Inbreeding and demography interact to impact the recovery of a bottlenecked crested ibis population

Domain: neuroscience
Published: 2026-02-14
Editorial outcome: accept

Abstract
Biodiversity loss driven by climate change and human activities poses a critical global challenge. Population restoration and reintroduction programs are essential for mitigating this threat to endangered species, yet their outcomes often remain unpredictable due to poorly understood success factors, such as the inevitable inbreeding during bottleneck events. The conservation programme of the crested ibis (Nipponia nippon) marks a successful example where the population rose from just seven individuals to over 9000 in the past four decades. By developing an individual-based model that simulates the restoration process and incorporates species-specific demography and inbreeding data, we conclude that this successful restoration is largely deterministic, as our results closely mirror empirical recovery time and population-level inbreeding coefficients. To establish general guidelines for reintroduction programs, we compare how inbreeding depression influences the recovery success of two reintroduction strategies involving small founder populations. Our simulations reveal that the ‘firework’ approach (one-source translocations) outperforms the ‘sequential’ (serial translocations) approach in restoration effectiveness. Furthermore, by expanding analyses over a broad demographic space, we demonstrate that the net effect of inbreeding varies with species-specific demography and highlight the importance of considering their interaction when interpreting conservation outcomes and designing future reintroduction programs.

Introduction
More than one in four species assessed by the IUCN is threatened with extinction, and biodiversity is expected to decline further as climate change and other anthropomorphic threats intensify1. To reverse this trend, effective conservation programmes are urgently needed2. Predicting the likelihood of population recovery from ecological threats, setting up more protected areas, and providing optimal species reintroduction strategies are therefore central to these efforts3–11. Despite the evident need, population restoration and reintroduction outcomes vary widely across species4,12–16, and the causes of failure are often not well understood15,17,18. In-depth analyses of empirical conservation outcomes can help identify drivers of success and failure, offering broader insights that can be applied to conservation efforts of other threatened species4,6,18,19.

Population bottlenecks can result from ecological catastrophes, yet are also common in reintroduction programmes, which inevitably begin with small populations due to financial constraints, conservation uncertainties, or to minimise negative impacts on the source population13,16,20. The primary goals of such programmes are to help endangered species maintain genetic diversity by establishing multiple self-sustaining populations or restoring species’ historical geographic ranges6,20,21. However, unavoidable inbreeding in small populations during early reintroduction phases often leads to reduced genetic diversity, which raises looming concerns about long-term conservation success4,17. Inbreeding is therefore a likely contributor to the variable outcomes of restoration efforts.

Inbreeding depression—the reduced fitness of a population due to mating between genetically close-related individuals—has been a central focus of conservation biology since its inception22, and is regarded as one of the most cryptic threats to population viability3,23,24. In wild animals, inbreeding is known to result in abnormal embryo development25,26, reduced fecundity23, survival rates3,27,28, and recruitment probability29,30, which ultimately threaten population viability through a reduced population growth rate19,31. These effects stem from the increased occurrence of partially recessive deleterious alleles in the homozygous state through identity-by-descent, as well as the accumulation of such alleles due to genetic drift, which invariably accompany inbreeding in small, endangered populations. Even in species that have recovered from bottlenecks, genome-wide sequencing studies have revealed that considerable inbreeding persists3,19,32,33. This raises concerns that the detrimental effects of inbreeding could undermine the viability of current steadily growing populations, or hinder the success of future reintroduction programmes19,23,32,34. A remarkable conservation success is the recovery of the endangered crested ibis (Nipponia nippon) in East Asia. This long-lived species faced a severe bottleneck in the last century due to habitat loss and pollution35. Fortunately, its population has been officially announced to have rebounded from just seven wild individuals to over 9000 (wild and captive) individuals in the past four decades, thanks to extensive conservation efforts in China36,37. As with many restoration programmes, however, it remains unclear how and why this species overcame the expected negative consequences of inbreeding, and what lessons can be learned to guide conservation efforts for other endangered species.

The crested ibis is thus an ideal empirical example for which a more extensive analysis of its conservation can be of great use—especially given that long-lived species are thought to be particularly vulnerable to extinction during bottleneck events19,23. For instance, their slow reproductive pace may hinder them from rapidly recovering from a small population size4,19. Despite this, the populations of some long-lived critically endangered species appear to have successfully recovered from past bottleneck events12,13,19,23,24,38. This has partially been attributed to the idea that repeated reproduction over a long lifespan can help buffer the harmful effects of inbreeding at the population level, thereby aiding in successful restoration23,24,39. In other words, lifetime fecundity can be substantial for species that have a slow birth rate yet continue to breed over decades. However, the influences of demography, such as fecundity and mortality rates, are often overlooked in predictions of how inbreeding impacts population viability3,6,19,28.

Therefore, in this study, we create an individual-based model incorporating both empirical inbreeding depression data and demographic rates from the crested ibis population restoration. Our first aim is to investigate to what extent such a theoretical model (Fig. 1A) can make predictions that align with empirical conservation outcomes and to understand whether the crested ibis restoration success was achieved by chance or is largely deterministic. We then conduct two additional mutually independent model analyses, as examples of broader lessons we can learn by applying this simulation framework to inform conservation practice. First, we use the same ibis restoration model to implement two idealised reintroduction approaches and compare their effectiveness (Fig. 1B): ‘firework’ and ‘sequential’. The ‘firework’ approach involves simultaneously establishing multiple independent populations using founders taken from a successfully restored source population (analogous to sparks radiating outward from a firework). In addition to the one-time release of founders to establish isolated populations, we also simulate a variant in which immigrants are regularly translocated from the source population after the initial reintroduction. The ‘sequential’ approach involves establishing new populations in a stepwise manner, where founders are taken from newly recovered populations, resembling a chain of translocation events extending over time. We choose to study these idealised reintroduction approaches because they are the basic building blocks that can be combined to produce more complex and diverse reintroduction programmes used in conservation practice. This comparison aims to provide general reintroduction recommendations for endangered species that require careful management for population expansion. Lastly, we investigate more generally how demography and inbreeding interact to impact population viability in restoration programmes. To do so, we compare the simulation results with and without inbreeding depression in a large demographic parameter space beyond that of the crested ibis.

Results
Model overview
The simulation model begins with a bottlenecked population consisting of a few individuals. These individuals mate randomly to form breeding pairs that remain together for subsequent breeding seasons (Fig. 1). Each pair reproduces once per year. Their reproductive success is determined by the species’ clutch size, hatching success (influenced by the offspring’s inbreeding coefficients), and fledging success of the hatchlings. An individual’s inbreeding coefficient is calculated by tracking a pedigree matrix that contains all individuals that have ever appeared in the population (see ‘Methods’ and Supplementary Methods for details). After reproduction, individuals survive based on stage-specific probabilities (juvenile or adult survival rates). If both partners of a breeding pair survive, they will maintain the pair bond and breed again in the next season. If one partner dies or reaches the maximum reproductive age, the other individual randomly pairs with an unpaired adult of the opposite sex. This generates a population of overlapping generations. Simulations continue until the population reaches a threshold size or goes extinct.

Model predictions align well with the empirical crested ibis population restoration
To investigate the empirical restoration of the crested ibis, we incorporated species-specific biological information into the model, from empirical data (see the Supplementary Notes and the online repository40). The information includes kinship of the founder population, the negative effect of the inbreeding coefficient on hatching success (derived from empirical pedigree data analysis), clutch size, fledging success, nest survival, and stage-specific mortality rates (for details see Methods and Table 1). Of 300 simulations, 291 replicates (97%) resulted in successful population recovery, reaching a threshold population size of 9000 (Fig 2A, B, Fig. S2), suggesting that the empirical restoration success of ibis restoration is largely deterministic. Furthermore, the time required for successful restoration among simulation replicates (median: 44 years, mean ± sd: 46.5 ± 10.0 years) is close to the empirical restoration time of 41 years (grey dashed lines in Fig. 2A, Fig. S2).

Among simulations that resulted in successful restoration (Fig. 2B, green lines), most populations entered exponential growth (i.e., a straight line on the log scale) after short initial fluctuations. In contrast, populations in unsuccessful restorations (Fig. 2B, purple lines) remained small, never entered steady exponential growth, and eventually decreased to extinction—often rapidly (median: 8 years, mean ± sd: 15.8 ± 20.7 years). During restoration, the population’s average inbreeding coefficient first increases until reaching a plateau (Fig. 2C). The initial increase of the population-level inbreeding coefficient resulted from unavoidable inbreeding caused by the small size of the founder population. Once the population survives this initial phase, fewer inbred individuals can produce more offspring, contributing to faster population growth. Also, as population size increases, mating with close kin becomes less likely, leading to a decline in the variance of inbreeding coefficients among individuals. Among the successful replicates, the median population-level inbreeding coefficient in the final restoration year (0.19) was similar to the empirical estimate in the sampled population (0.17, 95% CI: 0.155–0.175, N = 321, grey dashed line in Fig. S3A).

The effect of inbreeding on hatching success was a central assumption of the crested ibis population restoration model. While this relationship was estimated from empirical data (see ‘Methods’), we also performed a sensitivity analysis to test model robustness. Varying the parameter value (s0) by ±50% did not substantially change the results (median population restoration time ranged from 40 to 50 years, and restoration success rate ranged from 95% to 99%, Fig. S4). More notable differences occurred when the value of s0 was doubled, leading to a decrease in restoration success (to below 90%) and longer restoration time (median: 58 years), although this does not affect the average inbreeding level in the successfully restored populations (Fig. S4). We also varied the relatedness between the adult founders, ranging from full siblings, half-siblings, to unrelated. All scenarios showed high restoration success rates (93.7–97.3%), though simulated restoration times suggest that the empirical founders were likely to have ranged from half-siblings to unrelated (Fig. S5). When inbreeding was assumed to not only impact hatching success but also reduce the survival of juveniles or adults, restoration success declined, but the population-level inbreeding coefficient when reaching restoration remained similar (Fig. S6).

In the main model, we implemented hard selection (i.e., mortality rates were independent of population density) for simplicity. However, soft selection is known to potentially hinder population recovery by negatively affecting individual fitness at population density41. To test whether this influences our model results, we additionally investigated how density regulation affects simulation outcomes. The results were robust to soft selection, as density dependence primarily slowed population growth during later stages of recovery, when the population size became large, but did not reduce the probability of successful restoration (Figs. S7 and S8, corresponding to two different ways of density regulation). Intuitively, this is because restoration success hinges on the early stage, which determines whether a population can enter stable exponential growth, whereas density effects only become important later.

The alignment between simulation results and the empirical data (i.e., restoration time and population-level inbreeding coefficients) and the robustness of the model suggests that our model provides a good fit for the real-world restoration dynamics of the crested ibis population.

Population reintroduction success depends crucially on the origin and number of founders
Having shown that our theoretical model fits well with the empirical restoration of the crested ibis, we conducted further model analyses to draw broader conclusions. Our first analysis using the theoretical model includes model variants corresponding to two idealised reintroduction strategies, which we term ‘firework’ and ‘sequential’ approaches. These strategies differ in the source of founders used to establish newly introduced populations. In the ‘firework’ approach, founders of the newly introduced populations were taken from the original source population, after it was successfully restored. The new populations were either established solely by these founders (Fig. 3A1) or also with additional immigrants translocated from the source population at regular intervals (Fig. 3A2). In the ‘sequential’ approach, the founders of the first round of reintroduction also came from the restored source population, but subsequent reintroduction rounds drew founders from the most recently restored population in a stepwise, chain-like fashion. For clarity and ease of comparison, only a few representative trajectories of population reintroduction are shown in Fig. 3; however, our simulations explored a wider range of scenarios, varying the number of unrelated founder pairs from three to 13 for each reintroduction approach, with 50 independent replicates for each scenario (Fig. S9).

With the ‘firework’ reintroduction approach, increasing the number of founders resulted in lower inbreeding levels in the reintroduced population, regardless of whether immigrants were added (Fig. 3A1 and A2; compare the trajectories with three and 11 founder pairs). However, adding immigrants further slowed the accumulation of population-level inbreeding coefficients (Fig. 3A1 and A2; compare trajectories with the same number of founder pairs) and accelerated growth of the reintroduced population (Fig. S10). For example, a scenario with three initial founder pairs supplemented by the repeated addition of three immigrant pairs from the source population across five rounds (Fig. 3A2) yielded comparable population growth dynamics to a one-time reintroduction of 11 founder pairs (Fig. 3A1). These two scenarios showed similar final-year population average inbreeding coefficients (0.21 vs. 0.21, Fig. 3A1 and A2) and population sizes (285 vs. 280 individuals, Fig. S10).

In population reintroductions following the ‘sequential’ approach, there is a notable accumulation of the inbreeding coefficient over consecutive rounds (Fig. 3B). This approach resulted in more frequent population reintroduction failures, especially with a small number of founders (Fig. S9B). For instance, with only three founder pairs, there is a faster increase in the population-level inbreeding coefficient, resulting in sudden population collapse at the beginning of the fourth reintroduction round (Fig. 3B). In contrast, introducing 11 founder pairs allowed the population to complete all ten rounds of reintroduction, despite the continuous accumulation of inbreeding in each consecutively reintroduced population. Overall, the full programme of ten reintroduction rounds under the ‘sequential’ approach was only possible when each reintroduction round involved more than seven founder pairs (Fig. S9).

Our simulations showed that, for both reintroduction approaches, increasing the number of founders leads to faster population growth and mitigates the accumulation of inbreeding coefficients over reintroduction steps. As founder numbers increased, the restoration effectiveness gap between the two approaches narrowed. Nonetheless, the ‘firework’ approach generally outperformed the ‘sequential’ approach by yielding higher success probability, shorter restoration times of newly established populations, and requiring fewer founder pairs to achieve successful reintroduction.

The net effect of inbreeding depression on population restoration depends on demography
We further analysed the theoretical model to explore how inbreeding and demography interact to influence population viability under a broader demographic parameter space. Specifically, we varied clutch size, juvenile mortality rate, and adult mortality rate within ranges informed by demographic parameters of 41 bird species (Table S1). For each parameter combination, we ran simulations both with and without inbreeding depression, reducing hatching success. This comparison allowed us to disentangle the interactions between demographic parameters and inbreeding depression in shaping population viability after a bottleneck event.

From a full analysis across these parameter combinations, we can categorise species into three types (markers I–III in Fig. 4A–C) based on how demographic rates and inbreeding jointly affect population viability. Type I species (of which the crested ibis is an example) have favourable demographic rates (e.g., low juvenile and adult mortality rates). For these species, inbreeding depression has a negligible impact on the restoration success after a bottleneck (Fig. 4C), as they show a high recovery probability regardless (Fig. 4A, B). In contrast, type III species have unfavourable demographic rates that alone lead to low recovery probabilities (Fig. 4A, B), making population extinction during bottleneck events almost inevitable regardless of inbreeding depression (Fig. 4C). Type II species occupy an intermediate zone: they have demographic rates that result in a good chance of population restoration when inbreeding is assumed to be neutral (Fig. 4A), but restoration is unlikely when inbreeding reduces reproductive fitness (Fig. 4B, C). All three types are reflected by the distribution of the 41 species in the full simulation analysis (Fig. 5), and variation in clutch size introduces further complexity. Specifically, small clutch sizes considerably hinder recovery in species with high adult mortality, whereas in species with larger clutches, population viability is more constrained by high juvenile mortality. Although the model assumes a uniform effect of inbreeding depression across species, the net impact of inbreeding on population recovery from a bottleneck varies considerably depending on the demographic context. Given the large variation in avian demography (Table S1), our model results highlight the necessity to consider the interactions between a species’ demography and the impact of inbreeding depression when evaluating the likelihood of population recovery from bottleneck events.

Methods
Ethics declarations
All fieldwork was conducted under the guidance of the Ethics Committee of the Institute of Zoology, Chinese Academy of Sciences. The collection of pedigree information and captivity data was permitted by Dongzhai National Nature Reserve, and carried out in accordance with the guidelines of the Institutional Animal Care and Use Committee of the Institute of Zoology, Chinese Academy of Sciences.

Study system
The crested ibis is currently categorised as an endangered species in the IUCN Red List of threatened species57. It was declared locally extinct in Russia, Korea and Japan in the last century, and was rediscovered in 1981 in a mountain village of Yang County, Shaanxi Province, China. At the time, the wild population had only seven individuals, including two breeding pairs, one of which had three nestlings58. Since then, extensive conservation efforts—both in situ and ex situ—have been undertaken. As of 2022, the crested ibis has officially been reported by the State Council of China to have recovered to a population size exceeding 9000 individuals over the past 41 years36.

Quantification of the inbreeding effect
The empirical dataset used in this study was collected from the Crested Ibis Breeding Centre at Dongzhai National Nature Reserve (DNNR) in Henan Province, China. A pedigree was constructed based on recorded breeding partnerships and parental information for 321 captive-bred crested ibises from 2008 to 2023 using the R package ‘pedantics’59. Individual inbreeding coefficients were calculated from this pedigree using the same package, yielding a population mean of 0.17 (95% CI: 0.155-0.175). We used mixed linear models to quantify the effects of inbreeding on fitness during early-life stages—specifically fertilisation, hatching, and fledging (see Supplementary Notes for details of the statistics). The effects of inbreeding on juvenile and adult survival were not estimated due to the lack of such information for birds living in captivity. Instead, we used simulations to explore the potential effects of inbreeding on mortality rates at different life stages and evaluate how this affects population restoration dynamics (Fig. S6).

Field data collection for estimating demographic parameters
Breeding biology information was collected from the wild crested ibis population derived from the 122 individuals released at Dongzhai National Nature Reserve since 2014. We monitored breeding activity throughout the breeding season from February to June during 2021–2023. The crested ibis nests were searched over 549.66 km2 of mountainous terrain. Most nests were found in Masson pine (Pinus massoniana), with an average nest height of 12.58 ± 1.70 m (N = 33 nests). Nests were checked every other day via binoculars or drones (DJI Mini 4 Pro) to identify clutch size, the number of hatchlings (30 days after clutch completion) and the number of fledglings (42 days after hatching). Daily survival rate (DSR) was estimated using the RMark package in R60,61. A total of 40 nests were continuously monitored in the wild. Those with incomplete records were excluded from downstream analyses. Juveniles (22 individuals) and adults (40 individuals) were tracked with GPS devices (HQBG3621L, from Hunan Global Xinshi Technology Co., Ltd.).

Demographic parameters used in the model include clutch size, nest survival rate, hatching success, fledging success, and the mortality rates of juveniles and adults. The wild individuals originated from released offspring of the captive population living in the same nature reserve, and thus are likely to share similar fitness effects of inbreeding as the captive population. Details on how these demographic parameters were estimated are provided in the Supplementary Note.

Calculating inbreeding coefficients from a simulated pedigree
The inbreeding coefficient F measures the level of inbreeding, which is the probability that two alleles at a given locus in an individual are identical by descent from a common ancestor. This can be estimated by analysing the pedigree to track the kinship of all common ancestors of an individual’s parents. We calculated inbreeding coefficients by constructing a numerator relationship matrix (A) using the tabular method62. Specifically, all individuals in the pedigree were numbered from 1 to N, and the N × N matrix A contains the pairwise relationship coefficients between any two individuals. The diagonal element corresponding to a focal individual i is given by ai,i = 1 + 0.5ap,q, where p and q are the parents of the focal individual i, located in the p-th and q-th row of the matrix; and ap,q is thus the relationship coefficient between them (Supplementary Methods). The off-diagonal entries in the lower triangle of A are computed recursively as ai,j = 0.5(ai,p + ai,q), where p and q are the parents of individual j. Following this method, all elements of A can be generated through pedigree tracking. The inbreeding coefficient of individual i is then derived from its corresponding diagonal element in A by Fi = ai,i − 1. We programmed the pedigree matrix and the calculation of F in C++ (version 22) using a memory-efficient algorithm that significantly reduced the storage demands for the matrix. The algorithm pseudo-code is provided in the Supplementary Methods, and the C++ code is accessible in the Zenodo repository40.

Model simulation details for crested ibis restoration
We parameterised the individual-based model based on the breeding system and demographic data of the crested ibis. Simulations were initiated with a small population of seven individuals from two families—two breeding pairs, one of which had three nestlings—resembling the population state when the species was rediscovered in the wild in 198135. Because the kinship between the four adult founders was unknown, we explored different assumptions about their relatedness (i.e., full siblings, half siblings, and unrelated; Fig. S5). Pedigree analysis of one sampled population revealed that inbreeding primarily reduced brood hatching success, with no significant influence on fertilisation success or nestling survival (relevant analyses are provided in the Supplementary Note and the Zenodo repository40). We therefore model only the effect of inbreeding depression on hatching success here, but consider the effect of inbreeding depression on different life stages in the Supplementary Method and Fig. S6. We modelled the average number of hatchlings V per brood as a function of clutch size C and inbreeding-dependent hatching success, as follows:

V = C(H0 − s0F), (1)

where H0 is the baseline hatching success, s0 quantifies the negative effect of inbreeding depression, and F is the inbreeding coefficient. We performed a sensitivity analysis to explore how the parameterisation of s0 affects the simulated outcomes of population recovery (Fig. S4).

The number of fledglings was drawn from a Poisson distribution with a mean value of VRf, where Rf represents the fledging success of the hatchlings. We also incorporated the empirical nest survival rate Rn, which reflects the probability a nest survives the breeding season without complete reproductive failure due to damage or predation. As crested ibises remain in the juvenile stage without breeding for two years, we modelled mortality rates across three life stages based on empirical data: first-year juvenile (j1), second-year juvenile (j2), and adult (a). The values of all parameters are listed in Fig. 1. The survivorship of juveniles and adults in the population after a breeding season is determined by sampling a Bernoulli distribution with their corresponding life-stage-dependent mortality rates as the mean. Survivors enter a new breeding cycle, except for newborns and first-year juveniles. Simulations were terminated once the population reached 9000 individuals to compare the simulated population recovery with the empirical restoration outcomes. We here assumed no carrying capacity for population growth, but density-dependence as a type of soft selection could potentially hinder population recovery by negatively affecting individual fitness41. We therefore explored the effects of how density regulation can affect population recovery in the Supplementary Method, Fig. S7 and Fig. S8. All simulation code was written in C++ and is available in the Zenodo repository40. Simulation and empirical data were analysed and visualised in R 4.2.2.

Model analysis 1: comparing the ‘firework’ and ‘sequential’ reintroduction approaches
Based on the crested ibis model, we developed a reintroduction analysis that includes two model variants to compare the conservation effectiveness of two applied reintroduction strategies, the ‘firework’ approach and the ‘sequential’ approach. In each independent simulation of the ‘firework’ approach, we first generated a source population containing over 1000 individuals using the core crested ibis model. From this population, a fixed number of founder pairs were randomly sampled ten times to initialise ten independent reintroduction events. Each reintroduction event was terminated when the population either recovered to over 1000 individuals or went extinct. We tested different founding population sizes, ranging from three to 13 pairs, and simulated each scenario ten times.

To evaluate the impact of immigration on reintroduction outcomes, we ran additional simulations by simultaneously translocating groups of founders following two alternative processes: (1) translocating founders to establish a new population with no subsequent immigrants (same as the ‘firework’ simulations described above); (2) translocating founders to establish a new population and adding the same numbers of new immigrant pairs from the source population to the new population every three years for five rounds (i.e., in years 3, 6, 9, 12 and 15). We simulated scenarios with three and 11 pairs of reintroduced founders for these two alternatives, which led to four new populations being established simultaneously. The simulations were terminated once any of the four reintroduced populations reached 1000 individuals. Each combination was run for ten replicates.

In the ‘sequential’ approach, founders were always taken from the most recently recovered population that had reached 1000 individuals, creating a series of reintroductions. The number of founder pairs also ranged from three to 13. Each reintroduction proceeded sequentially: a new round began after the previous reintroduced population had recovered. Simulations were terminated either after 10 rounds of successful reintroduction or when a newly reintroduced population went extinct. We ran 50 independent simulation replicates for each number of founder pairs.

Model analysis 2: evaluating the more general impact of inbreeding on species-specific demography
To evaluate the net effects of inbreeding depression on the probability of population recovery in a bottleneck scenario, we implemented two model variants: hatching success declines with inbreeding (s0 = 1), and inbreeding has no effect on hatching success (s0 = 0). To generalise beyond the crested ibis, we excluded ibis-specific parameters such as nest survival and fledging success, and varied other demographic parameters across wider ranges: the mortality rate of juveniles (mpj) and adults (mpa), and clutch size (Cp) (Table 1). Specifically, we explored 11 values of mpj, 17 values of mpa, and six values of Cp, with full factorial combinations of mpj, mpa and Cp, and each unique combination was simulated with 100 independent replicates. Simulations began from a small, unrelated founding population consisting of three unrelated pairs. All individuals older than one year were allowed to breed. The linear correlation between inbreeding coefficients and hatching success was kept the same as in the crested ibis population restoration model, as relevant data for other species were unavailable. Nest failure and hatchling death were also excluded for simplicity and generality. To contextualise the model outcomes, we mapped 41 avian species with available stage-dependent mortality data from the COMADRE Database (2024) (Available from: https://www.compadre-db.org/[15 July 2024, Version 4.23.3.1]) to the simulation outcomes to provide implications of varied inbreeding effects on species with diverse demographic rates under our model assumptions. From all available avian data in COMADRE, we filtered species to ensure they were not too dissimilar in life-history to the crested ibis, such that we can explore parameter space beyond that of our focal species while ensuring that the model remains a biologically appropriate tool to do so. Specifically, we included only species with lifespans exceeding 10 years and average clutch sizes between one and six. As a larger clutch size contributes to improved restoration success (see Fig. 5), we rounded the average clutch size up to the next integer (rather than the closest integer) for all the species mapped to the simulation outcomes, to be more conservative in attributing the extinction risk to the effects of inbreeding and juvenile and adult mortality.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This paper uses simulations to explore the effects of restorations strategy (introducing many individuals at once into multiple\nnew populations [“firework”] versus iteratively adding individuals [stepping stone]) demography, and inbreeding depression\non the viability of reintroduced populations. The study is motivated by the successful reintroduction and expansion of the\ncrested ibis and uses approximate demographic parameters for this species to parameterize the simulations. The authors\nfind that the wildly successful reintroduction of crested ibis is not surprising under the assumptions of the simulation model,\nand that, more generally, the impact of inbreeding on reintroduction success depends on demographic parameters of the\nspecies/population in question.\nWhile the crested ibis recovery is quite interesting, I cannot tell how the simulations were parameterized, what is the quality\nof the empirical demographic data used, and thus strongly question whether the simulations are actually informative of the\npopulation dynamics of the species.\nThe general contribution of the simulations that incorporate a wider range of demographic parameters (“model analysis 2”)\nis also unclear to me, in particular because we already know that population recovery (essentially a function of population\ngrowth rate) is strongly affected by demographic parameters (age- and sex-specific survival and reproduction) in every\nspecies, and it is unclear that the model of inbreeding depression in these simulations is realistic for any of the modeled\nscenarios.\nMarty Kardos\nSpecifics:\n24-26: Inbreeding depression has been a central focus of the field of conservation biology since its inception. See Michael\nSoulé’s books from the 1980s. However, it is true that there have been many papers on inbreeding published recently\nbecause we can now measure inbreeding precisely in any population where we can sequence genomes and map reads to\na good genome assembly.\n27-29: nothing is said here about effects on the population growth rate but this is the central concern for effects on population\nviability (https://onlinelibrary.wiley.com/doi/full/10.1111/mec.17608).\n49-51: This is not very convincing. Reference 6 is a paper about alpine ibex where genetic variation is associated with\npopulation growth rate, directly contradicting the statement. Reference 17 did not actually measure inbreeding depression so\nits relevance is tenuous at best. These are the only two of these study systems that I a intimately familiar with. I therefore\nsuggest reconsidering this argument. There are also other studies that directly contradict this statement, including one of my\nown (https://www.nature.com/articles/s41559-023-01995-0), and many others depending on how one defines ‘long-lived’\n(e.g., soay sheep, red deer on the Isle of Rum), many species in captivity (Ralls et al papers from the 1980s). I am actually\nnot aware of any reason to expect inbreeding depression to be weaker on average in long lived compared to short lived\nspecies.\n72-74: It is kind of circular to investigate how demography impacts population viability because population viability is by\nnecessity a direct consequence of population growth rate, which is a direct consequence of cumulative birth and death rates.\n78: Formation of long-term breeding pairs is not consistent with random mating, where parents are picked at random from all\npotential parents in a population. I suggest clarifying this.\n***The parameterization of inbreeding effects on fitness and the base line demographic parameters are absolutely critical to\nthis paper (https://onlinelibrary.wiley.com/doi/full/10.1111/mec.17608). For the simulation model to be informative of how\nlikely the observed outcome was (recovery from 7 individuals) requires the assumed model parameters to closely match the\nreal ones BEFORE and DURING the population decline and recovery. What are the sample sizes for the empirical analysis\nof demographic vital rates and inbreeding depression? What animals were used for the analyses? Were they done in\ncaptivity or in the wild? How much statistical uncertainty is associated with the estimated vital rates and estimated effects of\ninbreeding depression? Crucially, when were the empirical analyses done? Before the bottleneck or after? The empirical\ndata on these effects are apparently not published, and the link to the referenced data on Dryad (reference 33) is broken so I\ncannot evaluate this. These critical data should be added to the manuscript if they are not published somewhere else\nalready.\nThe simulations begin with “a small population of seven individuals from two families (two pairs and three nestlings),\nresembling the population state when the species was rediscovered in 1981 in the wild” (lines 307-310). However, the\nrealized kinship among these seven individuals does not depend only on the family structure, but also depends critically on\nwhat happened in the population beforehand. For example, while the realized kinship coefficient of full siblings sampled\nfrom an infinitely large and randomly mating population is 0.25, the realized kinship is expected to be much higher than 0.25\nfor full sibs sampled from a population that has been small for a long time. The potentially large effects of recent historical\ndemography on realized inbreeding during the population bottleneck appear to be assumed to be absent here. It is also\nentirely unclear how large the assumed effects of inbreeding on fitness were, or what is the source of this information. How\nmany lethal equivalents were there for different vital rates? Howe were these effects incorporated into the simulations? Were\nthe vital rates estimated using the same individuals that were used to estimated inbreeding depression? Were the effects of\ninbreeding already incorporated into the average vital rate estimates? Were the effects different for males versus females, or\nyoung versus old individuals? The lack of clarity here is a major weakness of the paper.\nIt is unclear what the motivation is behind the comparison of the ‘firework’ and ‘stepping stone’ reintroduction models. I\nespecially question the relevance of the stepping stone model bercause I have never heard of this approach being used in\npractice, probably because it ensures serial population bottlenecks as new reintroductions are done, and this is why\ninbreeding increases so rapidly in this scenario (Figure 3b). It would probably be more informative to compare scenarios\nwhere new immigrants are versus aren’t added repeatedly to reintroduced populations either from the original source or\nanother population in an effort to maintain genetic variation, especially in cases where a reintroduced population does not\nbegin to recover immediately.\nFigure2: It is unclear why population size is shown on a log scale. I suggest showing the raw population size so that readers\ndo not have to do any math to interpret the figure. It is also unclear why there is variation in the population size at year zero,\nwhen it seems each population replicate should have a value of log10(7) = 0.84 at year zero.\nFigure 3: I assume that figure three shows a single simulation replicate, correct? I suggest making this clear in the caption.\nModel analysis 2: here the authors use a wider range of combinations of demographic vital rates to attempt to gain an\nunderstanding of the effects of inbreeding and demography on population recovery.\n359-361: Inbreeding depression has been estimated empirically in may study systems. Why not incorporate those data here\ninstead of assuming your estimates for the crested ibis apply to all species?\nMore generally, we know that inbreeding depression arising from deleterious genetic variation can have widely varying\neffects of population dynamics and viability depending on which vital rates are affected, what is the form of selection (soft\nversus hard), environmental conditions and other ecological factors (climate, predation, intra- and inter-specific competition),\nand historical population size. These effects do not seem to be considered anywhere in the paper, which makes for a\nsignificant omission in my opinion. See https://doi.org/10.1146/annurev-ecolsys-110411-160257,\nhttps://onlinelibrary.wiley.com/doi/full/10.1111/mec.17608, and citations therein.", "reviewer_2": "Inbreeding and demography interact to impact population recovery from bottlenecks.\nThis manuscript addresses a fundamental question in conservation biology: How do demographic and genetic factors\ninteract in species conservation programs? This is a very important and timely question given the increased reliance on\nspecies reintroductions, and one that needs more careful analyses of empirical examples. This paper presents such a\ncareful analysis of the crested ibis restoration.\nI very much enjoyed reading the paper. I particularly enjoyed the fact that the crested ibis results were carefully put into a\nlarger context. Figure 5 is an excellent example of how the authors achieve general insights from putting a single species\nstudy into a broad perspective.\nBelow are some comments that will hopefully help in the revision of the manuscript. I'll beginn with some general comments,\nfollowed by more specific ones.\n1) Studies of the effects of inbreeding on population dynamics have long recognised that these effects differ when selection\nis hard or soft (see e.g. Bell et al. 2021, Ecology Letters). When selection is density- or frequency dependent (soft selection),\ninbreeding depression may have little effect on population dynamics, while under density- or frequency independent\nselection (hard selection) the effects of inbreeding depression translate more directly into reduced population growth. In this\nmanuscript, selection is assumed to be invariably hard (eq. 1). I think this is a point that the authors should discuss in detail,\nespecially since the softness of selection is an important aspect of the interactions between inbreeding and demography that\nmake up the title of this manuscript. That selection is always completely hard represents a very strong assumption. Ideally,\nthis is something that would be explored explicitly with the simulations in this manuscript, but if that isn't possible it needs to\nbe acknowledged and discussed both in light of the density-dependence seen in some crested ibis subpopulations (Li et al.\n2022, Lands) and in light of the population dynamics of reintroduced populations in general.\n2) Based on empirical evidence from the crested ibis, this manuscript models inbreeding effects on a single life history trait,\nhatching success. It is well known that the life history stages that are affected by inbreeding have a marked impact on the\ndegree to which inbreeding affects population dynamics (see e.g. https://onlinelibrary.wiley.com/doi/10.1111/mec.17608 for\na recent illustration). Hence, it would make this work even more relevant to a broader audience, if the authors also modelled\na situation where another life history trait (e.g. adult survival) showed inbreeding depression. I realise that simulation studies\nare a bottom-less pit and that one cannot always ask for yet another scenario. If it is not feasible to run another scenario with\ninbreeding depression in adult survival or another life-history stage, then this caveat should be brought up in the discussion.\n3) The crested ibis recovered from just seven to over 9000 individuals in just four decades. This is a very fast recovery. Other\nspecies recover more slowly, and this may affect how well different reintroduction strategies perform (see e.g.\nhttps://zslpublications.onlinelibrary.wiley.com/doi/full/10.1111/acv.12299 for an example). It would be interesting to know\nhow sensitive the results of this work are to the speed of recovery. If more simulations are not feasible, a verbal discussion of\nthis issue would be helpful.\nSpecific comments:\n- Lines 7-9: There is a considerable primary literature on the various factors that influence reintroduction success, and books\nthat summarise the state of the field. Some of the primary literature (e.g. Griffith et al., Science 1989; Sarazin & Barbault,\nTREE 1996; Fischer & Lindenmayer, Biol. Conserv. 2000) and a couple books (e.g.\nhttps://onlinelibrary.wiley.com/doi/book/10.1002/9781444355833, https://www.ucpress.edu/books/reintroduction-of-fish-and-\nwildlife-populations/hardcover) should perhaps be cited here to provide interested readers with the background.\n- Line 9-10: Maybe 'Retrospective' would be more appropriate here rather than 'Subsequent'?\n- Lines 17-19: I would switch the order of the goals here. I think that from a conservation perspective 'multiple self-sustaining\npopulations' comes first, and genetic diversity comes second because genetic diversity is a condition for populations to be\nself-sustaining in the long run.\n- Lines 29-30: The wording here could be misunderstood. The primary cause of inbreeding depression is the increased\noccurrence of partially recessive deleterious alleles in homozygous state through identity-by-descent. The decreased\ngenetic variation and the accumulation of mildly deleterious recessive alleles are a consequence of the genetic drift that\ninvariably accompanies inbreeding in endangered species.\n- Lines 30-31: It is true that many vertebrates do not seem to avoid inbreeding, but the statement that inbreeding is common\nwould need to be more specific to be helpful here. Close inbreeding, for example, is rare even in many endangered species.\nI would suggest to replace this sentence with a statement to the effect that inbreeding is a direct consequence of the small\npopulation size that makes a species be considered endangered.\n- Lines 36-41: I missed a reference here to the paper by Li et al. (2022, https://doi.org/10.3390/land11101817) which showed\nthat exogenous environmental factors are major drivers of the very fast recovery of the crested ibis. This seems relevant for\nthe discussion of hard versus soft selection.\n- Lines 49-53: I think this wording could easily be misunderstood. As Taylor et al. 2017 (reference #6 here) have shown,\nsubstantial inbreeding depression is very likely do go unnoticed in growing, reintroduced populations. It is not the case that\nthe negative fitness consequences of bottlenecks are strikingly negligible in long-lived endangered species (killer whales,\nreference #2 in the manuscript, and ibex, reference #5, serve as examples for this in the literature cited in the manuscript).\nRather, it is the fact that they are difficult to detect without good fitness data that leads to the appearance of an absence in\ngrowing populations.\n- Line 63, 100, and Abstract: In all these places the authors used the term 'repeatable' which to me implies that if one was to\ndo another restoration of the crested ibis it would unfold in a similar way. I don't think this is what the authors mean. What\nthey seem to mean is that the process is largely deterministic. Perhaps this would be a better term?\n- Line 66 and Abstract: I see why the authors introduce the term 'firework' here but I think it would help readers if the authors\nspelled out the analogy. At least the way I understand the analogy, this reintroduction strategy establishes many new\npopulations simultaneously, just the way that fireworks send out multiple lights simultaneously. If this interpretation is correct,\nit might be worth while to make it explicit.\n- Line 68 and Abstract: The other reintroduction strategy is called the ‘stepping-stone’ approach. Stepping-stone models\nhave a clearly defined meaning in population genetics, at least since Kimura & Weiss's 1964 paper in Genetics. To avoid\nconfusion, I would therefore not use this term here. 'Sequential approach' would work for me as an alternative but the authors\nmay have other preferences.\n- Line 101 and elsewhere: Please clarify whether SD refers to standard deviations among simulation replicates or to\nstandard deviations within populations. I assume the former but please specify.\n- Lines 132-133: I didn't understand completely why the variance of inbreeding coefficients would decline. Perhaps the\nauthors could elaborate? Also, does this statement refer to the variation among simulation replicates or within populations?\n- Lines 154-184: I did not understand whether these simulations were based on 'firework' or 'stepping-stone'. Please specify.\n- Line 196, fewer founders: True, but does 'firework' not require more founders at the initial stage? In most recovery programs\nthe number of animals available for release at any given time is limited. This may be a non-trivial advantage of non-firework\napproaches.\n- Lines 210-212: It does not become clear here whether these statements refer specifically to the conservation project of the\nSeychelles Magpie-robin, or whether they are general comments. Please clarify.\n- Lines 236-237: Am I right in thinking that by 'converging individual variation in F' the authors mean that the variance in F\namong individuals declines because all individuals are starting to be inbred to similar degrees? This may be something\nworth explaining in a few more words.\n- Line 246: Would it help to write '... current population growth ...' here to emphasise that growth rate is predicted to become\nnegative in the future in this example?\n- Line 254: Does '... due to this unfavorable demography ...' refer to the low survival and reproductive rates? Please clarify.\n- Line 345: Proceeding with another round of reintroductions once the population size reached 5000 leads to very long time\nintervals between successive reintroductions (ca. 30-50 years). This seems quite unrealistic in actual reintroduction\nprograms. How sensitive are the results to this choice of time intervals?\n- Fig 3: There are a couple aspects of the figure that I did not understand. First, with 'firework' and 11 pairs (Fig. 3A), the\naverage inbreeding declines at the very beginning. Why is this? Also, in Fig. 3B why is the average inbreeding at the\nbeginning (purple dot) of the 11 pairs scenario substantially higher than in Fig. 3A?", "reviewer_3": "This study presents simulation results on how population recovery is influenced by inbreeding depression and the\ndemography of long-living avian species. The results are backed up with empirical data on the Crested Ibis. I think this\nmanuscript provides some important considerations for conservation and rewilding programs. The methods presented could\nbe used as practical guides to evaluate the potential outcomes of conservation projects and/or prioritise between\nreintroduction schemes. The paper is well-written, with easy-to-follow logic and interpretation of the data.\nAt the end of the introduction, can you explain the main differences between the “firework” and “stepping-stone” approaches\nwith bit more details (L66-69), as these are first mentioned here, and the current description wasn’t immediately clear at first\n(e.g. how they are sequentially introduced). Also, it should be added somewhere why these two reintroduction approaches\nwere chosen (and not others) for the analysis.\nWhen presenting the “firework” vs. “stepping-stone” simulation results, it would be good to mention how many simulations\nthese are based on (L122), even though it’s later explained with more detail in the methods.\nThe results are well presented. I especially liked the Supplementary Figure 3B that clearly shows the amount of\n(un)successful outcomes in the different scenarios.\nIn methods, it could be better described how the 41 species of birds were selected, i.e. what thresholds were used to\nconsider a species long-living and why no other bird species with shorter lifespans were included.\nMinor comments:\nIn general: I would recommend to follow the IOC World Bird List when using the English name of bird species in the text.\nL358: “consisting of”\nSupplementary Table: “of 41 long-lived avian species analysed in this study” – as there are more than 41 long-lived bird\nspecies.\nFigure 4: For more detailed description on the different parameter spaces (I, II, III) it would be good to refer to text.\nSupplementary Figure 4 is not referenced anywhere in the text."}, "author_response": "Dear Dr. Kardos,\nThanks for your thoughtful and constructive comments. Above, you raised two major concerns: 1. Details of empirical data and its use in simulation parameterization; 2. The usefulness of “model analysis 2”, which is related to your comments on L72-74 and L356–361 below. We addressed concern 1 by adding the section “Quantification of inbreeding effect and life history parameters” to the Methods and providing a Supplementary Text “Empirical data of the crested ibis”. Please also see our response #1.6. Concern 2 was addressed by better explaining the logic of this analysis and revising the manuscript accordingly. Please see our responses #1.4 and #1.12 for details.\nPlease see our point-by-point reply to your specific comments below.\nWorking through your comments and suggestions helped us improve the paper substantially. We hope you find our revisions satisfactory.\nDr. Jia Zheng on behalf of all authors\nSpecifics:\n24-26: Inbreeding depression has been a central focus of the field of conservation biology since its inception. See Michael Soulé’s books from the 1980s. However, it is true that there have been many papers on inbreeding published recently because we can now measure inbreeding precisely in any population where we can sequence genomes and map reads to a good genome assembly.\nResponse #1.1: We rephrased this sentence and cited the book you recommended (now ref. [21]): “Inbreeding depression -- the reduced fitness of a population due to mating between genetically close-related individuals -- has been a central focus of conservation biology since its inception [21], and is regarded as one of the most cryptic threats to population viability…” (L53–55)\n27-29: nothing is said here about effects on the population growth rate but this is the central concern for effects on population viability (https://onlinelibrary.wiley.com/doi/full/10.1111/mec.17608).\nResponse #1.2: We incorporated the reference (now ref. [30]) and rephrased the sentence: “In wild animals, inbreeding is known to result in abnormal embryo development [24,25], reduced fecundity [22], survival rates [2,26,27], and recruitment probability [28,29], which ultimately threaten population viability through a reduced population growth rate [18,30].” (L56–58)\n49-51: This is not very convincing. Reference 6 is a paper about alpine ibex where genetic variation is associated with population growth rate, directly contradicting the statement. Reference 17 did not actually measure inbreeding depression so its relevance is tenuous at best. These are the only two of these study systems that I am intimately familiar with. I therefore suggest reconsidering this argument. There are also other studies that directly contradict this statement, including one of my own (https://www.nature.com/articles/s41559-023-01995-0), and many others depending on how one defines ‘long-lived’ (e.g., soay sheep, red deer on the Isle of Rum), many species in captivity (Ralls et al papers from the 1980s). I am actually not aware of any reason to expect inbreeding depression to be weaker on average in long lived compared to short lived species.\nResponse #1.3: The sentence was indeed misleading, as also pointed out by Reviewer 2, sorry for causing the confusion. We have rephrased it for clarity: “Despite this, the populations of some long-lived critically endangered species appear to have successfully recovered from past bottleneck events [11,12,18,22,23,38]. This has partially been attributed to the idea that repeated reproduction over a long lifespan can help buffer the harmful effects of inbreeding at the population level, thereby aiding in successful restoration [22,23,39].” (L75–79)\n72-74: It is kind of circular to investigate how demography impacts population viability because population viability is by necessity a direct consequence of population growth rate, which is a direct consequence of cumulative birth and death rates.\nResponse #1.4: Our focus here is not merely on the effect of demographic parameters but their interaction with the effect of inbreeding. We rephrased the sentence to avoid the impression of circular reasoning: “Lastly, we investigated more generally how demography and inbreeding interact to impact population viability in restoration programs. To do so, we compared the simulation results with and without inbreeding depression in a large demographic parameter space beyond that of the crested ibis.” (L100-103)\n78: Formation of long-term breeding pairs is not consistent with random mating, where parents are picked at random from all potential parents in a population. I suggest clarifying this.\nResponse #1.5: We rephrased the sentence to clarify this: “These individuals mate randomly to form breeding pairs that remain together for subsequent breeding seasons (Fig. 1).” (L106–108)\n***The parameterization of inbreeding effects on fitness and the base line demographic parameters are absolutely critical to this paper (https://onlinelibrary.wiley.com/doi/full/10.1111/mec.17608). For the simulation model to be informative of how likely the observed outcome was (recovery from 7 individuals) requires the assumed model parameters to closely match the real ones BEFORE and DURING the population decline and recovery. What are the sample sizes for the empirical analysis of demographic vital rates and inbreeding depression? What animals were used for the analyses? Were they done in captivity or in the wild? How much statistical uncertainty is associated with the estimated vital rates and estimated effects of inbreeding depression? Crucially, when were the empirical analyses done? Before the bottleneck or after? The empirical data on these effects are apparently not published, and the link to the referenced data on Dryad (reference 33) is broken so I cannot evaluate this. These critical data should be added to the manuscript if they are not published somewhere else already.\nResponse #1.6: We have now added two sections to the Methods (i.e., “Study system” and “Quantification of inbreeding effect and life history parameters”, L332–351), where we provided relevant information to answer your questions. In particular, the pedigree analysis of the effect of inbreeding depression has been done with a captive population of 321 individuals from 2008 to 2023, while the demographic vital rates were extracted from analyzing 122 wild individuals that lived and bred in the same natural reserve since 2014. The wild individuals originated from released offspring of the captive population living in the same natural reserve, and thus are likely to share similar fitness effects of inbreeding as the captive population. No information on this species was available before the bottleneck.\nWe also provided a Supplementary Text “Empirical data of the crested ibis” (L653-708) with a more extensive description of the data analysis and statistics. The statistical uncertainties are further addressed by performing several sensitivity analyses to test the robustness of our model results (more details please see responses below).\nThe empirical data is available on Zenodo: https://doi.org/10.5281/zenodo.15813404 The link is also provided in the section Data Availability (L467--469).\n“All data and code supporting the findings of this study is accessible on Zenodo: https://doi.org/10.5281/zenodo.15813404”\nThe simulations begin with “a small population of seven individuals from two families (two pairs and three nestlings), resembling the population state when the species was rediscovered in 1981 in the wild” (lines 307-310). However, the realized kinship among these seven individuals does not depend only on the family structure, but also depends critically on what happened in the population beforehand. For example, while the realized kinship coefficient of full siblings sampled from an infinitely large and randomly mating population is 0.25, the realized kinship is expected to be much higher than 0.25 for full sibs sampled from a population that has been small for a long time. The potentially large effects of recent historical demography on realized inbreeding during the population bottleneck appear to be assumed to be absent here.\nResponse #1.7: Good point. We performed a series of additional simulations assuming different levels of relatedness between the founders (Fig. S4). The results showed that the population would still have more than a 90% chance of recovering, even if all founder adults were full siblings, although population restoration would take much longer, and the population level of inbreeding coefficient would be much higher than what the empirical data suggests. More details of this analysis can be found in L146–149 in the Results and the section “Model simulation details for crested ibis restoration” in Methods (L370-372).\nL146–149: “We also varied the relatedness between the adult founders, ranging from full siblings, half-siblings, to unrelated. All scenarios showed high restoration success rates (93.7% to 97.3%), though simulated restoration times suggest that the empirical founders were likely to have ranged from half-siblings to unrelated (Fig. S4).”\nL370-372: “Because the kinship between the four adult founders was unknown, we explored different assumptions about their relatedness (i.e., full siblings, half siblings, and unrelated, Fig. S4).”\nFig. S4. Effects of founder relatedness on population restoration. (Full caption see manuscript page 31).\nIt is also entirely unclear how large the assumed effects of inbreeding on fitness were, or what is the source of this information. How many lethal equivalents were there for different vital rates? How were these effects incorporated into the simulations? Were the vital rates estimated using the same individuals that were used to estimated inbreeding depression? Were the effects of inbreeding already incorporated into the average vital rate estimates? Were the effects different for males versus females, or young versus old individuals? The lack of clarity here is a major weakness of the paper.\nResponse #1.8: The information about estimating the effects of inbreeding on fitness is available in the Method section “Quantification of inbreeding effect and life history parameters” and the Supplementary Text “Empirical data of the crested ibis”. In particular, the effect of inbreeding on hatching success was estimated using captive individuals whose pedigree information was available, while the vital rates such as nest survival rate, fledging rate, and the survival rates of juveniles and adults were estimated using data on wild individuals.\nThe effect of inbreeding on hatching success was incorporated into the simulations through parameters in Eq. 1 (Method section “Model simulation details for crested ibis restoration”, in L384-389).\nWe also explored the effect of possible inbreeding effects on the survival rates of juveniles and adults through parameters, as described in the Supplementary Method “Simulation details of additional analyses of the crested ibis population restoration model” (L766-772). In our model, the effects of inbreeding were assumed to differ between life stages but not between sexes.\nIt is unclear what the motivation is behind the comparison of the ‘firework’ and ‘stepping stone’ reintroduction models. I especially question the relevance of the stepping stone model because I have never heard of this approach being used in practice, probably because it ensures serial population bottlenecks as new reintroductions are done, and this is why inbreeding increases so rapidly in this scenario (Figure 3b). It would probably be more informative to compare scenarios where new immigrants are versus aren’t added repeatedly to reintroduced populations either from the original source or another population in an effort to maintain genetic variation, especially in cases where a reintroduced population does not begin to recover immediately.\nResponse #1.9: We have renamed the ‘stepping-stone’ to the ‘sequential’ approach, following the recommendation of reviewer 2. The rationale for implementing the two approaches is now included in the Introduction: “We chose to study these idealised reintroduction approaches because they are the basic building blocks that can be combined to produced more complex and diverse reintroduction programs used in conservation practice. This comparison aims to provide general reintroduction recommendations for endangered species that require careful management for population expansion.” (L97–100).\nFurthermore, we followed your suggestion to incorporate immigrants in the ‘firework’ reintroduction approach and studied its effect on the population average inbreeding coefficients (Fig. 3 compare A1 and A2) and population growth rate (Fig. S9). We added the following sentences to the Results (L182–189):\n“However, adding immigrants further slowed the accumulation of population-level inbreeding coefficients (Fig. 3A1 and A2; compare trajectories with the same number of founder pairs) and accelerated growth of the reintroduced population (Fig. S9). For example, a scenario with three initial founder pairs supplemented by the repeated addition of three immigrant pairs from the source population across five rounds (Fig. 3A2, pink line) yielded comparable population growth dynamics to a one-time reintroduction of 11 founder pairs (Fig. 3A1, orange line). These two scenarios showed similar final-year population average inbreeding coefficients (0.21 vs. 0.21, Fig. 3A1 and A2) and population sizes (285 vs. 280 individuals, Fig. S9).”\nFig. S3. Comparing the effectiveness of the ‘firework’ and ‘sequential’ reintroduction approaches (Full caption see manuscript page 7).\nFig. S9 Population dynamics of the simultaneous simulations in the four ‘firework’ scenarios (Full caption see manuscript page 34).\nFigure 2: It is unclear why population size is shown on a log scale. I suggest showing the raw population size so that readers do not have to do any math to interpret the figure. It is also unclear why there is variation in the population size at year zero, when it seems each population replicate should have a value of log10(7) = 0.84 at year zero.\nResponse #1.10: We adopted your suggestion to plot the raw population size in Fig. S1A. In the main text, we chose to plot population size on a log scale for two reasons: (1) It allows us to visualize and compare the trajectories of successful and failed restoration trajectories in the same panel (i.e., the failed restoration trajectories are not visible in Fig. S1A). (2) In log scale, exponential growth appears as a straight line, and this allows readers to easily see a distinctive feature between successful and failed restorations – in successful cases, population growth enters stable exponential growth after initial fluctuation, while the population of failed restorations never entered stable exponential growth.\nAll simulations started with seven founders. The apparent “variation” of population size in the initial years was due to the plotting data from the first restoration year instead of initial conditions. We have updated Fig. 2 and Fig. S1 to now include year 0. For additional clarity, a solid dot was added at log10 7 ≈ 0.84 to indicate the starting population size.\nFigure 3: I assume that figure three shows a single simulation replicate, correct? I suggest making this clear in the caption.\nResponse #1.11: Yes, each trajectory in Fig. 3 represents a single simulation replicate. We have now made it clear in the caption: “One randomly selected simulation replicate from each different scenario is used to demonstrate the modelling outcomes.”\nModel analysis 2: here the authors use a wider range of combinations of demographic vital rates to attempt to gain an understanding of the effects of inbreeding and demography on population recovery.\n359-361: Inbreeding depression has been estimated empirically in may study systems. Why not incorporate those data here instead of assuming your estimates for the crested ibis apply to all species?\nResponse #1.12: This point relates to the classic trade off in model design among generality, realism, and precision of prediction (Levins, 1966). In this analysis, our goal was to provide a conceptual demonstration of how interactions between inbreeding depression and demographic parameters can shape population recovery dynamics. To achieve this, we prioritized generality while retaining a degree of realism by grounding the model in the life history characteristics and empirically estimated inbreeding depression of the crested ibis.\nWe agree that species-specific estimates of inbreeding depression exist for many systems. However, incorporating such data would require matching each estimate with equally detailed, system-specific demographic and life history data to maintain internal consistency — a scope beyond the aims of this study. Rather than attempting to generalize across disparate species-specific datasets, we opted to use a single, biologically grounded case to illustrate the broader conceptual framework. We have also highlighted in the final paragraph of the Discussion how the model could be adapted for other species or contexts where such detailed empirical data are available.\nReference:\nLevins, Richard. \"The strategy of model building in population biology.\" American scientist 54.4 (1966): 421-431.\nMore generally, we know that inbreeding depression arising from deleterious genetic variation can have widely varying effects of population dynamics and viability depending on which vital rates are affected, what is the form of selection (soft versus hard), environmental conditions and other ecological factors (climate, predation, intra- and inter-specific competition), and historical population size. These effects do not seem to be considered anywhere in the paper, which makes for a significant omission in my opinion. See https://doi.org/10.1146/annurev-ecolsys-110411-160257, https://onlinelibrary.wiley.com/doi/full/10.1111/mec.17608, and citations therein.\nResponse #1.13: We agree that the demographic consequences of inbreeding depression can depend strongly on which vital rates are affected, the nature of selection (soft vs. hard), and broader ecological and historical contexts. While a comprehensive exploration of all such environmental and ecological factors lies beyond the scope of this study, we have expanded our analysis to explore some of these dimensions in this new revision. Specifically, we examined the potential effects of inbreeding on additional vital rates, including the survival of juveniles and adults: “When inbreeding was assumed to not only impact hatching success but also reduce the survival of juveniles or adults, restoration success declined, but the population-level inbreeding coefficient when reaching restoration remained similar (Fig. S5).” (L149–152)\nIn response to a related comment by Reviewer 2, we also incorporated soft selection by implementing density regulation and added to the Results: “Soft selection – for example, through density dependence – is known to potentially hinder population recovery by negatively affecting individual fitness [40]. To address this, we additionally investigated how density regulation affects our model outcomes. The results were robust to these assumptions, as density dependence primarily slowed population growth during later stages of recovery, when the population size became large, but did not reduce the probability of successful restoration (Figs. S6 and S7, corresponding to two different ways of density regulation). Intuitively, this is because restoration success hinges on the early stage, which determines whether a population can enter stable exponential growth, whereas density effects only become important later” (L153–160)\nReviewer #2 (Remarks to the Author):\nInbreeding and demography interact to impact population recovery from bottlenecks.\nThis manuscript addresses a fundamental question in conservation biology: How do demographic and genetic factors interact in species conservation programs? This is a very important and timely question given the increased reliance on species reintroductions, and one that needs more careful analyses of empirical examples. This paper presents such a careful analysis of the crested ibis restoration.\nI very much enjoyed reading the paper. I particularly enjoyed the fact that the crested ibis results were carefully put into a larger context. Figure 5 is an excellent example of how the authors achieve general insights from putting a single species study into a broad perspective.\nThank you for your supportive feedback and for providing several insightful ideas to improve the paper. In particular, we adopted your suggestion to explore the effect of density-dependent soft selection (Fig. S6 and S7), stage-dependent inbreeding effects (Fig. S5), and the effect of implementing a lower threshold population size for successful population reintroduction (Fig. 3 and Fig. S9).\nPlease see our point-by-point reply below for details.\nBelow are some comments that will hopefully help in the revision of the manuscript. I'll beginn with some general comments, followed by more specific ones.\n1) Studies of the effects of inbreeding on population dynamics have long recognised that these effects differ when selection is hard or soft (see e.g. Bell et al. 2021, Ecology Letters). When selection is density- or frequency dependent (soft selection), inbreeding depression may have little effect on population dynamics, while under density- or frequency independent selection (hard selection) the effects of inbreeding depression translate more directly into reduced population growth. In this manuscript, selection is assumed to be invariably hard (eq. 1). I think this is a point that the authors should discuss in detail, especially since the softness of selection is an important aspect of the interactions between inbreeding and demography that make up the title of this manuscript. That selection is always completely hard represents a very strong assumption. Ideally, this is something that would be explored explicitly with the simulations in this manuscript, but if that isn't possible it needs to be acknowledged and discussed both in light of the density-dependence seen in some crested ibis subpopulations (Li et al. 2022, Lands) and in light of the population dynamics of reintroduced populations in general.\nResponse #2.1: We explored the effect of soft selection by implementing two different forms of density regulation on the mortality rates (Methods: L400-403, SI Methods section “The effects of density-dependent soft selection”, L773–780), and varied the intensity of density effects.\nWe found: “Soft selection – for example, through density dependence – is known to potentially hinder population recovery by negatively affecting individual fitness [40]. To address this, we additionally investigated how density regulation affects our model outcomes. The results were robust to these assumptions, as density dependence primarily slowed population growth during later stages of recovery, when the population size became large, but did not reduce the probability of successful restoration (Figs. S6 and S7, corresponding to two different ways of density regulation). Intuitively, this is because restoration success hinges on the early stage, which determines whether a population can enter stable exponential growth, whereas density effects only become important later.” (L153–160)\nWe also added the relevant citation to Bell et al. (2021) (now ref. [61] in L153 and L402) and Li et al. (2022) (now ref. [51], in L289, 290).\n2) Based on empirical evidence from the crested ibis, this manuscript models inbreeding effects on a single life history trait, hatching success. It is well known that the life history stages that are affected by inbreeding have a marked impact on the degree to which inbreeding affects population dynamics (see e.g. https://onlinelibrary.wiley.com/doi/10.1111/mec.17608 for a recent illustration). Hence, it would make this work even more relevant to a broader audience, if the authors also modelled a situation where another life history trait (e.g. adult survival) showed inbreeding depression. I realise that simulation studies are a bottom-less pit and that one cannot always ask for yet another scenario. If it is not feasible to run another scenario with inbreeding depression in adult survival or another life-history stage, then this caveat should be brought up in the discussion.\nResponse #2.2: We adopted your suggestion and explored the potential effects of inbreeding on hatching success, the morality of juveniles and adults, as well as their combinations. We found: “When inbreeding was assumed to not only impact hatching success but also reduce the survival of juveniles or adults, restoration success declined, but the population-level inbreeding coefficient when reaching restoration remained similar (Fig. S5).” (L149–152)\n3) The crested ibis recovered from just seven to over 9000 individuals in just four decades. This is a very fast recovery. Other species recover more slowly, and this may affect how well different reintroduction strategies perform (see e.g. https://zslpublications.onlinelibrary.wiley.com/doi/full/10.1111/acv.12299 for an example). It would be interesting to know how sensitive the results of this work are to the speed of recovery. If more simulations are not feasible, a verbal discussion of this issue would be helpful.\nResponse #2.3: We performed an additional sensitivity analysis to explore how strongly the effect of inbreeding influences the chance and speed of population recovery: “The effect of inbreeding on hatching success was a central assumption of the crested ibis population restoration model. While this relationship was estimated from empirical data (see Methods), we further performed a sensitivity analysis to test model robustness. Varying the parameter value by ±50% did not substantially change the results (median population restoration time ranged from 40 to 50 years, and restoration success rate ranged from 95% to 99%, Fig. S3).” (L142–146)\nWe further added the following discussion regarding the speed of recovery in different species:\n“This vortex also contributes to the exponential growth in the simulations, aligned with population dynamics in seven watershed subpopulations of crested ibises [51]. However, such rapid recovery has not occurred in the Floreana mockingbird Mimus trifasciatus and some other crested ibis subpopulations [51,52], probably due to factors including habitat quality (related to density-dependent soft selection) or external threats, such as predation risks and disease outbreaks.” (L287–291)\nSpecific comments:\n- Lines 7-9: There is a considerable primary literature on the various factors that influence reintroduction success, and books that summarise the state of the field. Some of the primary literature (e.g. Griffith et al., Science 1989; Sarazin & Barbault, TREE 1996; Fischer & Lindenmayer, Biol. Conserv. 2000) and a couple books (e.g. https://onlinelibrary.wiley.com/doi/book/10.1002/9781444355833, https://www.ucpress.edu/books/reintroduction-of-fish-and-wildlife-populations/hardcover) should perhaps be cited here to provide interested readers with the background.\nResponse #2.4: Thanks for pointing us to these relevant references. We cited them in the revised paper: “Predicting the likelihood of population recovery from ecological threats, setting up more protected areas, and providing optimal species reintroduction strategies are therefore central to these efforts [2–10].” (L38–40)\n- Line 9-10: Maybe 'Retrospective' would be more appropriate here rather than 'Subsequent'?\nResponse #2.5: The word “subsequent” was not necessary. We removed it.\n- Lines 17-19: I would switch the order of the goals here. I think that from a conservation perspective 'multiple self-sustaining populations' comes first, and genetic diversity comes second because genetic diversity is a condition for populations to be self-sustaining in the long run.\nResponse #2.6: We adopted your suggestion to modify the sentence: “The primary goals of such programs are to help endangered species maintain genetic diversity by establishing multiple self-sustaining populations or restoring species' historical geographic ranges [5,19,20].” (L47–49)\n- Lines 29-30: The wording here could be misunderstood. The primary cause of inbreeding depression is the increased occurrence of partially recessive deleterious alleles in homozygous state through identity-by-descent. The decreased genetic variation and the accumulation of mildly deleterious recessive alleles are a consequence of the genetic drift that invariably accompanies inbreeding in endangered species.\nResponse #2.7: Thanks for pointing out this error. We rephrased the sentence: “These effects stem from the increased occurrence of partially recessive deleterious alleles in homozygous state through identity-by-descent, as well as the accumulation of such alleles due to genetic drift, which invariably accompany inbreeding in small, endangered populations.” (L58–60)\n- Lines 30-31: It is true that many vertebrates do not seem to avoid inbreeding, but the statement that inbreeding is common would need to be more specific to be helpful here. Close inbreeding, for example, is rare even in many endangered species. I would suggest to replace this sentence with a statement to the effect that inbreeding is a direct consequence of the small population size that makes a species be considered endangered.\nResponse #2.8: We followed your suggestion to remove this sentence, as it is ambiguous in the context. We rephrased to connect the sentence above and below: ”... as well as the accumulation of such alleles due to genetic drift, which invariably accompany inbreeding in small, endangered populations. Even in species that have recovered from bottlenecks, genome-wide sequencing studies have revealed that considerable inbreeding persists [2,18,31,32].” (L59-62)\n- Lines 36-41: I missed a reference here to the paper by Li et al. (2022, https://doi.org/10.3390/land11101817) which showed that exogenous environmental factors are major drivers of the very fast recovery of the crested ibis. This seems relevant for the discussion of hard versus soft selection.\nResponse #2.9: We added this reference (see Response #2.1 above for details).\n- Lines 49-53: I think this wording could easily be misunderstood. As Taylor et al. 2017 (reference #6 here) have shown, substantial inbreeding depression is very likely do go unnoticed in growing, reintroduced populations. It is not the case that the negative fitness consequences of bottlenecks are strikingly negligible in long-lived endangered species (killer whales, reference #2 in the manuscript, and ibex, reference #5, serve as examples for this in the literature cited in the manuscript). Rather, it is the fact that they are difficult to detect without good fitness data that leads to the appearance of an absence in growing populations.\nResponse #2.10: The sentences were indeed misleading, as also pointed out by Reviewer 1, sorry for causing the confusion. We have rephrased it for clarity: “Despite this, the populations of some long-lived critically endangered species appear to have successfully recovered from past bottleneck events [11,12,18,22,23,38]. This has partially been attributed to the idea that repeated reproduction over a long lifespan can help buffer the harmful effects of inbreeding at the population level, thereby aiding in successful restoration [22,23,39].” (L75–79)\n- Line 63, 100, and Abstract: In all these places the authors used the term 'repeatable' which to me implies that if one was to do another restoration of the crested ibis it would unfold in a similar way. I don't think this is what the authors mean. What they seem to mean is that the process is largely deterministic. Perhaps this would be a better term?\nResponse #2.11: We adopted your suggestion and replaced ‘repeatable’ with ‘largely deterministic’ throughout (L24 in Abstract, L87, L126).\n- Line 66 and Abstract: I see why the authors introduce the term 'firework' here but I think it would help readers if the authors spelled out the analogy. At least the way I understand the analogy, this reintroduction strategy establishes many new populations simultaneously, just the way that fireworks send out multiple lights simultaneously. If this interpretation is correct, it might be worth while to make it explicit.\nResponse #2.12: Thanks for the suggestion. We rephrased the sentence accordingly: “The ‘firework’ approach involves simultaneously establishing multiple independent populations using founders taken from a successfully restored source population (analogous to sparks radiating outward from a firework).” (L90–93)\n- Line 68 and Abstract: The other reintroduction strategy is called the ‘stepping-stone’ approach. Stepping-stone models have a clearly defined meaning in population genetics, at least since Kimura & Weiss's 1964 paper in Genetics. To avoid confusion, I would therefore not use this term here. 'Sequential approach' would work for me as an alternative but the authors may have other preferences.\nResponse #2.13: We followed your suggestion and replaced ‘stepping stone’ with ‘sequential’ throughout the manuscript.\n- Line 101 and elsewhere: Please clarify whether SD refers to standard deviations among simulation replicates or to standard deviations within populations. I assume the former but please specify.\nResponse #2.14: Yes, the SD refer to standard deviation among simulation replicates. We rephrased the sentence to specify this: “Furthermore, the time required for successful restoration among simulation replicates (median: 44 years, mean ± sd: 46.5 ± 10.0 years) is close to the empirical restoration time of 41 years (gray dashed lines in Fig. 2A, Fig. S1).” (L126-128)\n- Lines 132-133: I didn't understand completely why the variance of inbreeding coefficients would decline. Perhaps the authors could elaborate? Also, does this statement refer to the variation among simulation replicates or within populations?\nResponse #2.15: We rephrased the sentence to clarify these questions: “Once the population survives this initial phase, less inbred individuals can produce more offspring, contributing to faster population growth. Also, as population size increases, mating with close kin becomes less likely, leading to a decline in the variance of inbreeding coefficients among individuals.” (L135–138)\n- Lines 154-184: I did not understand whether these simulations were based on 'firework' or 'stepping-stone'. Please specify.\nResponse #2.16: This is an independent model analysis separate from the reintroduction analyses in the previous section but is another extension of the first crested ibis model. We clarified this both in the Introduction and Methods: “We then conducted two additional mutually independent model analyses, as examples of broader lessons we can learn by applying this simulation framework to inform conservation practice.” (L87–89) and “To evaluate the net effects of inbreeding depression on the probability of population recovery in a bottleneck scenario, we implemented two model variants: hatching success declines with inbreeding (s0 = 1); and inbreeding has no effect on hatching success (s0 = 0). To generalise beyond the crested ibis, we excluded ibis-specific parameters such as nest survival and fledgling success, and varied other demographic parameters across wider ranges...” (L432-436).\n- Line 196, fewer founders: True, but does 'firework' not require more founders at the initial stage? In most recovery programs the number of animals available for release at any given time is limited. This may be a non-trivial advantage of non-firework approaches.\nResponse #2.17: Thanks for your suggestion. We added this potential advantage of the ‘sequential’ reintroduction approach to the Discussion: “In practice, consistently sourcing individuals from the original population is often more difficult than from reintroduced populations. Therefore, given constraints from policy regulations, limited time or financial resources [15,48,49], the ‘sequential’ approach can sometimes have a practical advantage over the ‘firework’ approach.” (L267–270)\n- Lines 210-212: It does not become clear here whether these statements refer specifically to the conservation project of the Seychelles Magpie-robin, or whether they are general comments. Please clarify.\nResponse #2.18: We modified the sentence to clarify that the statement refers only to the Seychelles Magpie-robin case: “The varied mortality risks induced by local ecological threats are proposed to play a role in this species…” (L253)\n- Lines 236-237: Am I right in thinking that by 'converging individual variation in F' the authors mean that the variance in F among individuals declines because all individuals are starting to be inbred to similar degrees? This may be something worth explaining in a few more words.\nResponse #2.19: Yes, the converging variation in F was due to all individuals becoming inbred to similar degrees. We added the following sentence to explain why this happened: “The reduction of individual variation in inbreeding levels in the population is mainly caused by diminishing chances of mating with close kin in an expanding population.” (285–287)\n- Line 246: Would it help to write '... current population growth ...' here to emphasise that growth rate is predicted to become negative in the future in this example?\nResponse #2.20: We adopted your suggestion (L297). Thank you.\n- Line 254: Does '... due to this unfavorable demography ...' refer to the low survival and reproductive rates? Please clarify.\nResponse #2.21: We rephrased the sentence to “However, even with little or no impact of inbreeding depression, populations with unfavourable demographic rates, such as low survival and/or reproduction, can still face high extinction risks,…” (303–305)\n- Line 345: Proceeding with another round of reintroductions once the population size reached 5000 leads to very long time intervals between successive reintroductions (ca. 30-50 years). This seems quite unrealistic in actual reintroduction programs. How sensitive are the results to this choice of time intervals?\nResponse #2.22: We performed a new series of ‘sequential’ reintroduction simulations, where we proceeded with a new round of reintroduction once the size of the reintroduced population reached a threshold of 200, 500, or 1000. As shown in the figure below, this did not produce qualitatively different results. In the revised manuscript, we consistently used a population size of 1000 as the threshold (Fig. 3B).\n- Fig 3: There are a couple aspects of the figure that I did not understand. First, with 'firework' and 11 pairs (Fig. 3A), the average inbreeding declines at the very beginning. Why is this? Also, in Fig. 3B why is the average inbreeding at the beginning (purple dot) of the 11 pairs scenario substantially higher than in Fig. 3A?\nResponse #2.23: We revised Fig. 3 to add a case of ‘firework’ reintroduction with immigrants following the suggestion of Reviewer 1. The current Fig. 3A1 corresponds to Fig. 3A in the previous version. At the beginning of a reintroduction, the population size was very small, and therefore, the average inbreeding level of the population is subject to large random fluctuations depending on the relatedness between the founders and whether they happen to mate with close kin or not. Such random fluctuations have caused, for example, the average inbreeding level to first decrease in the 3 pairs case in the current Fig. 3A1.\nThe differences in starting points in Fig. 3B arise because founders in the first round of sequential reintroductions were drawn from source populations generated by different simulation replicates. For example, as shown in Fig. S2A, the average inbreeding level of source populations varies across replicates. Such variation across source populations leads to different initial inbreeding levels in Fig. 3B. However, this variation does not affect the overall pattern of reintroduction success – as demonstrated in Fig. S8, which summarises outcomes from 50 independent simulations per reintroduction scenario.\nAgain, we thank you for your constructive comments and suggestions. They greatly helped us improve the paper.\nReviewer #3 (Remarks to the Author):\nThis study presents simulation results on how population recovery is influenced by inbreeding depression and the demography of long-living avian species. The results are backed up with empirical data on the Crested Ibis. I think this manuscript provides some important considerations for conservation and rewilding programs. The methods presented could be used as practical guides to evaluate the potential outcomes of conservation projects and/or prioritise between reintroduction schemes. The paper is well-written, with easy-to-follow logic and interpretation of the data.\nThank you for your supportive feedback. Please see our point-by-point reply below to your specific comments and suggestions.\nAt the end of the introduction, can you explain the main differences between the “firework” and “stepping-stone” approaches with bit more details (L66-69), as these are first mentioned here, and the current description wasn’t immediately clear at first (e.g. how they are sequentially introduced). Also, it should be added somewhere why these two reintroduction approaches were chosen (and not others) for the analysis.\nResponse #3.1: We followed your suggestion to explain the differences between the reintroduction approaches and the reasons for choosing to study them. Please note that we renamed the “stepping stone” approach as the “sequential” approach, following the suggestion of Reviewer 2.\nIn the revised Introduction, we wrote:\n“The ‘firework’ approach involves simultaneously establishing multiple independent populations using founders taken from a successfully restored source population… The ‘sequential’ approach involves establishing new populations in a stepwise manner, where founders are taken from newly recovered populations, resembling a chain of translocation events extending over time.\nWe chose to study these idealised reintroduction approaches because they are the basic building blocks that can be combined to produce more complex and diverse reintroduction programs used in conservation practice.” (L90–99)\nWhen presenting the “firework” vs. “stepping-stone” simulation results, it would be good to mention how many simulations these are based on (L122), even though it’s later explained with more detail in the methods.\nResponse #3.2: We added the number of simulation replicates: “For clarity and ease of comparison, only a few representative trajectories of population reintroduction are shown in Fig. 3; however, our simulations explored a wider range of scenarios, varying the number of unrelated founder pairs from three to 13 for each reintroduction approach, with 50 independent replicates for each scenario (Fig. S8).” (L175–179)\nThe results are well presented. I especially liked the Supplementary Figure 3B that clearly shows the amount of (un)successful outcomes in the different scenarios.\nResponse #3.3: Thank you!\nIn methods, it could be better described how the 41 species of birds were selected, i.e. what thresholds were used to consider a species long-living and why no other bird species with shorter lifespans were included.\nResponse #3.4: We sourced the empirical data for this model analysis from COMADRE, a demographic database that contains annual juvenile and adult mortality rates necessary to parameterise our model. This initially restricted us to avian species available in COMADRE. We have added to the Methods our further filtering criteria:\n“From all available avian data on COMADRE, we filtered species to ensure they were not too dissimilar in life-history to the crested ibis – such that we can explore parameter space beyond that of our focal species while ensuring that the model remains a biologically appropriate tool to do so. Specifically, we included only species with lifespans exceeding ten years and average clutch sizes between one and six.” (L446-450).\nAlso, as the term “long-lived” is subjective, we have removed it from the relevant parts of the model.\nMinor comments:\nIn general: I would recommend to follow the IOC World Bird List when using the English name of bird species in the text.\nResponse #3.5: Done. See revised text and Supplementary Table “Demographic information of the 41 avian species presented in this study”.\nL358: “consisting of”\nResponse #3.6: Done. (L439)\nSupplementary Table: “of 41 long-lived avian species analysed in this study” – as there are more than 41 long-lived bird species.\nResponse #3.7: We updated the Table caption to “Demographic information of the 41 avian species presented in this study”.\nFigure 4: For more detailed description on the different parameter spaces (I, II, III) it would be good to refer to text.\nResponse #3.8: We added “(see main text for details)” to the end of the Figure caption.\nSupplementary Figure 4 is not referenced anywhere in the text.\nResponse #3.9: Since this supplementary figure is not essential, we removed it in the revised manuscript.\nWe thank you again for the very useful feedback!\nReferences:\nTaylor SS and IG Jamieson (2008) No evidence for loss of genetic variation following sequential translocations in extant populations of a genetically depauperate species. Mol Ecol 17: 545-556\nTielke, A. K., & Vos, M. (2024). Successful reintroduction of species: improving on windows of opportunity for biodiversity repair. Restoration Ecology, 32(3), e14091.\nDetailed Response to reviewers\nReviewer #2 (Remarks to the Author):\nI appreciate all the effort that the authors have put into revising their manuscript.\nI just have a few points that I think the authors can easily address in their final submission.\nThese points are, in roughly the order in which they appear in the text:\nResponse: We thank the reviewer for the positive feedback and thoughtful comments. We address all the final points carefully and provide detailed point-to-point replies below.\n1) Lines 144-146 report the results of a sensitivity analysis to test model robustness. The text emphasises that varying parameter values by ± 50% did not substantially change the results. This is correct but Figure S3 shows that doubling the magnitude of inbreeding depression reduces restoration success substantially. Since the precision of inbreeding depression estimates is commonly not very high, particularly when the effect size is on the small side, the manuscript should also mention the effects of varying parameter values by ± 100%.\nResponse: Thanks for your suggestion. We added the following sentence (L151–154):\n“More notable differences occurred when the value of s0 was doubled, leading to a decrease in restoration success (to below 90%) and longer restoration time (median: 58 years), although this does not affect the average inbreeding level in the successfully restored populations (Fig. S3).”\n2) On lines 153 ff. (and later on in the Discussion) the authors now address the effects of soft selection on their results. However, they do not state explicitly that their main model assumes hard selection. I think it would help readers if that were made explicit in the text.\nResponse: We have now revised the text (L160–161) to state explicitly that our main model assumed hard selection. Because our sensitivity analysis showed that hard or soft selection does not change the main conclusions of the model, we choose to avoid over-emphasizing this detail.\n3) The paper now provides more detail on the empirical estimation of the parameters from the ibis population, especially on the estimation of the magnitude of inbreeding depression in hatching success. This is very valuable information. This information also raises two issues, which I think should be addressed in the manuscript:\na) The authors report inbreeding depression estimates from a logistic and a linear model regression model (lines 661-666). Neither of these estimates corresponds to a standardised way of quantifying inbreeding depression. To be able to put the magnitude of inbreeding depression in the crested ibis in perspective, the authors should report estimates of lethal equivalents following the recommendations in Nietlisbach et al. 2019, Evolutionary Applications. Moreover, the authors should provide an estimate of the uncertainty in these parameter estimates, since this affects the interpretation of the sensitivity analyses as indicated above.\nResponse: We followed your suggestion to implement GLMMs with Poisson-distributed errors and a logarithmic link function to estimate inbreeding effects on hatching success, fertilisation success and fledging success, and used sandwich estimations to evaluate the uncertainty in the parameter estimate. We also estimated the diploid lethal equivalents (2B) following Nietlisbach et al. (2019). The updated results are now provided in the revised manuscript (L693–701).\nThe alternative method produced qualitatively similar estimates. We further confirmed this by implementing simulations of crested ibis population restoration using inbreeding effects based on the new estimates. The results (Fig. S10) are quantitatively similar to that of our main model (restoration time 40 vs 44 years, success rate 98% vs 97%), further supporting the robustness of our results.\nb) Assuming that the linear regression model used to quantify the magnitude of inbreeding depression is something similar to eq. 2 in Ralls et al. 1988 (Conservation Biology 2: 185-193), inbreeding depression in hatching success of crested ibis seems to be fairly weak. This should be verified as indicated under 3a) above, and if it turns out to be the case, it should be highlighted in the manuscript. In particular, this information should be used to put the finding in perspective that inbreeding depression seems to have no or a minor effect on the population dynamics of the crested ibis (see e.g. lines 301-303). If inbreeding depression is weak, it makes sense that it does not affect population dynamics very much.\nResponse: We followed Ralls et al. (1988) to estimate the intensity of inbreeding depression on hatching success (i.e., i value) and compared our estimate for the crested ibis to the values of 40 mammalian populations provided in Table 2 of their paper. As shown in the following figure, the cost of inbreeding of the crested ibis low to intermediate. We have provided this information (L705–708) and added the following discussion: “In the case of the crested ibis, along with remarkable conservation effort, a combination of relatively low cost of inbreeding and repeated reproduction attempts enabled by the species' longevity synergistically contributed to its rapid population recovery.” (L314–317)\nSome minor details:\n- Line 323, Reference 57: Reference 57 points to a paper about calculating inbreeding coefficients rather than a paper about Allee effects in crested ibis.\nResponse: Thanks for pointing out this error. We have replaced it with Li et al. (2022), currently reference [57]. (L333)\n- Reference 42: \"haliaeetus\" and \"scotland\" should be capitalised.\nResponse: We corrected this reference. Thank you.\n- Table S1: The rounding procedure for clutch size in Table S1 seems to have involved rounding up. It would be good to provide a brief explanation in the supplementary material as to why the authors chose to round up, and not to the closest integer.\nResponse: We appreciate the reviewer’s keen observation. As shown in Figure 5, smaller clutch sizes are less favourable for successful population restoration. By choosing to round up, rather than to the closest integer, we intended to be more conservative in attributing the extinction risk of the listed species to the effects of inbreeding and demographic parameters. We added a sentence to the Methods to clarify this. (L460–464)\nReviewer #3 (Remarks to the Author):\nI thank the authors for addressing my and the other reviewers' comments.\nResponse: We thank the reviewer again for their constructive feedback, which contributed greatly to improving the paper."}]

Decision letter