calculated using the ‘autocov_dist’ function from the spdep R package. The ‘autocov_dist’ response variable was the residuals from the first GLM. For unsampled points in the neighbourhood the inverse-distance weighting method was used. This method attributes a value to an unsampled point based on the weighted average of sampled values in the neighbourhood (Lu & Wong, 2008). The weights are related to the distance of unsampled to sampled point (ibid). The resulting autocovariate values were added to the second GLM as predictor ‘acres’.

With the available predictors, the best GLM needed to be determined. Deciding which was the best GLM was based on the Akaike Information Criterion (AIC). The AIC estimates the quality and adequacy of a model (Wagenmakers & Farrell, 2004). The best possible model has the lowest AIC value (ibid). Instead of making 63 GLMs, one for each unique combination of the possible (7) predictors with a minimum of 1 predictor per model; 8 models were made (Tab. 2). These models were based on the fact that four predictors had p-values off lower than 0.001 in the GLM with all seven predictors and the added ‘acres’ predictor. Thus each of the 8 GLMs included: altitude, perimeter, temperature, precipitation and acres. The signifance level for this research is set to 95% (p-value < 0.05).

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3. Results

This section presents the results from: (1) determining which lakes became ice-free during a certain time step. (2) calculating the RSL change per lake. (3) the GLM with the lowest AIC value.

3.1 Lakes ice-free

For 467 lakes from LG1 and LG2 it was determined in which time step the land in which they formed became ice-free (fig. 5) The bright yellow lakes in figure 5 were still underneath the SIS at 10 ka. Therefore, it is unsure when exactly they became ice-free. It is certain that this was at least 9 ka but it might have been at a later time step (<9 ka). Since the earliest time step in which lakes became free is 22 ka, every evaluated lake from LG1 and LG2 became ice-free after 23 ka. Table 1indicates how many lakes from LG1, LG2 and in total became ice-free during each time step.

Table 1: it displays how many lakes from either LG1 or LG2 became free of ice during a time step. In addition, it indicates how many lakes in total became ice-free during that time step.

Time step LG1 LG2 Total

22 ka 0 4 4 21 ka 0 11 11 20 ka 0 49 49 19 ka 0 0 0 18 ka 0 27 27 17 ka 0 51 51 16 ka 0 33 33 15 ka 0 9 9 14 ka 3 26 29 13 ka 14 36 50 12 ka 12 12 24 11 ka 102 4 106 10 ka 56 0 56 >=9 ka 17 0 17

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Figure 5: This map displays the time step in which lakes became ice-free. The lake polygons and points are colored according to that. The map also includes the lakes without a glaciation history, those are displayed in red.

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3.2 RSL change per lake

The RSL change is calculated per lake for all 658 lakes thus including the lakes from LG4. The values are rounded to their nearest integer. Since there are 244 unique values, the RSL change in figure 6 is displayed in 9 classes with an interval of 52,4.

3.3 The generalized linear models

Running each of the GLMs results in differing AIC values for each model. GLM 6 has the lowest AIC value of 3731.2. Since GLM 6 achieved the lowest AIC value, it is the preferred GLM, of these examined GLMs, to predict gastropod richness in a lake. The predictors included in GLM 6 are: altitude, area, perimeter, temperature, precipitation and RSL change. Of these predictors, ‘area’ appeared to be non significant. In each model ‘area’ and ‘isolation’ were non significant. RSL change was significant in every GLM that included it as a predictor.

Figure 6: This map displays the RSL change in 9 classes due to the high number of unique values. However, the absolute RSL is calculate for all 658 lakes.

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13 Table 2: displays the coefficient estimate and the standard error for each predictor per model. Significance of a predictor is indicated by a *. In addition, the AIC value for each model is included in the table.

GLM Intercept Altitude Perimeter Temperature Precipitation Area Isolation RSL change AIC 1 1.88* (0.017) -0.23* (0.021) 0.12* (0.009) 0.32* (0.018) -0.48* (0.025) X X X 3733.6 2 1.87* (0.017) -0.23* (0.021) 0.15* (0.018) 0.32* (0.018) -0.48* (0.025) -0.02 (0.016) X X 3733.2 3 1.87* (0.017) -0.23* (0.021) 0.12* (0.009) 0.32* (0.018) -0.48* (0.025) X 0.01 (0.013) X 3735.7 4 1.87* (0.017) -0.27* (0.025) 0.12* (0.009) 0.26* (0.033) -0.47* (0.026) X X -0.08* (0.031) 3732.5 5 1.87* (0.017) -0.23* (0.021) 0.15* (0.018) 0.32* (0.018) -0.48* (0.025) -0.02 (0.016) 0.01 (0.013) X 3735.3 6 1.87* (0.017) -0.27* (0.025) 0.15* (0.018) 0.26* (0.033) -0.47* (0.026) -0.03 (0.016) X -0.09* (0.031) 3731.2 7 1.87* (0.017) -0.27* (0.025) 0.12* (0.009) 0.26* (0.033) -0.47* (0.026) X 0.00 (0.013) -0.08* (0.031) 3734.6 8 1.87* (0.017) -0.27* (0.025) 0.15* (0.018) 0.26* (0.033) -0.47* (0.025) -0.03 (0.016) 0.00 (0.013) -0.09* (0.031) 3733.1 ** These GLMs are corrected for spatial autocorrelation by adding acres as explanatory variable. However, its value is trivial to predicting richness and therefore not included in this table.

4 Discussion

This section will discuss the results presented in the previous section. Which answered the 3 sub questions of this research. The first question, when did the land in which a lake formed become ice-free, is answered by figure 5. This map visualizes in which time step a lake became ice-free as the SIS receded. These results are further discussed in §4.1. In addition, for each of the 658 lakes within the research area the RSL change is calculated (fig.6). Therefore, the second question is answered as well and each absolute RSL change value for all lakes is documented in appendix 7A and 7D. The RSL change values are in closer detail reviewed in §4.2. Lastly, it is determined that RSL change is in fact a significant predictor for gastropod richness. This clarifies the last sub question if whether or not RSL change is a significant predictor for gastropod richness in lakes within the research area. And naturally this outcome is further discussed in §4.3. The answer to the main research question is formulated in this last section as well.

4.1 Lakes ice-free

In the determinations of when a lake became ice-free there were a few obstacles. First of all, the SIS was modelled from 25 to 10 ka but the SIS still advanced slightly after 25 ka. Therefore, to delineate when a lake became ice-free was not as straightforward as could have been. For example, lakes that were ice free during the time step of 23 ka could still get covered by ice in a later time step. Or a lake that was covered by ice at 21 ka but uncovered at 20 ka could get

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14 covered by ice again at 19 ka. Therefore, a lake was determined to be ice-free in a certain time step; only if it was not covered by ice again in a later time step. However, it was not possible to conclude the last time step a lake was covered by ice in ArcGIS. Therefore, this was computed in Excel for each lake (LG1, LG2) and manually added to the ‘mc_free’ field in ArcGIS. This process is quite error prone and with more time to fully master ArcGIS there might have been a better and easier way to determine the ‘ice freeness’ of a lake.

In addition, the ‘free_mc’ field could not support an empty input for LG4 lakes. Therefore, these are arbitrarily assigned the value 26 as they are at least since 26 ka free of ice as they never had a glaciation history (Georgopoulou et al., 2016a). As the most recent ice cap model by Hughes et al. (2016) is 10 ka, the 17 lakes that still intersected with the SIS at 10 ka are assigned a 9. This should be interpreted as ‘the lakes are =< 9 ka ice free’. However, it is plausible that those lakes became ice- free during 10 - 9 ka (time step 9 ka) as scandinavia became ice-free approximately 9.8 - 8.5 ka (Andrén et al., 2011; Georgopoulou et al., 2016a). The fact that lakes at a higher latitude became ice-free at later time steps is an expected result as the SIS receded towards the North Pole (Hughes et al., 2016).

4.2 RSL change per lake

For 658 lakes the RSL change is calculated. However, this is not necessarily the RSL change for each lake since it formed. But rather the RSL change since the land in which the lake formed became ice-free. The output of the ‘Extract to Point’ tool in ArcGIS was an added column to the input point features. Therefore, separate output files again needed to be combined in Excel and manually transferred to the ‘RSL_change’ field in the polygon shapefile with all 658 lakes. During this process the calculated RSL changes were rounded to the nearest integer since the attribute table field would not accept decimals. However, nearing the end of this study, it became apparent that certain settings needed to be changed in order to add decimals. Due to time constraints it was not possible to change the rounded RSL change values for all 658 to values with 2 (or more) decimals. But it is expected that the effect this may have had on the outcome of the GLMs is minor (Swindel & Bower, 1972). Due to the fact a sample size of 658 lakes is quite large (ibid).

Lakes in the Southern parts of the studied area have a negative value for RSL change and include all 191 lakes from LG4 and 146 lakes from LG2. This is easily explained due to the teeter-totter effect of isostatic uplift (Vink et al., 2007). As northern areas of Scandinavia are uplifting, more southern areas such as The Netherlands and Germany are experiencing crustal subsidence (Mörner, 1979; Vink et al., 2007). This includes areas which were never glaciated. Therefore, it partly explains why lakes from LG4 do not have a RSL change of 0. In addition, areas that had a positive uplift rate could transition into a negative uplift rate (ie. subsidence). Which, for example, is expressed by the function: y’ = -0.0225x4 + 0.5016x3 - 4.2129x2 + 16.3612x - 24.57 from Uscinowicz (2003) whom modeled uplift rates from 17.5 ka to 3 ka.

As explained, the RSL change value for a lake incorporates its absolute uplift or subsidence and the evolution of the geoid. Initially, the aim for this study was not to study the effect of RSL change on gastropod richness but the effect of only isostatic uplift and subsidence. However, the available DEMs by Erik Koene accounts for the geoid as well. Thus in order to extract the the uplift values from the DEMs by Erik Koene it is required to acknowledge the geoid change as well. And modelling the geoid for each time step to calculate the uplift/subsidence values from the DEMs was out of scope for this research. The geoid is defined as the eustatic sea level for this research. Therefore, the RSL change value can be interpreted as follows: a lake has sunken or uplifted with the RSL value in comparison to the sea level (ie. geoid) during the time step in which the lake became ice-free.

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4.3 The generalized linear models

The GLMs resulted in AIC values which lie very close together. Burnham and & Anderson (2004) stated that if the difference between the preferred and the second best model is less than 2; the evidence against the second model is slight and there is still substantial support for that model. The difference between the preferred model (GLM 6) and the second best model (GLM 4) is 1.3. Therefore, the proposition that GLM 4 is an appropriate model to predict gastropod richness is very credible. However, both models incorporate RSL change as a significant predictor. This implies that even if the second best model is not necessarily discarded; RSL change is still included in the model that describes the gastropod richness best.

The coefficient estimate and its standard error are quite vague descriptors of the effect that RSL change has on gastropod richness. In linear models the model parameters are interpreted linearly. For GLMs the interpretation is less straightforward (Agresti, 2003). To interpret the coefficient of RSL change correctly the natural exponential function is used (ibid). Therefore, to interpret the effect of RSL change in GLM 6, the exp(-0.09) is calculated. Which concludes: if RSL change increases with 1 unit, the mean (7.25) gastropod richness is multiplied by 0.91 (Agresti, 2003). For the obtained RSL values this implies that lakes with a high positive RSL change have a lower richness. This interpretation indirectly answers the main research question of this study. This question was: To what extent is the gastropod richness of lakes,

within the research area, influenced by the RSL change of those lakes? The gastropod richness

is negatively influenced by the RSL change. The mean richness declines by 9% with each increase of RSL change with 1 unit.

However, it is slightly debatable whether this is due to the RSL change itself or due to the fact that these lakes are probably younger since they became ice-free at a later stage (Georgopoulou et al., 2016a). Therefore, those lakes have had a shorter period of recolonization which could have influenced the gastropod richness (Georgopoulou et al., 2016b). Further research on possible correlations between the lakes becoming ice-free and their RSL change and how this might influence the gastropod richness was not possible due to time constraints. However, this is a subject that could be explored in the future.

5. Conclusion

This research has studied the effect of RSL change on gastropod richness in 654 lakes. The main research question that needed to be answered was: To what extent is the gastropod

richness of lakes, within the research area, influenced by the RSL change of those lakes?. And

it is concluded that the RSL change negatively influences the gastropod richness of the studied lakes. However, as mentioned this could be due to the fact that lakes with a high RSL change are relatively young since they became ice-free at a later time step.

With the ice sheet models by Hughes et al. (2016) it was determined when each lake with a glaciation history became ice-free. Thereby answering the first subquestion for 467 lakes: When did the land in which a lake formed become ice-free? With this knowledge the second subquestion could be answered: (2) What is the RSL change of the land, in which a lake formed, since it became ice-free? The RSL change for each lake was calculated using the DEM for the corresponding time step in which a lake became ice-free. The RSL change for LG4 lakes was determined by subtracting the oldest DEM from the 0 ka DEM. As it is certain that those lakes have at least experienced that RSL change. It should be noted that the values for RSL change were rounded to the nearest integer.

After calculating the RSL change for 658 lakes, RSL change was added as a predictor value to the GLMs. However, 4 lake names in the attribute table of the provided shapefile by Georgopoulou et al. (2016a) did not match with a lake in the csv file. Although this file was provided by the same study. Therefore, the final input for the GLMs consisted of 654 lakes. 8

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16 GLMs were designed and GLM 6 is the preferred model as it has the lowest AIC value (3731.2). In each GLM, that included RSL change as a predictor, RSL change was a significant predictor. And as the coefficient of RSL change is -0.09 in GLM 6, the mean value of gastropod richness (7.25) has to be multiplied by 0.91 for each increase in RSL change by 1 unit.

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6. Bibliography

1. Agresti, A. (2003). Categorical data analysis (Vol. 482). John Wiley & Sons.

2. Allen, A. P., & Gillooly, J. F. (2006). Assessing latitudinal gradients in speciation rates and biodiversity at the global scale. Ecology letters, 9(8), 947-954.

3. Andrén, T., Björck, S., Andrén, E., Conley, D., Zillén, L., & Anjar, J. (2011). T In The Baltic Sea Basin (pp. 75-97). Springer Berlin Heidelberg.

4. Bergström, A. K., Blomqvist, P., & Jansson, M. (2005). Effects of atmospheric nitrogen deposition on nutrient limitation and phytoplankton biomass in unproductive Swedish lakes. Limnology and Oceanography, 50(3), 987-994.

5. Burnham, K. P., & Anderson, D. R. (2004). Multimodel inference: understanding AIC and BIC in model selection. Sociological methods & research, 33(2), 261-304.

6. Clark, P. U., Dyke, A. S., Shakun, J. D., Carlson, A. E., Clark, J., Wohlfarth, B., ... & McCabe, A. M. (2009). The last glacial maximum. science, 325(5941), 710-714.

7. Conley, D. J., Paerl, H. W., Howarth, R. W., Boesch, D. F., Seitzinger, S. P., Havens, K. E., Lancelot, C. & Likens, G. E. (2009). Controlling eutrophication: nitrogen and phosphorus. Science, 323(5917), 1014-1015.

8. Crase, B., Liedloff, A. C., & Wintle, B. A. (2012). A new method for dealing with residual spatial autocorrelation in species distribution models. Ecography, 35(10), 879-888.

9. Denton, G. H., Anderson, R. F., Toggweiler, J. R., Edwards, R. L., Schaefer, J. M., & Putnam, A. E. (2010). The last glacial termination. Science, 328(5986), 1652-1656.

10. Dormann, C. F. (2007). Assessing the validity of autologistic regression. ecological modelling, 207(2-4), 234-242.

11. Georgopoulou, E., Neubauer, T. A., Harzhauser, M., Kroh, A., & Mandic, O. (2016a). Distribution patterns of European lacustrine gastropods: a result of environmental factors and deglaciation history. Hydrobiologia, 775(1), 69-82.

12. Georgopoulou, E., Neubauer, T.A., Strona, G., Kroh, A., Mandic, O., Harzhauser, M. (2016b). Beginning of a new age: How did freshwater gastropods respond to the Quaternary climate change in Europe? Quaternary Science Reviews, 149, 269-278.

13. Guisan, A., Edwards Jr, T. C., & Hastie, T. (2002). Generalized linear and generalized additive models in studies of species distributions: setting the scene. Ecological modelling, 157(2-3), 89-100.

14. Hebbeln, D., Dokken, T., Andersen, E. S., Hald, M., & Elverhøi, A. (1994). Moisture supply for northern ice-sheet growth during the Last Glacial Maximum. Nature, 370(6488), 357. 15. Hewitt, G. M. (1999). Post-glacial re-colonization of European biota. Biological journal of the Linnean Society, 68(1-2), 87-112.

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18 16. Hughes, A. L., Gyllencreutz, R., Lohne, Ø. S., Mangerud, J., & Svendsen, J. I. (2016). The last Eurasian ice sheets–a chronological database and time‐slice reconstruction, DATED‐ 1. Boreas, 45(1), 1-45.

17. Humborg, C., Fennel, K., Pastuszak, M., & Fennel, W. (2000). A box model approach for a long-term assessment of estuarine eutrophication, Szczecin Lagoon, southern Baltic. Journal of Marine Systems, 25(3-4), 387-403.

18. Koene, E. (2017). Paleo Sea Level Modelling. accompanying text for the Digital Elevation Models.

19. Lambeck, K., & Chappell, J. (2001). Sea level change through the last glacial cycle. Science, 292(5517), 679-686.

20. Lu, G. Y., & Wong, D. W. (2008). An adaptive inverse-distance weighting spatial interpolation technique. Computers & geosciences, 34(9), 1044-1055.

21. Mittelbach, G. G., Steiner, C. F., Scheiner, S. M., Gross, K. L., Reynolds, H. L., Waide, R. B., Willig, M. R., Dodson, S. I. & Gough, L. (2001). What is the observed relationship between species richness and productivity?. Ecology, 82(9), 2381-2396.

22. Mörner, N. A. (1971). Eustatic changes during the last 20,000 years and a method of separating the isostatic and eustatic factors in an uplifted area. Palaeogeography, Palaeoclimatology, Palaeoecology, 9(3), 153-181.

23. Mörner, N. A. (1976). Eustasy and geoid changes. The Journal of Geology, 84(2), 123-151. 24. Mörner, N. A. (1979). The northwest European “sea-level laboratory” and regional Holocene eustasy. Palaeogeography, Palaeoclimatology, Palaeoecology, 29, 281-300.

25. Morner, N. A. (1984). Differential Holocene sea level changes over the globe; evidence for glacial eustasy, geoidal eustasy, and crustal movements.

26. Neubauer, T. A., Harzhauser, M., Georgopoulou, E., Kroh, A., & Mandic, O. (2015). Tectonics, climate, and the rise and demise of continental aquatic species richness hotspots. Proceedings of the National Academy of Sciences, 112(37), 11478-11483.

27. Nicholls, A. O. (1989). How to make biological surveys go further with generalised linear models. Biological Conservation, 50(1-4), 51-75.

28. Swindel, B. F., & Bower, D. R. (1972). Rounding errors in the independent variables in a general linear model. Technometrics, 14(1), 215-218.

29. Taberlet, P., & Cheddadi, R. (2002). Quaternary refugia and persistence of biodiversity. Science, 297(5589), 2009-2010.

30. Vink, A., Steffen, H., Reinhardt, L., & Kaufmann, G. (2007). Holocene relative sea-level change, isostatic subsidence and the radial viscosity structure of the mantle of northwest Europe (Belgium, the Netherlands, Germany, southern North Sea). Quaternary Science Reviews, 26(25-28), 3249-3275.

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19 31. Wagenmakers, E. J., & Farrell, S. (2004). AIC model selection using Akaike weights. Psychonomic bulletin & review, 11(1), 192-196.

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7. Appendix

7A: The final GLM data

Thesis_Leonie_Bouma.zip → Statistics → 658_lakes_RSL01 7B: The ice sheet models

Thesis_Leonie_Bouma.zip → ArcGIS → Data → Shapefiles → Ice sheet models by Hughes et al. (2016)

7C: Lakes ice-free shapefiles

Thesis_Leonie_Bouma.zip → ArcGIS → Data → Shapefiles →Lakes ice-free 7D: Final shapefiles with all 658 lakes

Thesis_Leonie_Bouma.zip → ArcGIS → Data → Shapefiles →Final 658 lakes shp 7E: Intersection shapefiles

Thesis_Leonie_Bouma.zip → ArcGIS → Data → Shapefiles → Intersection results 7F: Detailed methods

To determine which lakes were located inside the extent of the DEMs by Koene the ‘select by attributes’ tool was used. In the SQL statement the lakes from LG3 were also excluded. I used the statement: "xcent" < 4 OR "ycent" < 44 OR “xcent” > 38 OR “ycent” > 71 OR “age = ‘LG3’. The xcent and ycent are the center coordinates of the lake which were included as a field in the shapefile provided by Georgopoulou et al. (2016). ‘Age’ expressed in the lakes groups was also an included field.

For the remaining 658 lakes I have calculated the time step in which the lakes (ie. the land in which the lakes formed) became ice-free. Using the ‘Intersect’ tool in ArcGIS gave an shapefile output containing all the lakes that intersected with the MC model of the SIS for the time step that I choose. I used the ‘Intersect’ tool for all 15 MC models of the SIS and the Max models of the SIS for the lakes that did not intersect with the MC models of SIS but did have a glaciation history. For each output shapefile I added in the field ‘free_mc’ an integer representing the time step the lake intersected with the SIS (e.g. 18, 17 or 16). But a lake that became ice-free at 11 ka of course intersected with the SIS not only at 12 ka but also earlier time steps. To determine when a lake last intersected with the SIS I had to export the output shapefiles of the intersections to a csv file. These I could open in Excel.

In Excel I combined all the exported csv files into one workmap. I then had to use a few excel functions such as IF, SEARCH and ISNA and write a recursive function to find the minimum value in the column ‘free_mc’ for each lake. I manually added the resulting time steps to the field “free_mc’ in the feature shapefile with all 658 lakes. Since it was not possible to export a single column into an existing feature shapefile as an additional field. For the lakes from LG4 the ‘free_mc’ field does not have a value as they were never covered by ice and thus never became ice-free during the last interglacial.

After determining for the 466 lakes with a glaciation history (LG1, LG2) when they became ice-free, I had to calculate the RSL change per lake. To do so I first subtracted the 21 ka - 9 ka DEMs by Koene from the 0 ka (present-day) according to the formula provided by Erik Koene. The output RSL change rasters were used to compute the RSL change per lake. Then I converted the polygon shapefile with all the 658 lakes to a point shapefile. For this I used the ‘Feature to Point’ data management tool and checked the ‘inside’ box. Thus each

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21 created point is the center of a polygon. Thereafter I had to make separate feature layers for each time step in which certain lakes became ice-free. This resulted in 12 point shapefiles for lakes becoming free of ice in or earlier than 21 ka (with a glaciation history), 20 ka, 18 ka, 17 ka, 16 ka, 15 ka, 14 ka, 13 ka, 12 ka, 11 ka, 10 ka and in or later that 9 ka (app. 7C). In the time step of 19 ka there were not any lakes that became ice-free. made a separate point shapefile for the lakes in LG4. However, I did calculate the RSL change for lakes in LG4 using the DEM of 21 ka. As this is the oldest DEM available.

To calculate the RSL change for each lake I overlayed the ‘lake points’ layers with the corresponding RSL change raster. For example, I overlayed the point layer which contained the lakes that became ice free at 20 ka with the RSL change raster for 20 ka (0 ka - 20 ka). With the ‘Extract Values to Points’ tool in ArcGIS I calculated the RSL change per lake. This tool extracted the RSL change value from the raster for each lake (point) at the location that the lake overlapped the raster. This value was added to a new field (RASTERVALU) in the output shapefile.

I have tried to transfer the values in the RASTERVALU field from the output shapefiles to the corresponding lakes in the polygon shapefile with ‘attribute transfer’ in the spatial adjustment editor. However, this tool did not open a dialog box which should have happened. Therefore, I had to manually add the RSL change values to the corresponding lakes in the polygon shapefile. To minimize the risk of making mistakes I exported all shapefiles to a csv file and combined them in Excel. I then ordered all the lakes alphabetically so that the order in which the lakes were displayed in the Excel file was the same as in the attribute table in ArcGIS. I checked the added RSL values to the attribute table twice to correct potential errors. Lastly, I exported the updated shapefile to a csv file and added the RSL change to the corresponding lakes in the Excel file with the predictors. To complete this last step I again used IF and SEARCH functions in Excel.

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