Using a monotone single-index model to stabilize the propensity score in missing data problems and causal inference

The augmented inverse weighting method is one of the most popular methods for estimating the mean of the response in causal inference and missing data problems. An important component of this method is the propensity score. Popular parametric models for the propensity score include the logistic, probit, and complementary log-log models. A common feature of these models is that the propensity score is a monotonic function of a linear combination of the explanatory variables. To avoid the need to choose a model, we model the propensity score via a semiparametric single-index model, in which the score is an unknown monotonic nondecreasing function of the given single index. Under this new model, the augmented inverse weighting estimator (AIWE) of the mean of the response is asymptotically linear, semiparametrically efficient, and more robust than existing estimators. Moreover, we have made a surprising observation. The inverse probability weighting and AIWEs based on a correctly specified parametric model may have worse performance than their counterparts based on a nonparametric model. A heuristic explanation of this phenomenon is provided. A real-data example is used to illustrate the proposed methods.     

补脾益肾方联合温针灸治疗重症肌无力疗效及对患者免疫功能的影响

目的:探讨补脾益肾方联合温针灸治疗对重症肌无力(MG)疗效及对免疫功能的影响。方法:随机分配84例MG病例为西药组和针药组,每组各42例,西药组给予常规西药治疗,即泼尼松片中剂量冲击,小剂量隔日维持治疗,针药组基于以上用药基础给予补脾益肾方联合温针灸治疗,治疗3个月后,统计两组治疗前后的中医证候积分,评估两组中医证候疗效,对比治疗前后的颈部血管流速、T淋巴细胞亚群水平和血清可溶性白细胞介素6受体水平。结果:治疗后,两组中医证候积分显著降低,针药组的变化幅度大于西药组(P<0.05); 针药组的中医证候总有效率低于西药组(P<0.05); 治疗后,两组颈内动脉(ICA)、颈总动脉(CCA)、颈外动脉(ECA)显著提高(P<0.05),两组T淋巴细胞中CD₃⁺、CD₄⁺亚群所占比和CD₈⁺、CD₄⁺比值显著降低(P<0.05),两组血清slL-6R水平均显著降低(P<0.05),以上指标针药组变化幅度大于西药组(P<0.05)。结论:补脾益肾方联合温针灸治疗能缓解MG患者的中医证候症状,提高疗效,促进其颈部血管循环,纠正患者自身机体免疫功能紊乱。     

浅谈“从温治咳”

咳嗽病因病机复杂多变,宣降失司、肺气上逆是发病的关键。外感咳嗽,辛温与宣降并用,驱邪理肺,宣畅气机,则咳止;内伤致咳,温补肺脾肾三脏,通调水道,排除多余水液,使痰无由生,又可调畅气机,从而减少咳嗽;感染后咳嗽为本虚标实,宜重温阳润肺,则余邪自散,咳嗽得止;素体阳虚者,当温补脾肾,使邪气无由生,咳嗽无由发。因此,对于临床常见症状咳嗽的治疗,应重视温法的应用,然切记以正确辨证为前提,不可一味温补。     

“治未病”思想在老年高血压病防治中的应用探讨

老年高血压病以肾气亏虚为主要病机,具有特殊的发病基础、临床症状、传变规律和预后。以"治未病"思想为指导,在老年高血压病发生、发展、预后的各个阶段进行提前干预,有利于扶助正气,增强抗病能力,延缓病情进展。具体而言,未病之时,应通过调整生活方式、服用中药保养和培补肾气,做到未病先防。已病之时,既病防变,阴阳俱虚者,治以补益肾气,方选肾气丸加减;肾阴虚者,治以滋阴补肾,方选左归丸合天麻钩藤饮加减;肾阳虚者,治以温补肾阳,方选右归丸加减。疾病初愈之时,继续以中药补肾虚、调气血,同时避免六淫邪气与情志内伤对机体的损害,以防疾病复发。     

疏风温阳法治疗慢性肾脏病蛋白尿的经验

目的本文介绍了治疗反复发作的慢性肾脏病蛋白尿的经验。方法蛋白尿是加重肾损害的独立危险因素,是精微物质外泄的表现,是治疗的重点和难点。作者认为阳气不足,感受风邪,是形成蛋白尿的原因,提出了疏风温阳法。首先阐释了疏风温阳法治疗蛋白尿和水肿的病因病机,以及疏风温阳法在具体应用中,如何应用疏风、温阳药物的用药经验,并举病案进一步说明临床应用此方法治疗的诊疗过程和治疗效果。结果总结了治疗蛋白尿的临证经验。结论疏风温阳法治疗慢性肾脏病蛋白尿疗效确切,为慢性肾脏病蛋白尿的治疗提供方法。     

蒙医温针治疗赫依偏盛型失眠症的随机对照试验

目的评价蒙医温针治疗赫依偏盛型失眠症的近期疗效及安全性。方法将80例赫依偏盛型失眠症患者随机分为治疗组和对照组各40例。治疗组给予蒙医温针治疗,对照组采用Streitberger针进行安慰剂针刺。观察2组治疗前后失眠严重程度指数(ISI)量表评分及睡眠脑电图的变化情况。结果治疗组治疗前后ISI评分有显著性差异(P<0.05);治疗组治疗后睡眠总时间延长、睡眠潜伏期缩短、睡眠效率相应提高,且睡眠结构有所变化,即N1期睡眠比例减少,REM睡眠比例增多(均P<0.05)。组间比较,除N2期睡眠及N3+N4期睡眠时间无差异,其余睡眠参数差异均具有统计学意义(均P<0.05)。结论蒙医温针可改善赫依偏盛型失眠患者的睡眠质量,调节失眠症患者睡眠结构及睡眠进程,且安全性高。     

温针灸阳陵泉穴治疗膝关节骨性关节炎临床疗效观察

目的:观察温针灸阳陵泉穴治疗膝关节骨性关节炎的临床疗效。方法:将2015年1月至2019年1月本院收治的膝关节骨性关节炎患者120例,根据随机数字表法分为对照组和观察组,每组60例。对照组给予等速肌力训练治疗,观察组在对照组的基础上加用温针灸阳陵泉穴治疗。观察两组患者膝关节屈曲度、伸直度,白细胞介素(interleukin,IL)-6及IL-18水平,VAS评分及膝关节症状和功能评分。结果:观察组治疗后屈曲度及伸直度均高于对照组,差异有统计学意义(P<0.05);观察组治疗后IL-6及IL-18水平均低于对照组,差异有统计学意义(P<0.05);观察组治疗后VAS评分低于对照组,差异有统计学意义(P<0.05);观察组治疗后症状和功能评分高于对照组,差异有统计学意义(P<0.05);观察组有效率95.0%,对照组有效率83.3%,观察组有效率高于对照组,差异有统计学意义(P<0.05)。结论:温针灸阳陵泉穴治疗膝关节骨性关节炎,可有效改善患者膝关节活动度,降低炎症因子,减轻疼痛,提高临床疗效。     

“阳化气，阴成形”：卵巢癌的中医证治

卵巢癌属于妇科恶性肿瘤之一,其发病率逐年上升趋势,属中医的"癥瘕"范畴。秉承《素问》"阳化气,阴成形"之旨来探讨卵巢癌的病机及治疗,认为"阳化气"不足,"阴成形"太过为卵巢癌发病的一个重要原因,并由此提出温补阳气的卵巢癌治疗原则,指出该原则应贯穿整个卵巢癌治疗的始终。     

Low potential for evolutionary rescue from climate change in a tropical fish

Climate change is increasing global temperatures and intensifying the frequency and severity of extreme heat waves. How organisms will cope with these changes depends on their inherent thermal tolerance, acclimation capacity, and ability for evolutionary adaptation. Yet, the potential for adaptation of upper thermal tolerance in vertebrates is largely unknown. We artificially selected offspring from wild-caught zebrafish (Danio rerio) to increase (Up-selected) or decrease (Down-selected) upper thermal tolerance over six generations. Selection to increase upper thermal tolerance was also performed on warm-acclimated fish to test whether plasticity in the form of inducible warm tolerance also evolved. Upper thermal tolerance responded to selection in the predicted directions. However, compared to the control lines, the response was stronger in the Down-selected than in the Up-selected lines in which evolution toward higher upper thermal tolerance was slow (0.04 ± 0.008 °C per generation). Furthermore, the scope for plasticity resulting from warm acclimation decreased in the Up-selected lines. These results suggest the existence of a hard limit in upper thermal tolerance. Considering the rate at which global temperatures are increasing, the observed rates of adaptation and the possible hard limit in upper thermal tolerance suggest a low potential for evolutionary rescue in tropical fish living at the edge of their thermal limits.

Globally, both mean and extreme environmental temperatures are increasing due to climate change with mean temperatures predicted to increase by 0.3–4.8 °C by the end of the century (1, 2). Aquatic ectotherms are particularly vulnerable to rising temperatures as their body temperature closely tracks the environmental temperature (3). These organisms can avoid thermal stress by migrating to cooler waters, acclimating, and/or adapting genetically (4–6). For species with a limited dispersal ability (e.g., species from shallow freshwater habitats; ref. 7), acclimation and evolutionary adaptation are the only possible strategies. Furthermore, for ectotherms living at the edge of their upper thermal limits, an increase in extreme temperatures may generate temperature peaks that exceed physiological limits and cause high mortality (5, 8–10). Although this is expected to cause strong selection toward higher upper thermal tolerance, it is largely unknown, particularly within vertebrates, whether and at what rate organisms may adapt by evolving their thermal limits (11–14). These are important issues because constrained or limited evolvability (15) of upper thermal tolerance could lead to population extinctions as climate change increases the severity of heat waves.Ectotherms can also increase their thermal limits through physiological and biochemical adjustments, in a process known as thermal acclimation when they are exposed to elevated temperatures for a period of time (16, 17). Thermal acclimation, sometimes called thermal compensation, is here used interchangeably with the term physiological plasticity as outlined by Seebacher et al. (18). In the wild, individuals may experience days or weeks of warmer temperatures prior to a thermal extreme. Through physiological plasticity, the severity of an ensuing thermal extreme may be reduced, thus increasing the chance for survival (19). Furthermore, in some cases, adaptation can be accelerated by plasticity (20–22). This requires that the physiological mechanisms responsible for acclimation are also (at least partly) involved in the acute response; that is, that there is a positive genetic correlation between physiological plasticity and (acute) upper thermal tolerance. It is therefore crucial to quantify the evolutionary potential of upper thermal tolerance of fish populations threatened by climate change (23, 24) and to understand the link between the evolutionary response of upper thermal tolerance and physiological plasticity.Previously detected evolution of upper thermal tolerance generally points toward a slow process (12, 13, 25–31). However, estimates of the evolutionary potential in upper thermal tolerance mostly come from studies on Drosophila (12, 25, 27, 32), and empirical evidence in aquatic ectotherms and specifically vertebrates is limited. The few studies that have been performed on fish show disparate responses to selection on heat tolerance even within the same species. Baer and Travis (33) detected no response to selection yet Doyle et al. (34) and Klerks et al. (28) detected selection responses with heritabilities of 0.2 in killifish (Heterandria formosa). Despite the typical asymmetry of thermal performance curves (3, 35), studies in vertebrates are limited to unidirectional estimates of evolutionary potential (28, 31, 33) or do not account for the direction of evolution when estimating heritability in upper thermal tolerance from breeding designs (36, 37). Furthermore, while several studies have found that populations with different thermal histories have evolved different levels of heat tolerance (29–31), we still lack a good understanding of how physiological plasticity within a generation, in response to a short heat exposure, interacts with genetic changes during evolution of thermal tolerance.To investigate possible asymmetry in the evolutionary potential of upper thermal tolerance in a vertebrate species, we artificially selected offspring of wild-caught zebrafish (Danio rerio) to increase and decrease upper thermal tolerance for six generations. Furthermore, to disentangle the contribution of acclimation from the genetic response to increase upper thermal tolerance, we selected two lines that were exposed to a period of warm acclimation prior to a thermal challenge. The size (>20,000 phenotyped fish) and duration (six generations) of this study are unique in a vertebrate species for a climate change-relevant selection experiment, and the results provide critical and robust information on how tropical fish may adapt to a changing climate.Being a freshwater and tropical species, zebrafish are likely to be especially vulnerable to climate change (7, 38). In the wild, zebrafish can already be found living only a few degrees below their thermal limits (17, 39) and live in shallow streams and pools (40) that have the potential to rapidly warm during heat waves. Zebrafish therefore represent a species living at the edge of its thermal limit in which rapid adaptation of thermal tolerance would be particularly beneficial for its survival. Wild-caught zebrafish originating from different sites in West Bengal, India (17, 40), were used to maximize the genetic diversity of the parental population. These wild-caught zebrafish (n = 2,265) served as parents of the starting F₀ generation (n = 1,800) on which we selected upper thermal tolerance for six generations. Upper thermal tolerance was measured as the critical thermal maximum (CT_max), a commonly used measure of an organism’s acute upper thermal tolerance (16, 41). CT_max is defined as the temperature at which an individual loses equilibrium (i.e., uncontrolled and disorganized swimming in zebrafish; ref. 42) during thermal ramping. Measuring CT_max is rapid, repeatable, and does not appear to harm zebrafish (42). CT_max is ecologically relevant because it is highly correlated with both tolerance to slow warming (43) and to the upper temperature range boundaries of wild aquatic ectotherms (9).Our selection experiment consisted of four treatment groups (Up-selected, Down-selected, Acclimated Up-selected, and Control) with two replicate lines in each treatment. We established these lines by selecting fish on their CT_max in the F₀ generation with each line consisting of 150 individuals (see Methods for further details of F₀ generation). The offspring of those fish formed the F₁ generation that consisted of 450 offspring in each line. At each generation, the Up, Down, and Control lines were all held at optimal temperature (28 °C) (39), whereas the Acclimated Up-selected lines were acclimated to a supraoptimal temperature (32 °C) for 2 wk prior to selection (17). From the F₁ to F₆ generations, we measured CT_max for all 450 fish in each line and selected the 33% with the highest CT_max in the Up-selected and in the Acclimated Up-selected lines, and the 33% with the lowest CT_max in the Down-selected lines. In the Control lines, 150 fish were randomly selected, measured, and retained. Thus, CT_max was measured on a total of 3,000 fish per generation and 150 individuals remained in each of the eight lines after selection, forming the parents for the next generation. The nonselected lines (Control) represented a control for the Up-selected and Down-selected lines, while the Up-selected lines represented a control for the Acclimated Up-selected lines, because these two treatments solely differed by the acclimation period to which the latter were exposed before selection. Thus, differences in CT_max between Up-selected and Acclimated Up-selected lines represent the contribution of physiological plasticity to upper thermal tolerance. If the difference between these two treatments increases during selection, it would suggest that plasticity increases during adaptation to higher CT_max (i.e., the slope the reaction norm describing the relationship between CT_max and acclimation temperature would become steeper).After six generations of selection, upper thermal tolerance had evolved in both the Up-selected and the Down-selected lines (Fig. 1). In the Up-selected lines, upper thermal tolerance increased by 0.22 ± 0.05 °C ($\bar{x}$ ± 1 SE) compared to the Control lines whereas the Down-selected lines displayed a mean upper thermal tolerance 0.74 ± 0.05 °C lower than the Control (Fig. 1B; estimates for replicated lines combined). The asymmetry in the response to selection was confirmed by the estimated realized heritability, which was more than twice as high in the Down-selected lines (h² = 0.24; 95% CI: 0.19–0.28) than in the Up-selected lines (h² = 0.10; 95% CI: 0.05–0.14; Fig. 2).Open in a separate windowFig. 1.Upper thermal tolerance (CT_max) of wild-caught zebrafish over six episodes of selection. Duplicated lines were selected for increased (Up-selected, orange lines and triangles) and decreased (Down-selected, blue lines and squares) upper thermal tolerance. In addition, we had two Control lines (green dashed lines and diamonds). The Up, Down, and Control lines were all acclimated to a temperature of 28 °C. In addition, two lines were selected for increased upper thermal tolerance after 2 wk of warm acclimation at 32 °C (Acclimated Up-selected, red lines and circles). At each generation, the mean and 95% CIs of each line are shown (n ∼ 450 individuals per line). (A) Absolute upper thermal tolerance values. (B) The response to selection in the Up and Down lines centered on the Control lines (dashed green line). Difference between Up-selected and Acclimated-Up lines are shown in Fig. 3. The rate of adaptation (°C per generation) is reported for each treatment using estimates obtained from linear mixed effects models using the Control-centered response in the Up-selected and Down-selected lines and the absolute response for the Acclimated-Up lines (SE = ±0.01 °C in all lines).Open in a separate windowFig. 2.Realized heritability (h²) of upper thermal tolerance (CT_max) in wild-caught zebrafish. The realized heritability was estimated for each treatment as the slope of the regression of the cumulative response to selection on the cumulative selection differential using mixed effect models passing through the origin with replicate as a random effect. Slopes are presented with their 95% CIs (shaded area) for the Down-selected lines (blue) and Up-selected lines (orange). Data points represent the mean of each replicate line (n ∼ 450) over six generations of selection. Average selection differentials are 0.57 (Down) and 0.39 (Up), respectively, see SI Appendix, Table S1 for more information.At the start of the experiment (F₀), warm acclimation (32 °C) increased thermal tolerance by 1.31 ± 0.05 °C (difference in CT_max between the Up-selected and Acclimated Up-selected lines in Figs. 1A and ​and3),3), which translates to a 0.3 °C change in CT_max per 1 °C of warming. In the last generation, the effect of acclimation had decreased by 25%, with the Acclimated-Up lines having an average CT_max 0.98 ± 0.04 °C higher than the Up lines (Fig. 3). This suggests that, despite a slight increase in CT_max in the Acclimated Up-selected lines during selection, the contribution of plasticity decreased over the course of the experiment.Open in a separate windowFig. 3.Contribution of acclimation to the upper thermal tolerance in the Acclimated-Up selected lines at each generation of selection. The contribution of acclimation was estimated as the difference between the Up and Acclimated-Up selected lines. Points and error bars represent the estimates (±SE) from a linear mixed effects model with CT_max as the response variable; Treatment (factor with two levels: Up and Acclimated Up), Generation (factor with seven levels), and their interaction as the predictor variables; and replicate line as a random factor.During the experiment, the phenotypic variation of CT_max that was left-skewed at F₀ increased in the Down-selected lines and decreased in the Up-selected lines (Fig. 4). At the F₆ generation, phenotypic variance was four times lower in the Up-selected lines (0.09 ± 0.01 and 0.12 ± 0.02 °C²; variance presented for each replicate line separately and SE obtained by nonparametric bootstrapping) than in the Down-selected lines (0.41 ± 0.03 and 0.50 ± 0.04 °C²), which had doubled since the start of the experiment (F₀: 0.20 ± 0.01 °C², see SI Appendix, Fig. S1). In the Acclimated Up-selected lines, the phenotypic variance that was already much lower than the Control at the F₀ also decreased and reached 0.06 ± 0.01 °C² and 0.07 ± 0.01 °C² for the two replicates at the last generation (SI Appendix, Fig. S1).Open in a separate windowFig. 4.Distribution of upper thermal tolerance (CT_max) in selected lines. (A) Distribution for each line at each generation (F₀ to F₆). In the F₀ generation, histograms show the preselection distribution in gray for the nonacclimated fish, in dark green for the Control lines, and in red for the Acclimated-Up fish. In all subsequent generations the Down-selected lines are in blue, the Up-selected lines in yellow, the Control lines in dark green, and Acclimated-up lines in red. All treatments use two shades, one for each replicate line. Dashed lines represent the mean CT_max for each line (n ∼ 450 individuals). (B) Distribution of upper thermal tolerance at the start (F₀, in gray) and the end (F₆, in blue and yellow) of the experiment for the Up-selected and Down-selected lines. The dashed gray line represents the mean of the Up-selected and Down-selected lines in the F₀ generation preselection (n ∼ 900 individuals). Dashed blue and yellow lines represent the mean CT_max for Up and Down-selected lines for the F₆ generation (n ∼ 450 individuals).Together with the asymmetrical response to selection and the lower response of the Acclimated Up-selected lines, these changes in phenotypic variance suggest the existence of a hard-upper limit for thermal tolerance (e.g., major protein denaturation (44), similar to the “concrete ceiling” for physiological responses to warming (14)). Such a hard-upper limit is expected to generate a nonlinear mapping of the genetic and environmental effects on the phenotypic expression of CT_max. This nonlinearity will affect the phenotypic variance of CT_max when mean CT_max approaches its upper limit (SI Appendix, Fig. S2A). For example, with directional selection toward higher CT_max, genetic changes in upper thermal tolerance will translate into progressively smaller phenotypic changes. Similarly, warm acclimation that shifts CT_max upwards will also decrease phenotypic variation in CT_max (see differences in phenotypic variance between control and Acclimated lines at the F₀). This hard ceiling can also explain why an evolutionary increase in CT_max reduces the magnitude of physiological plasticity in CT_max achieved after a period of acclimation (Fig. 3 and see SI Appendix, Fig. S2B). If the sum of the genetic and plastic contributions to CT_max cannot exceed a ceiling value, this should generate a zero-sum gain between the genetic and plastic determinants of thermal tolerance. An increase in the genetic contribution to CT_max via selection should thus decrease the contribution of plasticity. Selection for a higher CT_max should therefore negatively affect the slope of the reaction norm of thermal acclimation because acclimation will increase CT_max more strongly at low than high acclimation temperature (SI Appendix, Fig. S2B).To test this hypothesis, we measured CT_max in all selected lines at the final generation (F₆) after acclimation to 24, 28, and 32 °C. At all three acclimation temperatures, the Acclimated-Up lines did not differ from the Up-selected lines (average difference 0.14 ± 0.08 °C; 0.12 ± 0.09 °C; 0.14 ± 0.09 °C; at 24, 28, and 32 °C respectively; Fig. 5). This suggests that warm acclimation prior to selection did not affect the response to selection. However, considering the within-treatment differences in CT_max between fish acclimated to 28 and 32 °C, we show that the gain in CT_max due to acclimation decreases in both the Up and Acclimated-Up treatments compared to the Control and Down treatments (SI Appendix, Fig. S3). This confirms a loss of thermal plasticity in both Up-selected treatments (Up and Acclimated-Up) at higher acclimation temperatures. Notably, the loss of thermal plasticity is not evident in fish acclimated to 24 and 28 °C, possibly because at these temperatures CT_max remains further away from its hard upper limit.Open in a separate windowFig. 5.Upper thermal tolerance (CT_max) of the selected lines measured at the last generation (F₆) after acclimation at 24, 28, and 32 °C. The response is calculated as the mean difference in upper thermal tolerance (CT_max) relative to the Control lines. Large points and whiskers represent mean ±1 SE for each treatment (n = 120 individuals): Up-selected (orange triangles), Down-selected (blue squares), Acclimated Up-selected (red circles), and Control (green diamonds). Smaller translucent points represent means of each replicate line (n = 60 individuals). See SI Appendix, Fig. S3 for absolute CT_max values and model estimates.Acclimated Up-selected lines are perhaps the most ecologically relevant in our selection experiment. In the wild, natural selection on upper thermal tolerance may not result from increasing mean temperatures but through rapid heating events such as heat waves (45). During heat waves, temperature may rise for days before reaching critical temperatures. This gives individuals the possibility to acclimate and increase their upper thermal tolerance prior to peak temperatures. Our results show that while warm acclimation allowed individuals to increase their upper thermal tolerance, it did not increase the magnitude or the rate of adaptation of upper thermal tolerance.For the past two decades it has been recognized that rapid evolution, at ecological timescales, occurs and may represent an essential mechanism for the persistence of populations in rapidly changing environments (24, 46, 47). Yet, in the absence of an explicit reference, rates of evolution are often difficult to categorize as slow or rapid (48). For traits related to thermal tolerance or thermal performance, this issue is complicated by the fact that the scale on which traits are measured (temperature in °C) cannot meaningfully be transformed to a proportional scale. This prevents us from comparing rates of evolution between traits related to temperature with other traits measured on different scales (49, 50). However, for thermal tolerance, the rate of increase in ambient temperature predicted over the next century represents a particularly meaningful standard against which the rate of evolution observed in our study can be compared.In India and surrounding countries where zebrafish are native, heat waves are predicted to increase in frequency, intensity, and duration, and maximum air temperatures in some regions are predicted to exceed 44 °C in all future climate scenarios (51). Air temperature is a good predictor of water temperature in shallow ponds and streams where wild zebrafish are found (17, 40, 52, 53). Thus, strong directional selection on the thermal limits of zebrafish is very likely to occur in the wild. At first sight, changes in the upper thermal tolerance observed in our study (0.04 °C per generation) as well as the heritability estimates (Down-selected: h² = 0.24, Up-selected: h² = 0.10) similar to those obtained in fruit flies (Drosophila melanogaster) selected for acute upper thermal tolerance (Down-selected: h² = 0.19, Up-selected: h² = 0.12; ref. 12), suggest that zebrafish may just be able to keep pace with climate change and acutely tolerate temperatures of 44 °C predicted by the end of the century. However, several cautions make such an optimistic prediction unlikely.First, such an extrapolation assumes a generation time of 1 y, which is likely for zebrafish but unrealistic for many other fish species. Second, such a rate of evolution is associated with a thermal culling of two-thirds of the population at each generation, a strength of selection that may be impossible to sustain in natural populations exposed to other selection pressures such as predation or harvesting. Third, the heritability and rate of adaptation toward higher upper thermal tolerance observed here may be considered as upper estimates because of the potentially high genetic variance harbored by our parental population where samples from several sites were mixed. While mixing of zebrafish populations often occurs in the wild during monsoon flooding (54, 55), there are likely to be some isolated populations that may have a lower genetic diversity and adaptation potential than our starting population. Finally, and most importantly, the reduced phenotypic variance and decreased acclimation capacity with increasing CT_max observed in our study suggest the existence of a hard-upper limit to thermal tolerance that will lead to an evolutionary plateau similar to those reached in Drosophila selected for increased heat resistance over many generations (12, 56). Overall, the rate of evolution observed in our study is likely higher than what will occur in the wild and, based on this, it seems unlikely that zebrafish, or potentially other tropical fish species, will be able to acutely tolerate temperatures predicted by the end of the century. It is possible that other fish species, especially those living in cooler waters and with wider thermal safety margins, will display higher rates of adaptation than the ones we observed here, and more studies of this kind in a range of species are needed to determine whether slow adaptation of upper thermal tolerance is a general phenomenon.Transgenerational plasticity (e.g., epigenetics) has been suggested to modulate physiological thermal tolerance (57). However, the progressive changes in CT_max observed across generations in our study indicate that these changes were primarily due to genetic changes because effects of transgenerational plasticity are not expected to accumulate across generations. Therefore, the effects of transgenerational plasticity in the adaptation of upper thermal tolerance may be insufficient to mitigate impacts of climate change on zebrafish, yet the potential contribution of transgenerational plasticity is still an open question.By phenotyping more than 20,000 fish over six generations of selection, we show that evolution of upper thermal tolerance is possible in a vertebrate over short evolutionary time. However, the evolutionary potential for increased upper thermal tolerance is low due to the slow rate of adaptation compared to climate warming, as well as the diminishing effect of acclimation as adaptation progresses. Our results thus suggest that fish populations, especially warm water species living close to their thermal limits, may struggle to adapt with the rate at which water temperatures are increasing.