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Data for non-human primatesWe obtained 30 datasets for six genera of non-human primates: sifaka (Propithecus spp), gracile capuchin monkey (Cebus spp), guenon (Cercopithecus spp), baboon (Papio spp), gorilla (Gorilla spp), and chimpanzee (Pan troglodytes) (Supplementary Data 1). Of these, 17 datasets correspond to long-term projects in the wild, while 13 were contributed by the non-profit Species360 from ZIMS18, which is the most extensive database of life history information for animals under human care.Basic demographic functionsLet X be a random variable for ages at death, with observations x ≥ 0, and let μ (x|θ) be a continuous, non-negative parametric hazards rate or mortality function defined as$$mu left(x,|,{boldsymbol{theta }}right)=mathop{{rm{lim}}}limits_{Delta xto 0}frac{{{Pr }}(x < Xle x+Delta x|X > x)}{Delta x},$$
(2)
given that the limit exists, where ({boldsymbol{theta }}in {{mathbb{R}}}^{p}) is a p-dimensional vector of mortality parameters. The cumulative hazards rate is$$Uleft(x|{boldsymbol{theta }}right)=int_{0}^{x}mu (t|{boldsymbol{theta }}){dt},$$
(3)
which results in the survival function$$S(x|{boldsymbol{theta }})={{exp }}[-U(x|{boldsymbol{theta }})].$$
(4)
The Cumulative distribution function (CDF) of ages at death is F (x | θ) = 1 – S (x | θ), and the probability density function (PDF) of ages at death is f (x | θ) = μ (x | θ) S (x | θ), for x ≥ 0. The remaining life expectancy after age x is calculated as$$eleft(x{rm{|}}{boldsymbol{theta }}right) = frac{{int }_{x}^{{{infty }}}{tf}(t|{boldsymbol{theta }}){dt}}{Fleft({{infty }}right)-Fleft(xright)}\ =frac{{int }_{x}^{{{infty }}}S(t|{boldsymbol{theta }}){dt}}{Sleft(xright)},$$
(5)
which yields a life expectancy at birth given by$$eleft(0{rm{|}}{boldsymbol{theta }}right)={int }_{0}^{{{infty }}}S(x|{boldsymbol{theta }}){dx}.$$
(6)
The lifespan inequality at birth, as proposed by Demetrius16,36 and later by Keyfitz17, is given by$$H(0|{boldsymbol{theta }}) =-frac{{int }_{0}^{{{infty }}}S(x|{boldsymbol{theta }}){{log }}[S(x|{boldsymbol{theta }})]{dx}}{e(0|{boldsymbol{theta }})}\ = frac{{int }_{0}^{{{infty }}}S(x|{boldsymbol{theta }})U(x|{boldsymbol{theta }}){dx}}{e(0|{boldsymbol{theta }})}.$$
(7)
Following Colchero et al.13, we define the lifespan equality as$$varepsilon (x|{boldsymbol{theta }})=-{{log }}[H(x|{boldsymbol{theta }})].$$
(8)
For simplicity, henceforth we note the life expectancy, lifespan inequality and lifespan equality at birth as e(0 | θ) = e, H (0 | θ) = H, and ε (0 | θ) = ε, respectively.Survival analysisTo estimate age-specific survival for all the wild populations of non-human primates, we modified the Bayesian model developed by Colchero et al.13 and Barthold et al.37. This model is particularly appropriate for primate studies that follow individuals continuously within a study area and when individuals of one or both sexes can permanently leave the study area (out-migration), while other individuals can join the study population from other areas (in-migration). Thus, it allowed us to make inferences on age-specific survival (or mortality) and on the age at out-migration.Here we use the five parameter Siler mortality function25, as in Eq. (1) where θ = [a0, a0, c, b0, b1] is a vector of parameters to be estimated, and where a0, b0 ({mathbb{in }}{mathbb{R}}) and a1, c, b1 ≥ 0. For all species we studied, individuals of one or both sexes often leave their natal groups to join other neighbouring groups in a process commonly identified as natal dispersal. For some species, individuals who have undergone natal dispersal can then disperse additional times, described as secondary dispersal. Although dispersal within monitored groups (i.e. those belonging to the study area) does not affect the estimation of mortality, the fate of individuals that permanently leave the study area to join unmonitored groups can be mistaken for possible death. We identify this process as “out-migration”, which we classify as natal or immigrant out-migration, the first for natal and the second for secondary dispersals to unmonitored groups. This distinction is particularly relevant because not all out-migrations are identified as such, and therefore the fate of some individuals is unknown after their last detection. For these individuals we define a latent out-migration state at the time they were last detected, given by the random variable indicator O, with observations oij ∈ {0,1}, where oij = 1 if individual i out-migrated and oij = 0 otherwise, and where j = 1 denotes natal out-migration and j = 2 for immigrant out-migration. For known out-migrations, we automatically assign oij = 1. The model therefore estimates the Bernoulli probability of out-migration, πj, such that Oij ~ Bern(πj). Those individuals assigned as exhibiting out-migration, as well as known emigrants and immigrants, contribute to the estimation of the distribution of ages at out-migration. Here, we define a gamma-distributed random variable V for ages at out-migration, with realisations v ≥ 0, where Vj | Oj = 1 ~ Gam(γj1, γj2) and where γj1, γj2  > 0 are parameters to be estimated with j defined as above. The probability density function for the gamma distribution is gV(v | γj1, γj2) for v ≥ 0, with v = xl – αj, where xl is the age at last detection and αj is the minimum age at natal or immigrant out-migration.In addition, since not all individuals have known birth dates, the model samples the unknown births bi as xil = til – bi, where til is the time of last detection for individual i. The likelihood is then defined as$$p({x}_{{il}},{x}_{{if}},|,{boldsymbol{theta}},{boldsymbol{gamma}}_{1},{boldsymbol{gamma}}_{2},{pi }_{j},{o}_{ij})=left{begin{array}{cc}frac{fleft({x}_{il}right)}{Sleft({x}_{if}right)}({1-pi }_{j})hfill& {text{if}}; o_{{ij}}=0\ frac{Sleft({x}_{{il}}right)}{Sleft({x}_{{if}}right)}{pi }_{j}{g}_{V}({x}_{{il}}-{alpha }_{j})& {text{if}}; o_{{ij}}=1end{array}right.,$$
(9)
where xif is the age at first detection, given by xif = tif – bi, with tif as the corresponding time of first detection. The parameter vectors γ1 and γ2 are for natal and immigrant out-migration, respectively. In other words, individuals with oij = 0 are assumed to have died shortly after the last detection, while those with oij = 1 are censored and contribute to the estimation of the distribution of ages at out-migration. The full Bayesian posterior is then given by$$pleft({boldsymbol{theta }}{boldsymbol{,}}{{boldsymbol{gamma }}}_{1},{{boldsymbol{gamma }}}_{2},{boldsymbol{pi }},{{bf{b}}}_{u},{{bf{o}}}_{u},|,{{bf{b}}}_{k},{{bf{o}}}_{k},{{bf{t}}}_{f},{{bf{t}}}_{l}right) propto ; pleft({{bf{x}}}_{l},{{bf{x}}}_{f},|,{boldsymbol{theta }},{{boldsymbol{gamma }}}_{1},{{boldsymbol{gamma }}}_{2},{boldsymbol{pi }},{bf{d}}right)\ , times pleft({boldsymbol{theta }}right)pleft({{boldsymbol{gamma }}}_{1}right)pleft({{boldsymbol{gamma }}}_{2}right)pleft({boldsymbol{pi }}right),$$
(10)
where the first term on the right-hand-side of Eq. (10) is the likelihood in Eq. (9), and the following terms are the priors for the unknown parameters. The vector π = [π1, π2] is the vector of probabilities of out-migration while the subscripts u and k refer to unknown and known, respectively.Following Colchero et al.13, we used published data, expert information and an agent-based model to estimate the mortality and out-migration prior parameters for each population. We assumed a normal (or truncated normal distribution depending on the parameter’s support) for all the parameters. We used vague priors for the mortality and natal out-migration parameters (sd = 10), and informative priors for the immigrant out-migration parameters (sd = 0.5). We ran six MCMC parallel chains for 25 000 iterations each with a burn-in of 5000 iterations for each population, and assessed convergence using potential scale reduction factor38.For the zoo data we used a simplified version of the model described above, which omitted all parts that related to out-migration. In order to produce Supplementary Figs. 1 and 2, we used the same method as for the zoo data on the human life tables. To achieve this, we created an individual level dataset from the lx column of each population, and then fitted the Siler model to this simulated data. It is important to note that the Siler model provides a close fit to the nonhuman primate data and to high-mortality human populations, although it does not provide the best fit to low-mortality human populations, in part due to the late life mortality plateau common among human populations39 (Supplementary Fig. 6). It is therefore possible that the values of the mortality parameter b1 we report in Supplementary Data 2 for the human populations are under-estimated. Nonetheless, and for the purposes of our analyses, the Siler fits to the human populations we considered here are reasonable (Supplementary Fig. 6) and we can therefore confidently state that the limitations of the Siler model do not affect the generality of our results.Estimation of life expectancy and lifespan equalityBased on the results of the Bayesian inference models, we calculated life expectancy at birth as$$e= int_{0}^{{infty}}Sleft(t| {hat{boldsymbol{theta }}}right){dt},$$
(11)
where S (x) is the cumulative survival function as defined in Eq. (4) and where (hat{{boldsymbol{theta }}}) is the vector of mortality parameters calculated as the mean of the conditional posterior densities from the survival analysis described above. We calculated the lifespan inequality17,36, H, as$$H=-frac{1}{e}int_{0}^{{{infty }}}Sleft(x{rm{|}}hat{{boldsymbol{theta }}}right){{log }}left[Sleft(x|hat{{boldsymbol{theta }}}right)right]{dx},$$
(12)
from which we calculated lifespan equality, ε, as in Eq. (8). We calculated both measures for each of the study populations, and performed weighted least squares regressions for each genus, with weights given by the reciprocal of the standard error of the estimated life expectancies.Sensitivities of life expectancy and lifespan equality to mortality parametersAs we mentioned above, for simplicity of notation, we will express all demographic functions by their variable notation (e.g. e = e (0 | θ), S = S (x | θ), etc.), while we will alternatively note first partial derivatives, for instance the derivative of e with respect to a given mortality parameter θ ∈ θ, as eθ or ∂e / ∂θ.Proposition: If ({S:}{{mathbb{R}}}_{ge 0}to left[{mathrm{0,1}}right]) is a continuous non-increasing parametric survival function with parameter vector ({boldsymbol{theta }}{boldsymbol{in }}{{mathbb{R}}}^{{boldsymbol{p}}}), with continuous differentiable cumulative hazards function ({U:}{{mathbb{R}}}_{ge 0}to {{mathbb{R}}}_{ge 0}), and with life expetancy at birth, lifespan inequality and lifespan equality as in Eqs. (4)-(6), respectively, then the sensitivity of life expectancy, e, to a given parameter θ ∈ θ is$${e}_{theta }=frac{partial e}{partial theta }=int_{0}^{{{infty }}}{S}_{theta }{dx},$$
(13)
while the sensitivity of lifespan equality to θ is$${varepsilon }_{theta }=frac{partial varepsilon }{partial theta }=frac{{e}_{theta }left(1+{H}^{-1}right)-{H}^{-1}{int }_{0}^{{{infty }}}{S}_{theta }{Udx}}{e},$$
(14)
where$${S}_{theta }=frac{partial }{partial theta }S(x|{boldsymbol{theta }})$$
(15)
is the sensitivity of the survival function at age x to changes in parameter θ.Proof. The sensitivity of lifespan equality to changes in θ is derived from$${e}_{theta }=frac{partial }{partial theta }int_{0}^{{{infty }}}{Sdx},$$
(16)
which, by Leibnitz’s rule, Eq. (16) becomes$${e}_{theta }=int_{0}^{{{infty }}}frac{partial S}{partial theta }{dx}=int_{0}^{{{infty }}}{S}_{theta }{dx}.$$
(17)
The sensitivity of lifespan equality to changes in θ can be calculated as$${varepsilon }_{theta } =frac{partial }{partial theta }left(-{{log }}, Hright)\ =-frac{partial }{partial theta }{{log }}, H\ =-frac{1}{H}frac{partial H}{partial theta }\ =-frac{1}{H}frac{partial }{partial theta }left(frac{{int }_{0}^{{{infty }}}{SUdx}}{e}right).$$
(18)
By the quotient and Leibnitz’s rules, Eq. (18) can be modified as$${varepsilon }_{theta } =-frac{1}{H{e}^{2}}left[frac{partial }{partial theta }left(int _{0}^{{{infty }}}{SUdx}right)e-left(int _{0}^{{{infty }}}{SUdx}right)frac{partial e}{partial theta }right]\ =-frac{1}{{He}}int _{0}^{{{infty }}}frac{partial }{partial theta }left({SU}right){dx}+frac{1}{{He}}frac{int _{0}^{{{infty }}}{SUdx}}{e}frac{partial e}{partial theta }.$$
(19)
The first term in Eq. (19) can be further decomposed by the product rule, while the second term can be modified following the equality for H in Eq. (7), which yields$${varepsilon }_{theta } =-frac{1}{{He}}int _{0}^{{{infty }}}left(frac{partial S}{partial theta }U+Sfrac{partial U}{partial theta }right){dx}+frac{1}{e}{e}_{theta }\ =-frac{1}{{He}}left(int _{0}^{{{infty }}}{S}_{theta }{Udx}+int _{0}^{{{infty }}}Sfrac{partial U}{partial theta }dxright)+frac{1}{e}{e}_{theta }.$$
(20)
By the chain rule, we have that (frac{partial U}{partial theta }=-frac{partial }{partial theta }{{log }},S=-frac{1}{S}frac{partial S}{partial theta }), which modifies Eq. (20) as$${varepsilon }_{theta } = , -frac{1}{{He}}left(int _{0}^{infty }{S}_{theta }{Udx}-int _{0}^{infty }frac{partial S}{partial theta }{dx}right)+frac{1}{e}{e}_{theta }\ = , -frac{1}{{He}}left(int _{0}^{infty }{S}_{theta }{Udx}-{e}_{theta }right)+frac{1}{e}{e}_{theta }\ = , -frac{int _{0}^{infty }{S}_{theta }{Udx}}{{He}}+frac{{e}_{theta }}{e}left(1+frac{1}{H}right)\ =, frac{{e}_{theta }left(1+{H}^{-1}right)-{H}^{-1}int _{0}^{infty }{S}_{theta }{Udx}}{e},$$
(21)
hence completing the proof. ∎Changes in parameters along the genus linesFrom the results in Eqs. (13) and (14), we calculated the vectors of change (gradient vectors) at any point (leftlangle {e}_{j},{varepsilon }_{j}rightrangle) of the life expectancy-lifespan equality landscape, as a function of each of the Siler mortality parameters (See Fig. 2A, B).To quantify the amount of change of each parameter along the genus lines, we derived the sensitivities of a given mortality parameter θ to changes in life expectancy and lifespan equality, namely (frac{partial theta }{partial e}=frac{1}{{e}_{theta }}) for ({e}_{theta }, ne, 0,) and (frac{partial theta }{partial varepsilon }=frac{1}{{varepsilon }_{theta }}) for ({varepsilon }_{theta }, ne, 0). With these sensitivities we calculated the gradient vector$$nabla theta =leftlangle frac{partial theta }{partial e},frac{partial theta }{partial varepsilon }rightrangle$$
(22)
for any parameter at any point along the genus lines. Here we find a linear relationship between life expectancy and lifespan equality, given by$$mleft({e}_{{ik}}right)={hat{varepsilon }}_{{ik}}={beta }_{0k}+{beta }_{1k}{e}_{{ik}},$$
(23)
for i = 1, …, nk, where nk is the number of populations for genus k, and ({hat{varepsilon }}_{{ik}})is the fitted value of lifespan equality for population i in genus k, and β0k and β1k are linear regresssion parameters for genus k. To estimate the amount of change in parameter θ along the line for genus k, we can solve the path integral$${Theta }_{k}=int _{{C}_{k}}nabla theta d{bf{r}},$$
(24)
where path Ck is determined by the linear model for genus k and (d{bf{r}}=leftlangle {de},dhat{varepsilon }rightrangle =leftlangle {de},{d; m}left(eright)rightrangle) is the rate of change in the velocity vector ({bf{r}}=leftlangle e,hat{varepsilon }rightrangle =leftlangle e,mleft(eright)rightrangle).In order to compare results between the different mortality parameters in vector θ, we use the transformation g(θ) = log θ, which yields the following partial derivatives$$frac{partial }{partial e}gleft(theta right)=frac{1}{theta }frac{partial theta }{partial e}$$
(25)
and$$frac{partial }{partial varepsilon }gleft(theta right)=frac{1}{theta }frac{partial theta }{partial varepsilon }.$$
(26)
Thus the gradient vector becomes$$nabla theta =leftlangle frac{partial }{partial e}gleft(theta right),frac{partial }{partial varepsilon }gleft(theta right)rightrangle$$
(27)
while the path integral in Eq. (24) is modified accordingly. In short, the path integral ({Theta }_{j}) provides a measure of the relative change in parameter θ along the genus line (Fig. 3). To allow comparisons between all genera, we scaled the values of each path integral by the length of each line.Applications to the Siler mortality modelThe Cumulative hazards for the Siler mortality model in Eq. (7) is given by$$Uleft(xright)=frac{{e}^{{a}_{0}}}{{a}_{1}}left(1-{e}^{{-a}_{1}x}right)+{cx}+frac{{e}^{{b}_{0}}}{{b}_{1}}left({e}^{{b}_{1}x}-1right),$$
(28)
The sensitivities in Eqs. (13) and (14) require calculating Sθ for all θ ∈ θ. Treating S (x) as the function composition W (V), where W = exp(x) and V = – U, then Sθ is$${S}_{theta }=frac{{dW}}{{dV}}{V}_{theta }=-S{U}_{theta },$$
(29)
where Uθ is the first derivative of U(x | θ) with respect to θ. For each of the Siler mortality parameters, we then have$${S}_{{a}_{0}}=S(x|{boldsymbol{theta }})frac{{e}^{{a}_{0}}}{{a}_{1}}left({e}^{-{a}_{1}x}-1right)$$
(30)
$${S}_{{a}_{1}}=S(x|{boldsymbol{theta }})frac{{e}^{{a}_{0}}}{{a}_{1}}left[frac{1}{{a}_{1}}-{e}^{-{a}_{1}x}left(x+frac{1}{{a}_{1}}right)right]$$
(31)
$${S}_{c}=-S(x|{boldsymbol{theta }})x$$
(32)
$${S}_{{b}_{0}}=S(x|{boldsymbol{theta }})frac{{e}^{{b}_{0}}}{{b}_{1}}left(1-{e}^{{b}_{1}x}right)$$
(33)
$${S}_{{b}_{1}}=S(x|{boldsymbol{theta }})left[{e}^{{b}_{1}x}left(frac{1}{{b}_{1}}-xright)-frac{1}{{b}_{1}}right].$$
(34)
All analyses were performed in the free open source programme R40. The R functions we created for this project can be found in41.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

Spatial and temporal variations of the SRHII at daytime and nighttimeSignificant seasonal differences are observed in the SRHII in the YRDUA (Figure A1 and A2, Appendix A). In the daytime, RHI was concentrated in the Nanjing, “Su-Xi-Chang”, Ningbo, Shanghai, and Hangzhou metropolitan areas. Due to the high built-up areas and PD, the distribution of surface RHI is denser and stronger than that in the north and southwest of the YRDUA. The built-up area can absorb heat and store heat energy, which makes the surface temperatures rise rapidly. In spring and autumn, the spatial distribution of the RHI in spring or autumn was similar to that in summer except the spatial extent was tapered. However, the RHI gradually shrinks and transfers to the southern area of the YRDUA in winter, such as Linhai and Ningbo City, which is due to the relatively high solar radiation of the geographic location of the southern cities. The distance of the RHI is gradually shortened between cities and even into one piece from 2003 to 2017 due to long-term urban expansion and rapid growth of construction land (Figure A1, Appendix A). In the nighttime, the spatial pattern of the RHI is very different from that of the daytime. RHI mainly concentrates on Taihu Lake, Dianshan Lake, Ge Lake in the center part, Hongzhe Lake in the northwest, and Qiandao Lake in the southwest. Because water has a high specific heat capacity, it has the function of preserving heat at nighttime. Some cities like Shanghai, Hangzhou, and Nanjing have the strongest heat island in winter and the weakest heat island in summer. Urban areas usually have dense buildings, PD, and energy emissions, so there are more energy emissions at night. High surface albedo in urban areas at night leads to lower heat storage4,40 and ultimately resulting in smaller UHI at nighttime (Figure A2, Appendix A).From spring to summer and then summer to winter, RHI increases first and then decreases, and it reaches a peak in summer. For example, the proportion of the RHI was 12.65%, 31.03%, 21.12%, and 5.49% in spring, summer, autumn, and winter in 2017, respectively (Fig. 2d). An upward trend in the area of the RHI is observed from 2003 to 2017 in summer. In detail, the proportion of the heat island zone is 21.74%, 22.17%, and 31.03% in the summer of 2003, 2010, and 2017, respectively (Fig. 2d). It is because the urban areas of YRDUA have increased from 3571.01 km2 to 8760.26 km2 in 2003 and 2017, respectively (Figure B1, Appendix B). Moreover, the area of the medium heat island and strong heat island increased by 41.08% and 66.40% from 2003 to 2017 (Fig. 2b,c). A gradual decreasing trend is observed for the four grades of the SRHII (2–4 °C, 4–6 °C,  > 6 °C,  > 2 °C) in winter from 2003 to 2017 (Fig. 2a–d). The area of the RHI in winter was 18,481 km2, 8640 km2, and 6280 km2 in 2003, 2010, and 2017, respectively (Fig. 2d). Vegetation coverage is low in winter and bare soil is formed after harvest. It leads to the RHI decrease in winter. The above results indicated that the SRHII became increasingly hot in summer and increasingly cold in winter and that the trend became more obvious as the SRHII increased in the ranges of 2–4 °C, 4–6 °C,  > 6 °C. However, the seasonal variation of the RHI in the nighttime is opposite to that in the daytime. From spring to summer and then to winter, the area of the RHI decreases first and then increases, and it falls in the lowest value in summer (Fig. 2e–g). For example, the area of RHI is 19,209 km2, 5659 km2, 34,621 km2, and 38,596 km2 in spring, summer, autumn, and winter in 2017, respectively (Fig. 2h). The annual average of RHI regular increases, with values of 17,510 km2, 20,042 km2, and 20,097 km2 in 2003, 2010, and 2017, respectively (Fig. 2h).Figure 2Seasonal and inter-annual variations of the SRHII during the daytime (a–d) and nighttime (e–h) of the YRDUA.Full size imageRelationship between the SRHII and influencing factorsResults showed surface biophysical factors have a higher correlation with SRHII than socio-economic factors and climate factors in the day and night. NDBI and EVI have a stronger effect on SRHII than other biophysical factors in the day. NDBI showed a significant positive correlation with SRHII, while EVI showed a negative correlation with SRHII. In detail, NDBI (r = 0.567, p  autumn  > winter. The dominant influencing factor was the MNDWI in spring, autumn and winter, while EVI had the largest contribution in summer at night. More

Overview of the study areaThe experimental algae P. parvum was collected from the fishponds in Dawukou, Ningxia, China. Algal water samples were filtered by medium size filter paper and centrifuged, and cultured with F/2 culture medium in the following environmental conditions for 5 days; light intensity of 5000 lx, light/dark ratio of 12 h: 12 h, water temperature of 18.5 ± 0.5 ℃, pH of 8.5 ± 0.1 and salinity of 1.2 ± 0.1 mg/l20,21. The plate separation method was used to separate and purify the cultured algae22. After microscopy, the colony of pure algal cells were transferred to different volumes of triangular glass bottles which contains sterilized F/2 medium for expansion culture. Algae P. parvum propagates vegetatively by cell division, the cell density of algae increases exponentially during the process of propagation thus requires more space. To accommodate this increasing space requirement, different sizes of the triangular glass bottles were used as 50 ml, 250 ml and 10 l. The expansion cultures were maintained in the environmental conditions similar to the initial culture. The algal cells were used for the experiment when they reach the logarithmic growth stage (the logarithmic growth stage was reached in 10 days).Data collection and experimentationThe water sample from the 10 L expansion culture of P. parvum was collected. The initial nutrient concentrations and environmental factors were determined using appropriate methods and equipment in the laboratory. The initial nutrient concentrations and environmental conditions of the algae culture used in this experiment is presented in Table 1.Table 1 Initial nutrient concentrations and environmental conditions of algae culture used in the experiment.Full size tableExperimental factors and their levels for each nutrient concentrations and environmental factors were designed based on the above reference as shown in Table 2. We have designed eight levels for environmental factors (i.e., water temperature, pH and salinity) and ten levels for nutrient concentrations (i.e., nitrogen, phosphorous, silicon and iron).

1.

Evaluation of the effects of environmental factors on the growth of P. parvum

Table 2 Experimental factors and their levels designed for the experiment.Full size tableTo study the effects of environmental factors on the growth of P. parvum, water temperature, pH and salinity were used as the experimental factors by adopting the uniform design23,24,25 of three factors and eight levels as shown in Table 3.Table 3 Combination of environmental factors used for the different levels in the uniform design.Full size tableA 250 ml triangular glass bottle was used to implement each level of the above experiment with three replicates for each level (total of 24 bottles). The algae culture was allowed to grow in F/2 culture medium in the nutrient solution of 100 ml with an inoculation ratio of 1:10 (V/V). These bottles were kept in the light intensity of 5000 lx with light/dark ratio of 12 h: 12 h, while maintaining all other growth conditions to meet the experimental design requirements. The nutrient concentrations of N, P, Si and Fe were maintained at the level of initial concentrations (Table 1). Inoculated algae were cultured in a shaker for 10 days until it reaches its logarithmic growth stage and the growth rate was quantified.

2.

Evaluation of the effects of nutrient concentrations on the growth of P. parvum

To study the effects of nutrient concentrations on the growth of P. parvum, nitrogen, phosphorus, silicon and iron were used as experimental factors by adopting the uniform design5,26 of four factors and ten levels as shown in Table 4. The culture medium was prepared with sodium nitrate (NaNO3) as the nitrogen source, monosodium phosphate (NaH2PO4) as the phosphorus source, sodium metasilicate (Na2SiO3) as the silicon source, and ferric citrate (FeC6H5O7) as a source iron to obtain the appropriate concentrations of nitrogen, phosphorous, silicon and iron as designed for this experiment (Table 2).Table 4 Combination of nutrient concentration used for the different levels in the uniform design.Full size tableA 250 ml triangular glass bottle was used to implement each level of the above experiment with three replicates for each level (total of 30 bottles). The algae culture was allowed to grow in F/2 culture medium with a volume of 100 ml and an inoculation ratio of 1:10 (V/V). These bottles were kept in the light intensity of 5000 lx, light/dark ratio of 12 h: 12 h, water temperature of 18.5 ± 0.5 ℃, pH of 8.5 ± 0.1 and salinity of 1.2 ± 0.1 mg/l. Inoculated algae were cultured in a shaker for 10 days until it reaches its logarithmic growth stage and the biomass density was quantified.

3.

Determination of the growth rate of P. parvum

The algal cell density of the culture of each experimental level was measured using a 0.1 ml count plate under an optical microscope (Leica biological microscope DM1000, Leica Corporation, Oskar-Barnack-Straße, Germany) both at the beginning of the experiment and following 10 days of incubation period as the growth of the algae can reach its logarithmic growth stage at 10 days. Based on the algal cell density measurement, biomass density was calculated using the following formula (Eq. 1) described by Wei and Zhang;$$ Growth;rate;left( K right) = 3.322 times left( {log (N_{t} ) – log left( {N_{0} } right)} right)/left( {t – t_{0} } right) $$
(1)
where t is the duration of the experiment in days, N0 is the initial cell density (cell/ml) at the beginning of the experiment, and Nt is the cell density (cell/ml) at the end of day t of the experiment.Data analysis and results

1.

Establishment of the regression model between environmental factors and the growth rate

The growth rate of P. parvum under different levels of environmental factors are shown in Table 5, and the growth curve with time is shown in Fig. 1.Table 5 Growth rates of Prymnesium parvum under the different levels of environmental factors in the uniform design.Full size tableFigure 1The growth curve of P. parvum with time under different environmental factor levels.Full size imageIn multiple quadratic stepwise regression analysis, water temperature (X1), pH (X2) and salinity (X3) were taken as independent variables, and the growth rate (Y) was taken as the dependent variable. From this analysis a quadratic polynomial regression equation (Eq. 2) was developed as follows:$$ Y = – 11.0371 + 0.0682X_{1} + 2.5559X_{2} + 0.7953X_{3} – 0.0019X_{1} ^{2} – 0.1523{text{ }}X_{2} ^{2} – 0.3223{text{ }}X_{3} ^{2} $$
(2)
Correlation coefficient (R) of the above equation was 0.9994 and probability (P) of the regression equation was 0.025 (p  X3  > X1. Thus, the contribution of pH  > salinity  > water temperature on the growth rate of P. parvum.

2.

Evaluation of the effect of environmental factors on the growth rate of P. parvum

The environmental conditions that would result in the maximum growth rate of P. parvum were determined by optimizing the regression equation (Eq. 2). The following simple regression models (Eqs. 3–5) of multiple quadratic stepwise regression analyses reveal the relationships between individual environmental factors and the growth rate. These models were obtained by dimensionality reduction analysis in which the other factors were maintained at optimal levels.$$ X_{{1WT}} :;Yleft( {X_{1} } right) = 0.1768 + 0.0682X_{1} – 0.0019X_{1} ^{2} $$
(3)
$$ X_{{2pH}} :;Yleft( {X_{2} } right) = – 9.9345 + 2.5559X_{2} – 0.1523{text{ }}X_{2} ^{2} $$
(4)
$$ X_{{3salinity}} :;Yleft( {X_{3} } right) = 0.2982 + 0.7953X_{3} – 0.3223{text{ }}X_{3} ^{2} $$
(5)
The influence curves of each environmental factor on growth rate of P. parvum are shown in Fig. 2. The behavior of the curves is similar where the growth rate increases initially, then reaches a theoretical maximum and finally declines with increasing level of each environmental factor. Accordingly, P. parvum reaches its theoretical maximum growth rate (0.789) when the water temperature, pH and salinity is 18.11 ℃, 8.39 and 1.23‰, respectively. Therefore, Fig. 2 can be considered as the growth model of P. parvum as affected each of the respective environmental factors.

3.

Establishment of regression model between nutrient concentrations and the growth rate

Figure 2The growth rate of P. parvum as affected by the water temperature (a), pH (b) and salinity (c).Full size imageThe growth rates of P. parvum under the different levels of nutrient concentrations are shown in Table 7, and the growth curve with time is shown in Fig. 3.Table 7 Growth rate of Prymnesium parvum under the different levels of nutrient concentration in the uniform design.Full size tableFigure 3The growth curve of P. parvum with time under different nutrient concentrations factor levels.Full size imageA quadratic polynomial regression equation (Eq. 6) was generated using N (Xi), P (Xii), Si (Xiii) and Fe (Xiv) as independent variables and the growth rate (Y′) as the dependent variable by using multiple quadratic stepwise regression analysis as follows:$$ Y^{prime } = – 1.856686 + 1.371680X_{i} + 0.390361X_{{ii}} + 0.150656X_{{iii}} + 0.587990X_{{iv}} – {text{ }}0.2011178X_{i} ^{2} – 0.186640{text{ }}X_{{ii}} ^{2} – 0.108764{text{ }}X_{{iii}} ^{2} – 0.550523{text{ }}X_{{iv}} ^{2} $$
(6)
Correlation coefficient (R) of the above equation was 0.9994 and probability (P) of the regression equation was 0.035 ( Xii  > Xiv  > Xiii. Therefore, the contribution of nitrogen  > phosphorous  > iron  > silicon for the growth of P. parvum.

4.

Evaluation of the effect of nutrient concentrations on the growth rate of P. parvum

Multifactor square stepwise regression model was used to analyze the influence of individual nutrient concentration following the dimensionality reduction. To evaluate the influence of individual nutrient concentration on the growth rate, following sub-models (Eqs. 7–10) were developed by fixing other factors at the optimal level.$$ X_{i} nitrogen:Y^{prime } (X_{i} ) = – 1.4432 + 1.3717X_{i} – 0.2012X_{i} ^{2} $$
(7)
$$ X_{{ii}} phosphorus:Y^{prime } (X_{{ii}} ) = 0.6916 + 0.3904X_{{ii}} – 0.1866X_{{ii}} ^{2} $$
(8)
$$ X_{{iii}} silicon:Y^{prime } (X_{{iii}} ) = 0.8436 + 0.1507X_{{iii}} – 0.1088X_{{iii}} ^{2} $$
(9)
$$ X_{{iv}} iron:Y^{prime } (X_{{iv}} ) = 0.7388 + 0.5880X_{{iv}} – 0.5505X_{{iv}} ^{2} $$
(10)
The influence curves of each nutrients on growth rate of P. parvum are shown in Fig. 4. The behavior of the curves shows an initial increase of the growth rate, then the growth rate reaches a theoretical maximum and finally declines with increasing level of concentrations of each nutrient. Accordingly, P. parvum reaches its theoretical maximum growth rate (0.896) when the concentration of nitrogen, phosphorous, silicon and iron is 3.41, 1.05, 0.69, 0.53 mgl−1, respectively. Therefore, Fig. 4 may be considered as the growth model of P. parvum as affected each of the respective nutrients.Figure 4The growth rate of P. parvum as affected by nitrogen (a), phosphorus (b), silicon (c) and iron (d).Full size image More

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Ethics and vertebrate animalsThe field surveys and collections were conducted on accessible public areas or private residential areas with property owners’ permission. The study did not involve human participants, or endangered or protected species. Laboratory mice were used as a blood source for mosquitoes. All experimental protocols were approved by the Institutional Animal Care and Use Committee (IACUC) of the University of California, Irvine (UCI) (IACUC protocol number: AUP-19-165). All methods were carried out in accordance with relevant IACUC guidelines and regulations.Study sites and mosquito larval habitat surveillanceThe study was carried out in Orange County, California, USA. Orange County is a highly urbanized county with an estimated population density of approximately 1470 people/km2 according to U.S. Census Bureau, an average annual low/high temperature range of 13–25 °C, 65% relative humidity, and annual precipitation of about 350 mm according to U.S. Climate Data. Annual rainfall was 261 mm, 311 mm, 198 mm and 475 mm for 2016, 2017, 2018 and 2019, respectively. A major drought event occurred in December 2017 and February 2018 when the total rainfall in the 3-month period was 20.6% of the 30-year average. Both Ae. aegypti and Ae. albopictus were discovered in the county in 20158. Culex quinquefasciatus is the most abundant mosquito in the county and breeds readily in a variety of residential, commercial and USDS water sources, and is the primary vector of West Nile virus in southern California18.Larval mosquito surveillance in Orange County was conducted from 2016 to 2019 by the Orange County Mosquito and Vector Control District (OCMVCD) through its routine mosquito surveillance and treatment program, following the recommendations of the California Department of Public Health and the Mosquito and Vector Control Association of California19. Briefly, OCMVCD staff conducted routine inspection for aquatic habitats in randomly selected public areas, and performed door-to-door mosquito larval and adult sampling on residential or commercial premises upon the request of the residents or business owners while distributing public education materials for vector control and personal protection. Arial photography was used to examine the presence of abandoned swimming pools in residential areas. In addition to surface aquatic habitats, subsurface habitats (e.g., catch basins, underground drains, manhole chambers, and public utility vaults) were examined for larval abundance of all mosquito species. In 2019, OCMVCD completed 5,622 mosquito service requests, and conducted 11,813 inspection and treatments on routine sites using a variety of public health-approved adulticides and larvicides. A total of 38,099 underground drains and catch basins and 6925 km of flood channels were treated. In addition, a total of 17,783 km of gutters and 3562 neglected swimming pools were inspected and treated. The larval distribution data reported here were based on this extensive field sampling effort20.Larval sampling used standard mosquito dippers or pipettes, and specialized modifications of these to sample hard to reach areas. Mosquito larvae from each source were collected, transferred into a uniquely-numbered vial with isopropyl alcohol (70%), and submitted to the laboratory for identification; if present, live pupae were collected and held in site-specific labelled rearing chambers (BioQuip Products, Inc., Rancho Dominguez, CA) until emergence. Third and fourth instar mosquito larvae (1–100, depending on sample size) and emerged adults were identified to species using a stereo microscope (40–50x) and morphological features described in taxonomic keys21,22. Results were uploaded to OCMVCD’s data management system, along with collection date, GPS location, and habitat type for each sample site. For this study, larval habitats were classified into six types: small container, underground system, ornamental water features, marsh, pools/spas, and creek (Table S1). The container classification included flowerpots/vases, saucers, tires, bowls, boxes, buckets, dishes, tree holes, etc. Underground storm drain system referred to larval habitats such as catch basins, manhole chambers, underground drains, and public utility vaults that were below the ground. Water feature included flood control channels, ponds, fountains, birdbaths, street gutters and small reservoirs, etc. Marsh included both fresh and salt water marshes.Mosquito strains and water source for laboratory studiesWe examined the effect of USDS water on oviposition substrate preference and larval development in microcosms in an insectary with climate control (27 ± 1 °C, 70 ± 10% relative humidity, and 12 h light/12 h dark photoperiod) at UCI. To minimize potential bias on behavior and ecology from mosquito colonization, this study did not use previously established laboratory mosquito colonies. Instead, we used Ae. aegypti and Ae. albopictus adults reared from field-collected eggs using ovicups in residential areas of Orange and Los Angeles Counties, California, respectively. Culex quinquefasciatus were also reared from eggs of field-collected, blood-engorged adult mosquitoes using gravid traps in Orange County23.All experiments reported here used two types of habitat water: (1) USDS water collected from seven manhole chambers or catch basins (33°47′01.9″N, 117°53′19.0″W, Orange City, manhole; 33°52′25.0″N, 117°57′02.6″W, Fullerton City, manhole; 33°44′44.4″N, 118°06′24.2″W, Seal Beach City, manhole; 33°55′38.9″N, 117°56′51.4″W, La Habra City, manhole; 33°52′48.9″N, 117°55′21.4″W, Fullerton City, catch basin; 33°54′35.2″N, 117°56′02.5″W, Fullerton City, catch basin; 33°52′25.0″N, 117°57′02.6″W, Fullerton City, catch basin); and 2) flowerpot water from vases of three cemeteries in Orange County (33°50′29.0″N, 117°53′57.9″W; 33°46′21.5″N, 117°50′35.8″W; 33°46′12.3″N, 117°50′21.4″W). Water (including sediments) from each breeding source was collected with mosquito dippers and mixed together by habitat type into 18.9 L (five-gallon) Nalgene™ containers. The containers were transported to the laboratory in shaded ice containers, and stored overnight in a refrigerator at 4 °C. The experiments described below were conducted on the field-collected water for the two habitat types. We selected flowerpot water as the comparison substrate because flowerpot containers showed the highest larval positivity rate in the study area.Oviposition preference testTo examine whether USDS water attracts or repels egg laying by Ae. aegypti and Ae. albopictus mosquitoes, a two-choice oviposition preference test was conducted. Briefly, this experiment used two ovicups placed within a mosquito cage (1 × 0.5 × 0.5 m3), one ovicup with 200 ml USDS water and another with 200 ml flowerpot water. Adult mosquitoes were bloodfed on mice; fully engorged females 3-days post-bloodfeeding were used for oviposition preference tests. Ten gravid Ae. aegypti females were released into a cage and allowed to lay eggs for three days, and the number of eggs in each ovicup were counted. Five replicates were used. The same experiment was conducted for Ae. albopictus.To evaluate whether the presence of Cx. quinquefasciatus larvae has any impact on the egg laying behavior of invasive Aedes mosquitoes, the two-choice oviposition preference test described above was used. One ovicup contained 200 ml USDS water and ten first-instar Cx. quinquefasciatus larvae, while the second ovicup contained 200 ml USDS water only. Ten gravid Ae. aegypti or Ae. albopictus females were released into a cage and allowed to lay eggs for three days. Five replicates were used. We also conducted this experiment using flowerpot water with the same design and same number of replicates to determine whether the impact of Cx. quinquefasciatus larvae on Aedes mosquito egg laying behavior was similar across different water substrate types.Egg hatchingTo investigate the effects of different habitat water sources on egg hatching, 50 Ae. aegypti or Ae. albopictus eggs on separate filter papers were introduced into ovicups with 200 ml USDS water or flowerpot water. Deoxygenized distilled water that we routinely use in laboratory mosquito colony maintenance was used as a positive control. The experiment was conducted in an insectary with climate control (27 ± 1 °C). The number of larvae hatched were counted daily for six days continuously. Five replicates were used.Larval survivorshipA life table study was conducted on Ae. aegypti and Ae. albopictus larvae to determine the effect of USDS water and flowerpot water on larval development and survivorship. Twenty-five newly hatched Ae. aegypti or Ae. albopictus larvae were introduced into a microcosm that contained 200 ml USDS or field flowerpot water. The number of dead and surviving larvae was recorded daily until they pupated. Pupae were counted, and removed to different paper cups for emergence to adults. Four replicates were used for each type of habitat water per species. We included Cx. quinquefasciatus in the larval life table study for method validation purposes because the larvae of this species were known to successfully develop into pupae and adults in USDS water in southern California10.Larval survivorship experiments were conducted in two different seasons. The first was in the summer (August–September) 2019 when the density of invasive Aedes species peaked19, and also insecticide runoff from mosquito and residential/agricultural pest control applications were at the highest levels in southern California24. The second was in the winter (December) 2019 when there was little insecticide treatment for mosquito and pest control. This design enabled us to examine seasonality in larval survivorship and the impact of environmental insecticide runoff in USDS water. To determine whether USDS water’s nutritional deficiency plays a major role in limiting Aedes larval development, we repeated the larval survival experiment by adding 0.1 g Tetramin Tropical Flakes, the standard larval mosquito diet in insectaries, to the microcosms every 2 days. The number of dead and surviving larvae, pupae, and emergent adults was recorded daily.Data analysisAll aquatic habitats that were positive or negative for the larvae of Ae. aegypti, Ae. albopictus and Cx. quinquefasciatus (the predominant species), were mapped using ArcGIS 10.7.1. The proportion of aquatic habitats positive for Ae. aegypti and Cx. quinquefasciatus was calculated for each habitat type from 2016 to 2019. To examine variation in Aedes and Culex larval positivity rate among different groups of larval habitats within the USDS, larval positivity rates for Ae. aegypti and Cx. quinquefasciatus were calculated for underground water retention vaults, underground catch basins/manholes, and underground pipelines/tunnels. The Chi-square test was used to examine the statistical significance. Culex quinquefasciatus was analyzed because it was the most common species, whereas Ae. albopictus was not included in the analysis due to insufficient number of Ae. albopictus positive habitats. To determine whether USDS water attracted or repelled oviposition of invasive Aedes mosquitoes, a pairwise t test was used to compare egg number in USDS water ovicups to flowerpot water ovicups for each Aedes species. Similarly, a pairwise t-test was used to test the effect of Cx. quinquefasciatus larvae on Aedes mosquito oviposition choice.To examine the effect of water sources on egg hatching, the t-test was used to analyze the egg hatching rate. The analysis of larval life table study data focused on pupation rates and larval-to-pupal development times. The pupation rate was calculated as the proportion of first-instar larvae that molted into pupae. The effect of water sources and larval food supplementation on pupation rate was analyzed using non-parametric Wilcoxon test. The t-test was used to analyze the duration of larval-to-pupal development. Kaplan–Meier survival analysis was used to determine the effects of food supplementation and water source on larval development for each species, and the log-rank test was conducted to determine their statistical significance. All statistical analyses were performed using JMP software (JMP 14.2, SAS Institute Inc.). More