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rename to main/_images/06c74463c88e2efca6214df563e00aca67f727323fd0c4681e01ea90c4b1dfb0.svg
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diff --git a/main/searchindex.js b/main/searchindex.js
index 4099cd5..3b53fd4 100644
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\ No newline at end of file
+Search.setIndex({"alltitles": {"A branch event": [[3, "a-branch-event"]], "A pulse of admixture": [[3, "a-pulse-of-admixture"]], "A split event": [[3, "a-split-event"]], "Answer": [[3, null], [3, null], [3, null]], "Appendix": [[2, "appendix"]], "Asymmetric migration": [[3, "asymmetric-migration"]], "Common concepts": [[2, "common-concepts"]], "Continuous migration": [[3, "continuous-migration"]], "Conventions and Terminology": [[2, "conventions-and-terminology"]], "Converting backwards time to forwards time": [[2, "converting-backwards-time-to-forwards-time"]], "Default values": [[3, "default-values"]], "Defaults": [[2, "defaults"]], "Deme": [[2, "deme"]], "Deme defaults": [[2, "deme-defaults"]], "Deme resolution": [[2, "deme-resolution"]], "Epoch": [[2, "epoch"]], "Epoch resolution": [[2, "epoch-resolution"]], "Example: sequential application of pulses": [[2, "example-sequential-application-of-pulses"]], "Excercise": [[3, null]], "Exponential size changes": [[3, "exponential-size-changes"]], "Gallery": [[0, null]], "Gutenkunst et al. (2009) Out-of-Africa expansion": [[0, "gutenkunst-et-al-2009-out-of-africa-expansion"]], "Human Data Model": [[2, "human-data-model"]], "Important considerations": [[2, "important-considerations"]], "Infinity": [[2, "infinity"]], "Introduction": [[1, null], [2, "introduction"]], "Jacobs et al. (2019) Denisovan admixture": [[0, "jacobs-et-al-2019-denisovan-admixture"]], "MDM documents": [[2, "mdm-documents"]], "Machine Data Model": [[2, "machine-data-model"]], "Metadata": [[2, "metadata"]], "Migration": [[2, "migration"]], "Migration resolution": [[2, "migration-resolution"]], "Multiple ancestors": [[3, "multiple-ancestors"]], "Multiple demes": [[3, "multiple-demes"]], "Note to Readers": [[2, "note-to-readers"]], "Population sizes": [[2, "population-sizes"]], "Pulse": [[2, "pulse"]], "Pulse resolution": [[2, "pulse-resolution"]], "Question": [[3, null], [3, null], [3, null]], "Reference parser implementation": [[2, "reference-parser-implementation"]], "Resolution": [[2, "resolution"]], "Schema": [[2, "schema"], [2, "sec-spec-hdm-schema"]], "Selfing and cloning": [[3, "selfing-and-cloning"]], "Setting defaults": [[3, "setting-defaults"]], "Software accepting the Demes format as input/output": [[1, "software-accepting-the-demes-format-as-input-output"]], "Software directly 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"spectrum": 2, "spell": 3, "squar": 3, "stabl": 2, "standard": 2, "standardis": 1, "start": [2, 3], "start_siz": [0, 3], "start_tim": 0, "step": [2, 3], "still": 2, "stop": 2, "str": 2, "straightforward": 2, "strictli": 2, "string": [2, 3], "strip": 2, "strongli": 2, "structur": 2, "style": 3, "subsequ": 2, "success": 2, "suffer": 3, "sum": 2, "support": 2, "suppos": 3, "syntax": [2, 3], "system": 3, "t": 2, "tab": 3, "tabl": [0, 1], "take": 2, "taken": 2, "task": 2, "technic": 2, "tediou": 1, "tempor": 2, "ten": [0, 2], "term": [2, 3], "termin": 3, "text": 2, "than": [2, 3], "thei": [2, 3], "them": 2, "therefor": 2, "thi": [0, 1, 3], "thing": 2, "think": [2, 3], "those": [1, 2], "thousand": 3, "three": 3, "through": [2, 3], "thu": [0, 2], "ti": 1, "time": [0, 1], "time_boundari": 2, "time_interv": 2, "time_unit": [0, 3], "titl": 2, "toler": 2, "tool": 1, "top": 3, "topolog": 2, "toward": [2, 3], "tracker": 2, "transcrib": 1, "transfer": 2, "transform": 2, "travel": 3, "treat": 3, "tri": 2, "trick": 2, "true": 2, "try": 3, "tskit": 1, "tutori": [1, 2], "two": [0, 2, 3], "type": [2, 3], "typeerror": 2, "ultim": 2, "understand": 2, "unfortun": 1, "union": 2, "uniqu": 2, "unit": 2, "unknown": 2, "unless": 2, "unresolv": 2, "until": 3, "up": [2, 3], "updat": 2, "url": 3, "us": [1, 2, 3], "user": [1, 2], "usual": 2, "utah": [0, 3], "v": 2, "validate_item": 2, "validator_nam": 2, "valu": 2, "valueerror": 2, "vari": 2, "variabl": 2, "variou": [0, 2, 3], "ve": 3, "veri": 3, "via": [2, 3], "visit": 2, "wa": [2, 3], "wai": [2, 3], "want": 3, "warn": 2, "we": [1, 2, 3], "well": [0, 3], "western": [0, 3], "what": 2, "when": [1, 2, 3], "where": 2, "wherea": 3, "whether": [2, 3], "which": [1, 2, 3], "while": 2, "who": 3, "why": 2, "wide": 2, "wiggl": 2, "wish": [2, 3], "within": [2, 3], "without": [2, 3], "word": [2, 3], "work": [1, 2], "worri": 3, "would": [2, 3], "writabl": 2, "write": [1, 2], "writer": 2, "written": [2, 3], "x": [2, 3], "y": [2, 3], "yaml": 2, "year": [0, 2, 3], "yml": 3, "yoruba": [0, 3], "you": [1, 2, 3], "youngest": 2, "your": [1, 2], "yri": [0, 3], "zero": [2, 3], "zigzag": 3, "zip": 2}, "titles": ["Gallery", "Introduction", "Specification", "Tutorial"], "titleterms": {"2009": 0, "2019": 0, "A": 3, "accept": 1, "admixtur": [0, 3], "africa": 0, "al": 0, "an": 3, "ancestor": [2, 3], "answer": 3, "appendix": 2, "applic": 2, "asymmetr": 3, "backward": 2, "branch": 3, "chang": 3, "clone": 3, "cloning_r": 2, "common": 2, "concept": 2, "consider": 2, "continu": 3, "convent": 2, "convert": 2, "data": 2, "default": [2, 3], "deme": [1, 2, 3], "denisovan": 0, "descript": 2, "dest": 2, "directli": 1, "document": 2, "doi": 2, "don": 3, "end_siz": 2, "end_tim": 2, "epoch": [2, 3], "et": 0, "event": 3, "exampl": 2, "excercis": 3, "expans": 0, "exponenti": 3, "format": 1, "forward": 2, "galleri": 0, "gener": 3, "generation_tim": 2, "gutenkunst": 0, "have": 3, "human": 2, "i": [1, 2, 3], "implement": 2, "import": 2, "infin": 2, "input": 1, "introduct": [1, 2], "jacob": 0, "level": 2, "machin": 2, "mdm": 2, "metadata": 2, "migrat": [2, 3], "model": [0, 2], "multipl": 3, "name": 2, "necessari": 1, "note": 2, "out": 0, "output": 1, "parser": 2, "popul": 2, "proport": 2, "puls": [2, 3], "question": 3, "rate": 2, "reader": 2, "refer": 2, "relat": 1, "resolut": 2, "schema": 2, "self": 3, "selfing_r": 2, "sequenti": 2, "set": 3, "size": [2, 3], "size_funct": 2, "softwar": 1, "sort": 2, "sourc": 2, "specif": [1, 2], "split": 3, "start_siz": 2, "start_tim": [2, 3], "support": 1, "symmetr": [2, 3], "t": 3, "terminologi": [2, 3], "thi": 2, "time": [2, 3], "time_unit": 2, "todo": [2, 3], "too": 3, "top": 2, "tutori": 3, "unit": 3, "valid": 2, "valu": 3, "what": [1, 3], "who": 2, "why": [1, 3], "yaml": 3, "zigzag": 0}})
\ No newline at end of file
diff --git a/main/specification.html b/main/specification.html
index fbe8717..bf4f347 100644
--- a/main/specification.html
+++ b/main/specification.html
@@ -2102,7 +2102,7 @@ <h4>pulses<a class="headerlink" href="#id41" title="Link to this heading">#</a><
             <span class="n">description</span><span class="o">=</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="kc">None</span><span class="p">),</span>
             <span class="n">start_time</span><span class="o">=</span><span class="p">((</span><span class="nb">str</span><span class="p">,</span> <span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">),</span> <span class="n">is_positive_or_json_infinity</span><span class="p">),</span>
             <span class="n">ancestors</span><span class="o">=</span><span class="p">(</span><span class="nb">list</span><span class="p">,</span> <span class="n">is_list_of_identifiers</span><span class="p">),</span>
-            <span class="n">proportions</span><span class="o">=</span><span class="p">(</span><span class="nb">list</span><span class="p">,</span> <span class="n">is_list_of_fractions</span><span class="p">),</span>
+            <span class="n">proportions</span><span class="o">=</span><span class="p">(</span><span class="nb">list</span><span class="p">,</span> <span class="n">is_list_of_proportions</span><span class="p">),</span>
         <span class="p">),</span>
     <span class="p">)</span>
 
@@ -2110,8 +2110,8 @@ <h4>pulses<a class="headerlink" href="#id41" title="Link to this heading">#</a><
         <span class="n">end_time</span><span class="o">=</span><span class="p">(</span><span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">,</span> <span class="n">is_non_negative_and_finite</span><span class="p">),</span>
         <span class="n">start_size</span><span class="o">=</span><span class="p">(</span><span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">,</span> <span class="n">is_positive_and_finite</span><span class="p">),</span>
         <span class="n">end_size</span><span class="o">=</span><span class="p">(</span><span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">,</span> <span class="n">is_positive_and_finite</span><span class="p">),</span>
-        <span class="n">selfing_rate</span><span class="o">=</span><span class="p">(</span><span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">,</span> <span class="n">is_fraction</span><span class="p">),</span>
-        <span class="n">cloning_rate</span><span class="o">=</span><span class="p">(</span><span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">,</span> <span class="n">is_fraction</span><span class="p">),</span>
+        <span class="n">selfing_rate</span><span class="o">=</span><span class="p">(</span><span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">,</span> <span class="n">is_rate</span><span class="p">),</span>
+        <span class="n">cloning_rate</span><span class="o">=</span><span class="p">(</span><span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">,</span> <span class="n">is_rate</span><span class="p">),</span>
         <span class="n">size_function</span><span class="o">=</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="kc">None</span><span class="p">),</span>
     <span class="p">)</span>
     <span class="n">check_defaults</span><span class="p">(</span><span class="n">global_epoch_defaults</span><span class="p">,</span> <span class="n">allowed_epoch_defaults</span><span class="p">)</span>
@@ -2130,7 +2130,7 @@ <h4>pulses<a class="headerlink" href="#id41" title="Link to this heading">#</a><
             <span class="p">),</span>
             <span class="n">ancestors</span><span class="o">=</span><span class="n">pop_list</span><span class="p">(</span><span class="n">deme_data</span><span class="p">,</span> <span class="s2">&quot;ancestors&quot;</span><span class="p">,</span> <span class="p">[],</span> <span class="nb">str</span><span class="p">,</span> <span class="n">is_identifier</span><span class="p">),</span>
             <span class="n">proportions</span><span class="o">=</span><span class="n">pop_list</span><span class="p">(</span>
-                <span class="n">deme_data</span><span class="p">,</span> <span class="s2">&quot;proportions&quot;</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">,</span> <span class="n">is_fraction</span>
+                <span class="n">deme_data</span><span class="p">,</span> <span class="s2">&quot;proportions&quot;</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">,</span> <span class="n">is_proportion</span>
             <span class="p">),</span>
         <span class="p">)</span>
 
@@ -2155,8 +2155,8 @@ <h4>pulses<a class="headerlink" href="#id41" title="Link to this heading">#</a><
                 <span class="n">end_size</span><span class="o">=</span><span class="n">pop_number</span><span class="p">(</span>
                     <span class="n">epoch_data</span><span class="p">,</span> <span class="s2">&quot;end_size&quot;</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="n">is_positive_and_finite</span>
                 <span class="p">),</span>
-                <span class="n">selfing_rate</span><span class="o">=</span><span class="n">pop_number</span><span class="p">(</span><span class="n">epoch_data</span><span class="p">,</span> <span class="s2">&quot;selfing_rate&quot;</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">is_fraction</span><span class="p">),</span>
-                <span class="n">cloning_rate</span><span class="o">=</span><span class="n">pop_number</span><span class="p">(</span><span class="n">epoch_data</span><span class="p">,</span> <span class="s2">&quot;cloning_rate&quot;</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">is_fraction</span><span class="p">),</span>
+                <span class="n">selfing_rate</span><span class="o">=</span><span class="n">pop_number</span><span class="p">(</span><span class="n">epoch_data</span><span class="p">,</span> <span class="s2">&quot;selfing_rate&quot;</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">is_rate</span><span class="p">),</span>
+                <span class="n">cloning_rate</span><span class="o">=</span><span class="n">pop_number</span><span class="p">(</span><span class="n">epoch_data</span><span class="p">,</span> <span class="s2">&quot;cloning_rate&quot;</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">is_rate</span><span class="p">),</span>
                 <span class="n">size_function</span><span class="o">=</span><span class="n">pop_string</span><span class="p">(</span><span class="n">epoch_data</span><span class="p">,</span> <span class="s2">&quot;size_function&quot;</span><span class="p">,</span> <span class="kc">None</span><span class="p">),</span>
             <span class="p">)</span>
             <span class="n">check_empty</span><span class="p">(</span><span class="n">epoch_data</span><span class="p">)</span>
@@ -2171,7 +2171,7 @@ <h4>pulses<a class="headerlink" href="#id41" title="Link to this heading">#</a><
     <span class="n">check_defaults</span><span class="p">(</span>
         <span class="n">migration_defaults</span><span class="p">,</span>
         <span class="nb">dict</span><span class="p">(</span>
-            <span class="n">rate</span><span class="o">=</span><span class="p">(</span><span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">,</span> <span class="n">is_fraction</span><span class="p">),</span>
+            <span class="n">rate</span><span class="o">=</span><span class="p">(</span><span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">,</span> <span class="n">is_rate</span><span class="p">),</span>
             <span class="n">start_time</span><span class="o">=</span><span class="p">((</span><span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">,</span> <span class="nb">str</span><span class="p">),</span> <span class="n">is_positive_or_json_infinity</span><span class="p">),</span>
             <span class="n">end_time</span><span class="o">=</span><span class="p">(</span><span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">,</span> <span class="n">is_non_negative_and_finite</span><span class="p">),</span>
             <span class="n">source</span><span class="o">=</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">is_identifier</span><span class="p">),</span>
@@ -2182,7 +2182,7 @@ <h4>pulses<a class="headerlink" href="#id41" title="Link to this heading">#</a><
     <span class="k">for</span> <span class="n">migration_data</span> <span class="ow">in</span> <span class="n">pop_list</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="s2">&quot;migrations&quot;</span><span class="p">,</span> <span class="p">[]):</span>
         <span class="n">insert_defaults</span><span class="p">(</span><span class="n">migration_data</span><span class="p">,</span> <span class="n">migration_defaults</span><span class="p">)</span>
         <span class="n">graph</span><span class="o">.</span><span class="n">add_migration</span><span class="p">(</span>
-            <span class="n">rate</span><span class="o">=</span><span class="n">pop_number</span><span class="p">(</span><span class="n">migration_data</span><span class="p">,</span> <span class="s2">&quot;rate&quot;</span><span class="p">,</span> <span class="n">validator</span><span class="o">=</span><span class="n">is_fraction</span><span class="p">),</span>
+            <span class="n">rate</span><span class="o">=</span><span class="n">pop_number</span><span class="p">(</span><span class="n">migration_data</span><span class="p">,</span> <span class="s2">&quot;rate&quot;</span><span class="p">,</span> <span class="n">validator</span><span class="o">=</span><span class="n">is_rate</span><span class="p">),</span>
             <span class="n">start_time</span><span class="o">=</span><span class="n">pop_number</span><span class="p">(</span>
                 <span class="n">migration_data</span><span class="p">,</span>
                 <span class="s2">&quot;start_time&quot;</span><span class="p">,</span>
@@ -2211,7 +2211,7 @@ <h4>pulses<a class="headerlink" href="#id41" title="Link to this heading">#</a><
             <span class="n">sources</span><span class="o">=</span><span class="p">(</span><span class="nb">list</span><span class="p">,</span> <span class="n">is_nonempty_list_of_identifiers</span><span class="p">),</span>
             <span class="n">dest</span><span class="o">=</span><span class="p">(</span><span class="nb">str</span><span class="p">,</span> <span class="n">is_identifier</span><span class="p">),</span>
             <span class="n">time</span><span class="o">=</span><span class="p">(</span><span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">,</span> <span class="n">is_positive_and_finite</span><span class="p">),</span>
-            <span class="n">proportions</span><span class="o">=</span><span class="p">(</span><span class="nb">list</span><span class="p">,</span> <span class="n">is_nonempty_list_of_fractions_with_sum_less_than_1</span><span class="p">),</span>
+            <span class="n">proportions</span><span class="o">=</span><span class="p">(</span><span class="nb">list</span><span class="p">,</span> <span class="n">is_nonempty_list_of_proportions_with_sum_less_than_1</span><span class="p">),</span>
         <span class="p">),</span>
     <span class="p">)</span>
     <span class="k">for</span> <span class="n">pulse_data</span> <span class="ow">in</span> <span class="n">pop_list</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="s2">&quot;pulses&quot;</span><span class="p">,</span> <span class="p">[]):</span>
@@ -2231,7 +2231,7 @@ <h4>pulses<a class="headerlink" href="#id41" title="Link to this heading">#</a><
                 <span class="s2">&quot;proportions&quot;</span><span class="p">,</span>
                 <span class="n">default</span><span class="o">=</span><span class="p">[],</span>
                 <span class="n">required_type</span><span class="o">=</span><span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">,</span>
-                <span class="n">validator</span><span class="o">=</span><span class="n">is_fraction</span><span class="p">,</span>
+                <span class="n">validator</span><span class="o">=</span><span class="n">is_proportion</span><span class="p">,</span>
             <span class="p">),</span>
         <span class="p">)</span>
         <span class="n">check_empty</span><span class="p">(</span><span class="n">pulse_data</span><span class="p">)</span>
@@ -2275,10 +2275,14 @@ <h4>pulses<a class="headerlink" href="#id41" title="Link to this heading">#</a><
     <span class="k">return</span> <span class="n">value</span> <span class="o">&gt;=</span> <span class="mi">0</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">math</span><span class="o">.</span><span class="n">isinf</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
 
 
-<span class="k">def</span> <span class="nf">is_fraction</span><span class="p">(</span><span class="n">value</span><span class="p">):</span>
+<span class="k">def</span> <span class="nf">is_rate</span><span class="p">(</span><span class="n">value</span><span class="p">):</span>
     <span class="k">return</span> <span class="mi">0</span> <span class="o">&lt;=</span> <span class="n">value</span> <span class="o">&lt;=</span> <span class="mi">1</span>
 
 
+<span class="k">def</span> <span class="nf">is_proportion</span><span class="p">(</span><span class="n">value</span><span class="p">):</span>
+    <span class="k">return</span> <span class="mi">0</span> <span class="o">&lt;</span> <span class="n">value</span> <span class="o">&lt;=</span> <span class="mi">1</span>
+
+
 <span class="k">def</span> <span class="nf">is_nonempty</span><span class="p">(</span><span class="n">value</span><span class="p">):</span>
     <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">0</span>
 
@@ -2295,12 +2299,12 @@ <h4>pulses<a class="headerlink" href="#id41" title="Link to this heading">#</a><
     <span class="k">return</span> <span class="n">is_list_of_identifiers</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">len</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">0</span>
 
 
-<span class="k">def</span> <span class="nf">is_list_of_fractions</span><span class="p">(</span><span class="n">value</span><span class="p">):</span>
-    <span class="k">return</span> <span class="nb">all</span><span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">)</span> <span class="ow">and</span> <span class="n">is_fraction</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">value</span><span class="p">)</span>
+<span class="k">def</span> <span class="nf">is_list_of_proportions</span><span class="p">(</span><span class="n">value</span><span class="p">):</span>
+    <span class="k">return</span> <span class="nb">all</span><span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">numbers</span><span class="o">.</span><span class="n">Number</span><span class="p">)</span> <span class="ow">and</span> <span class="n">is_proportion</span><span class="p">(</span><span class="n">v</span><span class="p">)</span> <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">value</span><span class="p">)</span>
 
 
-<span class="k">def</span> <span class="nf">is_nonempty_list_of_fractions_with_sum_less_than_1</span><span class="p">(</span><span class="n">value</span><span class="p">):</span>
-    <span class="k">return</span> <span class="n">is_list_of_fractions</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">len</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="ow">and</span> <span class="nb">sum</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="o">&lt;=</span> <span class="mi">1</span>
+<span class="k">def</span> <span class="nf">is_nonempty_list_of_proportions_with_sum_less_than_1</span><span class="p">(</span><span class="n">value</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">is_list_of_proportions</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">len</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="ow">and</span> <span class="nb">sum</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="o">&lt;=</span> <span class="mi">1</span>
 
 
 <span class="k">def</span> <span class="nf">validate_item</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">value</span><span class="p">,</span> <span class="n">required_type</span><span class="p">,</span> <span class="n">validator</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
diff --git a/main/tutorial.html b/main/tutorial.html
index 1b4bca0..4b61d56 100644
--- a/main/tutorial.html
+++ b/main/tutorial.html
@@ -463,7 +463,7 @@ <h2>YAML<a class="headerlink" href="#yaml" title="Link to this heading">#</a></h
 <input id="sd-tab-item-1" name="sd-tab-set-0" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-1">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/0d0e2e19b3fc4be5b48c133f40f883acd203f5d5fbf99a5b2346e189a6b9026a.svg" src="_images/0d0e2e19b3fc4be5b48c133f40f883acd203f5d5fbf99a5b2346e189a6b9026a.svg" />
+<img alt="_images/98298340836881856933de6aaf98fb4108b43a3f8db5305615d3b4d437b9f6b8.svg" src="_images/98298340836881856933de6aaf98fb4108b43a3f8db5305615d3b4d437b9f6b8.svg" />
 </div>
 </div>
 </div>
@@ -509,7 +509,7 @@ <h2>What is a deme?<a class="headerlink" href="#what-is-a-deme" title="Link to t
 <input checked="checked" id="sd-tab-item-3" name="sd-tab-set-1" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-3">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/2c3b5ff00e84efc4de6157db7126436e0ac7096f282ee7730de00f15d873fc22.svg" src="_images/2c3b5ff00e84efc4de6157db7126436e0ac7096f282ee7730de00f15d873fc22.svg" />
+<img alt="_images/c53daf74fa34bb8d89b7d9c5b86f8f79607ab3726703a5c7afd6af43b4a83407.svg" src="_images/c53daf74fa34bb8d89b7d9c5b86f8f79607ab3726703a5c7afd6af43b4a83407.svg" />
 </div>
 </div>
 </div>
@@ -553,7 +553,7 @@ <h3>Default values<a class="headerlink" href="#default-values" title="Link to th
 <input id="sd-tab-item-5" name="sd-tab-set-2" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-5">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/8319b81aaf94f417384134ba4d5cd3e92917575f01f7cedef2ba0511e79459b6.svg" src="_images/8319b81aaf94f417384134ba4d5cd3e92917575f01f7cedef2ba0511e79459b6.svg" />
+<img alt="_images/d5183d6d5c660eb452a9091e577465b5e33561bca976807521233dd37c614893.svg" src="_images/d5183d6d5c660eb452a9091e577465b5e33561bca976807521233dd37c614893.svg" />
 </div>
 </div>
 </div>
@@ -590,7 +590,7 @@ <h2>What is an epoch?<a class="headerlink" href="#what-is-an-epoch" title="Link
 <input checked="checked" id="sd-tab-item-7" name="sd-tab-set-3" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-7">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/1d13fd5b060a03a718716f8fbeb01c391251ebe395c7eaad348eaf015eee538c.svg" src="_images/1d13fd5b060a03a718716f8fbeb01c391251ebe395c7eaad348eaf015eee538c.svg" />
+<img alt="_images/bca47307066a90795636cf261663583775d8a5936561599d9b97903d5e3b27f4.svg" src="_images/bca47307066a90795636cf261663583775d8a5936561599d9b97903d5e3b27f4.svg" />
 </div>
 </div>
 </div>
@@ -625,7 +625,7 @@ <h2>What is an epoch?<a class="headerlink" href="#what-is-an-epoch" title="Link
 <input id="sd-tab-item-9" name="sd-tab-set-4" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-9">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/a9014aee1cd8a5a6074470c4f39ef918845d8a416f10b31cac20feddeb51f547.svg" src="_images/a9014aee1cd8a5a6074470c4f39ef918845d8a416f10b31cac20feddeb51f547.svg" />
+<img alt="_images/3728b1ec5eb006aa203c25f12412b0fd8ac1168ee76579aac5102c7d92ff2f3f.svg" src="_images/3728b1ec5eb006aa203c25f12412b0fd8ac1168ee76579aac5102c7d92ff2f3f.svg" />
 </div>
 </div>
 </div>
@@ -688,7 +688,7 @@ <h2>Exponential size changes<a class="headerlink" href="#exponential-size-change
 <input id="sd-tab-item-11" name="sd-tab-set-5" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-11">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/05111bc176a490f75a92812b51d6ba6672eba0be6f57368e8573aebce8161bb1.svg" src="_images/05111bc176a490f75a92812b51d6ba6672eba0be6f57368e8573aebce8161bb1.svg" />
+<img alt="_images/59bd7b981c682399c72521e58610de4a958df0f533027c4862598877e8fa4cc3.svg" src="_images/59bd7b981c682399c72521e58610de4a958df0f533027c4862598877e8fa4cc3.svg" />
 </div>
 </div>
 </div>
@@ -764,7 +764,7 @@ <h3>A split event<a class="headerlink" href="#a-split-event" title="Link to this
 <input id="sd-tab-item-13" name="sd-tab-set-6" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-13">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/109a221aa42c4279f4d3b33fc4b96df0bb18bbacd58267b85b6da729d2833125.svg" src="_images/109a221aa42c4279f4d3b33fc4b96df0bb18bbacd58267b85b6da729d2833125.svg" />
+<img alt="_images/e16e158834e932548ff3543e3e9f353f68e8ffd48e340e8175823426d808b64b.svg" src="_images/e16e158834e932548ff3543e3e9f353f68e8ffd48e340e8175823426d808b64b.svg" />
 </div>
 </div>
 </div>
@@ -814,7 +814,7 @@ <h3>A split event<a class="headerlink" href="#a-split-event" title="Link to this
 <input id="sd-tab-item-15" name="sd-tab-set-7" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-15">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/fa2d539bb8f1eea0c7783712cf189b2cedb6859971211d2e3538c1eea0f5350b.svg" src="_images/fa2d539bb8f1eea0c7783712cf189b2cedb6859971211d2e3538c1eea0f5350b.svg" />
+<img alt="_images/ec55914b094a933f6f2b601923a583d60fffe1c7efe551b6faaae6fcf3aec7ab.svg" src="_images/ec55914b094a933f6f2b601923a583d60fffe1c7efe551b6faaae6fcf3aec7ab.svg" />
 </div>
 </div>
 </div>
@@ -855,7 +855,7 @@ <h3>A branch event<a class="headerlink" href="#a-branch-event" title="Link to th
 <input id="sd-tab-item-17" name="sd-tab-set-8" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-17">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/80faeae10043fd01f3cd0585e2bba9e2ee1303386af78bde37d73d87f65b5b89.svg" src="_images/80faeae10043fd01f3cd0585e2bba9e2ee1303386af78bde37d73d87f65b5b89.svg" />
+<img alt="_images/1dae64ccdf0cbf0b0ed93ed417c0962260b44bb908ea079d121d8981e30086eb.svg" src="_images/1dae64ccdf0cbf0b0ed93ed417c0962260b44bb908ea079d121d8981e30086eb.svg" />
 </div>
 </div>
 </div>
@@ -902,7 +902,7 @@ <h2>Multiple ancestors<a class="headerlink" href="#multiple-ancestors" title="Li
 <input id="sd-tab-item-19" name="sd-tab-set-9" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-19">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/5de46ba0aeb3101833842078da0b79b8012f65f42f6c13de0364c4c3d5d49613.svg" src="_images/5de46ba0aeb3101833842078da0b79b8012f65f42f6c13de0364c4c3d5d49613.svg" />
+<img alt="_images/f84b2d4c1ac3026dbf1922893adc6c653d1128789e28290c16ccdf32df03c535.svg" src="_images/f84b2d4c1ac3026dbf1922893adc6c653d1128789e28290c16ccdf32df03c535.svg" />
 </div>
 </div>
 </div>
@@ -957,7 +957,7 @@ <h3>Asymmetric migration<a class="headerlink" href="#asymmetric-migration" title
 <input id="sd-tab-item-21" name="sd-tab-set-10" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-21">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/9333695097ea8cd7974aed01f43a765caebfd767f4843d7d281ed430718e8ba9.svg" src="_images/9333695097ea8cd7974aed01f43a765caebfd767f4843d7d281ed430718e8ba9.svg" />
+<img alt="_images/6434b1c946d1c32ce632a4bcb8458f1caa2da625384f01a34ba4fd31b5feacc1.svg" src="_images/6434b1c946d1c32ce632a4bcb8458f1caa2da625384f01a34ba4fd31b5feacc1.svg" />
 </div>
 </div>
 </div>
@@ -1002,7 +1002,7 @@ <h3>Asymmetric migration<a class="headerlink" href="#asymmetric-migration" title
 <input id="sd-tab-item-23" name="sd-tab-set-11" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-23">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/70317cb544769a3e7f6310ef3679ef589e307e3c1d1da4ad2d9ebc2d90424481.svg" src="_images/70317cb544769a3e7f6310ef3679ef589e307e3c1d1da4ad2d9ebc2d90424481.svg" />
+<img alt="_images/a1bee1f2646f2de6874d0fda85b5aafb3a9253b5d6131443f96d07542782f5d4.svg" src="_images/a1bee1f2646f2de6874d0fda85b5aafb3a9253b5d6131443f96d07542782f5d4.svg" />
 </div>
 </div>
 </div>
@@ -1043,7 +1043,7 @@ <h3>Asymmetric migration<a class="headerlink" href="#asymmetric-migration" title
 <input id="sd-tab-item-25" name="sd-tab-set-12" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-25">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/e8e4ac67dbb64e58297a4e661dea2c5397a56514c4bd63b9c7471c62016fd694.svg" src="_images/e8e4ac67dbb64e58297a4e661dea2c5397a56514c4bd63b9c7471c62016fd694.svg" />
+<img alt="_images/bc226e91c43274555b695e8b64be18c5aee7405dd84e4ad1750d28452f1ebd1c.svg" src="_images/bc226e91c43274555b695e8b64be18c5aee7405dd84e4ad1750d28452f1ebd1c.svg" />
 </div>
 </div>
 </div>
@@ -1100,7 +1100,7 @@ <h3>Symmetric migration<a class="headerlink" href="#symmetric-migration" title="
 <input id="sd-tab-item-27" name="sd-tab-set-13" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-27">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/5139f5ee49c93cf336d079034875465fb38c3e5bd9cb2929932e868078bff92f.svg" src="_images/5139f5ee49c93cf336d079034875465fb38c3e5bd9cb2929932e868078bff92f.svg" />
+<img alt="_images/e9df002179fb6e582b493e491a7cdc2b82f64ef64ea3fbf84e95d2e5a996619e.svg" src="_images/e9df002179fb6e582b493e491a7cdc2b82f64ef64ea3fbf84e95d2e5a996619e.svg" />
 </div>
 </div>
 </div>
@@ -1140,7 +1140,7 @@ <h3>Symmetric migration<a class="headerlink" href="#symmetric-migration" title="
 <input id="sd-tab-item-29" name="sd-tab-set-14" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-29">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/ae663ce4ae65b8e7772f1e00cb8f5f806f325c7a05aee7c3b60488ce8dbf4e89.svg" src="_images/ae663ce4ae65b8e7772f1e00cb8f5f806f325c7a05aee7c3b60488ce8dbf4e89.svg" />
+<img alt="_images/06c74463c88e2efca6214df563e00aca67f727323fd0c4681e01ea90c4b1dfb0.svg" src="_images/06c74463c88e2efca6214df563e00aca67f727323fd0c4681e01ea90c4b1dfb0.svg" />
 </div>
 </div>
 </div>
@@ -1188,7 +1188,7 @@ <h3>Symmetric migration<a class="headerlink" href="#symmetric-migration" title="
 <input id="sd-tab-item-31" name="sd-tab-set-15" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-31">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/c24ab025d2be1c62463cd970f8ede2dadffceae338c0d772e9725ed208b71f2f.svg" src="_images/c24ab025d2be1c62463cd970f8ede2dadffceae338c0d772e9725ed208b71f2f.svg" />
+<img alt="_images/ef59baf2315f4e1cdc4b704d14d76cd76f621ad3b0aa6b3f8b59036035223259.svg" src="_images/ef59baf2315f4e1cdc4b704d14d76cd76f621ad3b0aa6b3f8b59036035223259.svg" />
 </div>
 </div>
 </div>
@@ -1247,7 +1247,7 @@ <h2>A pulse of admixture<a class="headerlink" href="#a-pulse-of-admixture" title
 <input id="sd-tab-item-33" name="sd-tab-set-16" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-33">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/ba94776fd26aca1f63e8959a5dbaffbd7dd8c5272b62a84e09f913ff7a56b198.svg" src="_images/ba94776fd26aca1f63e8959a5dbaffbd7dd8c5272b62a84e09f913ff7a56b198.svg" />
+<img alt="_images/99efc9379290432ebfc8d6fe7b570ebcad216df1769c04401c15ac2e02be422e.svg" src="_images/99efc9379290432ebfc8d6fe7b570ebcad216df1769c04401c15ac2e02be422e.svg" />
 </div>
 </div>
 </div>
@@ -1333,7 +1333,7 @@ <h2>A pulse of admixture<a class="headerlink" href="#a-pulse-of-admixture" title
 <input id="sd-tab-item-35" name="sd-tab-set-17" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-35">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/32457e9f3de524715f458372c93c6726246e3799386134d4653ff097d8db11ca.svg" src="_images/32457e9f3de524715f458372c93c6726246e3799386134d4653ff097d8db11ca.svg" />
+<img alt="_images/6827c21dc326839074b255d8d15153d8b391216916096915ec85893a6a200181.svg" src="_images/6827c21dc326839074b255d8d15153d8b391216916096915ec85893a6a200181.svg" />
 </div>
 </div>
 </div>
@@ -1371,7 +1371,7 @@ <h2>A pulse of admixture<a class="headerlink" href="#a-pulse-of-admixture" title
 <input id="sd-tab-item-37" name="sd-tab-set-18" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-37">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/cc6c7255ce6a74bb8ec5bd9b39e259c72ce851879bfe2684ef403755d580525e.svg" src="_images/cc6c7255ce6a74bb8ec5bd9b39e259c72ce851879bfe2684ef403755d580525e.svg" />
+<img alt="_images/6d39786aa91211e7afd1f2951bc2a7a09cce298b3518a1c64c8a0fa6e23027e6.svg" src="_images/6d39786aa91211e7afd1f2951bc2a7a09cce298b3518a1c64c8a0fa6e23027e6.svg" />
 </div>
 </div>
 </div>
@@ -1414,7 +1414,7 @@ <h2>A pulse of admixture<a class="headerlink" href="#a-pulse-of-admixture" title
 <input id="sd-tab-item-39" name="sd-tab-set-19" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-39">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/15ccf483c46cd19fd9a7af92463da76d09b789afb3a0457eba5ed7178c92d4ff.svg" src="_images/15ccf483c46cd19fd9a7af92463da76d09b789afb3a0457eba5ed7178c92d4ff.svg" />
+<img alt="_images/e252e93e2f01e1c49550b68aace9e6d57b3388c44de8c529346f5ca9b2206560.svg" src="_images/e252e93e2f01e1c49550b68aace9e6d57b3388c44de8c529346f5ca9b2206560.svg" />
 </div>
 </div>
 </div>
@@ -1515,7 +1515,7 @@ <h2>Time units and generation time<a class="headerlink" href="#time-units-and-ge
 <input id="sd-tab-item-41" name="sd-tab-set-20" type="radio">
 <label class="sd-tab-label pt-0" for="sd-tab-item-41">
 Drawing</label><div class="sd-tab-content docutils">
-<img alt="_images/647cec3d5d3e76f699c79a8624fd5ec1a7fa72595eee089925b6f95850f80fef.svg" src="_images/647cec3d5d3e76f699c79a8624fd5ec1a7fa72595eee089925b6f95850f80fef.svg" />
+<img alt="_images/0bb82fcea005469a26e10f6677064d297c65dec94ff80ec041bfea65c3a1f7ed.svg" src="_images/0bb82fcea005469a26e10f6677064d297c65dec94ff80ec041bfea65c3a1f7ed.svg" />
 </div>
 </div>
 </div>