diff --git a/DESCRIPTION b/DESCRIPTION
index 71b1097..c7de546 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -2,8 +2,8 @@ Encoding: UTF-8
 Package: bigsnpr
 Type: Package
 Title: Analysis of Massive SNP Arrays
-Version: 1.12.9
-Date: 2024-05-15
+Version: 1.12.10
+Date: 2024-08-13
 Authors@R: c(
     person("Florian", "Privé", email = "florian.prive.21@gmail.com", role = c("aut", "cre")),
     person("Michael", "Blum", role = "ths"),
diff --git a/NEWS.md b/NEWS.md
index 7597a48..f1b1711 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,3 +1,7 @@
+## bigsnpr 1.12.10
+
+- In function `snp_ancestry_summary()`, add parameter `sum_to_one` to optionally allows for ancestry coefficients to have a sum lower than 1 (when `FALSE`; default is `TRUE`).
+
 ## bigsnpr 1.12.9
 
 - In function `snp_modifyBuild()`, you can now provide `local_chain` as a vector of two, for when using `check_reverse`. You can now also modify the `base_url` from where to download the chain files.
diff --git a/R/ancestry-summary.R b/R/ancestry-summary.R
index 1f1400d..6822bc8 100644
--- a/R/ancestry-summary.R
+++ b/R/ancestry-summary.R
@@ -15,6 +15,8 @@
 #'   Default is 0.4. When correlation is lower, an error is returned.
 #'   For individual genotypes, this should be larger than 0.6.
 #'   For allele frequencies, this should be larger than 0.9.
+#' @param sum_to_one Whether to force ancestry coefficients to sum to 1?
+#'   Default is `TRUE` (otherwise, the sum can be lower than 1).
 #'
 #' @return Vector of coefficients representing the ancestry proportions.
 #'   Also (as attributes) `cor_each`, the correlation between input
@@ -27,7 +29,7 @@
 #' @example examples/example-ancestry-summary.R
 #'
 snp_ancestry_summary <- function(freq, info_freq_ref, projection, correction,
-                                 min_cor = 0.4) {
+                                 min_cor = 0.4, sum_to_one = TRUE) {
 
   assert_package("quadprog")
   assert_nona(freq)
@@ -53,9 +55,9 @@ snp_ancestry_summary <- function(freq, info_freq_ref, projection, correction,
   res <- quadprog::solve.QP(
     Dmat = cp_X_pd$mat,
     dvec = crossprod(y, X),
-    Amat = cbind(1, diag(ncol(X))),
-    bvec = c(1, rep(0, ncol(X))),
-    meq  = 1
+    Amat = cbind(-1, diag(ncol(X))),
+    bvec = c(-1, rep(0, ncol(X))),
+    meq  = `if`(sum_to_one, 1, 0)
   )
 
   cor_pred <- drop(cor(drop(X0 %*% res$solution), freq))
diff --git a/docs/news/index.html b/docs/news/index.html
index e7febc0..1738759 100644
--- a/docs/news/index.html
+++ b/docs/news/index.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">bigsnpr</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">1.12.9</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">1.12.10</span>
       </span>
     </div>
 
@@ -91,6 +91,10 @@ <h1 data-toc-skip>Changelog <small></small></h1>
       <small>Source: <a href="https://github.com/privefl/bigsnpr/blob/HEAD/NEWS.md" class="external-link"><code>NEWS.md</code></a></small>
     </div>
 
+    <div class="section level2">
+<h2 class="page-header" data-toc-text="1.12.10" id="bigsnpr-11210">bigsnpr 1.12.10<a class="anchor" aria-label="anchor" href="#bigsnpr-11210"></a></h2>
+<ul><li>In function <code><a href="../reference/snp_ancestry_summary.html">snp_ancestry_summary()</a></code>, add parameter <code>sum_to_one</code> to optionally allows for ancestry coefficients to have a sum lower than 1 (when <code>FALSE</code>; default is <code>TRUE</code>).</li>
+</ul></div>
     <div class="section level2">
 <h2 class="page-header" data-toc-text="1.12.9" id="bigsnpr-1129">bigsnpr 1.12.9<a class="anchor" aria-label="anchor" href="#bigsnpr-1129"></a></h2>
 <ul><li>In function <code><a href="../reference/snp_modifyBuild.html">snp_modifyBuild()</a></code>, you can now provide <code>local_chain</code> as a vector of two, for when using <code>check_reverse</code>. You can now also modify the <code>base_url</code> from where to download the chain files.</li>
diff --git a/man/snp_ancestry_summary.Rd b/man/snp_ancestry_summary.Rd
index 4749293..c099f20 100644
--- a/man/snp_ancestry_summary.Rd
+++ b/man/snp_ancestry_summary.Rd
@@ -9,7 +9,8 @@ snp_ancestry_summary(
   info_freq_ref,
   projection,
   correction,
-  min_cor = 0.4
+  min_cor = 0.4,
+  sum_to_one = TRUE
 )
 }
 \arguments{
@@ -27,6 +28,9 @@ project allele frequencies.}
 Default is 0.4. When correlation is lower, an error is returned.
 For individual genotypes, this should be larger than 0.6.
 For allele frequencies, this should be larger than 0.9.}
+
+\item{sum_to_one}{Whether to force ancestry coefficients to sum to 1?
+Default is \code{TRUE} (otherwise, the sum can be lower than 1).}
 }
 \value{
 Vector of coefficients representing the ancestry proportions.
diff --git a/tests/testthat/test-5-match.R b/tests/testthat/test-5-match.R
index 4e5eed2..7412a3a 100644
--- a/tests/testthat/test-5-match.R
+++ b/tests/testthat/test-5-match.R
@@ -148,6 +148,13 @@ test_that("snp_ancestry_summary() works (with no projection here)", {
   res <- snp_ancestry_summary(y, X, Matrix::Diagonal(nrow(X), 1), rep(1, nrow(X)))
   expect_equal(res, prop, check.attributes = FALSE)
   expect_equal(attr(res, "cor_pred"), 1)
+  expect_equal(sum(res), 1)
+
+  res.2 <- snp_ancestry_summary(y, X, Matrix::Diagonal(nrow(X), 1), rep(1, nrow(X)),
+                                sum_to_one = FALSE)
+  expect_equal(res.2, prop, check.attributes = FALSE)
+  expect_equal(attr(res.2, "cor_pred"), 1)
+  expect_equal(sum(res.2), 1)
 
   expect_warning(res2 <- snp_ancestry_summary(
     y, X[, -1], Matrix::Diagonal(nrow(X), 1), rep(1, nrow(X))),
@@ -156,6 +163,24 @@ test_that("snp_ancestry_summary() works (with no projection here)", {
   expect_equal(res2, prop[-1], tolerance = 0.1, check.attributes = FALSE)
   expect_equal(attr(res2, "cor_pred"), drop(cor(y, X[, -1] %*% res2)))
 
+  expect_warning(res2.2 <- snp_ancestry_summary(
+    y, X[, -1], Matrix::Diagonal(nrow(X), 1), rep(1, nrow(X)), sum_to_one = FALSE),
+    "The solution does not perfectly match the frequencies.")
+  expect_true(all(res2.2 > prop[-1]))
+  expect_equal(res2.2, prop[-1], tolerance = 0.1, check.attributes = FALSE)
+  expect_equal(attr(res2.2, "cor_pred"), drop(cor(y, X[, -1] %*% res2.2)))
+  # better than when forced to sum to 1
+  expect_true(all(res2.2 < res2))
+  expect_gt(attr(res2.2, "cor_pred"), attr(res2, "cor_pred"))
+  expect_lt(sum(res2.2), 1)
+
+  res.3 <- snp_ancestry_summary(y, cbind(X, rbeta(1000, 1, 3)),
+                                Matrix::Diagonal(nrow(X), 1), rep(1, nrow(X)),
+                                sum_to_one = sample(c(TRUE, FALSE), 1))
+  expect_equal(res.3, c(prop, 0), check.attributes = FALSE)
+  expect_equal(attr(res.3, "cor_pred"), 1)
+  expect_equal(sum(res.3), 1)
+
   expect_error(res3 <- snp_ancestry_summary(
     y, X[, -3], Matrix::Diagonal(nrow(X), 1), rep(1, nrow(X)), min_cor = 0.6),
     "Correlation between frequencies is too low:")