Philippa Kaur

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Historically, species distributions have been modeled independently from each other due to unavailability of multispecies datasets and computational restraints. However, ecological datasets that provide insights about collections of organisms have become prevalent over the last decade thanks to efforts like Long Term Ecological Research Network (LTER), National Ecological Observatory Network (NEON), and citizen science surveys1. In addition, technology has improved our ability to fit modern statistical models to these datasets that account for both species environmental preferences and interspecies dependence. These advancements have allowed for the development of joint species distribution models (JSDM)2,3,4 that can model dependence among species simultaneously with environmental drivers of occurrence and/or abundance.Species distributions are shaped by both interspecies dynamics and environmental preferences5,6,7,8. JSDMs integrate both sources of variability and adjust uncertainty to reflect that multiple confounded factors can contribute to similar patterns in species distributions. Some have proposed that JSDMs not only account for biotic interactions but also correct estimates of association between species distributions and environmental drivers3,9, while others claim JSDMs cannot disentangle the roles of interspecies dependence and environmental drivers5. We address why JSDMs can provide inference distinct from their concomitant independent SDMs, how certain parameterizations of a JSDM induce confounding between the environmental and random species effects, and when deconfounding these effects may be appealing for computation and interpretation.Because of the prevalence of occupancy data for biomonitoring in ecology, we focus our discussion of community confounding in JSDMs on occupancy models, although we also consider a JSDM for species density data in the simulation study. The individual species occupancy model was first formulated by MacKenzie et al.10 and has several joint species extensions4,11,12,13,14,15,16. We chose to investigate the impacts of community confounding on the probit model since it has been widely used in the analysis of occupancy data4,13,17. We also developed a joint species extension to the Royle-Nichols model18 and consider community confounding in that model.We use the probit and Royle-Nichols occupancy models to improve our understanding of montaine mammal communities in what follows. We show that including unstructured random species effects in either occupancy model induces confounding between the fixed environmental and random species effects. We demonstrate how to orthogonalize these effects in the model and compare the resulting inference compared to models where species are treated independently.Unlike previous approaches that have applied restricted regression techniques similar to ours, we use it in the context of well-known ecological models for species occupancy and intensity. While such approaches have been discussed in spatial statistics and environmental science, they have not been adopted in settings involving the multivariate analysis of community data. We draw parallels between restricted spatial regression and restricted JSDMs but also highlight where the methods differ in goals and outcomes. We find that the computational benefits conferred by performing restricted spatial regression also hold for some joint species distribution models.Royle-Nichols joint species distribution modelWe present a JSDM extension to the Royle-Nichols model18. The Royle-Nichols model accounts for heterogeneity in detection induced by the species’ latent intensity, a surrogate related to true species abundance. Abundance, density, and occupancy estimation often requires an explicit spatial region that is closed to emmigration and immigration. In our model, the unobservable intensity variable helps us explain heterogeneity in the frequencies we observe a species at different sites without making assumptions about population closure. In the “Model” section, we further discuss the distinctions between abundance and intensity in the Royle-Nichols model.The Royle-Nichols model utilizes occupancy survey data but provides inference distinct from the basic occupancy model10. In the Royle-Nichols model, we estimate individual detection probability for homogeneous members of the population, whereas in an occupancy model, we estimate probability of observing at least one member of the population given that the site is occupied. Furthermore, the Royle-Nichols model allows us to relate environmental covariates to the latent intensity associated with a species at a site, while in an occupancy model, environmental covariates are associated with the species latent probability of occupancy at a site. Species intensity and occupancy may be governed by different mechanisms, and inference from an intensity model can be distinct from that provided by an occupancy model19,20,21. Cingolani et al.20 proposed that, in plant communities, certain environmental filters preclude species from occupying a site and an additional set of filters may regulate if a species can flourish. Hence, certain covariates that were unimportant in an occupancy model may improve predictive power in an intensity model.Community confoundingSpecies distributions are shaped by environment as well as competition and mutualism within the community8,22,23. Community confounding occurs when species distributions are explained by a convolution of environmental and interspecies effects and can lead to inferential differences between a joint and single species distribution model as well as create difficulties for fitting JSDMs. Former studies have incorporated interspecies dependence into an occupancy model4,11,12,13,14,15,16, and others have addressed spatial confounding1,17,24,25, but none of these explicitly addressed community confounding. However, all Bayesian joint occupancy models naturally attenuate the effects of community confounding due to the prior on the regression coefficients. The prior, assuming it is proper, induces regularization on the regression coefficients26 that can lessen the inferential and computational impacts of confounding27. Furthermore, latent factor models like that described by Tobler et al.4 restrict the dimensionality of the random species effect which should also reduce confounding with the environmental effects.We address community confounding by formulating a version of our model that orthogonalizes the environmental effects and random species effects. Orthogonalizing the fixed and random effects is common practice in spatial statistics and often referred to as restricted spatial regression27,28,29,30,31. Restricted regression has been applied to spatial generalized linear mixed models (SGLMM) for observations (varvec{y},) which can be expressed as$$begin{aligned} varvec{y}&sim [varvec{y}|varvec{mu }, varvec{psi }], end{aligned}$$
(1)
$$begin{aligned} g(varvec{mu })&= varvec{X}varvec{beta } + varvec{eta }, end{aligned}$$
(2)
$$begin{aligned} varvec{eta }&sim mathcal {N}(varvec{0}, varvec{Sigma }), end{aligned}$$
(3)
where (g(cdot )) is a link function, (varvec{psi }) are additional parameters for the data model, and (varvec{Sigma }) is the covariance matrix of the spatial random effect. In the SGLMM, prior information facilitates the estimation of (varvec{eta },) which would not be estimable otherwise due to its shared column space with (varvec{beta })30. This is analogous to applying a ridge penalty to (varvec{eta },) which stabilizes the likelihood. Another method for fitting the confounded SGLMM is to specify a restricted version:$$begin{aligned} varvec{y}&sim [varvec{y}|varvec{mu }, varvec{psi }], end{aligned}$$
(4)
$$begin{aligned} g(varvec{mu })&= varvec{X}varvec{delta } + (varvec{I}-varvec{P}_{varvec{X}})varvec{eta }, end{aligned}$$
(5)
$$begin{aligned} varvec{eta }&sim mathcal {N}(varvec{0}, varvec{Sigma }), end{aligned}$$
(6)
where (varvec{P}_{varvec{X}}=varvec{X}(varvec{X}varvec{X})^{-1}varvec{X}’) is the projection matrix onto the column space of (varvec{X}.) In the unrestricted SGLMM, the regression coefficients (varvec{beta }) and random effect (varvec{eta }) in (1) compete to explain variability in the latent mean (varvec{mu }) in the direction of (varvec{X})27. In the restricted model, however, all variability in the direction of (varvec{X}) is explained solely by the regression coefficients (varvec{delta }) in (4)31, and (varvec{eta }) explains residual variation that is orthogonal to (varvec{X}). We refer to (varvec{beta }) as the conditional effects because they depend on (varvec{eta }), and (varvec{delta }) as the unconditional effects.Restricted regression, as specified in (4), was proposed by Reich et al.28. Reich et al.28 described a disease-mapping example in which the inclusion of a spatial random effect rendered one covariate effect unimportant that was important in the non-spatial model. Spatial maps indicated an association between the covariate and response, making inference from the spatial model appear untenable. Reich et al.28 proposed restricted spatial regression as a method for recovering the posterior expectations of the non-spatial model and shrinking the posterior variances which tend to be inflated for the unrestricted SGLMM.Several modifications of restricted spatial regression have been proposed30,32,33,34,35. All restricted spatial regression methods seek to provide posterior means (text {E}left( delta _j|varvec{y}right)) and marginal posterior variances (text {Var}left( delta _j|varvec{y}right)), (j=1,…,p) that satisfy the following two conditions36:

1.

(text {E}left( varvec{delta }|varvec{y}right) = text {E}left( varvec{beta }_{text {NS}}|varvec{y}right)) and,

2.

(text {Var}left( beta _{text {NS,}j}|varvec{y}right) le text {Var}left( delta _{j}|varvec{y}right) le text {Var}left( beta _{text {Spatial,}j}|varvec{y}right)) for (j=1,…,p),

where (varvec{beta }_{NS}) and (varvec{beta }_{Spatial}) are the regression coefficients corresponding to the non-spatial and unrestricted spatial models, respectively.The inferential impacts of spatial confounding on the regression coefficients has been debated. Hodges and Reich29 outlined five viewpoints on spatial confounding and restricted regression in the literature and refuted the two following views:

1.

Adding the random effect (varvec{eta }) corrects for bias in (varvec{beta }) resulting from missing covariates.

2.

Estimates of (varvec{beta }) in a SGLMM are shrunk by the random effect and hence conservative.

The random effect (varvec{eta }) can increase or decrease the magnitude of (varvec{beta }), and the change may be galvanized by mechanisms not related to missing covariates. Therefore, we cannot assume the regression coefficients in the SGLMM will exceed those of the restricted model, nor should we regard the estimates in either model as biased due to misspecification. Confounding in the SGLMM causes (text {Var}left( beta _j|varvec{y}right) ge text {Var}left( delta _j|varvec{y}right)), (j=1,…,p), because of the shared column space of the fixed and random effects. Thus, we refer to the conditional coefficients as conservative with regard to their credible intervals, not their posterior expectations.Reich et al.28 argued that restricted spatial regression should always be applied because the spatial random effect is generally added to improve predictions and/or correct the fixed effect variance estimate. While it may be inappropriate to orthogonalize a set of fixed effects in an ordinary linear model, orthogonalizing the fixed and random effect in a spatial model is permissible because the random effect is generally not of inferential interest. Paciorek37 provided the alternative perspective that, if confounding exists, it is inappropriate to attribute all contested variability in (varvec{y}) to the fixed effects. Hanks et al.31 discussed factors for deciding between the unrestricted and restricted SGLMM on a continuous spatial support. The restricted SGLMM leads to improved computational stability, but the unconditional effects are less conservative under model misspecification and more prone to type-S errors: The Bayesian analogue of Type I error. Fitting the unrestricted SGLMM when the fixed and random effects are truly orthogonal does not introduce bias, but it will increase the fixed effect variance. Given these considerations, Hanks et al.31 suggested a hybrid approach where the conditional effects, (varvec{beta }), are extracted from the restricted SGLMM. This is possible because the restricted SGLMM is a reparameterization of the unrestricted SGLMM. This hybrid approach leads to improved computational stability but yields the more conservative parameter estimates. We describe how to implement this hybrid approach for joint species distribution models in the “Community confounding” section.Restricted regression has also been applied in time series applications. Dominici et al.38 debiased estimates of fixed effects confounded by time using restricted smoothing splines. Without the temporal random effect, Dominici et al.38 asserted all temporal variation in the response would be wrongly attributed to temporally correlated fixed effects. Houseman et al.39 used restricted regression to ensure identifiability of a nonparametric temporal effect and highlighted certain covariate effects that were more evident in the restricted model (i.e., the unconditional effects’ magnitude was greater). Furthermore, restricted regression is implicit in restricted maximum likelihood estimation (REML). REML is often employed for debiasing the estimate of the variance of (varvec{y}) in linear regression and fitting linear mixed models that are not estimable in their unrestricted format40. Because REML is generally applied in the context of variance and covariance estimation, considerations regarding the effects of REML on inference for the fixed effects are lacking in the literature.In ecological science, JSDMs often include an unstructured random effect like (varvec{eta }) in (1) to account for interspecies dependence, and hence can also experience community confounding between (varvec{X}) and (varvec{eta }) analogous to spatial confounding. Unlike a spatial or temporal random effect, we consider random species effects to be inferentially important, rather than a tool solely for improving predictions or catch-all for missing covariates. An orthogonalization approach in a JSDM attributes contested variation between the fixed effects (environmental information) and random effect (community information) to the fixed effect.We describe how to orthogonalize the fixed and random species effects in a suite of JSDMs and present a method for detecting community confounding. In the simulation study, we test the efficacy of our method for detecting confounding, show that community confounding can lead to computational difficulties similar to those caused by spatial confounding31, and highlight that, for some models, restricted regression can improve model fitting. We also investigate the inferential implications of community confouding and restricted regression in JSDMs by comparing outputs from the SDM, unrestricted JSDM, and restricted JSDM of the Royle-Nichols and probit occupancy models fit to mammalian camera trap data. Lastly, we discuss other inferential and computational methods for confounded models and consider their appropriateness for joint species distribution modeling. More

For a schematic overview of the experimental design, see Fig. 2.Experimental evolutionProtocolThe stock population (Stock population below) was allowed to expand for one generation and from this we established eight replicate experimental evolution populations, four selected for fighter morphs (F-lines) and four selected for scrambler morphs (S-lines). Each population was founded by 1,000 recently eclosed adults (500 random females and 500 random males of the desired morph). The classification of the morphs was based on visual inspection using a stereoscopic microscope and was unambiguous due to the discontinuous distribution of the phenotypes (Classifying male morphs below). Adults were allowed to interact freely for 6 days, all surviving adults (with previously laid eggs discarded) were transferred to a new container for 24 h of egg laying, after which adults were removed. The resulting offspring were allowed to mature over 13 days and 1,000 individuals from the newly eclosed adults selected for founding the following generation, again 500 random females and 500 random males of the desired morph, with this protocol repeated every generation (Extended Data Fig. 1). The isolation of nymphs to use virgins was unfeasible with our experimental design and population sizes. However, the period of 6 days after selecting the founders of the next generation and collecting eggs for the next generation was probably enough to displace most sperm stored by females mated with any unselected males due to the high number of remating that will be occurring over this duration (females on average remate after 80 min, ref. 88) and last male sperm precedence89. The timing of generation was chosen to reflect maturation rates from our stock population to avoid indirect selection on this trait. Moreover, a previous study90 showed there was no difference between male morphs in maturation rates and that over similar lengths of time to the protocol here the fertility of both morphs remains similar. Therefore, our protocol was not likely to impose strong differential selection on morph life histories.Tracking morph proportionWe assayed the proportion of male morph in each population every 6–7 generations, by isolating 200 larvae (ten per vial) from the container, allowing maturation within vials and recording the morph of all males that eclosed (mean n = 86 per population, per generation, range 71–109). Our selection protocol was highly effective in driving an increase in the frequency of the desired male morph to >90% after 20 generations in both treatments, with this effect considerably faster within F-lines indicted by a significant two-way interaction between proportion of the desired morph and generation (χ2 = 39.9, d.f. = 6, P 90% is probably a consequence of a longer interaction period (3 versus 6 days) in which the stored sperm of males before selection was able to be displaced and/or because selection was acting more efficiently in our larger populations. The difference between rate of changes in morph proportion between F- and S-lines in the current study, and also found by Plesnar-Bielak et al.39, may be associated with the genetic architecture of morph expression. Alternatively, selection could be less effective in scrambler lines if they are less efficient than fighters in displacing sperm of previous females’ partners, but this is unlikely as R. robini male morphs have previously been demonstrated to not differ in their sperm competiveness89.Stock populationWe established a stock population by mixing three laboratory populations that were collected from three sites in Poland (Krakόw, collected in 1998 and 2008, Kwiejce, collected in 2017 and Mosina, collected in 2017; Extended Data Fig. 1), where the line derived for material used in creating the reference genome (below) was also established from the same collections at Mosina in 2017. All populations were maintained in cultures with several hundred individuals per generation before mixing and establishment of the stock population. The mixing of distinct populations increased the genetic variance in the stock population, which otherwise would probably have been limited due to founder events and the limited population size of each of the contributing populations73, thus decreasing our power to detect the effects of SSTs on genetic variation. The newly mixed stock population was maintained with several hundred individuals per generation for roughly 12 generations before the onset of this experiment. This time period is probably enough to break linkage disequilibria that could have arisen due to mixing (for unlinked loci, linkage disequilibrium should decay by half each generation91).One generation before establishing experimental evolution populations the proportion of male morphs was determined from 176 random males, indicating a roughly equal morph ratio (95 fighters, 81 scramblers) of the stock population (Extended Data Fig. 3).General housing and husbandryThe stock population and experimental evolution populations were maintained in plastic containers (approximate length, 9.5 cm; width, 7 cm; height, 4.5 cm), filled with roughly 1 cm of plaster-of-Paris. The same containers were used when sampling mites for sequencing for the reference genome or resequencing from experimental evolution populations, but either replaced the plaster-of-Paris with 5% agarose gel or added a thin layer of 5% agarose gel above the plaster-of-Paris, respectively. The agarose gel was used to reduce the number of contaminates within our samples and on the basis of preliminary extractions that indicated that small pieces of plaster-of-Paris may reduce the quality of DNA during extractions. Individuals, pairs and small groups of ten mites were housed in glass vials (approximate height, 2 cm; diameter, 0.8 cm) and large groups of 60 or 150 mites in plastic containers (approximate height, 1.5 cm; diameter, 2 cm diameter or height, 1.5 cm; diameter, 3.5 cm diameter, respectively) all with an approximate 1 cm base of plaster-of-Paris. All plaster-of-Paris bases were completely soaked in water before mites were transferred into them. All mites were reared at a constant 23 °C, at high humidity ( >90%) and were provided an excess of powdered yeast ad libitum.Classifying male morphsTo illustrate the discontinuous distribution of the weapon and to demonstrate that this classification based on visual inspection is non-subjective, we performed phenotypic measurements from male mites from a population collected near Krakόw, Poland, that had previously been fixed onto microscope slides for a separate study66. The measurements taken were idiosoma (body without mouthparts) length and width of third proximal segment of the third right leg (genu). Measurements were preformed using Lecia DM5500B microscope and Lecia Application Suite v.4.6.1. We then performed an analysis to, first, determine whether the allometric relationship between idiosoma length and width of third pair of legs is best described as discontinuous and, second, to verify that classification by simple visual inspection matches the same classification from allometric analysis. One researcher performed all the measurements and classified each male as a fighter (n = 50) or scrambler (n = 50), a separate researcher was then given the measurements but not the classification of the male morph.Broadly, guidelines for the analysis of non-linear allometries92 were followed. The log–log scatterplots of idiosoma length against leg width were visualized, which showed there was clear evidence for non-linear scaling relationships. Next histograms of idiosoma length, leg width and relative leg width (leg width/idiosoma length) were visualized (Extended Data Fig. 2a–c). Where a normal distribution of idiosoma length, and a binomial distribution in leg width and relative leg width are further indications of a discontinuous relationship. On the basis of the lowest point between the two peaks of the density plot of relative leg width (Extended Data Fig. 2c) males were classified as scramblers (relative leg width 0.125). Replotting the log–log scatterplot of idiosoma length and leg width, and using the classification of morph described above clearly demonstrates the discontinuous allometric relationship of idiosoma length and leg width in R. robini (Extended Data Fig. 2d). Moreover, on the basis of the Akaike information criterion (AIC), the discontinuous model where males were assigned a morph (AIC = 646.5) clearly has a substantially better fit than a simple linear and quadratic models (AIC = 918.5 and 920.2, respectively). Further models were omitted from comparison (for example, breakpoint or sigmoidal) due to the clear discontinuous allometry observed. Finally, all 100 males were assigned the same morph by visual inspection and blind allometric analysis, demonstrating that the former is effective and accurate in classifying male morph.Phenotypic assaysFecundity assays were performed using experimental evolution females at F20 and F32. Eggs laid by females between days 4–8 were counted, encompassing the window of time of most evolutionary relevance for female fitness during maintenance of selection lines (that is, egg laying period in selection lines was between days 6–7) and also likely to capture variation in lifetime fecundity that remains largely consistent throughout the first 3 weeks of life93. Nymphs were individually isolated to gain virgin females, which on maturation females from each experimental evolution population (n = 30) were paired with a male from the stock population (15 with fighters and 15 with scramblers). Pairs were transferred to a new vial on day 4, with the pair being removed from the second vial after a further 4 days and all eggs in the second vial counted. If the male had died in the first vial, they were replaced with a stock male of the same morph. Any female deaths in the first or second vials were recorded.Longevity assays were also performed at F20 and F32. At F20, females used in fecundity assays, including the stock male they were paired with (replaced if dead), were transferred to a new vial at day 8. After this point, vials were then checked every 2 days for female deaths and pairs were moved to new vials every 4 days. Males were replaced with stock males of the same morph if found dead. Similarly, at F20, on maturation males from experimental evolution populations (n = 30) were paired with stock females, vials were checked every 2 days and changed every 4 days, with females being replaced if dead. At F32, only female longevity was determined and was performed in groups; 30 experimental evolution females and 30 stock males (15 of each morph) were placed in plastic containers, two per experimental population. This logistically easier estimate of longevity was done due to local restrictions during the SARS-CoV-2 pandemic and the imposed limitations on people working closely together. Groups were checked for dead females every other day and all remaining live mites transferred to a new container every 4 days. When mites were transferred to a new container the sex and morph ratio were balanced to that of the remaining females, by either removing or adding males of the desired morph from the stock population.To determine whether the survival of mites differed between F- and S-lines when competition between males was allowed, at F45 we created small colonies from each population and survival of males and females recorded over 6 days, the same period as used between selecting founders of the next generation and subsequent egg laying period. Colonies were at a 50:50 sex ratio, established with 150 newly eclosed mites placed into small plastic containers. This was approximately the same density after selection of the next generations founders during the maintenance of experimental evolution populations (150 mites in roughly 9.5 cm2 = 16 mites per 1 cm2; 1,000 mites in roughly 67 cm2 = 15 mites per 1 cm2). After 3 days, all colonies were checked and any dead mites identified by sex. After another 3 days, again dead mites were recorded and all surviving mites sexed and counted.Additionally, at F45 we performed further fecundity assays to obtain estimates of inbreeding depression within experimental evolution populations. To establish family groups, larvae were isolated and on maturation F0 males and females (n = 16) from within the same experimental evolution population were paired together. Pairs were allowed to produce eggs for 48 h, after which adults were removed from vials. After hatching from each pair, 12 F1 larvae were isolated into new vials. On their maturation, these F1 mites were either paired with a full sibling, that is, from the same family, or with an individual from a different family but from the same experimental evolution population. When possible, we made two inbred and two outbred pairs with same family lines used. Again, pairs were allowed to produce eggs for 48 h before their removal for the vial. After a further 5 days, vials were checked for larvae, if larvae were present in the first vial six were individually isolated and the second vial discarded, if no larvae were present in the first vial the second vial was checked for larvae and, if present, they were isolated. This protocol therefore produced inbred and outbred individuals from within the same experimental evolution population. Which, as above, on maturation F2 inbred and outbred females were paired with stock males (fighter males only) and number of eggs laid between days 4 and 8 counted. Only a single female from each unique inbred or outbred family was used. Either due to pairs failing to produce offspring or there being no F2 females, samples sizes were not exactly equal. In total, 59 outbred and 55 inbred females from F-lines, and 56 outbred and 54 inbred females from S-lines were paired with stock males.Phenotypic assay statistical analysesAll phenotypic analysis was conducted using R statistical software94 (v.3.5.2) and data were visualized using ggplot2 (ref. 95).Analysis of male morph proportion was performed using a generalized linear mixed model with binomial error structure, fitted using lme4 (ref. 96). Where the proportion of desired morph was compared in model with morph selection and generation (as a factor) including their two-way interaction as explanatory variables, and population included as a random effect.All fecundity data were analysed using generalized linear mixed models with Poisson error structures, fitted using lme4. Due to the differences in stock population males used between F45 and earlier generations, and slightly different rearing conditions between females in the fecundity assays from generations F20 and F32, they were analysed separately from data collected in F45. However, we noted that the fecundity of females in Fig. 5a was comparable to the outbred females in Fig. 5b. Explanatory variables fitted to fecundity data from F20 and F32 were, morph selection treatment, generation, including their two-way interaction term, and stock male morph. The explanatory variables fitted to fecundity data from inbreeding depression data were, morph selection treatment and status of female (that is, inbred or outbred), including their two-way interaction term. In both analyses, we included population as a random effect and an observation level random effect to account for overdispersion, we omitted fitting random slopes due to issues with increasing the complexity of random effects close to reaching a singular fit. Females that died before the end of the fecundity assay and those that laid zero eggs were removed from analysis. This excluded five females from F20 (three F-line and two S-line), 20 from F32 (13 F-line and seven S-line) and 16 from F45 (three inbred and three outbred F-line, and nine inbred and one outbred S-line).Longevities of females at F20 and F32, and males at F20, were analysed separately using mixed effects Cox models, fitted using coxme97. In all analyses, we included a random effect of population, with morph selection treatment as an explanatory variable and extra variable of male morph included in female longevity analysis at F20. Survival of mites over 6 days at F45 was analysed using a GLM with counts of dead and surviving mites fitted with a quasibinomial error structure, the model included morph selection treatment and sex, including their interaction term, as explanatory variables. If individuals were lost due to handling error (that is, killed or escaped) they were right-censored during analysis.Genome assemblySample originA line of R. robini originated from a wild-collected population from the Mosina region (Wielkopolska, Poland). In October 2017, onions were collected from the field and approximately 200 individuals of R. robini were identified under dissecting microscope. The line used for DNA isolation in the genome sequencing project was developed from full sib × sib mating for 14 generations (to maximize homozygosity) following and continuing the protocol described in ref. 67.DNA extractionFor DNA extraction we used only mite eggs, that were laid by 500 females, collected in a container (see above for a description) Females were kept in this container for 3 days. After that time, they were removed, and eggs were filtered using fine sieves and washed for 1 min in 0.3% sodium hypochlorite solution and in Milli-Q water for 2 × 2 min to remove any potential foreign DNA contamination. These eggs were collected in 1.5 ml Eppendorf tube and after short centrifugation, the remains of the water (supernatant) removed with a pipette. The sample was immediately transferred to ice and prepared for DNA extraction. DNA was extracted using Bionano Prep Animal Tissue DNA Kit for HMW DNA isolation according to the manufacturer’s instructions. Briefly, eggs were smashed with a sterile pellet pestle on ice in 500 μl homogenization buffer; the sample was fixed with 500 μl cold ethanol and incubated 60 min on ice, after that time the sample was centrifuged at 1500g for 5 min at 4 °C and the supernatant was discarded. Next, after resuspension in a homogenization buffer pellet, this was cast in four agarose plugs as described in the original protocol. Agarose plugs were incubated with Proteinase K and Lysis buffer solution for 2 h with intermittent mixing. After that time, the digestion solution was replaced with a freshly made one and incubated overnight with intermittent mixing. According to the original protocol, after RNase A digestion and plug washing, DNA was recovered by incubation of the plugs in TE buffer, followed by plug melting and addition of agarase. Recovered DNA was dialysed and homogenized on a membrane for 45 min at room temperature and transferred to a clean tube with a wide bore tip.SequencingSequencing was done using Oxford Nanopore Technologies (ONT, MinION). Isolated DNA purified using AMPure XP beads and resuspended in H2O before library preparation. Two separate libraries were prepared using ligation sequencing kit, SQK-LSK109 and Rapid Sequencing Kit SQK-RAD004, respectively, according to the manufacturer’s protocols and were sequenced on a FLO-MIN106 R9.4.1 SpotON flow cell on a MinION Mk 1B sequencer (ONT). The total yields from sequencing were 484,700 reads (2,417,068,187 nt) with a read-N50 of 10,044 nt (ranging from 216,403 to 100). Base calling of the raw reads was done using Guppy (v.3.3) resulting in a total sum of the reads 7,979,616,172, equivalent to 26× coverage aiming for a genome of 300 megabases (Mb). The reads N50/N90 were estimated at 7,958/1,719.Assembling reference genomeReads aligning with the Mitochondrion genome were identified using BLASTN and filtered from the raw reads before assembling the genome. The remaining ONT reads were assembled using the Flye software (v.2.6), with –min-overlap 3,000 to increase stringency at the initial overlay step, and default parameters including five rounds of polishing through consensus, contigs were additionally polished two times with Medaka (v.0.11.2). Illumina paired-end RNA dataset is assembled using CLC Assembler (CLC Assembly Cell). Both RNA assemblies and paired-end 10X genomic dataset (unpublished data) were mapped onto the contigs using minimap2 (v.2.16) and BWA mapper (v.0.7.17), respectively, and the assembly was further polished using PILON (v.1.20) to error correct potential low-quality regions. The resulting assembly yielded a genome of 307 Mb, assembled into 1,533 contigs ranging from 10,840,357 to 100 basepairs (bp) and an assembly-N50 of 1.670 Mb. Moreover, the BUSCO completeness analysis using the Arachnida (odb10) reference set confirmed our assembly represents the complete genome C:94.8%(S:89.1%,D:5.7%),F:0.9%,M:4.3%,n:2934 (=arachnida_odb10), only missing 126 genes from the whole reference set. Knowing that BUSCO only gives a rough estimation, we remain confident that this assembly represents well the bulb mite genome.Flow-cytometryWhole individual R. robini were homogenized in 500 μl of ice-cold LB01 detergent buffer along with the head of a male Drosophila melanogaster (1 C = 0.18 pg) as an internal standard. The homogenized tissue was filtered through a 30-μm nylon filter. Then 12 μl of propidium iodide with 2 μl of RNase was added, and stained for 1 h on ice in the dark. All samples were run on an FC500 flow cytometer (Beckman-Coulter) using a 488-nm blue laser, providing output as single-parameter histograms showing relative fluorescence between the standard nuclei and the R. robini nuclei. Six replicate samples were run to account for variation in fluorescence outputs. The genome size of R. robini was estimated at 0.30 pg, or about 293 Mb, and consistent with estimation of size from the genome assembly described above.Mitochondrial genomeONT reads aligned with R. robini mitochondrion genome were de novo assembled with Flye (v.2.6) assembler and polished with Racon. Mitochondrion genome is assembled in one single contig with a size of 15,335 bases.Gene predictionOn the polished final genome, protein coding genes have been predicted. For this, AUGUSTUS was used including hints coming from R. robini RNA-sequencing (RNA-seq) (samples SRR3934324, SRR3934325, SRR3934326, SRR3934327, SRR3934328, SRR3934329, SRR3934330, SRR3934331, SRR3934332, SRR3934333, SRR3934335, SRR3934337, SRR3934338 and SRR3934339 from the PRJNA330592 BioProject deposited at the National Center for Biotechnology Information (NCBI) Short Read Archive) and proteins coming from highly curated Tetranychus urticae (v.2020-03-20) as well as proteins from the previous version of the unpublished, Illumina-sequenced R. robini genome (https://public-docs.crg.eu/rguigo/Data/fcamara/bulbmite.v4a/). The PE RNA-seq reads were mapped on the genome using HISAT2 (-k 1 —no-unal) and further processed with Regtools to extract junction hints and filtered for junctions with a minimum coverage of 10. All the RNA-seq reads were also assembled with CLC Assembly Cell (v.5.2.0) software, setting the word size for the Bruijn graph at 50 and maximum bubble size at 31. The reads were assembled into 689,563 contigs (ranging from 10,675 to 180 bp), which were later mapped on the genome with GenomeTheader to generate complementary DNA hints. Protein hints were generated by using with Exonerate (v.2.2) with Protein2Genome model. To reduce the amount of overprediction due to repeated elements (transposable elements, simple sequence repeats) we de novo predicted high abundant repeats using RepeatModeler. The accompanying parameter file for extrinsic data for AUGUSTUS was adapted to include these hints as well as the softmasking of the genomic sequence. The resulting gene predictions from AUGUSTUS were further curated with EvidenceModeler using the same extrinsic data. The BUSCO analysis confirmed that our gene prediction indeed captured the expected genes well (C:94.6%(S:86.3%,D:8.3%),F:0.4%,M:5.0%,n:2934 (=arachnida_odb10)). The final predicted gene set was subsequently processed to be uploaded into ORCAE (https://bioinformatics.psb.ugent.be/orcae/overview/Rhrob)98.ResequencingGenomic sampling and mappingFor genomic analyses we sampled material from each of the morph selection lines (n = 8) at F1, F12 and F29. Following the experimental evolution protocols, after the first 24 h of egg laying all adults were transferred to a new container (described above) for a second 24 h to lay eggs and from these second dishes genomic material was sampled. On maturation, adults were transferred to and kept for 3 days in containers. Adults were then randomly selected and placed into Digestion Solution for MagJET gDNA Kit (F1&12) or ATL buffer (F29) before freezing at −20 °C. From each population two samples were collected consisting of 100 individuals (1 × 100 females and 1 × 100 males of random morph), the two samples separated by sex were used as technical replicates. The tissue from the 100 individuals within each sample was homogenized and DNA was extracted by Proteinase K digestion (24 h) followed by standard procedures using MagJET Genomic DNA Kit (ThermoScientific, F1&12) or DNeasy Blood and Tissue (Qiagen, F29). DNA concentration was controlled with the Qubit double-stranded DNA HS Assay Kit and DNA quality was assessed on agarose gels. The library preparation was performed using NEBNext Ultra II FS DNA Library Prep kit for Illumina.Whole-genome resequencing was carried out by National Genomics Infrastructure (Uppsala, Sweden) using the Illumina Nova-Seq 6000 platform with S4 flow cell to produce 2 × 150 bp reads (average 160.7 × 106: range 130.7 × 106 − 189.9 × 106). Adaptors were trimmed from reads using Trimmomatic99 software (v.0.39) and unpaired reads discarded. Fastq files were mapped to the assembled genome with bwa mem100 (v.0.7.17-r1188) using default settings. Sam files were converted to bam files, sorted, duplicates marked and ambiguously mapped reads removed using samtools101 (v.1.9). On average, 90% (range, 86–93%) of the reads from each sample were mapped successfully, of which an average of 17% (range, 15–19%) were marked as duplicates. This left us with an average of 117.7 × 106 pair end reads per sample, ranging between 99.6 × 106 and 145.9 × 106 (Supplementary Table 1).Genomic analysisFile preparation and filteringPreparation of files used in genomic analysis was done as follows: bam files were converted to a pile-up file using samtools, following which indels and surrounding windows (5 bp either side) were filtered, using identify-genomic-indel-regions.pl and filter-pileup-by-gtf.pl in PoPoolation102 (v.1.2.2) to avoid false SNPs, with the resulting filtered pile-up file converted to a sync file using mpileup2sync.pl in PoPoolation2 (ref. 103) (v.1.201). Using custom python scripts, the distribution of coverage from each sample (single sex) was determined by recording the coverage of positions every 10 kb across the genome from the sync file to give information on expected coverage (Supplementary Fig. 1). On the basis of this, we filtered the sync and pile-up files to contain only regions within a range of informative coverage, where the mean coverage of all samples at every position was between 50% of the expected coverage and 200% of the expected coverage (56×, range 23−112×). The pile-up and sync files containing individual male and female samples (48 in total) were then merged by sex to give files containing allele frequencies from 24 samples (eight populations across three generations), each consisting of allele frequencies of 200 individuals (100 males and 100 females, above) and used in all subsequent analysis (unless stated otherwise). Similarly, we drew coverage of a position every 10 kb from each sample in the sex-merged sync file to determine a distribution from which we decided to subsample to (Supplementary Fig. 1). We putatively identified X-linked contigs (below) and excluded them autosomal analysis. A similar, but, separate analysis on genes and SNPs from X-linked contigs was performed by using different parameters (below).Estimating nucleotide diversityUsing PoPoolation we determined various estimates of genetic diversity per sample (that is, 24 sex-merged samples). The pile-up file from each sample was subsampled using subsample-pileup.pl to a coverage of 63× (max coverage, 252×) to standardize estimations of genetic diversity across the genome, between populations and across generations. First, nucleotide diversity (Tajima’s Pi, π) and number of segregating sites (Watterson’s theta, ϴ) were estimated within genes. We performed analysis of exons using Syn-nonsyn-at-position.pl, in which genetic diversity of synonymous and non-synonymous positions were determined. Further analysis of overall genetic diversity within exons and introns were performed using Variance-at-position.pl, Tajima’s D (D) also estimated in the former. We used a minimum count of three (equal to a minor allele frequency of roughly 5%) for a SNP to be called, and a phred score >30 and a pool size of 400. Further analysis using 10 kb sliding windows (step size 10 kb) across the genome were performed using Variance-sliding.pl, and also included estimation of D. Estimates of D require the minimum count to be 2, but otherwise all the same parameters were used.We filtered genes to be included in our analysis (and all subsequent analysis) on the basis of a number of criteria. On the basis of extensive RNA-seq data from both males and females (Plesnar-Bielak, unpublished data with NCBI accession number PRJNA796800), we only included genes in our analyses that were expressed at a mean level of fragments per kilobase of transcript per million mapped reads >1 across 72 samples originated from both sexes and both morphs rearing in three different temperatures (18, 23 and 28 °C). A further filtering step was performed to remove genes with inconsistent mapping between samples, only genes with >60% exons mapped to (calculated from positions used to calculate parameters in the Syn-nonsyn-at-position.pl π outputs), with 63−252× coverage, in all 24 samples were included in the analysis. The final dataset contained 13,389 autosomal genes and subsequently used to filter other datasets to retain this set of genes only (see Supplementary Table 8 for a list of genes). Similarly, windows were discarded from outputs if 60% of genes being mapped to in all 24 samples) and reducing the final X-linked dataset to contain fewer than 200 genes. We therefore opted to reduce the target coverage further to 40×, in an attempt to retain more genes. This slight reduction of target coverage increased the number of genes in the final dataset substantially to 587 genes. We therefore opted to use a minimum coverage of 40× in all analysis of X-linked SNPs, genes and windows.Diverging SNPsTo determine divergent SNPs between F- and S-lines, we extracted the allele frequencies of all samples from the sex combined sync file. Samples from F29 were then used to filter the entire dataset to only contain SNPs on the basis of a number of criteria. First, positions within all samples were required to have a coverage >63× and 5% (that is, the average of all samples but not necessarily above >5% in all samples). Thus, our dataset contained only positions with the target coverage in all F29 samples and in which polymorphisms were unlikely to be a consequence of sequencing errors. After this filtering we were left with roughly 6 million SNPs used in further analysis. We performed a GLM, at each position by comparing the count of the major allele against counts of minor alleles at F29, to determine consistent allele frequency changes between treatments70. If any population had minor or major allele count of 0, +1 was added to minor and major alleles from all samples. To correct for multiple testing, we converted P values to q values using the qvalues R package (v.2.14.1)104 and applied a FDR with a q 900,000), GLMs were performed (identical to above) on the simulated major and minor allele counts. Using a FDR with a q  More

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This section is devoted to show results and to highlight eventual effects of the interplay between the nonlinearity characterizing the system dynamics and the presence of noisy fluctuations for the irradiance variable.Analysis of experimental dataThe need of taking into account noisy fluctuations of such an environmental variable is well demonstrated in Fig. 1. In the first panel (a) the experimental time behaviour of the irradiance is shown. This noisy curve is based on the experimental data (purple points) of the Boussole buoy located in the Gulf of Lion, collected over a period of nine years, precisely from 2004 to 2013. The time series of the experimental data presents quite a few gaps in time due to the malfunction of the buoy. This aspect has been remedied by merging the experimental data with those of the OASIM model validated for the Boussole site61 (yellow points). The latter is a multispectral atmospheric radiative transfer model that is in turn forced by experimental-model data based on ECMWF ERAINTERIM reanalyses which provide, for example, cloud cover data. The radiative model is partly stochastic since it considers the effects stemming from the presence of clouds, averaged along a single day (this explains why the yellow points are slightly less scattered). We see that the OASIM model accurately reproduces the profile which emerges from the experimental data. Further, we stress that the experimental data are only used in this initial analysis. In the biogeochemical simulations the irradiance signal is fully reconstructed starting from a realistic seasonal cycle combined with a range of different random fluctuations, and the information from OASIM is not used. In the second panel (b) the daily (black points) as well as the three-month (red points) running mean of the experimental series are plotted. Figure 1c shows the irradiance noisy fluctuations (INF) which have been obtained by subtracting the three-month running mean curve (3MRM, red curve in Fig. 1b) from the daily running mean one (DRM, black curve in Fig. 1b) and normalizing with respect to the mean of the 3MRM ((overline{3MRM})), namely (INF = (DRM – 3MRM) / overline{3MRM}). We see that a seasonal overall trend with higher oscillations during the winter time can be seen, implying that the characteristics of the noise may change over the year. Moreover, a slight imbalance between positive and negative values of the noisy fluctuations (that is, different values of the maximum fluctuation intensity) is present. The physical reason for the occurrence of such an aspect can be ascribed to the fact that the maximum value of solar irradiance corresponds to that measured during a sunny day. Conversely, the minimum level tends to zero corresponding to a dense darkness. While the former is close to the mean value of the solar irradiance (most of all in summer), the latter is much further away and then a natural asymmetry arises in the random fluctuations. However, it should be noted that, apart from the intense spikes, the asymmetry is not so pronounced, as proved by the mean value (red line in Fig. 1c) which is practically zero, namely (0.4%) of the (overline{3MRM}). Therefore, basing on this last observation, to model the noise affecting the irradiance dynamics, as a first approximation we consider a symmetric Gaussian autocorrelated noise as described in the next subsection.On the basis of such experimental results, we postulate the hypothesis that random fluctuations of light cannot be neglected, most of all in the study of ecological systems where light profoundly determines the system dynamics, governing fundamental processes at the basis of of the food web.Figure 1(a) Experimental data (purple points) of the stochastic solar irradiance collected by the Boussole buoy in a time-window of 9 years (2004-2013); the yellow points are the data generated by the OASIM model used to fill the gaps present in the experimental time-series due to malfunctioning of the buoy. (b) Daily (black points) and three-month (red points) running mean of the light curve in panel (a). (c) Irradiance noisy fluctuations (INF), obtained by subtracting the three-month running mean curve (3MRM) from the daily running mean one (DRM) and normalizing with respect to the mean value of 3MRM ((overline{3MRM})), namely (INF = (DRM – 3MRM) / overline{3MRM}); the red line represents the mean value of such fluctuations. Data already presented and validated in61.Full size imageSolar irradianceThe solar irradiance forcing is derived considering a deterministic seasonal oscillation combined with an Ornstein-Uhlenbeck process. The coefficient of variation (CV) of simulated light forcing, Fig. 2, (CV=sigma / mu) ((mu) and (sigma) being mean value and standard deviation calculated over both time and numerical realizations), is shown for 231 (D-tau) pairs. D and (tau) represent the intensity of a Gaussian noise source and the auto-correlation time of the fluctuations, respectively (see Eqs. (2) and (3)).Each pixel represents the mean value on time of CV calculated with respect to 1000 different stochastic realizations. Figure 2Coefficient of variation ((CV=sigma / mu)) of irradiance resulting from numerical integration of model equations for 231 (D-tau) different scenarios.Full size imageIt is easy to see the agreement between the results obtained from the numerical integration and the theoretical ones derivable from Eq. (5) by putting (text {var}{F_L(0)}=0) and (t gg 1), getting (sigma ^2_L=D / 2tau). In Fig. 2, indeed, the maximum values of (sigma) lie in the upper left part of the plot corresponding to small (high) values of (tau) (D). As it is clear the values of D have been chosen in order to obtain a relative standard deviation ranging from (5%mu) to (60%mu). We underline that, in this case, it is possible to interchangeably consider (sigma) and CV since the dependence of CV on D and (tau) does not differ from that of (sigma) (meaning that the dependence of (sigma) is not altered by dividing by (mu)) (results not shown).Effects on population dynamicsIn this section the noise-induced effects on the population dynamics are examined. The nine planktonic populations present a different qualitative behaviour of the CV, compared to that of the irradiance. In this case, the CV is characterized by a strong non-monotonic dependence on the parameter (tau). This aspect can be appreciated in Fig. 3 where different curves of CV versus the time correlation parameter are shown for different fixed values of D.Figure 3Coefficient of variation ((CV=sigma / mu)) of the nine planktonic populations resulting from numerical integration of model equations plotted versus the considered values of (tau); the different curves are related to different values of the noise intensity D.Full size imageThe existence of a maximum value for CV can be appreciated for each species. Although the qualitative behaviour is the same for all strains, particular attention has to be payed on diatoms and nanoflagellates. All the other species, indeed, present a percent variation of standard deviation between (2%) and (15%). In the case of nanoflagellates, instead, the D-dependent range is (20-90%), while diatoms reach values over the (100%) for the highest values of D. Therefore, these two species, in particular, and the whole system, in general, are extremely sensitive to the auto-correlation time which characterizes the noise.We note that the different curves related to the different selected values of D approach the horizontal axis, tending asymptotically to vanish as (tau) increases. Such a behaviour can be explained by the fact that high values of (tau) give rise to a more correlated dynamics, so that (tau rightarrow infty) implies fully correlated time-behaviours corresponding to the deterministic case. In this instance, then, all the different realizations give the same results, making the standard deviation vanish. The same happens, independently of the value of (tau), for low values of noise intensity for which the corresponding curves approach the same almost vanishing value (see orange, gray and yellow lines). Differently from the previous case, when (tau rightarrow 0) the noise tends to a delta-correlated noise, that is a white noise; for (tau ne 0), instead, the noise spectrum is not flat, being characterized by a Cauchy-Lorentz distribution. The strong nonmonotonicity of CV with respect to (tau), emerging when there are relatively high values of CV, implies a greater variability of the system biomass. Lower values of CV indicate that the system dynamics is less influenced by the presence of noise where very little or no differences with respect to the deterministic case are present. Conversely, high values of CV clearly demonstrate the remarkable signature of the presence of an impacting noise source. It is interesting to note that the noise influence on the ecosystem strongly depends on both (tau) and D, that is, just an intense noise is not enough to generate a greater response of the ecosystem. In particular, experimental data are characterized by a CV approximately equal to 0.361, which corresponds to values of D and (tau) lying on the diagonal strip in Fig. 2 ranging from ((tau ,D)=(0.5,10^4)) to ((tau ,D)=(365,10^7)). Finally we note the presence of a noise suppression effect. High values of D, indeed, can generate slight effects when the correlation time (tau) does not take on suitable values.The results shown here are an extension of the previous work by Benincà et al.56. There, the authors analyse a simpler, less realistic model of two interacting populations, whose dynamics is affected by a randomly fluctuating temperature. In that case, moreover, the deterministic oscillations of the temperature are suppressed, and the system exhibits intrinsic Lotka-Volterra oscillations whose frequency match with the characteristic one(s) of the noise. On the contrary, here, the observed maximum response (see Fig. 3) cannot be interpreted as a synchronization effect, since our model does not present intrinsic Lotka-Volterra-like oscillations and the periodic population variability is only due to the deterministic forcing(s).The nonmonotonic behaviour of the CV can be then interpreted as the signature of the intimate interplay between the ecological system and the noise. This interplay, indeed, has a pivotal role in both determining the dynamics of the populations and defining the characteristics of the ecosystem.In Fig. 3 it can be observed that the value of (tau) for which CV is maximum strongly depends on the noise intensity D. In particular, it is possible to note that the peaks in Fig. 3 move towards higher values of (tau) as the noise intensity increases. Thus, Fig. 3 demonstrates that the maximum-response effect to the random fluctuations is sensitive to the noise intensity D.However, it is important to underline that the response of the system to the noisy signal does not depend on the yearly oscillations induced by the deterministic forcings. Indeed, by considering constant the deterministic part of all external forcings (temperature, irradiance, wind and salinity), the non monotonic behaviour of CV with respect to both (tau) and D is still present, provided that the populations are not extinct (plot not shown). In this scenario indeed, besides dinoflagellates, diatoms and nanoflagellates are practically extinct as well, exhibiting thus a constant vanishing variance. All the other strains, instead, present qualitatively the same nonmonotonicity with only slight differences (shift of the peaks and different mean values of the CV curves), probably due to the extinction of diatoms and nanoflagellates which causes relevant differences in the system dynamics. More specifically, the system’s response seems to depend on both the noise intensity and the correlation time (see Fig. 3).In this scenario (absence of seasonal driving) we have studied the dependence on both parameters D and (tau) of the probability density functions (PDFs) of the non-vanishing populations. In Fig. 4, the PDFs of bacteria (B1), picophytoplankton (P3), microzooplankton (Z5) and etherotrophic nanoflagellates (Z6) are plotted for (tau =0.5) and eight different values of the parameter D.Figure 4Dependence of the probability density functions of non-vanishing populations on the parameter D for (tau =0.5). The curves are normalized within the interval taken into account. For this reason the relative peaks of the curves in the bottom panels have different values compared to those of the top panels. However, the figure aims at showing the existence of the value of the noise intensity for which the system is more sensitive as well as the generation of a stationary out-of-equilibrium state induced by the noise.Full size imageWe see that the mean value and the variance of these populations are strongly affected by the presence of random fluctuations in the irradiance. Specifically, as the noise intensity increases the mean values of picophytoplankton and bacteria concentrations exhibit a shift. In particular, the results indicate that picophytoplankton is disavantaged by the presence of a noisy component in the irradiance, which indeed tends to inhibit its ability to absorbe the solar light, slowing down its growth. As a consequence, since phytoplankton and bacteria compete for the same resources, as the former declines the latter are favoured, with a compensation mechanism which allows their predators (zooplankton populations) to be almost not affected by the noisy behaviour of the irradiance. Further, we note that for intermediate values of the noise intensity ((D = 10^4 – 10^5)) a maximum of the variance occurs (the PDFs are clearly spread on a wider range of values). Such an effect indicates that the noisy behaviour of irradiance strongly influences the whole ecosystem dynamics. Moreover, the nonmonotonic behaviour of the variance (its PDFs become larger and then tighter again as the noise intensity increases) indicates that the noise pushes the ecosystem away from equilibrium, driving it towards a non-equilibrium steady state. Finally, we note that the nonmonotonic behaviour of CV as a function of the noise intensity remains also in the presence of seasonal driving.Figure 5Coefficient of variation ((CV=sigma / mu)) of nine planktonic populations resulting from numerical integration of model equations plotted versus the considered values of D; different curves correspond to different values of the correlation time (tau).Full size imageFigure 5 shows indeed the nonmonotonic response of the ecosystem to the change of D when the deterministic seasonal cycling of the four environmental parameters (temperature, irradiance, wind and salinity) is present. It is easy to observe that also in this instance the major noise-induced effect appears in nanoflagellates and diatoms with a percent standard deviation of 50(%) and 100(%), respectively. The coalescence of different curves (related to different values of (tau)), as D decreases, is due to the fact that for (D rightarrow 0) the impact of the noise is negligible and the evolution of the system practically resembles the deterministic one. On the contrary, for higher values of D remarkable differences arise and clear peaks of CV appear in the considered range of variation.These plots show that, for a fixed value of (tau), there exists a value of the noise intensity for which the planktonic concentrations are maximally spread around their mean values (corresponding to the maximum value of CV and then of the variance). Moreover, such a nonmonotonic behaviour suggests the presence of a resonance, which can be interpreted as the effect of the interplay between the nonlinearity of the system and the environmental random fluctuations.Also in this case, the interplay between the two parameters D and (tau) in determining and characterizing the dynamics of the ecosystem transparently emerges. The value of D corresponding to the maximum value of CV, indeed, basically depends on the specific value of (tau).Finally, we point out that the different dynamic scenarios identified by the D-(tau) couples can be experienced by the system during the year, since the two parameters may seasonally vary depending on the different weather conditions. In other words, a seasonally varying noise (see Fig. 1c) may cause the nine populations explore different regions of the D-(tau) space during the year. Therefore, the results reported in this paper can highlight the detectable yearly variability of a marine ecosystem which does not stem from the deterministic seasonal variation of environmental parameters.Effects on the organic carbonIn this subsection the effects of the irradiance noise on the biogechemistry are analysed. In Fig. 6 the dependence on (tau) of both the CV [panel (a)] and the mean value concentration [panel (b)] of detritus, labile dissolved organic carbon (L-DOC), semi-labile dissolved organic carbon (SL-DOC) and gross primary production (GPP) are shown. All these biogeochemical properties are correlated with carbon cycling. Gross primary production is related to the amount of carbon entering in the ecosystem, and is related to the maximum energy available in the ecosystem progressively dissipated in the trophic web. Gross primary production is directly affected by light fluctuation and its CV shape is very similar to that of the irradiance, Fig. 2. We selected also detritus and DOC because they are important indicators for the carbon cycling dynamics and are related to the cycling of chemicals like heavy metals62. The different curves, related to different values of D, approach the same (vanishing) value for large (tau). As previously discussed for the CV [Fig. 6(a)] of biomass concentrations, this circumstance is due to the fact that, in this case, the system dynamics tends to the deterministic case, characterized by a unique possible realization implying a vanishing standard deviation. For high correlation times thus the system is insensitive to the noise intensity. On the contrary, for small values of (tau), different values of D lead to significant differences of the variance. In particular, detritus, L-DOC and SL-DOC exhibit a clear non-monotonic behaviour whose maximum value depends on the combined values of D-(tau). Only the GPP presents a decreasing monotonic behaviour.The dependence of the mean value concentration on (tau), instead, is qualitatively the same for all the four parameters. Also in this case we can note a diversification with respect to D occurring at small (tau) and a (deterministic) constant value arising for low (high) values of D ((tau)).These results manifest that not only the population dynamics, but also all the biogeochemical processes are profoundly affected by the presence of stochastic environmental variables. The values and the behaviour of the examined quantities are indeed determined by the intimate interplay between the intensity and the time correlation of the noise fluctuations.Figure 6(a) Coefficient of variation ((CV=sigma / mu)) and (b) mean value concentration ((mu)) of detritus, labile dissolved organic carbon (L-DOC), semi-labile dissolved organic carbon (SL-DOC) and gross primary production (GPP) resulting from numerical integration of model equations plotted versus the considered values of (tau); the different curves are related to different values of the correlation time D.Full size image More

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Growth conditions and plant materialsTwo experiments were conducted concurrently (sites A and B) in the same screen house in 2019 between the months of May and July at the Landmark University Greenhouse and Hydroponic Technology Center, a section of the Teaching and Research Farm of the University in Omu-Aran, Kwara State Nigeria. Experiment at site B was conducted simultaneously as A so as to validate the results of experiment A. Landmark University lies within Latitude 8° 7′ 26.21388″ and 5° 5′ 0.1788″. Both experiments (A & B) involved tomato (Solanum lycopersicum L. variety cherry) and cucumber (Cucumis sativus L. variety marketer) crops. For each crop, seeds were sown into a separate seed tray filled with coco peat (Coco peat, SRIMATHI EXPORT, INDIA). Cocopeat is the mesocarp tissue or husk after the grinding of coconut fruit. It has a lightweight and high water and nutrient holding capacities, it has an acceptable pH, electrical conductivity, and other chemical attributes27. Rice husk is the by-product of rice after milling. The rice husk used was collected from the rice processing mill of Landmark University. Rice husk is a highly porous and light weighted material with a very high specific area28.Two sets of seed trays (one for organic and another for inorganic fertilizers) were used each for tomato and cucumber crops in the nursery. Both were raised in the nursery for two weeks before transplanting. Black grow bags (30 × 17 cm) filled with a coco peat/rice husk (1:4 ratio by volume) mixture with a weight of about 10 kg were arranged in a screen house. Both the nursery and establishment of crop proper take place in a screen house. The screen house has a galvanized iron as the frame, a UV covering on top, side net for screening insect pests the floor fairly covered with granite. Temperature and relative humidity within the screen house during the period of the experiment was monitored using a Thermograph and a Barograph, and they were at an average of 31 °C and 75%, respectively.The grow bags were randomly placed in the screen house for the unbiased application of amendments. For both tomato and cucumber crops, the treatment comprised of six (6) levels of liquid organic fertilizer (5, 15, 25, 35, 45, 55 mL), in-organic fertilizer, and a control (ordinary borehole water). Levels of organic fertilizers were selected based on the recommendation of 20 mL of liquid organic fertilizer by29. The eight (8) treatments both for tomato and cucumber were arranged in a Completely Randomized Design replicated three times. One healthy plant was maintained per grow bag and four grow bags represent a treatment and there were 32 plants per block each for tomato and cucumber. For both crops, the experiment lasted for 90 days.Organic and in-organic nutrient solutionsThe liquid organic fertilizer used was obtained from the biomass of Mexican sunflower (Tithonia diversifolia). Fresh biomass (mainly leaves and stems) of the plant was collected from the Teaching and Research Farms of Landmark University, Nigeria. After rinsing, they were cut with a sterile knife into pieces of ≤ 1 cm size. A sample was taken for initial physicochemical analyses by grinding in a sterile mortal, diluted with sterile water and analyzed. The biomass was then soaked in sterile water inside a clean container, and allowed to ferment spontaneously for a period of 14 days. During the fermentation, samples were taken every 4 days for microbial analyses of the major players during the fermentation. At the end of fermentation, the mixture was separated using a sieve of mesh size ≤ 2 mm. The liquid portion was then refrigerated prior to the planting regime while another sample was taken to ascertain the physicochemical and microbial qualities of the produced liquid fertilizer. The chemical analysis is presented in Table 4. For inorganic fertilizer, Water soluble fertilizers employed in hydroponics were used (Hydroponics fertilizer, Anmol chemicals, India); calcium nitrate 650 mg L−1, potassium nitrate 450 mg L−1, magnesium 400 mg L−1, chelate 20 mg L−1, mono-ammonium phosphate 400 mg L−1. The electrical conductivity (EC) of the solution was 1.9 dS m-1.Irrigation and fertigationThe tomato and cucumber plants were fertigated morning and evening daily for one hour on each occasion according to the treatments. Preparation of the nutrient solution was with borehole water and was supplied to plants by an online pressure drip irrigation system set at 2.0 L h-1 using an arrowhead on each tomato and cucumber plant. Different tanks (250 L) were installed according to the various treatments making a total of 8 tanks. The organic fertilizer was diluted according to the various treatments equivalent to 1.25, 3.75, 6.25, 8.75, 11.25, and 13.75 L per 250 L of water respectively for 5, 15, 25, 35, 45, and 55 mL treatments. The nutrient solutions were refilled when the consumption is less than 20% of the initial volume (250 L) in the tank. One day per week, crops were irrigated with ordinary water to wash out pipes and prevent deposits of salts. The same concentration of nutrient was used from transplanting to the termination of the study for both tomato and cucumber crops, however, at the flowering of the crops, the volume of fertigation was increased to 3.0 L h-1 to be able to cope with the size of the plants.Trellising, pest and diseases controlFor both tomato and cucumber crops, plant vines were supported by twisting them around a wire that is- attached to the roof of the screen house and 2 m from the ground. Lateral outgrowths were cut off every week to ensure a sturdy single stem. Pests and diseases were scouted every day. Whiteflies, aphids, and other insects were controlled with orizon (Producer, location of producer) (active ingredient, acetamiprid, and abamectin) using 0.133% v/v. Fungi were controlled using ridomil gold (Producer, Location of producer) at 2% w/v.Determination of growth and yield of tomato and cucumberThree tomato and cucumber plants were randomly selected for each treatment for the determination of growth parameters (plant height, leaf area, number of leaves per plant, and stem diameter) at mid the flowering stage of tomato and cucumber plants.The leaf area of tomato was calculated using the model (A = KL2) developed by Lyon30, where L = Length of tomato leaf, K = constant which is 0.1551, and A = leaf area of tomato. Similarly, the leaf area of cucumber was calculated using A = 0.88LW – 4.27, where L = cucumber leaf length and W = cucumber leaf width, A = leaf area of cucumber31.Tomato fruits were ready for harvest from 65 days after transplanting, harvestings were done twice every week (Mondays and Fridays) for up to 85 days after transplanting. Similarly, harvesting of cucumber fruits started 35 days after transplanting and harvestings were also done twice a week (Mondays and Fridays), harvesting was carried out till 60 days after transplanting. Tomato and cucumber fruit yields were counted and weighed at each harvest.Analysis of tomato and cucumber leaves and fruitsAt the 50% flowering stage of tomato and cucumber plants, ten leaf samples were collected from each treatment. The leaf samples were oven-dried at 75 °C for 24 h and thereafter grounded. The grounded samples were later analyzed for nitrogen (N), phosphorous (P), potassium (K), calcium (Ca), and magnesium (Mg) content using the method of described by32. At harvest, four matured tomato and cucumber fruits of uniform size were selected per treatment, and their nutrient compositions were determined using the method of33.Statistical analysisAll data collected on the growth, yield, leaf, and fruit nutrient contents of tomato and cucumber were subjected to analysis of variance (ANOVA). The SPSS V 21.0 (New York, USA) software was used to perform ANOVA and Duncan’s multiple range test (DMRT) was used to compare means at a 5% probability level.
Ethical approvalI confirm that all the research meets ethical guidelines and adheres to the legal requirements of the study country.Compliance with international, national and/or institutional guidelinesExperimental research (either cultivated or wild), comply with relevant institutional, national, and international guidelines and legislation. Experimental studies were carried out in accordance with relevant institutional, national or international guidelines or regulation. More

Gamma source and dose modelingThe general literature contains conflicting results on whether the energies of photons interacting with fungi affects the radiotrophic response. As such, we sought to control critical variables while irradiating the fungi with ionizing radiation from a sealed Cs-137 source and a UV source. The Cs-137 source emitted a photon at 662 keV along with other lower energy photons near 30 keV (Table S1).A review of previous studies was conducted to identify the gamma dose rate and total dose that should be targeted for exposure (Table S2). Those dose rates ranged from 600,000 rad delivered in 1.5 h to 0.08 rad delivered in 16 h. Even among studies examining the same fungi attributes, the total dose varied dramatically. For the present study, we used a Health Physics code to target a 50-rad dose over a one-week exposure. This dose was selected as it changes blood count observed in most humans24. We hypothesized that this dose would induce physiological changes in the fungi without causing a high rate of lethality. A MicroShield (Grove Software, Inc.) model was created to identify the quantity of radioactive material and distance between source and sample necessary to achieve the dose of 50 rad in seven days. From a sensitivity analysis of the MicroShield model, it was determined that ~ 350 µCi of Cs-137 would create a dose rate of ~ 50 rad in seven days (Fig. 1; Table S3), if placed 1.8 cm from the surface of the fungi. It should be noted that Microshield values are often conservative and likely underestimate the actual dose on target. In addition, 50 rad falls in the middle of the large range for energies previously reported in the general literature (Table S2).Figure 1Time required on target to achieve an exposure of 50 rad determined in MicroShield and based on an activity of ~ 350 µCi for Cs-137 source and the vertical distance between the source and fungus.Full size imageThe dose from the Cs-137 source on the fungal mycelium is also dependent on the radial growth of the fungus from the center plug used to initiate growth. As the fungus grows away from the source, the leading edge will experience a lower total dose of radiation. Although a uniform dose would have been ideal, a source with activity sufficient to create a uniform radiation field would have initiated a variety of safety controls deemed impractical for this experiment. The background radiation dose at the testing site in Albuquerque is approximately 10 µrem h−1; the dose at the outermost area of the Petri dish was measured at 65,553 µrad h−1. As this dose was primarily from gamma emissions, rad and rem can be considered equivalent. To validate the simulation, a dose rate study was performed using thermoluminescent dosimeters (TLD) placed at varying distances from the center of the source. The TLD placed directly under the source measured ~ 100 rad over the seven-day exposure, which is double the prediction from the simulation (50 rad; Fig. 2A). However, at a radial distance of 3.5 cm, the measured and estimated total dose over seven days were much closer, 12.3 and 11.4 rad, respectively. A comparison of the measured and estimated dose on target demonstrated a non-linear correlation (Fig. 2B), in which the simulation better approximated the dose at larger radial distances from the source.Figure 2(A) The total gamma dose on the fungal mycelial at 7 days as a function of the radial distance from the central mycelium plug based on empirical measurements (-●-) and estimated from simulations (-○-). (B) Observed correlation between the measured and estimated doses at varying radial distances.Full size imageIn order to normalize the energy deposited in the fungi from Cs-137 and the UV lamp sources, the units of MeV g−1 s−1 were selected for additional simulations. Monte Carlo N-Particle transport code (MCNP) simulations were used to determine this quantity for the Cs-137. The materials and geometry of the Petri dish and fungus used for these simulations are shown in Fig. 3. The Cs-137 was simulated as a point source located 1.5 cm from the top of the fungi. The Petri dish was set on a bakelite table. The setup was located in the center of a notional 5 m × 5 m × 5 m room with 30 cm thick concrete walls and filled with air. Leads bricks set on the table surrounded the petri dish and source. The International Commission on Radiological Protection (ICRP) material definitions did not contain data for fungal mycelia. Thus, we selected for skin as the closest approximation of the properties of the fungal mycelium25. This simulation gave a result for the energy deposited per particle as 6.53 × 10–4 MeV g−1, which for a 350 μCi activity, the rate of energy deposition was determined to be 7907 MeV g−1 s−1.Figure 3Top (upper left) and side (upper right) view of the Petri dish and fungi materials and distances used to determine energy deposition rates in MCNP. The overall geometry used for the radiation transport simulations, including the lead bricks, is shown from the top down (lower left) and from the side (lower right).Full size imageUV source and irradiationOur intent was to match the energy absorbed by the fungi to control for all variables except the photon energy difference between the Cs-137 source and UV lamp. The spectrum of energies emitted from the Cs-137 source varied significantly from those of the UV lamp, which in this case was a 30 W deuterium lamp that emitted from 185 to 400 nm (Fig. S1). This wide bandwidth represented photon energies ranging from 3.1 to 6.7 eV. The bandwidth of the UV exposure was limited to 300–350 nm using a 50-nm bandpass filter centered at 325 nm to ensure that incident photons would be in the UV energy range and not form ozone. Because we chose to match the overall energy deposited from the UV source to the gamma source it was necessary to attenuate the beam to the right power level. We assumed that all the UV energy would be absorbed near the surface rather than in the bulk since the fungi were melanized. This simplified the calculations and reduced risk, given the challenge of accurately estimating the absorbance of the fungi. The power deposited by the gamma source was calculated as the rate of energy deposition was determined to be 7907 MeV g−1 s−1 (1.3 nW g−1 s−1). Given the initial size of the plug was 1 cm in diameter, the desired lamp fluence needed to be ~ 2.8 nW cm−2. Across the spectrum of interest, the lamp power was determined to be 3.202 × 10–4 mW, thus requiring an attenuation of 8.7 × 10–9 (OD 8.06), reducing the lamp power to ~ 3 pW cm−2 and achieving a reasonably close power density to the target. Due to the sensitivity of UV detectors, the required power densities could not be measured directly. Alternatively, we measured the neutral density filters to verify the prescription was indeed correct.Response of P. variotii to irradiationUniform plugs (~ 5-mm in diameter) of actively growing mycelia of P. variotii were cut using the end of a Pasteur pipette and transferred a Petri plate containing potato dextrose agar (PDA) one day prior to initiating exposure experiments. The diameter of the mycelium was measured from four images, separated by precisely six hours, over the course of seven days and used to measure the growth rate. Differences in the pigmentation of the fungi under the different conditions was quantified in Fiji26 through analysis of grayscale images collected at day seven, following the method described by Brilhante et al.27 A ratiometric value was derived from the grayscale values and the white background, which corrected for variations in lighting across or between images.Significant differences in the pigmentation but not growth rates of P. variotii were associated with exposure to UV and gamma to irradiation, based on One-Way ANOVA analyses (Fig. 4A; Table S4). P. variotii is a ubiquitous filamentous fungus commonly inhabiting soil, decaying plants, and food products and was reported to be present on the surface of the walls of Unit-4 at ChNPP22,28. P. variotii is also a common food contaminant and is resistant to high temperature and metals29,30, despite being more sensitive to gamma irradiation than other fungi such as Aspergillus fumigatus31. In the present study, we hypothesized that positive radiation-induced effects in P. variotii would result in enhanced growth rates due to gamma irradiation. Across all conditions, the average growth rate of P. variotii was ~ 5.6 ± 0.9 mm d−1 (mean ± standard deviation). While the growth rate of P. variotii exposed to gamma irradiation was greater compared with the control and UV-irradiated samples (Fig. 4A), the difference in the mean growth rates was not significant (P = 0.255) by ANOVA.Figure 4(A) Growth rate and pigmentation of control (orange square), gamma- (blue square), and UV- (red square) irradiated cultures of P. variotti (mean ± standard deviation). (B) Estimated total irradiation dose experienced by the mycelial as a function of the distance from the central source. Exponential decay fit: − 3.6 + 105.7*exp(− 0.75*x); Adjusted R2 = 0.998. (C) Graphical representation of the irradiation dose based on the growth rate and duration of exposure for zones of mycelia as a function of radial distance from the central plug.Full size imageWe also hypothesized that the pigmentation of P. variotii would increase with exposure to gamma and UV irradiation. While P. variotti does not produce melanin, it does produce a pigment, Ywa1, from a polyketide synthesis (PKS) gene cluster and has been shown to protect the fungus against UV-C irradiation28. In some melanized fungi, Ywa1 serves as precursor and can be hydrolyzed to 1,3,6,8-tetrahydroxynaphthalen (T4HN). T4HN may then be converted to 1,8-dihydroxynaphthalene (1,8-DHN) melanin through the DHN pathway32. However, Lim et al.28 concluded that P. variotii does not produce true melanin as the pigmentation was maintained when the DHN-melanin pathway was inhibited. Significant differences in the pigmentation of P. variotii were observed among the three different sample types (P  More