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An improved reference genome of P. alba var. pyramidalis
To identify the major structural variation between the genomes of these two species, we first produced a chromosome-level genome assembly of P. alba var. pyramidalis using single-molecule sequencing and chromosome conformation capture (Hi-C) technologies, and then performed comparative genomic analysis with a recently published genome assembly of P. euphratica37. The resulting assembly of P. alba var. pyramidalis consisted of 131 contigs spanning 408.08 Mb, 94.74% (386.61 Mb) of which were anchored onto 19 chromosomes (Supplementary Fig. S1 and Supplementary Tables S1–S3). A total of 40,215 protein-coding genes were identified in this assembly (Supplementary Table S4). The content of repetitive elements in the genome of P. alba var. pyramidalis (138.17 Mb, 33.86% of the genome) is 188.94 Mb less than that of P. euphratica (327.11 Mb, 56.95% of the genome), which contributes greatly to their differences in genome size (Supplementary Table S5).
3D organization of the poplar genomes
To characterize the spatial organization and evolution of poplar 3D genomes at a high resolution, we performed Hi-C experiments using HindIII for P. euphratica and P. alba var. pyramidalis, generating a total of 482.95 million sequencing read pairs. These data were mapped to their respective reference genome sequences. After stringent filtering, 81.72 and 94.61 million usable valid read pairs were obtained in P. euphratica and P. alba var. pyramidalis, respectively, and used for subsequent comparative 3D genome analysis (Supplementary Table S6). In addition, we profiled the DNA methylation and transcriptomes of the same tissue samples to provide a framework for understanding the relationships among epigenetic features and 3D chromatin architecture in poplar.
We first examined genome packing at the chromosomal level with a genome-wide Hi-C map at 50 kb binning resolution for P. euphratica and P. alba var. pyramidalis. As expected, the normalized Hi-C map from both species showed intense signals on the main diagonal (Fig. 1, and Supplementary Figs. S2 and S3) and a rapid decrease in the frequency of intrachromosomal interactions with increasing genomic distance, indicating frequent interactions between sequences close to each other in the linear genome (Supplementary Fig. S4). Strong intrachromosomal and interchromosomal interactions were also observed on the chromosome arms, implying the presence of chromosome territories in the nucleus, in which each chromosome occupies a limited, exclusive nuclear space16,38.
Fig. 1: Hi-C heatmaps with compartment region analysis results at 50-kb resolution of P. euphratica chromosome 1 (left) and P. alba var. pyramidalis chromosome 1 (right).

The heatmaps at the top are Hi-C contact maps at 50-kb resolution, which show global patterns of chromatin interaction in the chromosome. The chromosome is shown from top to bottom and left to right. The ICE-normalized interaction intensity is shown on the color scale on the right side of the heatmap. The track below the Hi-C heatmap shows the partition of A (red histogram, PC1  > 0) and B (green histogram, PC1 5 kb) structural variants ranging from 5 to 446 kb in length in the alignment of the two genomes, including 719 inversions, 476 translocations, and 7947 and 10,093 unique regions in P. alba var. pyramidalis and P. euphratica, respectively (Supplementary Tables S10 and S11).
To characterize the relationship between structural variation and spatial organization of the poplar genomes, we first analyzed the conservation of A/B compartments between P. alba var. pyramidalis and P. euphratica, using a 50-kb Hi-C matrix. The results showed that 71.52% (145.75 Mb in P. euphratica and 145.63 Mb in P. alba var. pyramidalis) of the total length of the syntenic regions have the same compartment status between the two species, while 43.68 and 43.71 Mb of the genomic regions exhibit A/B compartment switching in P. alba var. pyramidalis and P. euphratica, respectively (Fig. 3a). For the regions with structural variation, we found that 77% of the inversion events between the two genomes had no effects on their compartment status, while 61% of the translocation events occurred within the regions exhibiting compartment switching (Fig. 4a and Supplementary Table S10). Moreover, we also found that 38.59% and 33.39% of the nonsyntenic regions were identified as A compartments in P. alba var. pyramidalis and P. euphratica, respectively, indicating that the large-scale insertions and/or deletions are biased to occur at heterochromatic regions (Fig. 4b). We further assessed the conservation of genome organization at the TAD level by examining whether the orthologous genes within the same TAD in one species could still be located within the TAD in another species19,21,23. The results indicated that only 48.04% of TADs from P. alba var. pyramidalis and 40.95% from P. euphratica were substantially shared between the two species (Figs. 3b, c). Taken together, these results indicated that the 3D genome organization shows surprisingly low conservation across poplar species at both the compartmental and TAD levels.
Fig. 3: Evolutionary conservation of compartment status and TADs across P. euphratica and P. alba var. pyramidalis.

a Overlap of compartment status between syntenic regions in P. euphratica and P. alba var. pyramidalis. b Overlap of TADs between syntenic regions in P. euphratica and P. alba var. pyramidalis. c Example of conserved TAD structures across a syntenic region between P. euphratica and P. alba var. pyramidalis. The TADs are outlined by black triangles in the heatmaps, and the position of the TAD domains is indicated by alternating blue-green line segments. The mean cf value used to identify the domains is also shown. The orthology tracks of these conserved domains are shown at the bottom

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Fig. 4: Relationship between structural variation and spatial organization of the genomes of P. euphratica and P. alba var. pyramidalis.

a Analysis of compartment inversion (left) and translocation (right) across P. euphratica and P. alba var. pyramidalis. b Analysis of compartments of species-specific regions in P. euphratica (left) and P. alba var. pyramidalis (right)

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Relationship between chromatin interactions and expression divergence of WGD-derived paralogs
Poplar species have undergone a recent WGD event followed by diploidization, a process of genome fractionation that leads to functional and expression divergence of the duplicated gene pairs27,28,33. Although no biased gene loss or expression dominance was found between the two poplar subgenomes, there is evidence that nearly half of the WGD-derived paralogs have diverged in expression32,33. To explore the potential role of chromatin dynamics on the observed expression patterns of duplicated genes, we examined their differences in chromatin interaction patterns for both species. We first identified a total of 10,438 and 9754 paralogous gene pairs showing interchromosomal interactions in P. euphratica and P. alba var. pyramidalis, respectively. After correlating the frequency of chromatin interactions with their differences in expression, we found that gene pairs with biased expression (more than twofold differences in expression levels) interacted less frequently than gene pairs with similar expression levels in both species (P = 1.71 × 10−6 and 7.20 × 10−7 for P. euphratica and P. alba var. pyramidalis, respectively, Mann–Whitney U test; Fig. 5a). We also estimated the interaction score (the average of the distance-normalized interaction frequencies) for bins involved in the paralogous gene pairs and quantified their differences in interaction strength (Supplementary Fig. S7 and Supplementary Table S12)3,23. Our results showed that for gene pairs with biased expression, highly expressed gene copies have stronger interaction strengths than weakly expressed copies (P = 2.10 × 10−12 and 2.74 × 10−2 for P. alba var. pyramidalis and P. euphratica, respectively, Mann–Whitney U test), while no significant differences were observed for gene pairs with similar expression levels (Fig. 5b). We further investigated these phenomena at the level of high-order chromatin architecture and found that the gene pairs located in conserved TADs had similar expression levels (P = 2.68 × 10−3 and 7.86 × 10−6 for P. euphratica and P. alba var. pyramidalis, respectively, Mann–Whitney U test; Supplementary Fig. S8). Overall, our analyses indicate that the extensive expression divergence between WGD-derived paralogs in Populus is associated with the differences in their chromatin dynamics and 3D genome organization, and suggest that this organization may function as a key regulatory layer underlying expression divergence during diploidization.
Fig. 5: Comparison of interaction levels between WGD-derived paralogs with biased/similar expression in P. euphratica and P. alba var. pyramidalis.

a The box plot shows that the interaction frequency of WGD-derived paralogs with biased (fold change  > 2) and similar (fold change  More

Zoologist Alice Hughes leads the landscape-ecology research group at Xishuangbanna Tropical Botanical Garden in Menglun, Yunnan province, China.Credit: Michael C. Orr

British zoologist Alice Hughes has been working at the Xishuangbanna Tropical Botanical Garden in Menglun, Yunnan province, in southern China, for nearly eight years. She reveals what she has learnt about the country’s approach to ecological conservation ahead of its first United Nations biodiversity conference in Kunming, Yunnan, in May.
What is your current role?
I lead the landscape-ecology research group at one of China’s most diverse botanical gardens. My team aims to better understand the lives of animals and how they interact with their environments. This helps us to create more effective methods of conserving a biodiverse environment.
The 18-person team, which is part of the Chinese Academy of Sciences (CAS), does everything from mapping biodiversity to researching the illegal and legal trade in different species, to find out where and why our natural world is changing. We then develop actionable measures to help stem the worst effects of those changes.
For example, many members of my team are working on the various species of Rhinolophus bats. Our genetic research suggests that around 70% of the Rhinolophus bat species haven’t been described in scientific literature. If you can’t describe a species, then you can’t conserve it.
How did you come to work in China, and what’s it like?
In 2011, I moved to Thailand from the United Kingdom as part of my postdoctoral research, before heading to Australia and finally taking a position in China in 2013.
At first, I was naive about how different the culture might be in Asian countries and it’s definitely been a steep learning curve. Adaptability is important. I think that many people in the West are much too ready to disbelieve or find fault with actions from China, and Chinese scientists. As a result, there is sensitivity in China’s research community, especially around things that have frequently been an issue, such as the regulation of the trade of exotic wildlife. As a foreigner, it is a challenging balance to provide advice without it being seen as overly critical. I can participate in these discussions at a high level because I have worked here long enough: people know I will listen and provide my perspectives based on fact, rather than prejudice.

I’ve worked on some difficult and potentially sensitive topics, such as endangered species, wildlife trade and the Belt and Road Initiative, which aims to link global trade routes to China through international infrastructure development, for example. I focus on the possible impacts these might have on biodiversity and how to minimize them. China is wary of being accused of driving extensive biodiversity loss, especially as it is investing in scientific research to avert it.
I’ve been invited to join a variety of both central and regional government working groups. It’s a privilege to be in those groups and work with some of the country’s top scientists, especially when it comes to international or UN meetings.
Working for CAS is the equivalent to being an employee of the government. Many people outside China still find it surprising that foreigners work in scientific institutes here, even though the number is growing.
I’m also unusual because I’m a foreign woman. In the time I have worked here I don’t think I have met any other European women with full-time faculty positions in China. In my institute there are more than ten foreign men with such positions. It’s not easy for Chinese women either. At the institute, we have 43 research groups; only 3 are led by women.
It’s important for all conservation scientists to be open minded and willing to find out what’s going to work in any country and culture to help tackle the global problem of biodiversity loss, and develop solutions that work in that societal context. A good example of that came last year, when some specialists called for a global ban on wild-meat consumption, amid fears over new diseases that originate in wild animals and cause outbreaks in humans. Now that might sound like a great idea, but in many parts of Africa there is not enough water to raise livestock, and people depend on wild meat for food.
This means that rather than recommending a blanket ban, a better solution might be a system that monitors what is traded, and provides recommendations as to which species can be eaten safely and sustainably.

Xishuanganna tropical botanic garden in southwest China’s Yunnan Province.Credit: Xinhua/eyevine

Do foreign scientists need to speak Chinese to work in China?
For most of my team, neither English nor Chinese is their first language. We have around 12 different nationalities, so discussions take place predominantly in English, as a default.
I work closely with my Chinese colleagues to make sure that our research work is properly communicated when it’s published in Chinese. In meetings with Chinese colleagues, someone will translate pertinent points to me, or I’ll translate my slides into Chinese and present in English. I also have my reports and briefs translated, and with advances in translation software, we can get what is needed done.
It’s easy to have misunderstandings when you’re translating ideas between different languages, so we’re careful to look for any linguistic nuances that might change the perceived meaning.
How is China balancing urbanization with conservation?
It’s an ongoing challenge. The concept of an ecological civilization — the government’s vision for environmentally sustainable growth in China — was written into the country’s constitution in 2018 after it was made a national priority in 2012, which is a huge commitment to sustainability.
A principal policy is the ecological conservation red-line plan, an idea that has been developed over the past decade. Across China, large areas of land are now being protected from industrial and urban development, in part to ensure that crucial ecosystems, such as wetlands that limit floods, can continue to function effectively. Multimillion-dollar developments have been torn down during its roll-out. China is one of few countries to have enacted such a science-based, top-down vision of how to balance human need with the maintenance of ecological services and preservation of biodiversity.

It’s not all perfect, though: I know that on paper, these ecological red lines now exist and in certain biodiversity hotspots they have been enforced. But not every region is the same. Areas have high levels of autonomy and in Yunnan, where I live, there have been more challenges for the local government to work with provincial governments for many practical and political reasons. The saying goes, ‘The mountains are high, and the emperor is far away’: places that are far away from Beijing feel less pressure to enact centralized policies because there is less supervision.
The south of China has seen lots of deforestation, which is hugely damaging to biodiversity. Natural forests have been replaced with for-profit tree plantations, usually planted with rubber or eucalyptus, which have had a hugely negative impact on biodiversity. Sustainable forestry is a real issue across Asia.
China is leading an important biodiversity conference in May. What are your expectations?
It’s the first time that China will host the UN biodiversity conference and this puts the spotlight on what they are doing to help the situation.
I know there are a number of senior Chinese officials who would like to see China take on more of an international leadership role, in addition to making efforts to preserve biodiversity domestically.
The current set of UN goals for global biodiversity expired last year and the next set, which is planned to be agreed at the convention, must encourage countries to plant diverse, native species. Currently, there is no pressure coming from politicians to do that, even though we know we suffer biodiversity loss as a result: we’re often hung up on targets, even if those targets are virtue signalling, rather than real change.
Also, governments tend to try to meet their targets in the easiest and most economically beneficial way. So they meet their tree-planting targets by planting by just a few, non-diverse species that are often not even native to the country.
We still need to include more practical goals in policy documents, such as enabling sustainable supply chains, to focus on the mechanisms behind biodiversity loss.
What strikes you as unique about the Chinese ecological-research environment?
A Chinese ecologist needs to be fast to act. The time frame to submit an application for a grant can be very quick. Often you have less than 24 hours to respond. Also, most initiatives are tied to the government’s five-year plans, so our priorities need to adapt to reflect those five-year cycles.
In the past two years, there has been a complete inventory of all China’s marine and terrestrial protected areas so they can be accurately mapped and future targets can be based on them. That really is an unparalleled effort.
This involved mapping 400 marine protected areas, and 13,600 terrestrial ones. I haven’t heard of anything equivalent to this scale and speed in any other country.
The most positive thing for me is that science matters here. The annual budget for scientific research is increasing and the findings from our applied research inform national policy. That is something the West would do well to remember. More

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A mathematical model to simulate movement
For ‘attracting features’, such as nesting or roosting sites, we employ potential terms that are logarithmic in distance. Logarithmic potentials have been employed in diffusion models7 such as those involving long-range interactions8. The forces due to these are inversely proportional to distance from the features. Given a choice between locations, an animal would invariably drift towards ones that are closer. Additionally, they also command some influence for longer distances. We did consider alternatives such as a potential that corresponds to an inverse squared force but it diminishes much faster as the distance to the source increases. The ‘repulsive features’ such as human dominated areas are incorporated using Gaussian type potentials that would have an influence only when the animal is close to them. Such forces fall off exponentially fast as one goes away from the source location.
The corresponding Langevin equations can be written as:

$$begin{aligned} frac{dx}{dt}= & {} -gamma sum _{i}frac{ 2alpha times (x – x_{i})}{(x – x_{i})^2 + (y – y_{i})^2} nonumber \&+,gamma sum _{j}Big ((x-x_{j}) e^{-((x-x_{j})^2 + (y-y_{j})^2)}Big ) + root 2 of {2D}xi _x(t) end{aligned}$$
(1)

$$begin{aligned} frac{dy}{dt}= & {} -gamma sum _{i}frac{ 2alpha times (y – y_{i})}{(x – x_{i})^2 + (y – y_{i})^2} nonumber \&+,gamma sum _{j}Big ((y-y_{j}) e^{-((x-x_{j})^2 + (y-y_{j})^2)}Big ) + root 2 of {2D}xi _y(t) end{aligned}$$
(2)

where x and y denote the coordinates of an animal’s location. ((x_{i}), (y_{i})) and ((x_{j}), (y_{j})) denote locations of i attracting and j repelling features respectively. We only choose nests as points of attraction for breeding hornbills since their diurnal movements are strongly centred around the nests. The white noise terms (xi _x) and (xi _y) are Gaussian in nature and delta correlated—which means that no correlations exist between the noise values at different instances of time. (gamma ) and D denote the drift and diffusion coefficients respectively. The drift coefficient (gamma ) represents the directedness of motion, which could be interpreted as strength of bias towards/against certain features in the landscape. In contrast, D quantifies the strength of random undirected motion. The force term with coefficient (-gamma ) results from negative gradient of the logarithmic potential, whose choice we explained earlier:

$$begin{aligned} U = gamma sum _{i} log left{ (x – x_{i})^2 + (y – y_{i})^2 right} ^{alpha } ,,,. end{aligned}$$
(3)

The value of (alpha ) is determined from calculation of first passage times of the birds (discussed in the following section) and comparison of the values so obtained with observational (telemetry) data. We find that (alpha ) = 8 gives biologically sensible first passage times for hornbills (see “Calculating First Passage Times” in Methods section, Table 3 and Supplementary Tables 1, 2). If one observes an animal’s movement for a very long time, the probability of finding the animal would decrease more drastically away from a central feature for lower values of (alpha ). Such variations are captured by the steady-state probability distributions of space-use that we describe in the following section.
Fokker–Planck methods
Although the Langevin equations can generate trajectories of movement, the corresponding simulations need to be run for very long times to infer reliable information about spatial use. The time steps are further much smaller than the frequency of data recorded by the GPS. The step-lengths thus generated from simulated trajectories do not lend themselves to comparison against those from the recorded data. A convenient alternative is to solve a Fokker–Planck equation which has a direct correspondence with the Langevin equations. For our model, this takes the form:

$$begin{aligned} frac{ partial P(x,y,t)}{partial t}&= frac{partial }{partial x} left{ F_x + D frac{partial }{partial x} right} P(x,y,t) nonumber \&quad +, frac{partial }{partial y} left{ F_y + D frac{partial }{partial y}.right} P(x,y,t) end{aligned}$$
(4)

where

$$begin{aligned} F_x&= -gamma sum _{i} frac{ 2 alpha times (x – x_{i})}{(x – x_{i})^2 + (y – y_{i})^2} nonumber \&quad+, gamma sum _{j} (x – x_{j}) times e^{-( (x – x_{j})^2 + (y – y_{j})^2)} nonumber \ F_y&= -gamma sum _{i} frac{ 2 alpha times (y – y_{i})}{(x – x_{i})^2 + (y – y_{i})^2} nonumber \&quad+ gamma sum _{j} (y – y_{j}) times e^{-( (x – x_{j})^2 + (y – y_{j})^2)} end{aligned}$$
(5)

The Fokker–Planck equation describes the evolution of the probabilities of occurrence over a given region. The probability distribution eventually reaches a ‘steady state’ which captures the long-term occurrence probabilities for a given bird, and it does not change beyond this point in time. This steady-state probability distribution can be computed by setting the time derivative term to zero in Eq. (4). The numerical solution of the Fokker–Planck equation involves discretizing the spatial derivatives involved. The steady state probability distribution is consequently obtained on a spatial domain of discretized grids.
Interestingly, Giuggioli et al.9 considered logarithmic potentials in their work on home range estimation, where an exponent of 8 was found to have a very similar steady state distribution to that from a harmonic potential. Harmonic potential has been utilized in analyzing home ranges of Peromyscus maniculatus10.
Using the steady-state solution of the Fokker–Planck equation, we compute the mean square displacement averaged over different possible starting locations using the steady state distribution. A discrete version of the mean-square displacement (MSD) can be defined as:

$$begin{aligned} MSD = sum _i^N langle (x – x_i)^2 + (y – y_i)^2 rangle P_{0}(x_i,y_i) end{aligned}$$
(6)

where (P_0(x_i,y_i)) is the distribution of starting locations (x_i) and (y_i) from where displacements are calculated. The inner angular brackets represent a similar weighted average of the mid-points of all grids over the steady-state probability distribution (P_{text {st}}(x,y)). Many of the grids that we define to perform simulations lie outside the known home range of the birds. The probability of choosing a starting location is defined using a Gaussian distribution centred around the nest or the most visited roost site.
The square root of the MSD defines a characteristic length scale. This could be interpreted as home range length when the steady state distribution is computed over an infinite extent9. A logarithmic potential does not lend itself to such computations since it decays much more slowly such that the characteristic length continues to grow with the size of the area considered. We evaluate the characteristic length scale (L) on a domain that is not much larger in size compared to the observed home range.
We also calculate L from empirical data by using the probability of occurrence over space inferred from two-dimensional histograms of location data. The MSD in this case is evaluated in the same vein as above but now the displacements from initial locations are weighted over the probabilities of occurrence derived from the histograms. Since these probabilities are only available for each grid, we choose only the mid-points of grids as possible locations to find the result. The starting locations are chosen from a uniform distribution over the mid-points of the grids. This is definitely a crude way of evaluating L but it does give us some way of comparing our numerical solutions against data. Finding a joint-probability distribution over the two dimensions would have been ideal but it is complicated by the fact that the distribution over space is multi-modal owing to multiple roosts for some hornbills. When inferring MSD from the location coordinates directly, it increases before saturating as the sampling frequency is decreased. For very high sampling frequency (or very small time intervals), diffusion effects dominate which leads to an almost linear increase in MSD. The effects of drift are more prominent compared to diffusion for lower sampling frequencies which marks the saturation of the MSD values10.
A first-passage time model for heterogeneous environments
The temporal information about an animal’s whereabouts is highly scrambled in the data. An important quantity of interest that could be extracted from movement data is the search time to reach a given target. A very useful measure of search times is the ‘first passage time’. Very generally, first passage time is the time taken for a given state variable to reach a particular value. In the case of animal movement, it can be interpreted as the time taken to reach a particular target location. McKenzie et al.11 derived an interesting first passage time model which had a direct correspondence with a Fokker–Planck equation. We use the prescription of Moorcroft et al.12,13 to estimate the drift and diffusion coefficients. This assumes a movement kernel that is a product of exponential distribution of step lengths and von Mises distribution for the turning angles. (This may be seen in the “goodness of fit tests” section in Methods where we assess fit of our data to claimed distributions.) It can be expressed as:

$$begin{aligned} K({mathbf{X}} ,{mathbf{X}}’ ,tau )=, & {} frac{1}{rho } f_tau (rho ) k_tau (phi ) end{aligned}$$
(7)

$$begin{aligned} {rm{where}},,,,,,,,,,,, ,f_tau (rho )=, & {} lambda e^{-lambda rho }end{aligned}$$
(8)

$$begin{aligned} k_tau (phi )=, & {} frac{1}{2 pi I_0(kappa _tau )} exp [kappa _tau cos (phi )] end{aligned}$$
(9)

Here, ({mathbf{X}} ), ({mathbf{X}}’ ) denote the current and previous locations respectively, f is the exponential distribution of step lengths (rho ) with rate parameter (lambda ) and mean (bar{rho }_{tau } = 1/lambda ), and (k_{tau }) is the von Mises distribution of turning angles (phi ). (tau ) refers to the time taken to complete a given step. The turning angles are computed with respect to the nest/roost sites. (kappa _tau ) is the concentration parameter of the von Mises distribution which signifies the departure from a uniform distribution of movement directions. The normalizing factor (I_0(kappa _tau )) is a modified Bessel function of the first kind and of zeroth order. The drift and diffusion coefficients can be reliably estimated as:

$$begin{aligned} gamma= & {} lim _{tau rightarrow 0} frac{bar{rho }_{tau } kappa _tau }{2tau } end{aligned}$$
(10)

$$begin{aligned} D= & {} lim _{tau rightarrow 0} frac{bar{{rho _{tau }}^2}}{4tau } end{aligned}$$
(11)

Employing the formalism in McKenzie11 to derive the equation for the first passage time T, we obtain the following equation:

$$begin{aligned}&gamma sum _{i} left{ frac{ 2alpha times ({mathbf{X}} – {mathbf{X}} _{i})}{(x – x_{i})^2 + (y – y_{i})^2} right} cdot nabla T nonumber \&quad -, gamma sum _{j} left{ ({mathbf{X}} – {mathbf{X}} _{j}) e^{-( (x – x_{j})^2 + (y – y_{j})^2)} right} cdot nabla T nonumber \&quad +, D nabla ^2 T + 1 = 0 end{aligned}$$
(12)

The terms in dot product with (nabla T) are simply the drift coefficients with spatial dependence.
McKenzie et al.11 had a simpler version of the first passage time equation that only accounted for bias towards the home range centre. The authors mention that the task of solving the first passage time equation is computationally harder with terms that account for more complex types of heterogeneities. We transform the partial differential equation in (12) into polar coordinates which simplifies the process of solving it (see First Passage Time calculation in Methods). The first passage times obtained from this solution also help us fix the value of (alpha ) in the equation above and subsequently in the logarithmic potential in (3), and in Eqs. (1) and (2). On performing this analysis for different hornbills, we see that (alpha ) = 8 works very well for them irrespective of the species and distribution of heterogeneities around them (see First Passage Time calculation in Methods). First passage times are calculated from the roosting/nesting site that lies closest to the home range centre. In case of GHNBr2, we calculate the first passage times from the approximate home range centre where no roosts exist. This ensures that most points considered for computations lie within the actual extent of the bird’s recorded locations. We used the Minimum Convex Polygon method to estimate the approximate home range centre14. This helped in identifying a location for each bird—which was a roost/nest in most cases—from where first passage times were subsequently computed. The method used for home range estimation is not relevant in the context of our proposed model and results presented, and therefore we do not consider other alternatives. More