拟合具有递减趋势的 nls 函数的问题

问：

作为背景，我根据不同溶解氧浓度下物种的潜在不受影响的部分 （PNAF） 计算了 3 个功能多样性指数。为了拟合回归，我将 nls 函数与发布数据的 peper 提供的公式一起使用。在重现他们的结果时，我使用的拟合与以下代码配合得很好;

globalfit <- nls(PNAF ~ 1/(1 + exp(-(log10(LOEC)-a)/b)),
                 data = global,
                 start = c(a=0.3 , b=0.2))

我使用类似于以下内容的代码计算了每个功能索引的 PNAF

#Functional Divergence of fish
FDiv_fish <- data.frame(Divergence= FD_calc_fish$FDiv, LOEC= AllLOEC_fish)
#Calculate the fraction of functional evenness compared to the functional richness at 100% population
FDiv_fish$Divergence_frac[1] <- FDiv_fish$Divergence[1]/max(FDiv_fish$Divergence)
for (i in 2:nrow(FDiv_fish)) {
  FDiv_fish$Divergence_frac[i] <- FDiv_fish$Divergence[i]/FDiv_fish$Divergence[nrow(FDiv_fish)]
}
#Remove empty rows
FDiv_fish <- na.omit(FDiv_fish)

# Calculate species richness
SRic_fish <- rowSums(pnaf_matrix_fish)
SRic_fish <- data.frame(LOEC=AllLOEC_fish, SRic = SRic_fish)
SRic_fish$SRic_frac <- SRic_fish$SRic/max(SRic_fish$SRic)

函数散度指数的结果数据帧如下

FDiv_fish = {Divergence = c(0.889950737228376, 0.955047157345304, 
0.952619624560615, 0.935368469313814, 0.940003820276155, 0.942700206928084, 
0.942650807180955, 0.940289064256148, 0.943752991360123, 0.941559360809695, 
0.924050406506512, 0.926648389394962, 0.876447636275341, 0.881548684676512, 
0.886245224649011, 0.88218834971409, 0.885314645756991, 0.881492706719018, 
0.876662397962403, 0.886349294318137, 0.883035022314938, 0.8848327450232, 
0.881672831746863, 0.884156297551429, 0.881140906361141, 0.883534593605944, 
0.885833771865729, 0.88804392997383, 0.891027945817535, 0.888186735006869, 
0.893358872293167, 0.886332319236113, 0.888904363556696, 0.887038353743163, 
0.884779304420887, 0.897837333190895, 0.894509967650634, 0.891991192039641, 
0.899398165601533, 0.89549768133025, 0.885348372920148, 0.883072158209693, 
0.880708851749932, 0.870967680069655, 0.872686632273436, 0.870231057490782, 
0.871863360688521, 0.873455110028267, 0.888942354125257, 0.882187190419575, 
0.88359490643209, 0.832093698279846, 0.833758685259681, 0.837055666849556, 
0.838621975644644, 0.84572076038212, 0.853563980765286, 0.852846371924774, 
0.848690020275423, 0.848019579107283, 0.897076657728166, 0.886592898915272, 
0.875127667801321, 0.872745593426437, 0.870399511052835, 0.873366955360124, 
0.864058267778409, 0.852842506107893, 0.854601294578928, 0.852417777332101, 
0.854148580874727, 0.852008859522321, 0.854982653095199, 0.853592877986531, 
0.852255836650848, 0.844261486012797, 0.842393713964801, 0.851535546465613, 
0.845919707924595, 0.83799275396368, 0.839680366487134, 0.848107377439518, 
0.850662066070129, 0.843754962494148, 0.840898540618949, 0.839502768752552, 
0.841098849929625, 0.836293864179716, 0.831588394725384, 0.828942721595275, 
0.831778862465456, 0.827309791131041, 0.822929138401967, 0.82559644603514, 
0.823170938369431, 0.820778350271261, 0.818418016069642, 0.816089287920916, 
0.818746480527328, 0.81984077135057, 0.817565361142596, 0.819146561499075, 
0.820075084732484, 0.820993582920095, 0.820910837777695, 0.820524854216395, 
0.820811742816053, 0.822601708617993, 0.822873768873091, 0.823752214457896, 
0.82401613553359, 0.824880160298616, 0.825735443483524, 0.825986203258117, 
0.826234629738616, 0.826480755340803, 0.827312025301094, 0.827550864133838, 
0.832160021463369, 0.822561048178852, 0.81328819769379), LOEC = c(1.67053607, 
1.75484884, 1.80915198, 1.83058743, 1.86345512, 1.86774221, 1.8720293, 
1.89060669, 1.89489378, 1.90775505, 1.9149002, 1.95634207, 1.96920334, 
2.000642, 2.00778715, 2.02636454, 2.07780962, 2.0863838, 2.09495798, 
2.09924507, 2.11210634, 2.13068373, 2.16640948, 2.19070299, 2.21070941, 
2.21213844, 2.22785777, 2.23357389, 2.26929964, 2.27501576, 2.27644479, 
2.3578995, 2.36075756, 2.36790271, 2.39362525, 2.51366377, 2.51937989, 
2.69086349, 2.75945693, 2.83233746, 2.85806, 2.8723503, 2.91236314, 
2.93379859, 2.93951471, 3.08384674, 3.13957891, 3.35107535, 3.40394946, 
3.43967521, 3.44539133, 3.50826865, 3.59829754, 3.63973941, 3.65117165, 
3.74834569, 3.95698407, 4.00414206, 4.03558072, 4.03986781, 4.1298967, 
4.21992559, 4.24136104, 4.2727997, 4.39426725, 4.40712852, 4.50716062, 
4.52287995, 4.58004115, 4.58861533, 4.71008288, 4.71436997, 4.75724087, 
4.77010214, 4.8015408, 4.81011498, 4.83440849, 4.84155364, 4.85155685, 
4.95158895, 5.10449516, 5.14022091, 5.14736606, 5.16451442, 5.25311428, 
5.28598197, 5.29312712, 5.38315601, 5.67610716, 5.71612, 5.72326515, 
5.77471023, 5.78900053, 6.00764212, 6.02621951, 6.08623877, 6.13196773, 
6.14768706, 6.16197736, 6.18341281, 6.20913535, 6.41062858, 6.58068315, 
6.59354442, 6.68071525, 6.70786682, 6.72215712, 6.85076982, 7.02511148, 
7.04368887, 7.45810757, 7.5166978, 7.55099452, 7.94254874, 8.00113897, 
8.02114539, 8.07116144, 8.1026001, 8.56274776, 9.52162689, 10.24042898
), Divergence_frac = c(1.09426245179996, 1.17430347575865, 1.17131863865961, 
1.1501070247499, 1.15580654304549, 1.15912195652324, 1.15906121575844, 
1.15615727232055, 1.16041643544845, 1.15771919902396, 1.13619060147043, 
1.13938501999983, 1.0776593571143, 1.08393148600494, 1.0897062408653, 
1.08471800305928, 1.0885620229919, 1.08386265682772, 1.07792342302313, 
1.0898342024777, 1.08575905173458, 1.08796948920725, 1.0840841343167, 
1.08713774533873, 1.08343009139904, 1.08637331281992, 1.08920032822025, 
1.09191788654012, 1.09558696209313, 1.09209347624307, 1.09845301435141, 
1.08981333031692, 1.09297585539459, 1.0906814537067, 1.08790377990216, 
1.10395962432119, 1.0998683740735, 1.09677134694568, 1.10587878706702, 
1.10108284353514, 1.08860349311683, 1.08580471315554, 1.08289884723192, 
1.07092133211748, 1.07303491523433, 1.07001559835549, 1.07202263989669, 
1.07397981736989, 1.09302256770232, 1.08471657761807, 1.08644747204947, 
1.02312280030545, 1.02517002905481, 1.02922391991321, 1.0311498162923, 
1.03987831469865, 1.0495221536298, 1.04863979871238, 1.04352924668281, 
1.04270488802368, 1.10302431570011, 1.09013373294897, 1.07603635498817, 
1.07310741247844, 1.07022272488522, 1.07387142446761, 1.06242568160781, 
1.04863504539506, 1.05079761024725, 1.04811280890251, 1.05024096414629, 
1.04761001320114, 1.05126651969085, 1.04955768497198, 1.04791369045752, 
1.03808402532686, 1.035787456837, 1.04702803862183, 1.04012293590801, 
1.03037614014312, 1.03245118872767, 1.04281284278373, 1.04595402771406, 
1.03746121594627, 1.03394902692976, 1.03223281873891, 1.0341953225372, 
1.02828722530483, 1.02250149096407, 1.01924843363752, 1.02273568560825, 
1.01724062082422, 1.01185427347343, 1.01513393207506, 1.01215158501459, 
1.00920971507851, 1.00630750377344, 1.00344415452612, 1.00671137592924, 
1.00805689013484, 1.00525909937084, 1.00720330606284, 1.00834499634685, 
1.00947436007083, 1.0093726185939, 1.00889802230393, 1.00925077376457, 
1.01145167352805, 1.0117861924057, 1.01286630839323, 1.01319081952772, 
1.01425320401513, 1.01530484006165, 1.01561316837049, 1.0159186277159, 
1.01622125795557, 1.01724336790706, 1.01753703850676, 1.02320434972878, 
1.01140167841038, 1), category = c("LOEC<3.51", "LOEC<3.51", 
"LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", 
"LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", 
"LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", 
"LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", 
"LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", 
"LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", 
"LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", 
"LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", 
"LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", 
"LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", "LOEC<3.51", 
"LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", 
"LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", 
"LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", 
"LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", 
"LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", 
"LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", 
"LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", 
"LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", 
"LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", 
"LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", 
"LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", 
"LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", 
"LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", 
"LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51", "LOEC>=3.51")))}

当尝试将用于 SSD 曲线的公式与功能多样性指数的结果应用时，我有第三个数字，它显示发散度增加（当溶解氧矛盾减少时），在这种情况下，这转化为递减趋势。我似乎找不到一种方法来使 nls 建模适用于这个。

这是我到目前为止尝试过的代码

# PNAF of Functional richness
nls_FRic_fish <- nls(Richness_frac ~ 1/(1 + exp(-(log10(LOEC)-a)/b)),
                     data = FRic_fish,
                     start = c(a=0.3 , b=0.1))
# PNAF of Functional Evenness
nls_FEve_fish <- nls(Evenness_frac ~ 1/(1 + exp(-(log10(LOEC)-a)/b)),
                     data = filter(FEve_fish, LOEC>=3),
                     start = c(a=0.3 , b=0.1),
                     trace=TRUE)
# PNAF of Functional Divergence
nls_FDiv_fish <- nls(Divergence_frac ~ log(1/(1 + exp(-(log10(LOEC)-a)/b))),
                     data = FDiv_fish,
                     start = c(a=0.3 , b=0.1),
                     trace = TRUE)  
# Create a new variable to categorize LOEC values (identified 2 main behaviours)
FEve_fish$category <- ifelse(FEve_fish$LOEC < 3, "LOEC<3", "LOEC>=3")
FDiv_fish$category <- ifelse(FDiv_fish$LOEC < 3.51, "LOEC<3.51", "LOEC>=3.51")
# Plot
tiff('scatter.fish.tiff', width = 12, height = 4, units = 'in', res = 300)
plot1 <- ggplot(FRic_fish, aes(x = LOEC, y = Richness_frac)) +
      geom_point(size = 0.8) +
      geom_function(fun= function(x) 1/(1 + exp(-(log10(x)-coef(nls_FRic_fish)['a'])/coef(nls_FRic_fish)['b'])),
                       color="blue",
                       size=0.4) +
      labs(x = expression("Dissolved oxygen concentration " (~ mgO[2] ~ L^{-1})), y = "PNAF of functional richness") +
      xlim(0, 10.5) +
      theme_bw() +
      theme(panel.border = element_blank())
plot2 <- ggplot(FEve_fish, aes(x = LOEC, y = Evenness_frac)) +
      geom_point(size = 0.8) +
      geom_function(fun= function(x) 1/(1 + exp(-(log10(x)-coef(nls_FEve_fish)['a'])/coef(nls_FEve_fish)['b'])),
                    color="blue",
                    size=0.4) +
      labs(x = expression("Dissolved oxygen concentration " (~ mgO[2] ~ L^{-1})), y = "PNAF of functional evenness") +
       xlim(0,10.5) +
       theme_bw() +
       theme(panel.border = element_blank())
plot3 <- ggplot(FDiv_fish, aes(x = LOEC, y = Divergence_frac)) +
      geom_point(size = 0.8) +
      geom_function(fun= function(x) 1/(1 + exp(-(log10(x)-coef(nls_FDiv_fish)['a'])/coef(nls_FDiv_fish)['b'])),
                    color="blue",
                    size=0.4) +
      labs(x = expression("Dissolved oxygen concentration " (~ mgO[2] ~ L^{-1})), y = "PNAF of functional divergence") +
      xlim(0,10.5) +
      theme_bw() +
      theme(panel.border = element_blank())
grid.arrange(plot1, plot2, plot3, ncol = 3)
dev.off()

当尝试生成nls_SDiv_fish模型时，通常会弹出错误，例如 “阶跃因子 0.000488281 降低到 0.000976562 的'minFactor'以下”、“奇异梯度”、“初始参数估计时的奇异梯度矩阵”等。

我尝试使用不同的起始参数，包括负值，我尝试使用不同的算法和不同版本的 nls（nls2 和 nlsLM），但没有解决方案。 有谁知道如何解决这个问题？ 告诉我您是否需要查看我的更多代码。