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We have demonstrated that Mexican tetra fish can locate their depth with high fidelity by using hydrostatic pressure alone. Crucially, the fish can use hydrostatic pressure not only as a gradient, giving information about upward and downward movement but also as a distance-based cue that can allow precise localisation of their vertical position. This newly identified sensory capability indicates how fish can achieve the complex task of navigating through three-dimensional environments.The basis of navigation in all animals, hinges on the individual knowing the spatial relationship between their current location and an intended destination. Although all animals inhabit a three-dimensional world, many, including humans, are constrained to travelling over surfaces with three degrees of freedom: two translational and one rotational14. The addition of the vertical dimension enlarges the size of the navigable space from a two-dimensional plane to a three-dimensional volume2, leading to a multiplicative increase in the complexity of a navigational task14,15,16. Reliable information on vertical position would therefore be a significant benefit for three-dimensional navigation.Although it is likely that in the wild fish rely on multiple cues to navigate, a sense of pressure would be particularly useful when other cues are unavailable or unreliable, for example, in turbid waters where visual landmarks are absent or obscured, and in turbulent waters where olfactory plumes cannot provide fine-scale information. The stability and ubiquity of hydrostatic pressure in aquatic environments allow fish access to a reliable navigational cue and could explain why two separate experiments, each testing a different species, found that fish perceived vertical information as the more reliable cue when horizontal and vertical information conflicted.The physiological mechanism underlying depth perception in fish is yet to be identified, although the swim-bladder has been implicated. In this putative mechanism, absolute depth is estimated during fast, steady vertical displacements by combining a measurement of vertical speed with a measurement of the fractional rate of change of swim-bladder volume. If this is the mechanism that these and other bony fish are using to sense their depth, there are likely to be important ecological and welfare consequences for fish that suffer barotrauma from angling or transit through hydroelectric power facilities, where the damage caused from exposure to rapid changes in barometric pressure may cause swim bladder ruptures17. Therefore, governments need to be aware of key migratory paths that fish use to move between feeding and breeding sites to enable them to protect important species. Similarly, fish that contract parasitic infections of the swim bladder are likely to find their vertical navigation is severely compromised. While there are currently no studies on the pressure sensing in fish with parasitic infections of the swim bladder, previous research has reported that infected Koi carp (Cyprinus carpio) are less able to achieve and sustain neutral buoyancy and demonstrate abnormal swimming behaviour18. Similarly, silver eels (Anguilla Anguilla) infected with a swim bladder nematode experienced a loss of buoyancy resulting in them expending more energy while swimming, impeding their migration19.While the swim bladder appears to be a good candidate organ for sensing hydrostatic pressure in bony fish, many cartilaginous or deep-sea species do not possess a gas phase, despite still being able to navigate vertically. Previous research has suggested that instead of relying on fractional changes in swim bladder volume, these species may rely on the sensory afferents of their lateral line system; with evidence that swimming crabs (Callinectes ornatus), mud crabs (Panopeus herbstii) and dogfish (Scyliorhinus canicula) sense pressure changes via the bending of hair cells oriented to sense either vertical or horizontal displacements20. The ability of fish to use hydrostatic pressure to accurately locate a point in the vertical dimension may be important for fisheries management. Known points of interest, for example, food sites, refugia, heavily predated areas, present in the vertical column could be learned and remembered by fish, with them either returning to or avoiding these areas as necessary. Further field studies on individual fish and shoals of fish using hydrostatic pressure in this context are needed to identify how this cue is used both in the wild and in farmed fisheries.Our findings reveal novel sensory information that A. mexicanus, and possibly other fish species, use to gain detailed navigational information over short distances in the vertical dimension. Extrapolating from this, we argue that it is likely that fish could use pressure to navigate over larger distances as the pressure magnitudes will increase as the vertical distance increases. Together, this study reveals a new sensory capacity that has great adaptive value in the fish’s volumetric world. More

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Study site and demographic dataThe study was carried out in Volcanoes National Park, the Rwandan part of the Virunga massif, which is further shared with Uganda and the Democratic Republic of the Congo. We focused on habituated mountain gorilla groups monitored by the Dian Fossey Gorilla Fund’s Karisoke Research Center, often referred to as the Karisoke subpopulation. Since 1967, groups in this subpopulation have been followed on a near daily basis. Through the mid-2000s, the Karisoke groups generally numbered three but over the last decade, group fission events and new group formations resulted in an average of ten groups in the region (see42,43). During daily observations, detailed demographic data are recorded, such as group composition, birthdate and death date, group transfers (for further details see Strier et al.50). The data used for this study covers demographic data from 1967 to 2018 and includes 396 recognized individuals.Epidemiological dataWe obtained published data on four variables that control the disease dynamics of COVID-19 in humans, namely (a) the basic reproductive number (R0)34,35, (b) the infection fatality rate (IFR) based on estimates from China and Italy24,25,36,37, (c) the probability of developing immunity and (d) the duration of immunity37,38,39,41.Stochastic projection modelWe used the stochastic projection model proposed by Colchero et al.51, that models population dynamics for both sexes on fully age-dependent demographic rates. The model incorporates the yearly variance–covariance between demographic rates, while it accounts for infanticide as a function of the number of silverbacks (mature males > 12 years old) in the population51. Because of this relationship between infanticide and number of silverbacks, this source of mortality changes in time and cannot be assumed to be part of the infant mortality rate. To explore the extinction probability for the Karisoke subpopulation as a function of different diseases, we gathered information from the model on the proportion of individuals that died for each disease and the frequency of outbreaks (i.e., how often outbreaks occurred).Demographic-epidemiological projection model for COVID-19We constructed a predictive population model that combines the species’ baseline demographic rates with a model based on the susceptible-infected-recovered-susceptible (SIRS) framework. As the baseline demographic rates, we used the age-specific mortality and fecundity estimated by Colchero et al.51 for mountain gorillas (Karisoke subpopulation). We defined four epidemiological stages, namely (a) susceptible, (b) infected, (c) immune and (d) dead, each of which we further divided into a fully age-specific structure (Fig. 1). Based on recent research on COVID-19 on humans, we assumed that the dynamics of the model allowed for the recovered individuals to be divided into either susceptible or immune37,38,39,41. Furthermore, we incorporated the potential age-specific infection fatality rate (IFR) based on current estimates from medical and epidemiological research24,25,36,37, adjusted to the lifespan of the gorillas by means of the logistic function$$qleft(xright)=frac{{q}_{M}}{1+{text{exp}}left[-0.2left(x-25right)right]},$$
(1)
where qM is the maximum infected mortality probability. Similarly, we modeled the probability of developing immunity as a function of the strength of the disease, which, based on recent research, we measured as mirroring Eq. (1) as$$mleft(xright)=frac{{M}_{I}}{1+{text{exp}}left[-0.2left(x-25right)right]},$$
(2)
where MI is the maximum immunity probability (Fig. 2B).To explore the potential impact of COVID-19 on the growth rate of the Karisoke mountain gorilla subpopulation, we varied four of the critical epidemiological variables, namely (a) the basic reproductive number, R0, from 0.5 to 6 (which helps to simulate factors such as increased group density, which may increase the likelihood of transmission), (b) the maximum infected mortality probability, qM = (0.3, 0.6) (Fig. 2A), (c) the immunity duration, TI to 1, 3, 6, and 12 months, and (d) the maximum immunity probability, MI, from 0.2 to 0.8 (Fig. 2B). As time units we used year fractions in half months (i.e., t1 − t0 = 0.5/12), which allowed us to simplify the model, based on current information on the average time of serial interval and incubation period in humans21. This implementation assumes that susceptible individuals could become infected at the beginning of the time interval, while infected individuals in time interval t would either recover (immune or susceptible) or die in t + 1.The deterministic structure of the model implies that the number of individuals in each sex, age and epidemiological stage was given by the possible contribution from the other stages 1/2 month before. This is, the number of susceptible individuals of age x at time t is given by the difference equation$$begin{aligned} n_{s,x,t} & = p_{x – 1} left{ {n_{s,x – 1,t – 1} + n_{i,x – 1,t – 1} left[ {1 – qleft( {x – 1} right)} right]left[ {1 – mleft( {x – 1} right)} right]} right} \ & quad + n_{{m,x – T_{i} ,t – T_{i} }} prodlimits_{{j = x – T_{i} :j > 0}}^{x – 1} {p_{j} – n_{i,x,t} } , \ end{aligned}$$where the ns,x,t is the number of susceptible individuals of age x at time t, and subscripts i and m refer to infected and immune individuals, respectively. For simplicity of notation, we do not include a subscript for sex, although the model does distinguish between sexes. The probability px is the age-specific survival probability. Functions q(x) and m(x) are as in Eqs. (1) and (2). Similarly, the number of immune individuals at time t and age x are$${n}_{m,x,t}={n}_{i,x-1,t-1}left[1-qleft(x-1right)right]mleft(xright)+sum_{{j:0le jle {T}_{i}wedge x-j >0}}{p}_{x-j}{n}_{i,x-j,t-j}.$$We incorporated this mechanistic structure into a stochastic model, where all contributions from time t to t + 1 were drawn from binomial or Poisson distributions. For instance, the total new number of infected individuals, Ni,t, was obtained as a random draw from a Poisson distribution with expected value$$Eleft[{N}_{i,t}right]={text{min}}left[{{R}_{0}N}_{i,t-1},{N}_{t}right],$$where Nt is the total number of individuals in the study subpopulation. We then distributed randomly these individuals into different available ages and sex corresponding to the term ni,x,t, in the susceptible equation above. The number of newborns, Bx,t, at each age for which there were available females at time t was drawn from a binomial distribution with expected value$$Eleft[{B}_{x,t}right]=left({n}_{s,x,t}+{n}_{m,x,t}right){f}_{x}$$where fx is the age-specific average female fecundity rate and ns,x,t and nm,x,t refers to the number of susceptible and immune females, respectively, of age x at time t. The sex of each newborn was then determined by means of a Bernoulli draw with probability given by the proportion of males in the population. Thus, if the draw produced 1 for that individual, it became a male, and if 0 a female.For each scenario, we ran stochastic simulations for 2000 iterations for 10 years and recorded the average number of individuals at each age–sex and epidemiological state at every month. We then ran long-term stochastic simulations for four scenarios with R0 = 3 and maximum immunity probability MI = 0.2. For these, we recorded also the number of subpopulations that went extinct at each month. More

We assembled a unique dataset of range-wide observations of Yucca available from iNaturalist. These provided the bases for determining presence and absence of flowers for our two focal species, and while flowering Yucca are likely to be more photographed, we still had sufficient absences for these common and iconic species to use in downstream models. These models were effective at predicting flowering phenology of the two focal species with generally high accuracy during the normal flowering season. Unlike other frameworks for predicting phenology, our approach is not to estimate an onset, median or termination timing of a phenophase. Rather, our goal was to determine whether climate and daylength covariates provide a basis for predicting the probability of open flowers during normal and anomalous bloom periods. This approach is enabled by having dense reporting of presence-absence data generated by growing community science resources.Model fitting revealed that probability of flowering is determined by complex interactions between climate and daylength, suggesting the critical importance of climate context. This importance for arid-adapted Yucca is in line with other studies of phenology of desert plants, from Saguaro in the desert Southwest of North America9 to lilies in arid environments in Africa25. Yet, we were surprised that flowering of Yucca does not necessarily always rely on increased precipitation. We expected precipitation would be a critical limiting factor in desert environments, and for Mojave yucca in particular, precipitation is a strong driver positively influencing the odds of flowering during spring and summer. However, for both species, flowering odds are also relatively high during cold and drier conditions earlier in the season (Fig. 3). These results may relate to precipitation falling as snow rather than rain during late winter—another avenue for further exploration in follow up studies.Joshua trees and Mojave yucca have different growth forms and are of vastly different sizes at maturity, and therefore, may be expected to react differently to climatic drivers. However, our findings indicate that the same interacting climate variables drive flowering phenology for both species, and the overall shape of their seasonal phenology curves are similar (Fig. 2). The main differences in our models are likely attributed to adapted differences in overall bloom timing; in particular, Y. schidigera generally blooms later in the year than Y. brevifolia (Fig. 2). For example, Y. brevifolia only blooms under highest daylength conditions if it is unusually cold and wet, while Y. schidigera flowering odds can often exceed 50% under warm and wet conditions when daylength is long (Fig. 3). Conversely, while Y. brevifolia has better odds of blooming in cold, dry conditions early in the year, even under wet conditions it can bloom with odds above 25%. In contrast, Y. schidigera is rarely in bloom in colder, wetter early season conditions.We also note the importance of including a polynomial term for daylength (Table 1), which always dramatically improved models (Table 1). The outcome, clearly visible in Fig. 3, is that responses of phenology are strongly non-linear across gradients. In sum, our work corroborates the importance of context dependence, finding that daylength, temperature, and precipitation interact in complex, nonlinear ways to influence flowering times.A key question we sought to answer in this work is whether we predict anomalous flowering events. Accelerating climate change means that species will experience conditions outside the range experienced for centuries. How species respond phenologically to these novel conditions is an area of active research26, but the focus has predominantly been on using yearly anomaly data, e.g. warmest years on record or via warming experiments27. Our efforts here are trying to predict a seasonal anomaly, where plants seasonally flowered outside of their presumed normal periods (e.g. in fall rather than spring). A key question of interest was whether the fall-winter bloom in 2018–2019 was itself triggered by anomalous climate conditions mirroring those of the usual bloom period.We examined this question by testing whether models, which were fit using data from years with a known normal blooming period, were able to predict presences and absences during the 2018–2019 fall-winter season. Our results show that we can predict absences with low error rates (4.7–6.7%, Table 2). However, these models had much higher rates for false positives (32.1–50.2%, Table 2). Our model predicts more anomalous blooming than actually observed. This suggests that, while Yucca might have been triggered to bloom by atypical cooler and wetter conditions, there are still factors not included in our models that limited the extent of anomalous blooming.It remains possible that co-evolution between Yucca and their obligate pollinator or florivore community28 may extend to how phenology is cued. It may also be that Yucca are responding not only to instantaneous climate conditions, such as mean photoperiod, but whether days are shortening or lengthening, and if so, it may be that the modeling approach used here is not sensitive enough to capture these types of more dynamic seasonal cues. Our work may also point to out-of-normal season blooming simply being more common and widespread than previously suspected, given broadly suitable climate conditions. A next step is to use growing community-science reporting of Yucca plants in flower to determine the rate of seasonally anomalous flowering from dense, range-wide community science observations enabled via resources such as iNaturalist.Finally, we note the value of examining predictive power of models using climate measurements over shorter and longer temporal windows. While these different climate accumulation windows are by nature highly autocorrelated, we found that data from the longer temporal window led to modest improvement of models based on AUC statistics. It is likely that the longer temporal window captures more information about GDD and overall water input in the environment. For example, a classic paper by Beatley5 that focused on shrub phenology in the Mojave showed fall and winter rains were precursor triggers of phenological events in spring. We also note congruence with the findings of Clair and Hoines13, who showed strong positive correlations with the 30-year averages of temperature and precipitation and fruit and seed mass in Joshua trees, although they focused on broader temporal scale questions. Connecting these longer timescale and broad spatial phenology studies, and aligning lags over different time-scales is a frontier area in phenology research. Finally, our findings should not necessarily be extrapolated more broadly for arid-adapted plants, and traits such as perenniality or woody versus herbaceous habit with associated differences in costs for growth and reproduction, may condition thresholds for needed accumulation of heat or water.We close by noting that phenology modeling is often treated as a one-off exercise where models are built, and results shared. We argue that the accelerating growth of new data resources and flexible modeling frameworks provide a means for models to iteratively improve. One key step towards this goal is faster annotation of phenology state. Here we hand-coded two key states in Yucca photographs1. These carefully vetted classifications can now provide the basis for more automated approaches for annotating photographs, e.g. via machine learning29. These new results can be fed into current models to test and improve model performance.Expanding data resources for modeling flower presence is one key step, but the development of improved phenology models that include more fitness-relevant responses is also important, such as number of flowers or fruits, potentially in relation to vegetative biomass. Individual yucca plants, for example, do not bloom annually even in favorable conditions, because vegetative growth must precede production of a heavy, high-cost inflorescence10. More sophisticated species-level models that link the full range of environmental conditions populations experience across their range with seasonal vegetative and reproductive biomass proxies are uncommon, mostly due to data limitations. Rather, studies typically focus on single, local areas or transect approaches across broad-scales30, with associated limitations for further prediction or forecasting.We argue that the ability to develop ecophysiological-guided, range-wide models are in reach, using the same community science photographs that so far have only been used to generate simple states such as open flower presence. Such models hold promise in helping to provide a basis for improved understanding of mechanisms underlying flowering, and better detection of anomalous blooming events and their consequences. For example, we don’t yet know if anomalous blooms produce fewer or greater flower numbers, as compared to normal periods. Do these blooms ultimately lead to the production of fruit and, if so, how much? Such next-step approaches are particularly critical and necessary, because as we experience more unusual weather phenomena and novel conditions, phenology prediction and understanding the consequences of phenological changes becomes even more challenging. As weather forecasting was improved by assimilating more data and building better process parameters, our hope is that similar methods with richer data types can improve the most difficult phenology prediction challenges. More

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