diff --git a/R/aaa-auto.R b/R/aaa-auto.R
index 190ba1df80..6151c6d7f4 100644
--- a/R/aaa-auto.R
+++ b/R/aaa-auto.R
@@ -9730,6 +9730,7 @@ fundamental_cycles_impl <- function(
         call = rlang::caller_env()
       )
     }
+    start <- start - 1
   }
   bfs_cutoff <- as.numeric(bfs_cutoff)
   if (is.null(weights) && "weight" %in% edge_attr_names(graph)) {
@@ -9746,7 +9747,7 @@ fundamental_cycles_impl <- function(
   res <- .Call(
     R_igraph_fundamental_cycles,
     graph,
-    start - 1,
+    start,
     bfs_cutoff,
     weights
   )
@@ -9971,7 +9972,7 @@ minimum_spanning_tree_prim_impl <- function(
 
 random_spanning_tree_impl <- function(
   graph,
-  vid = 0
+  vid = NULL
 ) {
   # Argument checks
   ensure_igraph(graph)
@@ -9983,6 +9984,7 @@ random_spanning_tree_impl <- function(
         call = rlang::caller_env()
       )
     }
+    vid <- vid - 1
   }
 
   on.exit(.Call(R_igraph_finalizer))
@@ -9990,7 +9992,7 @@ random_spanning_tree_impl <- function(
   res <- .Call(
     R_igraph_random_spanning_tree,
     graph,
-    vid - 1
+    vid
   )
   if (igraph_opt("return.vs.es")) {
     res <- create_es(graph, res)
@@ -10316,6 +10318,7 @@ vertex_path_from_edge_path_impl <- function(
         call = rlang::caller_env()
       )
     }
+    start <- start - 1
   }
   edge_path <- as_igraph_es(graph, edge_path)
   mode <- switch_igraph_arg(
@@ -10331,7 +10334,7 @@ vertex_path_from_edge_path_impl <- function(
   res <- .Call(
     R_igraph_vertex_path_from_edge_path,
     graph,
-    start - 1,
+    start,
     edge_path - 1,
     mode
   )
diff --git a/R/trees.R b/R/trees.R
index 03adbc86ee..693f897627 100644
--- a/R/trees.R
+++ b/R/trees.R
@@ -152,7 +152,7 @@ to_prufer <- function(graph) {
 #' @param graph The input graph to sample from. Edge directions are ignored if
 #'   the graph is directed.
 #' @param vid When the graph is disconnected, this argument specifies how to
-#'   handle the situation. When the argument is zero (the default), the sampling
+#'   handle the situation. When the argument is `NULL` (the default), the sampling
 #'   will be performed component-wise, and the result will be a spanning forest.
 #'   When the argument contains a vertex ID, only the component containing the
 #'   given vertex will be processed, and the result will be a spanning tree of the
@@ -171,7 +171,7 @@ to_prufer <- function(graph) {
 #' @family trees
 #' @export
 #' @cdocs igraph_random_spanning_tree
-sample_spanning_tree <- function(graph, vid = 0) {
+sample_spanning_tree <- function(graph, vid = NULL) {
   random_spanning_tree_impl(
     graph = graph,
     vid = vid
diff --git a/man/sample_spanning_tree.Rd b/man/sample_spanning_tree.Rd
index 69efb56e52..1100e6a41a 100644
--- a/man/sample_spanning_tree.Rd
+++ b/man/sample_spanning_tree.Rd
@@ -4,14 +4,14 @@
 \alias{sample_spanning_tree}
 \title{Samples from the spanning trees of a graph randomly and uniformly}
 \usage{
-sample_spanning_tree(graph, vid = 0)
+sample_spanning_tree(graph, vid = NULL)
 }
 \arguments{
 \item{graph}{The input graph to sample from. Edge directions are ignored if
 the graph is directed.}
 
 \item{vid}{When the graph is disconnected, this argument specifies how to
-handle the situation. When the argument is zero (the default), the sampling
+handle the situation. When the argument is \code{NULL} (the default), the sampling
 will be performed component-wise, and the result will be a spanning forest.
 When the argument contains a vertex ID, only the component containing the
 given vertex will be processed, and the result will be a spanning tree of the
diff --git a/src/rinterface.c b/src/rinterface.c
index e627617568..b352b672e0 100644
--- a/src/rinterface.c
+++ b/src/rinterface.c
@@ -13168,7 +13168,7 @@ SEXP R_igraph_fundamental_cycles(SEXP graph, SEXP start, SEXP bfs_cutoff, SEXP w
     Rz_SEXP_to_vector(weights, &c_weights);
   }
                                         /* Call igraph */
-  IGRAPH_R_CHECK(igraph_fundamental_cycles(&c_graph, &c_basis, (Rf_isNull(start) ? 0 : c_start), c_bfs_cutoff, (Rf_isNull(weights) ? 0 : &c_weights)));
+  IGRAPH_R_CHECK(igraph_fundamental_cycles(&c_graph, &c_basis, (Rf_isNull(start) ? -1 : c_start), c_bfs_cutoff, (Rf_isNull(weights) ? 0 : &c_weights)));
 
                                         /* Convert output */
   PROTECT(basis=Ry_igraph_vector_int_list_to_SEXPp1(&c_basis));
@@ -13482,7 +13482,7 @@ SEXP R_igraph_random_spanning_tree(SEXP graph, SEXP vid) {
     c_vid = (igraph_integer_t) REAL(vid)[0];
   }
                                         /* Call igraph */
-  IGRAPH_R_CHECK(igraph_random_spanning_tree(&c_graph, &c_res, (Rf_isNull(vid) ? 0 : c_vid)));
+  IGRAPH_R_CHECK(igraph_random_spanning_tree(&c_graph, &c_res, (Rf_isNull(vid) ? -1 : c_vid)));
 
                                         /* Convert output */
   PROTECT(res=Ry_igraph_vector_int_to_SEXPp1(&c_res));
@@ -13869,7 +13869,7 @@ SEXP R_igraph_vertex_path_from_edge_path(SEXP graph, SEXP start, SEXP edge_path,
   IGRAPH_FINALLY(igraph_vector_int_destroy, &c_vertex_path);
   c_mode = (igraph_neimode_t) Rf_asInteger(mode);
                                         /* Call igraph */
-  IGRAPH_R_CHECK(igraph_vertex_path_from_edge_path(&c_graph, (Rf_isNull(start) ? 0 : c_start), &c_edge_path, &c_vertex_path, c_mode));
+  IGRAPH_R_CHECK(igraph_vertex_path_from_edge_path(&c_graph, (Rf_isNull(start) ? -1 : c_start), &c_edge_path, &c_vertex_path, c_mode));
 
                                         /* Convert output */
   igraph_vector_int_destroy(&c_edge_path);
diff --git a/tools/py-stimulus/src/stimulus/generators/r.py b/tools/py-stimulus/src/stimulus/generators/r.py
index 088964b58a..dc8a5023b8 100644
--- a/tools/py-stimulus/src/stimulus/generators/r.py
+++ b/tools/py-stimulus/src/stimulus/generators/r.py
@@ -255,7 +255,15 @@ def handle_argument_check(param: ParamSpec) -> str:
 
             if param.is_optional and param.is_input and res:
                 res = optional_wrapper_r(res)
-
+                # For optional VERTEX parameters, add the subtraction inside the NULL check
+                if param.type == "VERTEX":
+                    # Add the subtraction at the end of the wrapped block
+                    name = get_r_parameter_name(param)
+                    res = res.rstrip()
+                    if res.endswith("}"):
+                        # Insert before the closing brace
+                        res = res[:-1] + f"  {name} <- {name} - 1\n}}"
+                    
             # Replace template placeholders
             res = indent(res).replace("%I%", get_r_parameter_name(param))
             for i, dep in enumerate(param.dependencies):
@@ -299,9 +307,13 @@ def handle_argument_check(param: ParamSpec) -> str:
             name = get_r_parameter_name(param)
             call = type.get("CALL", name)
             if call:
-                call_formatted = call.replace("%I%", name)
-                # Add spaces around arithmetic operators
-                call_formatted = re.sub(r'(\w+)(\+|\-|\*|/)(\d+)', r'\1 \2 \3', call_formatted)
+                # For optional VERTEX parameters, subtraction is done in INCONV, so just use the name
+                if param.is_optional and param.type == "VERTEX":
+                    call_formatted = name
+                else:
+                    call_formatted = call.replace("%I%", name)
+                    # Add spaces around arithmetic operators
+                    call_formatted = re.sub(r'(\w+)(\+|\-|\*|/)(\d+)', r'\1 \2 \3', call_formatted)
                 parts.append(call_formatted)
 
         # Format .Call() as multi-line with each argument on its own line
diff --git a/tools/stimulus/functions-R.yaml b/tools/stimulus/functions-R.yaml
index 7470eaf8f5..f2f3d45946 100644
--- a/tools/stimulus/functions-R.yaml
+++ b/tools/stimulus/functions-R.yaml
@@ -992,7 +992,7 @@ igraph_minimum_spanning_tree_unweighted:
 igraph_minimum_spanning_tree_prim:
 
 igraph_random_spanning_tree:
-    PARAMS: GRAPH graph, OUT EDGE_INDICES res, OPTIONAL VERTEX vid=0
+    PARAMS: GRAPH graph, OUT EDGE_INDICES res, OPTIONAL VERTEX vid
 
 #######################################
 # Coloring