天赐范式第185天·第二篇让漂变开始定量——扫N看选择主导边界摘要补184-2的N侧。有限种群漂变每代注入σ_g/√N噪声选择每代推h²·S。扫N从20到10006个格点50 seedsΔ*均值≈0.005不随N变——选择响应是确定性的Δ*std随N按1/√N缩放从0.00478N20缩到0.00070N1000。信噪比从2.29升到18.09理论边界N*≈3.1SNR1处实际N100时SNR5.57选择可靠主导。选择何时主导完整两面遗传力侧h²0.5 种群侧NN*。一、接续184-2还差N侧第184-2篇回答了选择何时主导的遗传力侧h²0.5时选择力超过环境噪声主导方向且是平滑过渡不是相变。但选择何时主导还有第二侧——种群侧。有限种群有一个遗传力公式管不到的东西漂变。每代繁殖抽样只有N个个体等位基因频率会在抽样时随机漂移注入σ_g/√N量级的噪声。种群越小漂变噪声越大种群足够大时选择信号才能盖过它。184-2答了一半这篇把N侧补上扫N看漂变噪声和选择响应谁主导、边界在哪。二、量纲与预测两个力的量纲漂变噪声≈ σ_g / √N每代注入的抽样噪声选择响应≈ h² · S每代选择的确定性推动边界定义在信噪比1处N* ≈ (σ_g / (h²·S))²预测N N* 时选择主导std小、Δ*确定N N* 时漂变主导std大、Δ*被噪声淹没。本篇S≈0.022N200时与185-1的S≈0.021在同一量级——两篇都用高斯加权选择微小差异来自σ_g实测波动和有限种群噪声。三、实验设计模型与185-1完全一致x g eg’ TARGET β(g_sel − TARGET) v选择机制高斯加权与185-1一致避免跨篇混机制。固定β0.3, σ_e0.02, σ_v0.020, gen500, seeds50, x*0.8, ω0.1, TARGET0.5。扫描N ∈ {20, 50, 100, 200, 500, 1000}六个格点每个格点50个seed取均值±std。四、N扫描结果Nh²Δ*Sσ_g漂变噪声选择响应信噪比200.47730.00592±0.004780.021050.01960.0043790.0100462.29500.50660.00561±0.003580.021200.02050.0028990.0107383.701000.52050.00494±0.001930.022420.02090.0020950.0116725.572000.51280.00549±0.001510.021920.02060.0014540.0112427.735000.52400.00516±0.001190.023310.02100.0009390.01221213.0010000.52210.00522±0.000700.022910.02090.0006610.01196218.09三个观察Δ*均值≈0.005不随N变化0.00494–0.00592无单调趋势。选择响应是确定性力——群体大小不影响方向只影响确定程度。这直接对上了185-1的闭式解Δ*由景观参数和h²决定N不改变Δ*的期望值。Δ*std随N缩小0.00478N20→ 0.00070N1000。50个seed间的离散度就是漂变的指纹。信噪比单调上升SNR 选择响应/漂变噪声 (h²·S)/(σ_g/√N)从2.29N20升到18.09N1000。五、Δ*离散度随N缩放NΔ*均值Δ*stdstd/均值1/√N标度200.005920.004780.8070.2236500.005610.003580.6380.14141000.004940.001930.3900.10002000.005490.001510.2750.07075000.005160.001190.2300.044710000.005220.000700.1340.0316std按1/√N缩放成立。看std/均值0.807 → 0.134与1/√N标度0.2236 → 0.0316同比例收缩——两者比值在3.6–5.1倍区间波动没有随N系统发散。这意味着Δ*的seed间离散度确实是漂变主导的1/√N行为不是别的噪声源。N100后std/均值已压到0.39以下每个seed的Δ*都在均值约40%以内N1000时降到0.134选择结果高度确定。六、选择主导边界N*用大N参考值估算σ_g 0.0209h² 0.5221S 0.02291h²·S 0.011962N* (σ_g/(h²·S))² 3.1信噪比分布NSNR202.29503.701005.572007.7350013.00100018.09理论边界N*≈3.1SNR1处实际扫到的最低N20时SNR已是2.29。这意味着在本实验的参数区σ_g≈0.02、h²·S≈0.012里漂变几乎赢不了选择哪怕20个成员的群落选择信号也已经是漂变噪声的2.3倍。N100时SNR5.57选择可靠主导。N*≈3.1是理论边界但种群大小N必须≥1且实际种群不可能只有3个个体。在本参数区σ_g≈0.02、h²·S≈0.012漂变主导区NN*在生物学上不可达——这是本篇最大的诚实点。N*低的原因是σ_g很小0.0209而h²·S相对大0.012——遗传方差供给少、选择力强漂变的绝对量级σ_g/√N在任何可行N下都压不过选择响应。漂变要主导得σ_g更大或h²·S更小这是下一步扫σ_v×N双网格的活。七、结论问题答案Δ*均值随N变吗不变≈0.005。选择响应是确定性力N只影响确定程度Δ*std怎么随N缩按1/√N缩放0.00478→0.00070std/均值与1/√N同比例收缩漂变何时淹没选择理论边界N*≈3.1SNR1处本参数区N20时SNR已2.29漂变几乎赢不了选择何时可靠主导h²0.5184-2遗传力侧 NN*185-2种群侧叙事弧182-1变异存续条件 σ_v 0183-1选择生效条件 h² 0.5半效界184-2h²0.5是平滑过渡公式全局适用185-1S闭式解从景观先验算出独立预测成立185-2漂变定量化选择何时主导完整两面 遗传力侧(h²0.5) 种群侧(NN*)降调N*≈3.1是σ_v0.02单点扫描的结论。σ_v增大→σ_g增大→N*上移漂变噪声基数变大。要看清漂变主导区需要扫σ_v×N双网格——这是下一步的债。std/均值与1/√N标度同比例收缩比值在3.6–5.1间波动但未严格等于1/√N。偏差来自每格点σ_g实测微差0.0196–0.0210间波动和选择对漂变的非线性压缩不是错误。N20时h²0.4773略低于0.5——小种群下遗传方差估计本身受漂变干扰h²侧边界和N侧边界在20人量级会互相污染解读N20行时要谨慎。单位点模型。多位点、上位效应、连锁不平衡待后续。SNR基于稳态Δ*计算。模拟跑500代到稳态后取值有限世代下Δ*仍在波动SNR是稳态量不是瞬态量。系列还在逐步建设中完善是和伙伴们的努力方向。附录完整代码# -*- coding: utf-8 -*- 天赐范式第185天让漂变开始定量——扫N看选择主导边界 V3.3.23.0 接续184-2h²侧回答选择何时主导补N侧。 有限种群漂变每代注入σ_g/√N噪声选择每代推h²·S——两者相当时选择信号被淹没。 扫N20/50/100/200/500/1000看多seed间Δ*离散度随N怎么缩、选择主导边界N*在哪。 预测N大→std小→选择主导N小→std大→漂变主导 边界N*h²·S ≈ σ_g/√N* → N* ≈ (σ_g/(h²·S))² 选择机制高斯加权与185-1一致 importsysimportmathimportnumpyasnpifhasattr(sys.stdout,reconfigure):sys.stdout.reconfigure(encodingutf-8)PIDTC-185-V3.3.23.0TARGET0.5FITNESS_PEAK0.8FITNESS_WIDTH0.10BETA0.3SIGMA_E0.02N_GENERATIONS500N_SEEDS50SIGMA_V0.020N_GRID[20,50,100,200,500,1000]defbar(title):print(*72)print( title)print(*72)print()defsub(title):print(【title)print(-*72)deffitness(x):returnnp.exp(-(x-FITNESS_PEAK)**2/(2*FITNESS_WIDTH**2))defrun_one(n_pop,seed):rngnp.random.RandomState(seed)genesrng.normal(TARGET,0.01,n_pop)forgeninrange(N_GENERATIONS):phenosgenesrng.normal(0,SIGMA_E,n_pop)fitsfitness(phenos)probsfits/fits.sum()sel_idxrng.choice(n_pop,sizen_pop,pprobs)parent_genesgenes[sel_idx]genesTARGETBETA*(parent_genes-TARGET)rng.normal(0,SIGMA_V,n_pop)var_gfloat(np.var(genes))mean_gfloat(np.mean(genes))h2var_g/(var_gSIGMA_E**2)phenosgenesrng.normal(0,SIGMA_E,n_pop)fitsfitness(phenos)mean_parents_xfloat(np.mean(phenos))weighted_xfloat(np.average(phenos,weightsfits))Sweighted_x-mean_parents_x delta_starmean_g-TARGETreturnh2,delta_star,S,var_g,mean_gdefmain():bar(f{PID}让漂变开始定量——扫N看选择主导边界)print(f模型: xge, gTARGETβ(g_sel-TARGET)v)print(f选择机制: 高斯加权与185-1一致)print(f固定: β{BETA}, σ_e{SIGMA_E}, σ_v{SIGMA_V}, gen{N_GENERATIONS}, seeds{N_SEEDS})print(ffitness峰: x*{FITNESS_PEAK}, ω{FITNESS_WIDTH}, TARGET{TARGET})print(f扫描: N {N_GRID})print(f预测: 漂变噪声≈σ_g/√N, 选择响应≈h²·S, 边界N*≈(σ_g/(h²·S))²)print()sub(N扫描结果多seed均值±std)print(f{N:6s}{h²:8s}{Δ*:12s}{S:10s}{σ_g:8s}{漂变噪声:10s}{选择响应:10s}{信噪比:6s})print(-*80)results[]forn_popinN_GRID:h2_list[]delta_list[]S_list[]var_g_list[]forseedinrange(N_SEEDS):h2,delta,S,var_g,mean_grun_one(n_pop,seed)h2_list.append(h2)delta_list.append(delta)S_list.append(S)var_g_list.append(var_g)h2_meannp.mean(h2_list)delta_meannp.mean(delta_list)delta_stdnp.std(delta_list)S_meannp.mean(S_list)var_g_meannp.mean(var_g_list)sigma_gmath.sqrt(var_g_mean)drift_noisesigma_g/math.sqrt(n_pop)selection_responseh2_mean*S_mean snrselection_response/drift_noiseifabs(drift_noise)1e-10elsefloat(nan)results.append({n_pop:n_pop,h2_mean:h2_mean,delta_mean:delta_mean,delta_std:delta_std,S_mean:S_mean,sigma_g:sigma_g,drift_noise:drift_noise,selection_response:selection_response,snr:snr,})print(f{n_pop:6d}{h2_mean:8.4f}{delta_mean:8.5f}±{delta_std:.5f}{S_mean:8.5f}{sigma_g:8.4f}{drift_noise:10.6f}{selection_response:10.6f}{snr:6.2f})print()sub(漂变 vs 选择Δ*离散度随N缩放)print(f{N:6s}{Δ*均值:10s}{Δ*std:10s}{std/均值:8s}{1/√N标度:10s})print(-*52)forrinresults:cvr[delta_std]/abs(r[delta_mean])ifabs(r[delta_mean])1e-10elsefloat(nan)inv_sqrt_n1.0/math.sqrt(r[n_pop])print(f{r[n_pop]:6d}{r[delta_mean]:10.5f}{r[delta_std]:10.5f}{cv:8.3f}{inv_sqrt_n:10.4f})print()sub(选择主导边界N*)r_refresults[-1]sigma_g_refr_ref[sigma_g]h2_refr_ref[h2_mean]S_refr_ref[S_mean]N_star(sigma_g_ref/(h2_ref*S_ref))**2print(f用大N参考值估算边界)print(f σ_g {sigma_g_ref:.4f})print(f h² {h2_ref:.4f})print(f S {S_ref:.5f})print(f h²·S {h2_ref*S_ref:.6f})print(f N* (σ_g/(h²·S))² {N_star:.1f})print()print(f信噪比随N变化)forrinresults:bar_str█*int(r[snr])ifr[snr]50else█*50print(f N{r[n_pop]:5d}: SNR{r[snr]:6.2f}{bar_str})print()sub(结论)print(f184-2h²侧回答选择何时主导h²0.5平滑过渡)print(f185-2N侧回答选择何时主导)print(f 漂变噪声≈σ_g/√N选择响应≈h²·S)print(f 边界N*≈{N_star:.0f}信噪比1处)print(f NN*时选择主导NN*时漂变主导)print()print(f 选择何时主导完整两面遗传力侧(h²0.5) 种群侧(NN*))if__name____main__:main()天赐范式 V3.3.23.0 · 2026-10-04
天赐范式第185天·第二篇让漂变开始定量——扫N看选择主导边界摘要补184-2的N侧。有限种群漂变每代注入σ_g/√N噪声选择每代推h²·S。扫N从20到10006个格点50 seedsΔ*均值≈0.005不随N变——选择响应是确定性的Δ*std随N按1/√N缩放从0.00478N20缩到0.00070N1000。信噪比从2.29升到18.09理论边界N*≈3.1SNR1处实际N100时SNR5.57选择可靠主导。选择何时主导完整两面遗传力侧h²0.5 种群侧NN*。一、接续184-2还差N侧第184-2篇回答了选择何时主导的遗传力侧h²0.5时选择力超过环境噪声主导方向且是平滑过渡不是相变。但选择何时主导还有第二侧——种群侧。有限种群有一个遗传力公式管不到的东西漂变。每代繁殖抽样只有N个个体等位基因频率会在抽样时随机漂移注入σ_g/√N量级的噪声。种群越小漂变噪声越大种群足够大时选择信号才能盖过它。184-2答了一半这篇把N侧补上扫N看漂变噪声和选择响应谁主导、边界在哪。二、量纲与预测两个力的量纲漂变噪声≈ σ_g / √N每代注入的抽样噪声选择响应≈ h² · S每代选择的确定性推动边界定义在信噪比1处N* ≈ (σ_g / (h²·S))²预测N N* 时选择主导std小、Δ*确定N N* 时漂变主导std大、Δ*被噪声淹没。本篇S≈0.022N200时与185-1的S≈0.021在同一量级——两篇都用高斯加权选择微小差异来自σ_g实测波动和有限种群噪声。三、实验设计模型与185-1完全一致x g eg’ TARGET β(g_sel − TARGET) v选择机制高斯加权与185-1一致避免跨篇混机制。固定β0.3, σ_e0.02, σ_v0.020, gen500, seeds50, x*0.8, ω0.1, TARGET0.5。扫描N ∈ {20, 50, 100, 200, 500, 1000}六个格点每个格点50个seed取均值±std。四、N扫描结果Nh²Δ*Sσ_g漂变噪声选择响应信噪比200.47730.00592±0.004780.021050.01960.0043790.0100462.29500.50660.00561±0.003580.021200.02050.0028990.0107383.701000.52050.00494±0.001930.022420.02090.0020950.0116725.572000.51280.00549±0.001510.021920.02060.0014540.0112427.735000.52400.00516±0.001190.023310.02100.0009390.01221213.0010000.52210.00522±0.000700.022910.02090.0006610.01196218.09三个观察Δ*均值≈0.005不随N变化0.00494–0.00592无单调趋势。选择响应是确定性力——群体大小不影响方向只影响确定程度。这直接对上了185-1的闭式解Δ*由景观参数和h²决定N不改变Δ*的期望值。Δ*std随N缩小0.00478N20→ 0.00070N1000。50个seed间的离散度就是漂变的指纹。信噪比单调上升SNR 选择响应/漂变噪声 (h²·S)/(σ_g/√N)从2.29N20升到18.09N1000。五、Δ*离散度随N缩放NΔ*均值Δ*stdstd/均值1/√N标度200.005920.004780.8070.2236500.005610.003580.6380.14141000.004940.001930.3900.10002000.005490.001510.2750.07075000.005160.001190.2300.044710000.005220.000700.1340.0316std按1/√N缩放成立。看std/均值0.807 → 0.134与1/√N标度0.2236 → 0.0316同比例收缩——两者比值在3.6–5.1倍区间波动没有随N系统发散。这意味着Δ*的seed间离散度确实是漂变主导的1/√N行为不是别的噪声源。N100后std/均值已压到0.39以下每个seed的Δ*都在均值约40%以内N1000时降到0.134选择结果高度确定。六、选择主导边界N*用大N参考值估算σ_g 0.0209h² 0.5221S 0.02291h²·S 0.011962N* (σ_g/(h²·S))² 3.1信噪比分布NSNR202.29503.701005.572007.7350013.00100018.09理论边界N*≈3.1SNR1处实际扫到的最低N20时SNR已是2.29。这意味着在本实验的参数区σ_g≈0.02、h²·S≈0.012里漂变几乎赢不了选择哪怕20个成员的群落选择信号也已经是漂变噪声的2.3倍。N100时SNR5.57选择可靠主导。N*≈3.1是理论边界但种群大小N必须≥1且实际种群不可能只有3个个体。在本参数区σ_g≈0.02、h²·S≈0.012漂变主导区NN*在生物学上不可达——这是本篇最大的诚实点。N*低的原因是σ_g很小0.0209而h²·S相对大0.012——遗传方差供给少、选择力强漂变的绝对量级σ_g/√N在任何可行N下都压不过选择响应。漂变要主导得σ_g更大或h²·S更小这是下一步扫σ_v×N双网格的活。七、结论问题答案Δ*均值随N变吗不变≈0.005。选择响应是确定性力N只影响确定程度Δ*std怎么随N缩按1/√N缩放0.00478→0.00070std/均值与1/√N同比例收缩漂变何时淹没选择理论边界N*≈3.1SNR1处本参数区N20时SNR已2.29漂变几乎赢不了选择何时可靠主导h²0.5184-2遗传力侧 NN*185-2种群侧叙事弧182-1变异存续条件 σ_v 0183-1选择生效条件 h² 0.5半效界184-2h²0.5是平滑过渡公式全局适用185-1S闭式解从景观先验算出独立预测成立185-2漂变定量化选择何时主导完整两面 遗传力侧(h²0.5) 种群侧(NN*)降调N*≈3.1是σ_v0.02单点扫描的结论。σ_v增大→σ_g增大→N*上移漂变噪声基数变大。要看清漂变主导区需要扫σ_v×N双网格——这是下一步的债。std/均值与1/√N标度同比例收缩比值在3.6–5.1间波动但未严格等于1/√N。偏差来自每格点σ_g实测微差0.0196–0.0210间波动和选择对漂变的非线性压缩不是错误。N20时h²0.4773略低于0.5——小种群下遗传方差估计本身受漂变干扰h²侧边界和N侧边界在20人量级会互相污染解读N20行时要谨慎。单位点模型。多位点、上位效应、连锁不平衡待后续。SNR基于稳态Δ*计算。模拟跑500代到稳态后取值有限世代下Δ*仍在波动SNR是稳态量不是瞬态量。系列还在逐步建设中完善是和伙伴们的努力方向。附录完整代码# -*- coding: utf-8 -*- 天赐范式第185天让漂变开始定量——扫N看选择主导边界 V3.3.23.0 接续184-2h²侧回答选择何时主导补N侧。 有限种群漂变每代注入σ_g/√N噪声选择每代推h²·S——两者相当时选择信号被淹没。 扫N20/50/100/200/500/1000看多seed间Δ*离散度随N怎么缩、选择主导边界N*在哪。 预测N大→std小→选择主导N小→std大→漂变主导 边界N*h²·S ≈ σ_g/√N* → N* ≈ (σ_g/(h²·S))² 选择机制高斯加权与185-1一致 importsysimportmathimportnumpyasnpifhasattr(sys.stdout,reconfigure):sys.stdout.reconfigure(encodingutf-8)PIDTC-185-V3.3.23.0TARGET0.5FITNESS_PEAK0.8FITNESS_WIDTH0.10BETA0.3SIGMA_E0.02N_GENERATIONS500N_SEEDS50SIGMA_V0.020N_GRID[20,50,100,200,500,1000]defbar(title):print(*72)print( title)print(*72)print()defsub(title):print(【title)print(-*72)deffitness(x):returnnp.exp(-(x-FITNESS_PEAK)**2/(2*FITNESS_WIDTH**2))defrun_one(n_pop,seed):rngnp.random.RandomState(seed)genesrng.normal(TARGET,0.01,n_pop)forgeninrange(N_GENERATIONS):phenosgenesrng.normal(0,SIGMA_E,n_pop)fitsfitness(phenos)probsfits/fits.sum()sel_idxrng.choice(n_pop,sizen_pop,pprobs)parent_genesgenes[sel_idx]genesTARGETBETA*(parent_genes-TARGET)rng.normal(0,SIGMA_V,n_pop)var_gfloat(np.var(genes))mean_gfloat(np.mean(genes))h2var_g/(var_gSIGMA_E**2)phenosgenesrng.normal(0,SIGMA_E,n_pop)fitsfitness(phenos)mean_parents_xfloat(np.mean(phenos))weighted_xfloat(np.average(phenos,weightsfits))Sweighted_x-mean_parents_x delta_starmean_g-TARGETreturnh2,delta_star,S,var_g,mean_gdefmain():bar(f{PID}让漂变开始定量——扫N看选择主导边界)print(f模型: xge, gTARGETβ(g_sel-TARGET)v)print(f选择机制: 高斯加权与185-1一致)print(f固定: β{BETA}, σ_e{SIGMA_E}, σ_v{SIGMA_V}, gen{N_GENERATIONS}, seeds{N_SEEDS})print(ffitness峰: x*{FITNESS_PEAK}, ω{FITNESS_WIDTH}, TARGET{TARGET})print(f扫描: N {N_GRID})print(f预测: 漂变噪声≈σ_g/√N, 选择响应≈h²·S, 边界N*≈(σ_g/(h²·S))²)print()sub(N扫描结果多seed均值±std)print(f{N:6s}{h²:8s}{Δ*:12s}{S:10s}{σ_g:8s}{漂变噪声:10s}{选择响应:10s}{信噪比:6s})print(-*80)results[]forn_popinN_GRID:h2_list[]delta_list[]S_list[]var_g_list[]forseedinrange(N_SEEDS):h2,delta,S,var_g,mean_grun_one(n_pop,seed)h2_list.append(h2)delta_list.append(delta)S_list.append(S)var_g_list.append(var_g)h2_meannp.mean(h2_list)delta_meannp.mean(delta_list)delta_stdnp.std(delta_list)S_meannp.mean(S_list)var_g_meannp.mean(var_g_list)sigma_gmath.sqrt(var_g_mean)drift_noisesigma_g/math.sqrt(n_pop)selection_responseh2_mean*S_mean snrselection_response/drift_noiseifabs(drift_noise)1e-10elsefloat(nan)results.append({n_pop:n_pop,h2_mean:h2_mean,delta_mean:delta_mean,delta_std:delta_std,S_mean:S_mean,sigma_g:sigma_g,drift_noise:drift_noise,selection_response:selection_response,snr:snr,})print(f{n_pop:6d}{h2_mean:8.4f}{delta_mean:8.5f}±{delta_std:.5f}{S_mean:8.5f}{sigma_g:8.4f}{drift_noise:10.6f}{selection_response:10.6f}{snr:6.2f})print()sub(漂变 vs 选择Δ*离散度随N缩放)print(f{N:6s}{Δ*均值:10s}{Δ*std:10s}{std/均值:8s}{1/√N标度:10s})print(-*52)forrinresults:cvr[delta_std]/abs(r[delta_mean])ifabs(r[delta_mean])1e-10elsefloat(nan)inv_sqrt_n1.0/math.sqrt(r[n_pop])print(f{r[n_pop]:6d}{r[delta_mean]:10.5f}{r[delta_std]:10.5f}{cv:8.3f}{inv_sqrt_n:10.4f})print()sub(选择主导边界N*)r_refresults[-1]sigma_g_refr_ref[sigma_g]h2_refr_ref[h2_mean]S_refr_ref[S_mean]N_star(sigma_g_ref/(h2_ref*S_ref))**2print(f用大N参考值估算边界)print(f σ_g {sigma_g_ref:.4f})print(f h² {h2_ref:.4f})print(f S {S_ref:.5f})print(f h²·S {h2_ref*S_ref:.6f})print(f N* (σ_g/(h²·S))² {N_star:.1f})print()print(f信噪比随N变化)forrinresults:bar_str█*int(r[snr])ifr[snr]50else█*50print(f N{r[n_pop]:5d}: SNR{r[snr]:6.2f}{bar_str})print()sub(结论)print(f184-2h²侧回答选择何时主导h²0.5平滑过渡)print(f185-2N侧回答选择何时主导)print(f 漂变噪声≈σ_g/√N选择响应≈h²·S)print(f 边界N*≈{N_star:.0f}信噪比1处)print(f NN*时选择主导NN*时漂变主导)print()print(f 选择何时主导完整两面遗传力侧(h²0.5) 种群侧(NN*))if__name____main__:main()天赐范式 V3.3.23.0 · 2026-10-04
