diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 559bcc1d..2d6ac64b 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -22,6 +22,7 @@ jobs:
           - 3.4
           - 3.3
           - 3.2
+          - 3.1
 
     runs-on: ubuntu-latest
     container:
diff --git a/CHANGES.md b/CHANGES.md
index d8bad4f4..e42dd5da 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -1,6 +1,9 @@
 # Changes
 
 ## Unreleased
+- Fixed build error with GDAL 3.1
+
+ - <https://github.com/georust/gdal/pull/416>
 
 ## 0.15
 - **Breaking**: `RasterBand::actual_block_size` now takes two `usize` offsets instead of `(isize, isize)`
diff --git a/src/raster/mdarray.rs b/src/raster/mdarray.rs
index 18d07485..46c3c80b 100644
--- a/src/raster/mdarray.rs
+++ b/src/raster/mdarray.rs
@@ -15,9 +15,8 @@ use gdal_sys::{
     GDALGroupGetGroupNames, GDALGroupGetMDArrayNames, GDALGroupGetName, GDALGroupH,
     GDALGroupOpenGroup, GDALGroupOpenMDArray, GDALGroupRelease, GDALMDArrayGetAttribute,
     GDALMDArrayGetDataType, GDALMDArrayGetDimensionCount, GDALMDArrayGetDimensions,
-    GDALMDArrayGetNoDataValueAsDouble, GDALMDArrayGetSpatialRef, GDALMDArrayGetStatistics,
-    GDALMDArrayGetTotalElementsCount, GDALMDArrayGetUnit, GDALMDArrayH, GDALMDArrayRelease,
-    OSRDestroySpatialReference, VSIFree,
+    GDALMDArrayGetNoDataValueAsDouble, GDALMDArrayGetSpatialRef, GDALMDArrayGetTotalElementsCount,
+    GDALMDArrayGetUnit, GDALMDArrayH, GDALMDArrayRelease, OSRDestroySpatialReference, VSIFree,
 };
 use libc::c_void;
 use std::ffi::CString;
@@ -387,6 +386,7 @@ impl<'a> MDArray<'a> {
     ///
     /// TODO: add option to pass progress callback (`pfnProgress`)
     ///
+    #[cfg(any(all(major_is_3, minor_ge_2), major_ge_4))]
     pub fn get_statistics(
         &self,
         force: bool,
@@ -401,7 +401,7 @@ impl<'a> MDArray<'a> {
         };
 
         let rv = unsafe {
-            GDALMDArrayGetStatistics(
+            gdal_sys::GDALMDArrayGetStatistics(
                 self.c_mdarray,
                 self.c_dataset,
                 libc::c_int::from(is_approx_ok),
@@ -805,6 +805,7 @@ mod tests {
 
     #[test]
     #[cfg_attr(not(all(major_ge_3, minor_ge_4)), ignore)]
+    #[cfg(any(all(major_is_3, minor_ge_2), major_ge_4))]
     fn test_root_group_name() {
         let fixture = "/vsizip/fixtures/byte_no_cf.zarr.zip";
 
@@ -822,6 +823,7 @@ mod tests {
 
     #[test]
     #[cfg_attr(not(all(major_ge_3, minor_ge_4)), ignore)]
+    #[cfg(any(all(major_is_3, minor_ge_2), major_ge_4))]
     fn test_array_names() {
         let fixture = "/vsizip/fixtures/byte_no_cf.zarr.zip";
 
@@ -843,6 +845,7 @@ mod tests {
 
     #[test]
     #[cfg_attr(not(all(major_ge_3, minor_ge_4)), ignore)]
+    #[cfg(any(all(major_is_3, minor_ge_2), major_ge_4))]
     fn test_n_dimension() {
         let fixture = "/vsizip/fixtures/byte_no_cf.zarr.zip";
 
@@ -863,6 +866,7 @@ mod tests {
 
     #[test]
     #[cfg_attr(not(all(major_ge_3, minor_ge_4)), ignore)]
+    #[cfg(any(all(major_is_3, minor_ge_2), major_ge_4))]
     fn test_n_elements() {
         let fixture = "/vsizip/fixtures/byte_no_cf.zarr.zip";
 
@@ -883,6 +887,7 @@ mod tests {
 
     #[test]
     #[cfg_attr(not(all(major_ge_3, minor_ge_4)), ignore)]
+    #[cfg(any(all(major_is_3, minor_ge_2), major_ge_4))]
     fn test_dimension_name() {
         let fixture = "/vsizip/fixtures/byte_no_cf.zarr.zip";
 
@@ -918,6 +923,7 @@ mod tests {
 
     #[test]
     #[cfg_attr(not(all(major_ge_3, minor_ge_4)), ignore)]
+    #[cfg(any(all(major_is_3, minor_ge_2), major_ge_4))]
     fn test_dimension_size() {
         let fixture = "/vsizip/fixtures/byte_no_cf.zarr.zip";
 
@@ -942,6 +948,7 @@ mod tests {
 
     #[test]
     #[cfg_attr(not(all(major_ge_3, minor_ge_4)), ignore)]
+    #[cfg(any(all(major_is_3, minor_ge_2), major_ge_4))]
     fn test_read_data() {
         let fixture = "/vsizip/fixtures/byte_no_cf.zarr.zip";
 
@@ -968,6 +975,7 @@ mod tests {
 
     #[test]
     #[cfg_attr(not(all(major_ge_3, minor_ge_4)), ignore)]
+    #[cfg(any(all(major_is_3, minor_ge_1), major_ge_4))]
     fn test_read_string_array() {
         // Beware https://github.com/georust/gdal/issues/299 if you want to reuse this
         // This can't be Zarr because it doesn't support string arrays
@@ -1001,6 +1009,7 @@ mod tests {
 
     #[test]
     #[cfg_attr(not(all(major_ge_3, minor_ge_4)), ignore)]
+    #[cfg(any(all(major_is_3, minor_ge_2), major_ge_4))]
     fn test_datatype() {
         let fixture = "/vsizip/fixtures/byte_no_cf.zarr.zip";
 
@@ -1027,6 +1036,7 @@ mod tests {
 
     #[test]
     #[cfg_attr(not(all(major_ge_3, minor_ge_4)), ignore)]
+    #[cfg(any(all(major_is_3, minor_ge_2), major_ge_4))]
     fn test_spatial_ref() {
         let fixture = "/vsizip/fixtures/byte_no_cf.zarr.zip";
 
@@ -1052,6 +1062,7 @@ mod tests {
 
     #[test]
     #[cfg_attr(not(all(major_ge_3, minor_ge_4)), ignore)]
+    #[cfg(any(all(major_is_3, minor_ge_2), major_ge_4))]
     fn test_no_data_value() {
         let fixture = "/vsizip/fixtures/byte_no_cf.zarr.zip";
 
@@ -1073,6 +1084,7 @@ mod tests {
 
     #[test]
     #[cfg_attr(not(all(major_ge_3, minor_ge_4)), ignore)]
+    #[cfg(any(all(major_is_3, minor_ge_2), major_ge_4))]
     fn test_attributes() {
         let fixture = "/vsizip/fixtures/cf_nasa_4326.zarr.zip";
 
@@ -1124,6 +1136,7 @@ mod tests {
 
     #[test]
     #[cfg_attr(not(all(major_ge_3, minor_ge_4)), ignore)]
+    #[cfg(any(all(major_is_3, minor_ge_2), major_ge_4))]
     fn test_unit() {
         let fixture = "/vsizip/fixtures/cf_nasa_4326.zarr.zip";
 
@@ -1164,6 +1177,7 @@ mod tests {
 
     #[test]
     #[cfg_attr(not(all(major_ge_3, minor_ge_4)), ignore)]
+    #[cfg(any(all(major_is_3, minor_ge_2), major_ge_4))]
     fn test_stats() {
         // make a copy to avoid writing the statistics into the original file
         let fixture = TempFixture::fixture("byte_no_cf.zarr.zip");