Philippa Kaur

For this initial compilation, we focused on gathering traits from field guides and species accounts rather than the primary research literature because each represents the culmination of a comprehensive effort to describe a regional flora/fauna by local experts25. Authors of these guides have already done the hard work of scouring the literature, corresponding with fellow naturalists, and compiling occurrence records to support range, phenology, and habitat associations26. We began by performing a comprehensive review of all the holdings in the Florida Museum of Natural History’s McGuire Center for Lepidoptera and Biodiversity library, at the University of Florida. This, and subsequent searches in online databases, allowed us to compile a list of references that currently has more than 800 relevant resources.We initially identified the categories of trait information available in each resource and its format to target volumes for trait extraction and processing. Given the unequal availability of resources among regions, we had the explicit goal of identifying a corpus that would maximize the number of extractable trait data from as many butterfly species as evenly across the globe as possible. This led to our choice of 117 volumes within several global regions (Fig. 2, Supplementary Material S1) and a focus on measurements (wingspan/forewing length), phenology (months of adult flight and total duration of flight in months) and voltinism (the number of adult flight periods per year), habitat affinities, and host plants as traits (Table 1, Supplementary Material S2).Table 1 The total number of species represented by each trait in LepTraits 1.0.Full size tableTo process these resources, we developed a protocol to scan each volume, extract verbatim natural language descriptions, provide quality control for extraction, and then resolve given taxonomic names to a standardized list27. This provided a database of trait information in which each “cell” included all text from a single resource relevant to one trait category of a single taxon. In order to “atomize” the raw text into standardized metrics or a controlled list of descriptive terms, we developed a methodology appropriate to each trait. This resulted in a more fine-grained dataset in which each “cell” included a single, standardized trait value. Since the values of these taxon-specific traits frequently differed among resources, we then calculated “consensus” traits for each species, for example, the average forewing length (Table 1). A graphical representation of this process with an example trait is illustrated in Fig. 1.Fig. 1A graphical illustration of the processing workflow used to compile, scan, digitize, extract, atomize, and compile species trait records from literature resources. (1) Literature resources were examined for potential trait data and compiled into a single library; (2) each literature resource was scanned into.pdf format so that text could be readily copy and pasted from species accounts; (3) each.pdf file was uploaded to an online database with associated metadata for each literature resource; (4) trait extractors utilized an online interface to extract verbatim, raw text from designated resources; (5) verbatim, raw text extracts were either automatically (via regular-expressions and keyword searches) or manually atomized to a controlled vocabulary; (6) species consensus traits were calculated by aggregating resource-level records by name-normalized taxonomy. Rulesets were used for consensus trait building and are detailed in the supplementary material. Both resource-level and species consensus traits are presented in the dataset.Full size imageResource compilation and ingestionText sources from the master list were digitized by multiple participating institutions. They scanned each page of the book and converted the images to editable text with Abbyy FineReader optical character recognition (OCR) software (abbyy.com). These PDFs with copy-and-pastable text were then uploaded to a secure, online database that included citation information about each resource. The geographic breadth covered by each resource was designated using the World Geographic Scheme (WGS)28; this information was used to assess geographic evenness of our trait compilation efforts. Resource metadata, including the WGS scheme, were kept with each resource in an online database where individuals could access scanned copies of the resource for trait extraction.Verbatim data extractionIndividual workers were assigned to a resource and instructed to copy verbatim trait information from the original source. They then pasted that text into the relevant data field in a standardized, electronic form on an online portal designed to facilitate extraction and processing. Most field guides and other book-length resources are organized within a taxonomic hierarchy to describe traits of a family with a contiguous block of text, for example, family, then genus, species, and finally subspecies within species. We call these text blocks describing a single taxon “accounts” (e.g., family account, species account), and we recorded data at the taxonomic resolution provided in the original source. These taxonomic ranks included family, subfamily, tribe, genus, species, and subspecies. When information for a taxon was encountered outside its own account, the “extractor” (project personnel trained to manually extract verbatim text) assigned to glean data from the book entered this text into a separate entry for the taxon. Trait information from figure captions and tables were also extracted from the resource. Graphical representations of phenology and voltinism were common, and these visual data were converted to text descriptions. Each resource was extracted in stages, and each stage was subjected to a quality assurance and control process (see Technical Validation). This process corrected mistakes and attempted to find unextracted data overlooked by the extractor. These problems were corrected before the extractor could proceed with further trait extraction from the resource and were also used for training purposes.AtomizationVerbatim text extracts were subjected to an “atomization” process in which raw text was standardized into disaggregated, readily computable data. This conversion into the final trait data format (numerical, categorical, etc.) was two-pronged and involved both manual editing and semi-automated atomization of verbatim text. Regular expressions were used for most semi-automated atomization, including extraction of wing measurements, which were converted into centimeters. Keyword searches were also performed in the semi-automated pipeline for phenology, voltinism, and oviposition traits. For example, “univoltine” or “uni*” was searched for across the voltinism raw text, along with other search terms. All semi-automated atomization outputs were subject to quality assurance and control detailed further in Technical Validation. Manual atomization tasks were performed by multiple team members for traits which presented higher complexity. For example, habitat affinities and host plant associations were atomized manually along with a quality control protocol based on predefined rule sets that are described further in the Supplementary Material S3.Normalization and consensus traitsTo provide consensus traits at the species (and sometimes genus) level, we standardized nomenclature through a process we called “name-normalization,” which harmonizes taxonomy across all of our resources29. This name-normalization procedure relied on a comprehensive catalog of valid names and synonyms27. Following taxonomic harmonization, we compiled consensus traits based on rule sets specified in the metadata of each trait. For example, species-level consensus of primary and secondary host plant families required that at least one-third of the records for a given taxon list a particular family of plants (when multiple records were available).Categorical traits such as voltinism list all known voltinism patterns for a species regardless of geographic context. To this end, it is important that users of these data are aware that not all traits may be applicable to their study region. For example, some species may be univoltine at higher latitudes or elevations, but bivoltine elsewhere. We therefore present both the resource-level records as well as the species consensus traits for use in analysis.For this initial synopsis of butterfly species traits, we extracted records from 117 literature/web-based resources, resulting in 75,103 individual trait extraction records across 12,448 unique species, out of the ca. 19,200 species described to date27. Figure 2 indicates the geographic regions covered by our 117 resources, mapped at the resolution level-two regions in the World Geographic Scheme28. A full list of resources can be found in the Supplemental Material S1 as a bibliography. Similarly, the geographic distribution of trait records is indicated in Fig. 3. Resource and consensus species trait records varied in number and in the scope of taxonomic coverage. Table 1 indicates the number of unique records and species level records for each trait. Table 2 indicates the number of species-level records by family. Measurement traits, including wingspan and forewing length, were the most comprehensive traits extracted from our resource set. This represents one of the largest trait datasets and the most comprehensive dataset for butterflies to date.Fig. 2Geographic breadth of our butterfly trait resources. Using a global map of level-two regions (World Geographic Scheme, Brummitt 2001), we have indicated the total number of resources available within each geographic area). Grey areas indicate that no resources were extracted from that region.Full size imageFig. 3Geographic breadth of our butterfly trait records. Using a global map of level-two regions(World Geographic Scheme, Brummitt 2001), we have indicated the total number of trait records from each geographic region). Grey areas indicate that trait records were not extracted from that region.Full size imageTable 2 The number of species represented within each family in LepTraits 1.0.Full size table More

There are two phases involved in supporting the technical quality of the dataset: (i) the process used by Taronga when collecting data for each shark-bite incident, and (ii) the consistency modifications that we made during manuscript development.Phase oneFor each shark-bite incident, Taronga attempts to contact the most-relevant person involved in the event as possible — e.g., victim, victim’s family, witnesses. Those contacted are asked to complete a questionnaire with information relating to the shark bite. If applicable, questionnaires can also be completed by a fisheries officer in the relevant State and sent to Taronga. Taronga works closely with experts in each State’s fisheries department to validate information sourced in media reports. Each shark-bite case is unique, so the validation process varies depending on details specific to each incident. Forensic shark scientists within each State department are contacted after each shark bite to confirm details related to the incident. For example, validating species responsible for the bite often requires forensic analysis through expert examination of bite marks or artefacts21,22,23,24,25. When available, video footage is analysed for validation of information, such as confirmation of shark species and length.The database is cross-checked annually for the previous year with the International Shark-Attack File in Florida, USA, as well as with fisheries officers to ensure consistency. The database is cross-checked with the acknowledgement that there are discrepancies between versions due to differences in inclusion criteria. For example, the International Shark-Attack File includes bites where the victim was bitten aboard a boat, whereas the database we present here does not include bites aboard a boat.We acknowledge the limitations associated with this database, such as differences in reporting over time. For example, incidents might be reported more in recent decades due to technological advances making reporting more accessible or media publicising these events more widely18. There might also be reporting biases, for example, victims could be more likely to report a bite by a large, potentially dangerous shark (e.g., white, tiger, or bull shark) rather than a smaller, less-dangerous shark species (e.g., wobbegong shark). We also completed a quality assessment of the original database fields and redesigned the data acquisition and entry process (see Phase two) to allow exploration of shark-bite trends and patterns in Australia.Phase twoWe identified errors and inconsistencies in database fields. To avoid additional errors and inconsistencies, and to obtain a quality-controlled database, we redesigned the process for gaining and entering information into the database. This included creating a data descriptor (Supplementary File 2) used as a protocol to inform which questions to ask in the questionnaire. The data descriptor also directs the format of database entries by specifying information required in each field and by indicating the format of each entry (i.e., numeric, descriptive, or categorical). We manually inspected all previously entered data and adapted them to match the data descriptor. We checked each entry using the filter function in Microsoft Excel to identify any spelling and grammatical errors in the fields and ensure that all categories were grammatically identical. We standardised all metrics during this process (e.g., the data descriptor now stipulates that all length measurements should be recorded in metres).We validated and standardised the geographical locations of shark bites by converting all coordinates into decimal degrees using Microsoft Excel. We subsequently plotted all coordinates using the ggmap library27 in R (Version 4.0.2) (R Core Team 2020) (Fig. 2). We corrected any unusual coordinates (e.g., outside of Australian waters) and crosschecked them with site descriptions and states to ensure validity.Fig. 2Geographical locations of 1,196 shark bites in Australia. Each shark-bite incident is indicated by a red dot. (a) all shark-bite incidents; (b) bites most likely inflicted by bull sharks, (c) tiger sharks, and (d) white sharks. Two bite incidents that occurred at the Australian external territory, Cocos (Keeling) Islands, are not included on these maps. Background layers show elevation and major, perennial watercourses.Full size imageDuring the development of the data-descriptor protocol, we converted some previous descriptive columns into categorical columns. These columns included (but are not limited to) victim activity, attractant, injury location, injury severity, and weather condition. Converting these columns into categories facilitates analysis to investigate shark-bite patterns. For example, we converted victim activity into a categorical field to restrict answers to the following: snorkelling, motorised boating, unmotorised boating, boarding, swimming, standing, diving, fishing, or other, rather than allowing answers in any format. We used this information to create a time series to show the activity of shark-bite victims in Australia over time (Figs. 3 and 4). Shark bites have increased for boarders (including surfboarding, bodyboarding, kiteboarding, sailboarding, wakeboarding, and stand-up paddle boarding) over time, particularly since 1960 (Figs. 3b, 4). This is likely due to the increase in popularity of board sports, particularly surfing, since the 1960s28. This trend is likely not reflected in Fig. 3a because shark bites are unlikely to be classed as ‘provoked’ during board riding.Fig. 3Number of shark bites (black, dashed line) and proportion of activity done by the victim at the time of shark-bite incidents in Australia from 1900 to 2022. Panels represent shark bites in Australia that are; (a) provoked or (b) unprovoked. Boarding includes surfboarding, bodyboarding, kiteboarding, sailboarding, wakeboarding, and stand-up paddle boarding. Swimming includes snorkelling, spearfishing, freediving, body surfing, clinging to an object, falling into water, floating, or wading. Diving includes scuba-diving, hookah diving, or hard-hat diving. Fishing includes cleaning fish. No data for years 1908 and 1970.Full size imageFig. 4Number of shark bites (black, dashed line) and proportion of activity done by the victim at the time of shark-bite incidents in Australia from 1900 to 2022. Panels represent shark bites in Australia that are; (a) fatal or (b) non-fatal. Boarding includes surfboarding, bodyboarding, kiteboarding, sailboarding, wakeboarding, and stand-up paddle boarding. Swimming includes snorkelling, spearfishing, freediving, body surfing, clinging to an object, falling into water, floating, or wading. Diving includes scuba-diving, hookah diving, or hard-hat diving. Fishing includes cleaning fish. No data for years 1908 and 1970.Full size imageThe column representing a shark-bite victim’s recovery status also requires a categorical response, restricting answers to: fatal, injured, or uninjured (Fig. 5). Since 1900, the proportion of shark-bite-related fatalities has decreased (Fig. 5). This trend is also true for the three species most attributed to shark-bite-related fatalities, white (Carcharodon carcharias), tiger (Galeocerdo cuvier), and bull (Carcharhinus leucas) sharks. The decrease in shark-bite-related deaths is likely due to advancements in medical responses to shark-bite victims over time14 and better understanding among surfers about using tourniquets to stem bleeding following increased certification as first responders in workplace occupational health and safety requirements. Bites resulting in an uninjured victim includes interactions where the shark might have bitten the victim’s equipment (i.e., surfboard, bodyboard, kayak) rather than biting the person.Fig. 5Proportion of victim-recovery status (fatal = grey; red = injured; blue = uninjured) resulting from all unprovoked shark bites in Australia between 1900–2022. Blank years represent years without any reported occurrences. (a) all shark-bite incidents, (b) bites most likely inflicted by bull sharks, (c) tiger sharks, or (d) white sharks. No data for years 1908 and 1970.Full size imagePreviously, entries in the injury location column were descriptive. We converted the column to a categorical field restricting answers to the following: arm, hand, lower arm, upper arm, shoulder, neck, head, torso, leg, foot, calf, thigh, pelvic region, or other. During the analyses process, we further categorised these injury locations into four body areas (head, arm, torso, and leg) to assess how injury location affects recovery status (fatal or injured) (Fig. 6). Fatality most often occurred following shark bites to the torso (Fig. 6). This is likely due to the injuries to organs and major arteries resulting in blood loss, which is a leading cause of shark-bite fatalities29. This is the first time that the location of a shark bite on the body has been assessed relative to recovery status.Fig. 6Proportion of Australian shark bites resulting in either fatality or injury categorised by injury location on the victim’s body (left panel; 250 bites resulting in fatal injury, 723 bites resulting in non-fatal injury) and by species (right panel; bites by 201 tiger, 170 bull, 258 white, and 303 bites other sharks).Full size imageUnderstanding how the location of a shark-bite wound relates to victim recovery has value in informing the development of shark-bite mitigations. For example, the development of shark-bite-resistant wetsuits could potentially result in higher survival rates of the user if the fabric is concentrated around the torso region30,31. Redesigning data acquisition and entry process to allow for categorical columns permits these types of analyses.Some detail of a shark-bite incident might be lost by converting previously descriptive columns into categorical columns. We addressed this by complementing categorical columns with accompanying fields to retain details of the incident. For example, injury location and injury severity columns are both categorical and allow for user-friendly data analysis, whereas the injury description column is descriptive and provides added detail about the victim’s injuries if applicable. Individually, all three columns address certain aspects of the victim’s injuries, and together, all three columns comprehensively summarise injuries to the shark-bite victim.Our analysis of the Australian Shark-Incident Database suggests that tiger sharks are proportionally responsible for the most fatalities of all shark species in Australia (38% of all tiger shark bites result in fatality), followed by bull sharks (32% of all bull shark bites result in fatality), and white sharks (25% of all white shark bites result in fatality) (Fig. 6). We emphasise that these figures represent the overall percentage of bites resulting in fatality since 1791 and do not account for possible changes over time. These figures are also proportional to the number of bites by each respective species. In Australia, white sharks are responsible for the largest number of bites on humans (361 total) compared to tiger (229 total) and bull sharks (197 total). At the time of publication, white and tiger sharks were each responsible for 91 and 86 total fatalities on humans in Australia, respectively.There were 540 incidents in which time of day was recorded. We used these data to assess whether particular shark-bite incidents are more likely to occur at specific times of day (Fig. 7). To standardise reported 24-hour times, we took the location (latitude, longitude) information and reported time and date of each incident using the getSunlightTimes function in the suncalc library in R32 to calculate whether the incident occurred in one of four light-availability categories: dawn, day, dusk, or night. Shark bites occur mostly during the day, which likely reflects time of day when there are more ocean users present. However, there is a slightly higher proportion of bites at dusk for bull sharks compared to tiger and white sharks (Fig. 7). Identifying these trends can assist authorities in developing data-driven educational messaging as a shark-bite mitigation measure. This is important considering that enhanced education is the preferred mitigation measure scored by ocean users in New South Wales33.Fig. 7Period of day (corrected for local time) distribution of provoked and unprovoked shark bites in Australia by shark species from 1791 to 2022 (n = 540 bites from all species, 70 from bull, 59 from tiger, and 217 from white sharks).Full size imageThese examples demonstrate that the Australian Shark-Incident Database will be useful for scientists to analyse environmental, social, and biological related shark-bite patterns in Australia. Use of the newly developed data descriptor to standardise future applications and account for quality assurance and control will aid in keeping the database consistent for ease of analysis and interpretation. Ultimately, the publishing of this database will improve our understanding of shark-bite incidents in Australia and will equip us with the knowledge to aim to avoid or predict these events in the future. More

Model descriptionThe system dynamics model divided an urban dog population into the following subpopulations: (i) free-roaming dogs (both owned and unowned free-roaming, i.e. unrestricted dogs found on streets), (ii) shelter dogs (unowned restricted dogs living in shelters), and (iii) owned dogs (owned home-dwelling restricted dogs) (Fig. 1). The subpopulations change in size by individuals flowing between the different subpopulations or from flows extrinsically modelled (i.e. flows from subpopulations not included in the systems model; the acquisition of dogs from breeders and friends to the owned dog population, and the immigration/emigration of dogs from other neighbourhoods).Ordinary differential equations were used to describe the dog population dynamics. The models were written in R version 3.6.128, and numerically solved using the Runge–Kutta fourth order integration scheme with a 0.01 step sizes using the package “deSolve”29,30. For the baseline model, Eqs. (1–3) were used to describe the rates of change of dog subpopulations in the absence of management.Baseline free-roaming dog population (S):$$frac{dS}{dt}={r}_{s}times Stimes left(1-frac{S}{{K}_{s}}right)+alpha times O-delta times S$$
(1)
In the baseline model, the free-roaming dog population (Eq. 1) increases through the free-roaming dog intrinsic growth rate (rs), and the abandonment and roaming of dogs from the owned dog population (α) and decreases through adoption to the owned dog population (δ). The intrinsic growth rate is the sum of the effects of births, deaths, immigration, and emigration, which are not modelled separately. In this model, the growth rate of the free-roaming dog population is reduced depending on the population size in relation to the carrying capacity, through the logistic equation (rreal = rmax(1 − S/Ks))31. In the baseline simulation, the free-roaming dog population rises over time, until it stabilises at an equilibrium size.Baseline shelter dog population (H):$$frac{dH}{dt}=gamma times O-beta times H- {mu }_{h}times H$$
(2)
The shelter dog population (Eq. 2) increases through relinquishment of owned dogs (γ) and decreases through the adoption of shelter dogs to the owned dog population (β), and through the shelter dog death rate (µh). There is no carrying capacity for the shelter dog population as we assumed that more housing would be created as the population increases. This allowed calculation of the resources required to house shelter dogs.Baseline owned dog population (O),$$frac{dO}{dt}={r}_{o} times Otimes (1-frac{O}{{K}_{o}})+beta times H+delta times S-alpha times O-gamma times O$$
(3)
The owned dog population (Eq. 3) increases through the owned dog growth rate (ro), adoption of shelter dogs (β), and adoption of free-roaming dogs (δ); and decreases through abandonment/roaming (α) and relinquishment (γ) of owned dogs to the shelter dog population. The growth rate of the owned dog population (ro) combines the birth, death, and acquisition rates from sources other than the street or shelters (e.g. breeders, friends) and was modelled as density dependent by the limit to growth logistic formula (1 − O/Ko).Parameter estimatesDetailed descriptions of parameter estimates are provided in the supplementary information. The simulated environment was based on the city of Lviv, Ukraine. This city has an area of 182 km2 and a human population size of 717,803. Parameters were estimated from literature, where possible, and converted to monthly rates (Table 1). Initial sizes of the dog populations were estimated for the baseline simulation, based on our previous research in Lviv32. The carrying capacity depends on the availability of resources (i.e. food, shelter, water, and human attitudes and behaviour33) and is challenging to estimate. We assumed the initial free-roaming and owned dog populations were at carrying capacity. Initial population sizes for simulations including interventions were determined by the equilibrium population sizes from the baseline simulation (i.e. the stable population size, the points at which the populations were no longer increasing/decreasing).Table 1 Parameter description, parameter value, and minimum and maximum values used in the sensitivity analysis for the systems model.Full size tableEstimating the rate at which owned dogs are abandoned is difficult, as abandonment rates are often reported per dog-owning lifetime32,34 and owners are likely to under-report abandonment of dogs. Similarly, it is challenging to estimate the rate that owned dogs move from restricted to unrestricted (i.e. free-roaming). For simplicity, we modelled a combined abandonment/roaming rate (α) of 0.003 per month, estimated based on our previous research in Lviv and from literature34,35,36. We derive the owned dog relinquishment rate (γ) from New et al.37. We estimated shelter (β) and free-roaming adoption rates (δ) from shelter data in Lviv. We set the maximum intrinsic growth rate for the free-roaming dogs (rs) at 0.03 per month, similar to that reported in literature17,19,38. We assumed that demand for dogs was met quickly through a supply of dogs from births, breeders and friends and set a higher growth rate for the owned dog population (ro) at 0.07 per month.We assumed shelters operated with a “no-kill” policy (i.e. dogs were not killed in shelters as part of population management) and included a shelter dog death rate (µh) of 0.008 per month to incorporate deaths due to euthanasia for behavioural problems or health problems, or natural mortality. We modelled neutered free-roaming dog death rate (µn) explicitly for the CNR intervention at a minimum death rate of 0.02 per month38,39,40,41.InterventionsSix intervention scenarios were modelled (Table 2): sheltering; culling; CNR; responsible ownership; combined CNR and responsible ownership; and combined CNR and sheltering, representing interventions feasibly applied and often reported27. Table 2 outlines the equations describing each intervention. To simulate a sheltering intervention, a proportion of the free-roaming dog population was removed and added to the shelter dog population at sheltering rate (σ). In culling interventions, a proportion of the free-roaming dog population was removed through culling (χ).Table 2 Description of intervention parameters and coverages for simulations applied at continuous and annual periodicities.Full size tableFree-roaming dog population with sheltering intervention:$$frac{dS}{dt}={r}_{s}times Stimes left(1-frac{S}{{K}_{s}}right)+alpha times O-delta times S-sigma times S$$
(4)
Shelter dog population with sheltering intervention:$$frac{dH}{dt}=gamma times O-beta times H- {mu }_{h}times H+sigma times S$$
(5)
Free-roaming dog population with a culling intervention:$$frac{dS}{dt}={r}_{s}times Stimes left(1-frac{S}{{K}_{s}}right)+alpha times O-delta times S-chi times S$$
(6)
To simulate a CNR intervention, an additional subpopulation was added to the system (Eq. 7): (iv) the neutered free-roaming dog population (N; neutered, free-roaming). In this simulation, a proportion of the intact (I) free-roaming dog population was removed and added to the neutered free-roaming dog population. A neutering rate (φ) was added to the differential equations describing the intact free-roaming and the neutered free-roaming dog populations. Neutering was assumed to be lifelong (e.g. gonadectomy); a neutered free-roaming dog could not re-enter the intact free-roaming dog subpopulation. Neutered free-roaming dogs were removed from the population through the density dependent neutered dog death rate (µn); death rate increased when the population was closer to the carrying capacity. The death rate was a non-linear function of population size and carrying capacity modelled using a table lookup function (Fig. S1). Neutered free-roaming dogs were also removed through adoption to the owned dog population, and we assumed that adoption rates did not vary between neutered and intact free-roaming dogs.Neutered free-roaming dog population:$$frac{dN}{dt}=varphi times I-{mu }_{n}times N-delta times N$$
(7)
Intact free-roaming dog population with neutering intervention.$$frac{dI}{dt}={r}_{s}times Itimes left(1-frac{(I+N)}{{K}_{s}}right)+alpha times O-delta times I-varphi times I$$
(8)
To simulate a responsible ownership intervention, the baseline model was applied with decreased rate of abandonment/roaming (α) and increased rate of shelter adoption (β). To simulate combined CNR and responsible ownership, a proportion of the intact free-roaming dog population was removed through the neutering rate (φ), abandonments/roaming decreased (α) and shelter adoptions increased (β). In combined CNR and sheltering interventions, a proportion of the intact free-roaming dog population (I) was removed through neutering (φ) and added to the neutered free-roaming dog population (N), and a proportion was removed through sheltering (σ) and added to the shelter dog population (H).Intact free-roaming dog population with combined CNR and sheltering interventions:$$frac{dI}{dt}={r}_{s}times Stimes left(1-frac{(I+N)}{{K}_{s}}right)+alpha times O-delta times I-varphi times I- sigma times I$$
(9)
Intervention length, periodicity, and coverageAll simulations were run for 70 years to allow populations to reach equilibrium. It is important to note that this is a theoretical model; running the simulations for 70 years allows us to compare the interventions, but does not accurately predict the size of the dog subpopulations over this long time period. Interventions were applied for two lengths of time: (i) the full 70-year duration of the simulation; and (ii) a five-year period followed by no further intervention, to simulate a single period of investment in population management. In each of these simulations, we modelled the interventions as (i) continuous (i.e. a constant rate of e.g. neutering) and (ii) annual (i.e. intervention applied once per year). Interventions were run at low, medium, and high coverages (Table 2). As the processes are not equivalent, we apply different percentages for the intervention coverage (culling/neutering/sheltering) and the percent increase/decrease in parameter rates for the responsible ownership intervention. Intervention coverage refers to the proportion of dogs that are culled/neutered/sheltered per year (i.e. 20%, 40% and 70% annually) and, for responsible ownership interventions, the decrease in abandonment/roaming rate and increase in the adoption rate of shelter dogs (30%, 60% and 90% increase/decrease from baseline values). To model a low (20%), medium (40%) and high (70%) proportion of free-roaming dogs caught, but where half of the dogs were sheltered and half were neutered-and-returned, combined CNR and sheltering interventions were simulated at half-coverage (e.g. intervention rate of 0.7 was simulated by 0.35 neutered and 0.35 sheltered). For continuous interventions, sheltering (σ), culling (χ), and CNR (φ) were applied continuously during the length of the intervention. For annual interventions, σ, χ, and φ were applied to the ordinary differential equations using a forcing function applied at 12-month intervals. In simulations that included responsible ownership interventions, the decrease in owned dog abandonment/roaming (α) and the increase in shelter adoption (β) was assumed instantaneous and continuous (i.e. rates did not change throughout the intervention).Model outputsThe primary outcome of interest was the impact of interventions on free-roaming dog population size. For interventions applied for the duration of the simulation, we calculated: (i) equilibrium population size for each population; (ii) percent decrease in free-roaming dog population; (iii) costs of intervention in terms of staff-time; and (iv) an overall welfare score. For interventions applied for a five-year period, we also calculated: (v) minimum free-roaming dog population size and percent reduction from initial population size; and (vi) the length of time between the end of the intervention and time-point at which the free-roaming dog population reached above 20,000 dogs (the assumed initial free-roaming dog population size of Lviv, based on our previous research32, see Supplementary Information for detail).The costs of population management interventions vary by country (e.g. staff salaries vary between countries) and by the method of application (e.g. method of culling, or resources provided in a shelter). To enable a comparison of the resources required for each intervention, the staff time (staff working-months) required to achieve the intervention coverage was calculated. While this does not incorporate the full costs of an intervention, as equipment (e.g. surgical equipment), advertising campaigns, travel costs for the animal care team, and facilities (e.g. clinic or shelter costs) are not included, it can be used as a proxy for intervention cost. Using data provided from VIER PFOTEN International, we estimated the average number of staff required to catch and neuter the free-roaming dog population and to house the shelter dog population in each intervention, using this data as a proxy for catching and sheltering/culling. The number of dogs that can be cared for per shelter staff varies by shelter. To account for this, we estimated two staff-to-dog ratios (low and high). Table 3 describes the staff requirements for the different interventions.Table 3 Staff required for interventions and the number of dogs processed per staff per day.Full size tableUsing the projected population sizes, the staff time required for each staff type (e.g. number of veterinarian-months of work required) was calculated for each intervention. Relative salaries for the different staff types were estimated (Table 3). The relative salaries were used to calculate the cost of the interventions by:[Staff time required × relative salary ] × €20,000.Where €20,000 was the estimated annual salary of a European veterinarian, allowing relative staff-time costs to be compared between the different interventions. Average annual costs were reported.To provide overall welfare scores for each of the interventions, we apply the estimated welfare scores on a one to five scale, for each of the dog subpopulations, as determined by Hogasen et al. (2013)22. This scale is based on the Five Freedoms (freedom from hunger and thirst; freedom from discomfort; freedom from pain, injury, or disease; freedom to express normal behaviour; freedom from fear and distress42,43) and was calculated using expert opinions from 60 veterinarians in Italy22. The scores were weighted by the participants’ self-reported knowledge of different dog subpopulations, which resulted in the following scores: 2.8 for shelter dogs (WH); 3.5 for owned dogs (WO); 3.1 for neutered free-roaming dogs (WN); and 2.3 for intact free-roaming dogs (WI)22.Using these estimated welfare scores, we calculated an average welfare score for the total dog population based on the model’s projected population sizes for each subpopulation (Eq. 10). For interventions running for the duration of the simulation, the welfare score was calculated at the time point (t) when the population reached an equilibrium size. For interventions running for five years, the welfare score was calculated at the end of the five-year intervention. The percentage change in welfare scores from the baseline simulation were reported.$$Welfare score= frac{{H}_{t}times {W}_{H}+{O}_{t}times {W}_{O}+{N}_{t}times {W}_{N}+{I}_{t}times {W}_{I}}{{H}_{t}+{O}_{t}+{N}_{t}+{I}_{t}}$$
(10)
Model validation and sensitivity analysisA global sensitivity analysis was conducted on all parameters described in the baseline simulation and all interventions applied continuously, at high coverage, for the full duration of the simulation. A Latin square design algorithm was used in package “FME”44 to sample the parameters within their range of values (Table 1). For the global sensitivity analysis on interventions, all parameter values were varied, apart from the parameters involved in the intervention (e.g. culling, neutering, abandonment/roaming rates). The effects of altering individual parameters (local sensitivity analysis) on the population equilibrium was also examined for the baseline simulation using the Latin square design algorithm to sample each parameter, individually, within their range of values. Sensitivity analyses were run for 100 simulations over 50 years solved with 0.01 step sizes. More

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Lehtonen12 presents three simple models with the same broad structure: a single mutant individual with divergent mating behaviour arises in a population of ‘residents’ that all play the same strategy, and the success of that mutant is then followed (Figs. 1, 2). Specifically, Lehtonen investigates the fitness benefits of increased mating for mutant males in comparison to mutant females. Two important parameters can be varied: (i) the degree of anisogamy (defined here as the ratio of sperm number to egg number), which captures how divergent males and females are in the size (and thus number) of gametes they produce, and (ii) the efficiency of fertilisation, which determines how easily gametes can find and fuse with each other. If fertilisation is highly efficient, then gametes of the less numerous type will achieve nearly full fertilisation; on the other hand, inefficient fertilisation can result in gametes of both sexes going unfertilised.Fig. 2: Structure of the three models of Lehtonen12, showing differences in mating behaviour between resident males (green), resident females (blue) and mutant males and females (both yellow).For illustration, we suppose that females produce four eggs each and males produce eight sperm (the anisogamy ratio in nature is typically much higher). In Model 1, resident individuals spawn monogamously in a ‘nest’ (black outline), whereas mutant males and females can bring additional partners to their nest to spawn in a group. In Model 2, resident individuals divide their gametes equally among m spawning groups, each consisting of m individuals of each sex (shown here with m = 2). Mutant males and females instead divide their gametes among a larger or smaller number of groups, mmutant (shown here with mmutant = 4). In Model 3, there is a further sex asymmetry in addition to anisogamy: Fertilisation takes place inside the female’s body. Resident individuals mate with m partners (shown here with m = 2), whereas mutant males and females mate with a larger or smaller number of partners, mmutant (shown here with mmutant = 4).Full size imageIn the first two models, fertilisation is external and no assumptions are made about pre-existing differences between the sexes apart from the number of gametes they produce. In other words, males and females are identical except that males produce sperm in greater numbers than females produce eggs. In Model 1, resident individuals are assumed to mate monogamously, whereas a mutant can monopolise multiple partners of the opposite sex (Fig. 2). Importantly, both male and female mutants can bring additional partners back to their ‘nest’ to spawn in a group. When fertilisation is highly efficient, females can fertilise all of their eggs by bringing back a single male, and there is simply no benefit (in this model) of seeking further partners (Fig. 1A). In contrast, anisogamy means that males always produce at least some gametes in excess, and thus can benefit from seeking additional mates. When fertilisation is inefficient, however, both sexes benefit from increasing the concentration of opposite-sex gametes at their ‘nest’ (Fig. 1B). This latter benefit is sex-symmetric, whereas the former continues to apply only to males. As a consequence, the Bateman gradients are always steeper for males than for females (Fig. 1A, B), confirming Bateman’s argument.Model 2 similarly assumes external fertilisation, but in this case the resident males and females meet in groups consisting of m individuals of each sex (Fig. 2). Fertilisation occurs via group spawning. It is assumed that each resident individual divides its gametes evenly across M groups, whereas mutant individuals can instead spread their gametes over a larger or smaller number of groups (note that the author assumes that M = m, but this assumption could be relaxed without undermining the core argument). Spreading gametes out across a larger number of spawning groups does not increase the concentration of opposite-sex gametes they encounter (Fig. 2). However, a mutant that spreads its gametes more widely reduces the density of its own gametes across those groups in which it spawns. This in turn results in there being more opposite-sex gametes for each gamete of the mutant’s sex in those groups. For example, in Fig. 2, mutant males spawn in twice as many groups as resident males and thereby halve the density of their own sperm in each group. The resulting egg-to-sperm ratio of (frac{4}{6}=frac{2}{3}) is more favourable than the ratio of (frac{4}{8}=frac{1}{2}) that the resident males experience. Mutant females can similarly increase local sperm-to-egg ratios by spreading their eggs over more groups. However, in contrast to males, this only leads to fitness benefit if fertilisation is inefficient, and even then the benefit to females is very modest (scarcely perceptible in Fig. 1D). Gamete spreading reduces wasteful competition among the mutants’ own gametes for fertilisation. Such ‘local’ gamete competition, like gamete competition more generally, is stronger among sperm than among eggs because sperm are more numerous under anisogamy13,14. Consequently, as in Model 1, Bateman gradients are always steeper in males (Fig. 1C, D). Recall that the results of the above models emerge in the absence of any assumptions beyond the sex difference in the number of gametes produced.The third and final model allows for a further pre-existing difference between the sexes in addition to anisogamy: internal fertilisation, which is common and widespread in animals (Fig. 2)15. Each female is assumed to mate with m males, while each male divides his gametes evenly among m females. As in the previous two models, males benefit more than females from additional matings under most conditions. However, in the particular case where fertilisation is highly inefficient and the ratio of sperm to eggs is not too large, the pattern can theoretically reverse, such that female Bateman gradients exceed their male counterparts (Fig. 1F). The reason is that the effects of gamete concentration are asymmetric under internal fertilisation: Multiple mating by a female increases the local concentration of sperm its eggs experience, whereas a male’s multiple mating does not increase the concentration of eggs around its sperm (Fig. 2). Under conditions of severe sperm limitation—due to both weak anisogamy and highly inefficient fertilisation—this can lead to females benefitting more from additional matings than males (Fig. 1F). Although intriguing, it is unclear whether this finding has any empirical relevance, as sperm limitation is probably rarely severe in internal fertilisers. Under more realistic conditions of moderate to high fertilisation rates, sex differences in the degree of local gamete competition once again become decisive, and male Bateman gradients exceed their female counterparts (Fig. 1E). More