Present address: School of Biosciences, Cardiff University, Cardiff CF13TL, UK.
Evaluating the severity of the population bottleneck in the Mauritius kestrel Falco punctatus from ringing records using MCMC estimation
Article first published online: 26 MAR 2002
Journal of Animal Ecology
Volume 70, Issue 3, pages 401–409, May 2001
How to Cite
Groombridge, J. J., Bruford, M. W., Jones, C. G. and Nichols, R. A. (2001), Evaluating the severity of the population bottleneck in the Mauritius kestrel Falco punctatus from ringing records using MCMC estimation. Journal of Animal Ecology, 70: 401–409. doi: 10.1046/j.1365-2656.2001.00502.x
- Issue published online: 26 MAR 2002
- Article first published online: 26 MAR 2002
- Bayesian estimation;
- endangered species;
- Markov Chain Monte Carlo;
- minimum viable population size;
- 1The Mauritius kestrel Falco punctatus (Temminck 1823) has recovered from very low numbers. In order to evaluate the severity of the population bottleneck that it experienced, we have developed a method for estimating the productivity of the nests that escaped detection. This method uses ringing records for MCMC estimation of parameters describing the recruitment of adults to the breeding population and the growth in productivity of undiscovered nests.
- 2Comparison of the estimates for the two restored populations (eastern and western) showed a far lower proportion of undiscovered nests in the former, as predicted because of widespread use of nestboxes. This served to verify the method of estimation. The estimates show a steady increase in population size, in contrast with field estimates indicating a recent reduction in growth.
- 3The results suggest that the alarmingly low estimates of population size in 1974 (two breeding pairs) were accurate, and that few undiscovered nests existed during the bottleneck.
- 4The recovery of the population seems to have been initiated by the intensive conservation effort. The most rapid period of population growth coincides with the reintroduction programme. The results imply that the eastern population is much more reliant on intensive management for its future growth.
Population-viability theory suggests that a species’ chances of survival will be severely affected by extended periods of small population size (Schonewald-Cox et al. 1983; Gilpin & Soulé 1986; Lande & Barrowclough 1987; Nunney & Campbell 1993). However, there are several examples of species restored from extremely low numbers whose capacity to recover does not seem to have been affected, including the Chatham Island Black Robin Petroica traversi (Butler & Merton 1992), Hawaiian goose Branta sandvicensis (Black & Banko 1994) and the Cook Island kakerori Pomarea dimidiata (Robertson et al. 1994). One of the most dramatic recoveries is that of the Mauritius kestrel, from a recorded wild population of only four individuals in 1974 to 101 monitored breeding pairs in 1998. An intensive captive-breeding and reintroduction programme was implemented from 1984 to 94, with reintroduced birds moving into previously unused areas (Jones et al. 1991; Cade & Jones 1993; Jones et al. 1995).
Despite detailed records of population size during the severest part of the bottleneck, there has been some suggestion and theoretical grounds for believing that unrecorded nests during this time were numerous enough to have made an important contribution to the Mauritius kestrels’ recovery. Fox, Fox & Bailey (1985) gave an estimate of over 50 individuals in 1985, describing the surviving wild population as having a ‘healthy productivity and density, but a distribution limited by habitat’. Other reports regard this figure as an over-estimate, in view of the small number of nests located for that year (Cade & Jones 1993; Jones et al. 1995). One indication that the population had been over-estimated is that it led to predictions of population-growth rates (Temple 1986) that were not subsequently realized, and carrying capacities (66 individuals) that have been subsequently surpassed (Jones 1987; Jones et al. 1995). Here we develop a new method to estimate the importance of undetected nests; it makes use of annual ringing data to estimate their contribution to the growth of the adult breeding population for 1973–97.
In mark–resight field studies that focus on small, closed populations, such as the Mauritius kestrel, accurate population estimates might be expected. In some birds, for example the green-rumped parrotlets studied by Casagrande & Beissinger (1997), conventional mark–resight techniques can be used since birds appear to be resighted independently and with equal probability. However, as in many ringing studies, conventional mark–release–recapture methods (Lebreton et al. 1992) cannot be used to estimate the kestrel population size. A standard assumption is violated: different individuals are not equally likely to be detected, because ringed adults were mostly identified at nest sites. Since adult Mauritius kestrels show great fidelity to their nest sites, those that have been recorded once are much more likely to be observed in subsequent years. We overcame this problem by developing a new analytical method. As our basic data, we used the relative frequency of ringed and unringed birds in newly established pairs. Over all years and sites there was a greater proportion of unringed birds than would be predicted from the proportion of fledglings that had been ringed in preceding year’s records of fledglings. The most straightforward explanation is that the excess unringed birds were fledged from undetected nests. Each year’s data thus give an estimate of this productivity from undetected nests. Each annual estimate is, however, imprecise as a consequence of small sample size; we therefore developed a method that combined information across years.
The species’ history
The Mauritius kestrel is a small Indian Ocean falcon endemic to Mauritius. Formerly distributed throughout the island (McKelvey 1977; Temple 1977; Jones 1987), the species’ range was restricted to the island’s mountainous areas by early this century following human colonization (Jones 1987). Pesticide contamination during an antimalarial campaign from 1948 to 70 (Ricaud 1975; Cheke 1987) brought about the catastrophic decline of the kestrel population (Safford & Jones 1997). By the 1960s the kestrel was regarded as critically endangered (Brown & Amadon 1968; Staub 1971), and in 1974 the wild population comprised only four known individuals (Temple 1974, 1977; Collar & Stuart 1985). Consequently, the Mauritius kestrel became the focus of intensive conservation efforts, and between 1974 and 1988 five adult Mauritius kestrels, seven fledglings and 14 individuals from wild-laid eggs were taken from the wild to initiate a captive population. A 10-year (1984–94) programme of captive-breeding and reintroduction was implemented (Jones et al. 1991; Cade & Jones 1993; Jones et al. 1995). By 1994 a total of 331 kestrels had been reintroduced successfully, many of which moved into new areas of habitat. By 1997 the total wild population was thought to be over 400 birds (Safford & Jones 1997), and consisted of the original western population and a separate eastern population established entirely from reintroduced birds.
The western and eastern kestrel populations differ in both habitat and number of known pairs. The habitat of the larger, western population is more precipitous; the smaller eastern population centres around more open habitat and includes many areas cleared for cultivation. Consequently the western population nests predominantly in cliff cavities, whereas in the eastern population nest boxes have provided sites for over 90% of recorded nesting attempts between 1988 and 94 (Jones et al. 1995). We analyse both eastern and western populations separately. Because the eastern population is almost entirely reliant on nest-boxes, the population size is essentially known. The analysis of the eastern population therefore provides a test of many of the assumptions used in our analysis.
Materials and methods
Background and data collection
Mauritius kestrels breed annually from September to February, are monogamous and generally return to the same nest site location each season (Jones 1987). Captive-breeding techniques for the restoration programme were adapted from those used for other birds of prey (Cade 1986). Reintroduction methods involved fostering of young nestlings to wild pairs, and the falconry technique of releasing captive-reared juveniles into the wild (‘hacking’; see Newton 1979). Both methods have previously been applied to other raptors (Temple 1978) and other avian taxa (Cade 1988; Butler & Merton 1992; Cade 1993). The methods used for the release of captive-reared kestrels are given by Jones & Owadally (1985) and Jones et al. (1991). Jones et al. (1995) gives a detailed chronology of the Mauritius kestrel restoration programme.
Monitoring of breeding success of the western and eastern kestrel populations since 1974 has resulted in increasing numbers of known breeding pairs, with captive-bred and released birds forming established pairs within the population. The routine ringing of wild adults and young, as well as released birds, has enabled estimates of survival parameters. By 1994 a total of 331 kestrels had been released on Mauritius over a 10-year period, with 257 (78%) surviving to independence and approximately two-thirds of these surviving their first winter (Jones et al. 1995). Subsequently, of a total of 46 breeding pairs, 44 (96%) successfully reared at least one young to fledging.
The monitoring of the western population since 1973 has involved location of pairs, identification of ringed individuals and evaluation of breeding success, as well as surveys for newly established pairs at the start of each season. The eastern population became extinct during the 1950s and was reinstated via reintroductions from 1987 to 1994. Comparable field methodology and data collection for the species monitoring programme was carried out in the east population from 1987 to 98.
Banding of wild-caught adult kestrels and young fledglings at the nest was carried out opportunistically, depending on nest-site topography and accessibility. Banding of adult kestrels and their young involved a single numbered metal ring on one leg and two coloured metal or plastic rings on the other leg for individual identification in the field. Wherever necessary, birds in the wild were caught to confirm identity.
Although the pair-by-pair population data extend back to 1974, the ringing of kestrel fledglings at the nest did not become routine until 1984. However, during these early years new unringed juveniles entering the population could be identified from field observations of characteristic juvenile behaviour. Annual surveys for new breeding pairs continued throughout each breeding season. Each breeding season, field data for every territorial pair included nest site location and identity of the male and female. Data were recorded on laying date, clutch size, number hatched and number fledged. Nestlings were ringed at around 9–25 days old, with confirmation of successful fledging at 35–45 days old. In the western population most cliff nest sites were reached by abseil, but some sites were inaccessible, and offspring from those sites remained unbanded. The reliance of the eastern population on nest boxes meant that these could be easily monitored and almost all fledglings were ringed.
The records for each year included the number of known pairs, the number of offspring fledged and the ringing records for newly established pairs. The total recorded as offspring included those fledged from wild nests, those captive-reared and fostered under wild pairs and those released by hacking. Table 1 shows the data sets for both western and eastern populations.
|Fledgling escaping ringing||0||3||0||5||4||3||2||3||0||2||2||10||5||4||4||4||1||9||1||17||10||4||6||6||8|
|Ringed subadult new breeders||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||3||2||3||0||8||8||18||12||18||12|
|1-year-old new breeders||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||2||2||3||0||7||5||15||6||10||4|
|2-year-old new breeders||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||1||3||2||3||4||5|
|3-year-old new breeders||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||1||1||2||1|
|4-year-old new breeders||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||1||0||2|
|5-year-old new breeders||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||0||1||2||0|
|Unringed subadult new breeders||0||0||0||0||0||0||0||0||2||0||1||0||2||0||0||1||2||3||2||7||4||15||19||14||12|
|Eastern population (the Eastern population was extinct from 1950 until the release programme in 1987)|
|Fledgling escaping ringing||0||0||0||0||1||3||3||3||1||3||6|
|Ringed subadult new breeders||0||4||12||6||10||12||17||11||33||16||20|
|1-year-old new breeders||0||4||11||4||3||10||9||7||24||10||13|
|2-year-old new breeders||0||0||1||1||5||1||6||3||8||2||1|
|3-year-old new breeders||0||0||0||1||1||1||1||1||1||2||2|
|4-year-old new breeders||0||0||0||0||1||0||1||0||0||1||2|
|5-year-old new breeders||0||0||0||0||0||0||0||0||0||1||1|
|Unringed subadult new breeders||0||0||0||0||0||1||1||4||3||2||1|
The ringing records for adults in newly established nests can be summarized by six values for each year. First, the number that were unringed: x0t. The subscript 0 indicates unringed and t specifies the year of first nesting. Secondly, the number that had rings showing that they fledged in each of the previous five years: x1t, x2t, x5t.
The relative size of each count was modelled using eight parameters: a1, a2–a5, r, k and p1 that are defined as follows. The values of a1-a5 lie between 0 and 1. They represent the relative contribution of birds fledging 1–5 years beforehand to newly established pairs. For the ringed birds we calculate the relative probability of being recruited from each age category as:
where Nr(t−i) is the number of fledglings ringed i years before the nest was established. The value c is simply a constant that ensures the probabilities of all outcomes sum to one (Σiπit = 1). The values of ai were assumed to remain constant throughout the study period. This does not mean that the rate of survival and nesting remains constant, but only that the relative contribution of the five year-classes remains unchanged. We evaluated this assumption examining the change in relative size of x1t and x2t, which were the only common categories. The ratio would be expected to depend on the proportions fledging in the respective years, but there was no other obvious trend, and none detected by a regression (assuming binomial error and with expected proportions as a covariate, F2,5 = 3·5, NS).
Unringed adults could be the offspring of known nests that escaped ringing or the offspring of undiscovered nests. The relative frequency of unringed individuals was therefore modelled as the sum of these two sources:
where p(t−i) is the effective number of fledged young from undiscovered nests i years beforehand and Nu(t-i) the number of fledglings from known nests that escaped ringing.
The p(t−i) values are, by definition, unknown but are determined by the parameters r, k and p1. The values were calculated according to:
where r is the intrinsic rate of increase; k, the notional carrying capacity. The third parameter, p1, is the first in the series which, in biological terms, is the productivity in 1980 (1987 for the eastern population). We do not restrict the p(t) values to whole numbers because fledglings from undiscovered nests might be more or less effective in surviving and forming pairs than ringed birds. For example, it might take 1·5 fledglings from undiscovered nests to have the same chance of producing a breeding adult as one ringed fledgling.
For any combination of the eight parameters (a1–a5, r, k and p1) we can calculate the probability of the observed data (the counts x0t, x1t, x5t) in a particular year, t, according to the multinomial probability:
where θ represents the parameter combination and m is a constant. We do not need to evaluate the constant in the estimation process, just the relative likelihood for any parameter combination, which is obtained from the product over years:
The metropolis algorithm
The parameters θ (i.e. a1–a5, r, k and p1) were estimated separately for the eastern and western populations using the Metropolis algorithm (Metropolis et al. 1953; Gelman et al. 1995). This is a Markov chain Monte Carlo (MCMC) procedure that steps through parameter combinations in such a way that, given enough time, the probability of a parameter combination appearing in the chain is proportional to its posterior probability.
At each step in the algorithm a new set of parameters, θnew, was chosen near to the current values θold. The new values were drawn from uniform distributions on either side of the old with widths 0·1, 0·1, 2 and 1 for a, r, k and p1, respectively. The following ratio of probabilities was then calculated:
where P(θ) represents the prior probability of a parameter combination. The numerator and denominator are each proportional to the posterior probabilities given by Bayes’ rule (Gelman et al. 1995). The prior distributions were obtained from our knowledge of the kestrel’s ecology and are set out below. The stepping rule is to accept θnew if D > 1 and with probability D if D < 1. Otherwise, the old values are retained for the next step.
The run started with an arbitrary combination of parameters chosen from the prior distributions. After a burn-in period of 5000 iterations the chain was run for 100 000 iterations. Replicate runs with the same priors gave essentially indistinguishable results. The prior distributions were based on records of the density of nests, productivity per nest and the observation that extensive searching for undiscovered nests was without success at the start of the study period. We also noted that the most recently fledged birds were consistently over-represented among the newly established pairs. Each of the priors encompasses a range that amply covers what we consider the biologically plausible values.
We chose the following distributions: for k, log-normal with parameters m = 100, σ = 0·1 (m = 40, σ = 0·1 for the eastern population) (see Hastings & Peacock 1974); for r, log-normal with parameters m = 0·4, σ = 0·4; for p1, the curve from the exponential family that interpolates the Poisson distribution with mean 0·5; for ai, uniform in the region 1 > ai > a(i+1) > 0.
These prior distributions predict a range of pt values (productivity in year t) that are shown in Fig. 1. In Fig. 1c and 1d we show the upper and lower limits of the envelope that contains 95% of pt values when the parameters r, k and p1 are drawn from the prior distribution. The values plotted are pt/0·85 (pt/1·25 for eastern population) to make them comparable with nest counts. The denominators are the average productivity of nests, so that by dividing we calculate the ‘effective’ number of pairs. The upper limit for our prior in 1985 is close to 18 undiscovered breeding pairs (i.e. 50 + breeding birds) in the western population 1985. This fits our prior beliefs, but not the estimate given by Fox et al. (1985). We therefore constructed a prior closer to the alternative view, by changing the prior on r to a log-normal distribution with parameters m = 0·6, σ = 0·4. The corresponding 95% envelope is also shown in Fig. 1c.
The algorithm is described at http://www.qmw.ac.uk/~ugbt112/.
The posterior estimates are shown in Fig. 1c,d as upper and lower limits including 95% of the pt values given by the 100 000 parameter combinations from the chain. The much tighter range of our posterior distribution, compared to the priors in Fig. 1c,d illustrates that there was considerable information in the ringing data. Most notable is the low predicted number of undiscovered nests for the western population from 1980 to 87, followed by a sharp increase from around 1989 onwards (Fig. 1c). The results for the eastern population (Fig. 1d) agree very closely with the field data, showing very low estimates of undiscovered nests, with an upper limit of only six undiscovered nests by 1996. Figure 1a,b shows the observed number of nests, in black, plus the median of our posterior estimate in grey. The total heights therefore show our estimate of the change in total population size. Whereas the field counts for the western population suggest a recent reduction in population growth rate from 1994 to 1997, our estimates of total size continue to show pronounced growth, with no indication of stabilizing population size.
This study has demonstrated a new method of extracting demographic trends from breeding-success data for an endangered species. Previous bird studies have used count data as indices of abundance to estimate population trajectory rather than to estimate absolute population size, e.g. transect counts (Robbins, Bystrak & Geissler 1986; Link & Sauer 1997, 1998), roost counts (Casagrande & Beissinger 1997), aerial counts (Sagar et al. 1999) and numbers of carcasses (Newton, Wyllie & Dale 1999). Other studies have used a marked sample of individuals to estimate survival parameters (Newton 1988, 1989, 1995; Kenward, Marcstrom & Karlbom 1999), population turnover (Village 1985), to infer population trajectory (Green, Pienkowski & Love 1996; Hiraldo et al. 1996), or to estimate population size from resighting records that are assumed to be independent (Arnason, Schwarz & Gerrard 1991). One way of estimating absolute size is to mark the whole population (Butler & Merton 1992; Brook & Kikkawa 1998), but this is labour-intensive and is rarely feasible. We have solved this problem for the Mauritius kestrel by applying a model that is insensitive to variable search effort, and which combines information across years to reduce the broad confidence intervals associated with other resight techniques (see Casagrande & Beissinger 1997).
Our model is, however, based on assumptions that allow the number of birds in each category (no ring, 1-year-old ring, 2-year-old ring … 5-year-old ring) to be described by a multinomial distribution with the relative probabilities we have specified. First, we assume that the birds with and without rings are mixing freely before pairing to nest. This is reasonable given that the records of ringed birds do not appear to show territory inheritance from parents, or other clearly non-random patterns. There may, however, be populations of undiscovered nests that are too distant to contribute new adults. For example, we detected no mixing between eastern and western populations. The productivity of populations away from known nests could, then, be underestimated because they are under-represented in the sampling. However, wide-ranging surveys are conducted over the island each year and substantial pockets are unlikely to have been missed.
The model assumes that the growth of the undiscovered population can be described by a smooth curve of logistic shape. The growth in number of known nests certainly has this form (Fig. 1) and so this assumption seems reasonable. If the population levels off, the number of nests escaping detection could begin to decline because, once found, nests are much easier to revisit. In our case, we do not appear to have reached this point. This problem could be overcome with a different model for the change in pt.
We have tested the assumption that the relative contribution of different age classes (to new pairs) has not changed through time. This test did, however, have low power. Nevertheless, any such changes are unlikely to have had a severe effect on our results because most of the new breeders are from the two youngest age classes, and the size of these two classes is strongly correlated. Any new application of our approach should carefully consider the suitability of this assumption.
Our findings are relevant to the assessment of (i) the ability of field-monitoring data to reflect population size accurately, (ii) the severity of the population bottleneck, (iii) the impact of the reintroduction programme on the population’s recovery and (iv) the future demographic trends of the Mauritius kestrel population.
The recent reduction in growth rate of the western population suggested by field data implies that the population is nearing carrying capacity, whereas our estimates indicate continued growth. Therefore, it would seem that, in recent years, a ceiling of field monitoring efficiency has been reached, and that the use of field data as a direct index of population size is no longer effective.
Our results indicate that the species’ population recovery was poor before the reintroduction programme began, suggesting that the captive-breeding and release programme has been highly instrumental in accelerating the recovery of the western population. The acceleration in population-growth coincides with the restoration programme (Table 1, Fig. 1). The results from the model (Fig. 1) also indicate that, despite the end of releases into the western population in 1993, the population growth rate still remains substantial. The results for the eastern population show only slight deviation from the known number of pairs, and indicate negligible population expansion beyond that confirmed by field data. Only after 1993 does the model suggest the presence of any undiscovered nests in the eastern population. The implication for the future of the eastern population is that in situ management, in the form of provision of nest boxes, may continue to be necessary. The provision of nest boxes as a management tool has been successful in other raptor species, such as the peregrine falcon Falco peregrinus (Cade 1988).
Jones (1987) provides a detailed description of numbers of known wild pairs and their breeding success each year. A total of two wild pairs (one did not breed) were known in 1974, four in 1982 and seven in 1985. The severity of the genetic consequences depends on the bottleneck being sustained (e.g. Nei, Maruyama & Chakraborty 1975) rather than the lowest size. Our estimates provide evidence that the population was close to the field counts, and remained well below 25 pairs during the 17 years since its lowest size in 1973–90. The population estimate by Fox et al. (1985), of approximately 50 individuals in the 1984 post-breeding season, suggested that the population was considerably larger than the field sightings, and that the wild population was showing signs of natural recovery. This implied that the kestrels’ recovery from the bottleneck would be relatively rapid, but our results show a considerably longer period of low population size. This conclusion is robust to a change in the prior distribution to make rapid early growth more likely. The estimates of population growth at the end of the study period are more sensitive to a change in the prior. This is not unexpected, as the rate of change of slope seems rapid in this region. The broad biological message is unaltered, however. The population has grown at a greater rate than suggested by the field counts.
For how much longer will the population growth continue? The prediction by Temple (1978a) of a carrying capacity of 100–120 birds for all of Mauritius assumed that it would only persist in the remnants of pristine forest. Cade (1982) suggested an ancestral island population of only 164–328 kestrel pairs, taking into account known range size and suitable habitat, yet our estimates suggest that the current island population could exceed this in the next 5 years. The unexpected flexibility shown by released Mauritius kestrels in occupying a wide range of habitats including suburban gardens and areas of invading exotic vegetation was not widely anticipated. Our results imply that the western population may have further potential for population growth, whereas the eastern population may be closely tied to nest box provision.
The density of the populated area is approximately in the region of two individuals per km2, giving a revised estimate of 3730 birds for pristine Mauritius. This is still over 10 times lower than the effective population size (Ne) on pristine Mauritius estimated from the genetic variation in the ancestral population at microsatellite loci scored from museum skins (Groombridge et al. 2000). This value is two orders of magnitude larger than would be expected for a single isolated population, for which Ne is typically 10 times lower than census size in wildlife populations (Frankham 1995). Greater kestrel densities on pristine Mauritius are unlikely to account for such a high ancestral Ne, which could be explained in two further ways. There could have been immigration on to Mauritius, but mitochondrial DNA data suggest that the island population has been isolated from the nearest islands for approximately 750 000 generations (R.A. Nichols, unpublished data). Alternatively, the ancestral population could have been subdivided. At first this might seem implausible for a raptor on an island only 35 km by 50 km. However, ringing records do suggest subdivision: there have been no recorded movements between the eastern and western populations in 13 years. Instances of dispersal of up to 14 km have been documented but are rare (Jones et al. 1995).
The estimation of population size is an essential component in the conservation of critically endangered birds. Our evidence suggests that population size has outstripped the available effort for field counts, so the analysis of ringing returns will continue to be useful to monitor growth. It is hoped that long-term population monitoring will continue at annual intervals to ensure the total independence of the Mauritius kestrel from conservation management. Accurate and comparable estimates of population size will be an integral part of future goals for the Mauritius Kestrel Restoration Programme, including assessment of habitat carrying capacity, the impact of reintroductions on population growth, as well as the severity of the population bottleneck.
Our method is widely applicable to other marked bird populations in which nest-site fidelity renders conventional survey techniques unsuitable.
For help with fieldwork on Mauritius we are particularly grateful to M. Nicoll, D. Birch, R. Chapman, S. Paul, M. Burgess, T.-A. Parry, R. Mitchell and A. Budden. All logistical support was provided by the Mauritius Wildlife Foundation. The work was funded by the Durrell Wildlife Conservation Trust, Institute of Zoology and the Mauritius Wildlife Foundation.
- 1991) Estimating closed population size and number of marked animals from sighting data. Journal of Wildlife Management, 55, 716 – 730. , , (
- 1994) Is the Hawaiian Goose saved from extinction? Creative Conservation: interactive management of wild and captive animals (eds G.M.Mace, P.J.Olney & A.T.C.Feistner), pp. 394 – 419. Chapman & Hall, London. & (
- 1998) Examining threats faced by island birds: a population viability analysis on the Capricorn silvereye using long-term data. Journal of Applied Ecology, 35, 491 – 503. & (
- 1968) Eagles, Hawks and Falcons of the World. Country Life, London. & (
- 1992) The Black Robin: saving the world’s most endangered bird. Oxford University Press, Auckland. & (
- 1982) The Falcons of the World. Collins, London. (
- 1986) Propagating diurnal raptors in captivity: a review. International Zoo Yearbook, 325//25, 1 – 20. (
- 1988) The breeding of peregrines and other falcons in captivity: a historical summary. Peregrine Falcon Populations, Their Management and Recovery (eds T.J.Cade, J.H.Enderson, C.G.Thelander & C.M.White), pp. 539 – 547. The Peregrine Fund, Inc., Boise, Idaho. (
- 1993) Re-introduction of birds. Overview by the chairman of the RSG Birds Section. Re-Introduction News, 7, 4 – 6. (
- 1993) Progress in restoration of the Mauritius kestrel. Conservation Biology, 7, 169 – 175. & (
- 1997) Evaluation of four methods for estimating parrot population size. Condor, 99, 445 – 457. & (
- 1987) An ecological history of the Mascarene Islands, with particular reference to extinctions and introductions of land vertebrates. Studies of Mascarene Island Birds (ed. A.W.Diamond), pp. 5 – 89. Cambridge University Press, Cambridge. (
- 1985) Threatened Birds of Africa and Related Islands. ICBP/IUCN Red Data Book (1), 3rd edn. International Council for Bird Preservation and International Union for Conservation of Nature and Natural Resources, Cambridge. & (
- 1985) The predation ecology of the Mauritius Kestrel. Falco Punctatus. Interim Report. The Peregrine Fund, Boise, Idaho. , , (
- 1995) Effective population size/adult population size ratios in wildlife: a review. Genetical Research, Cambridge, 66, 95 – 107. (
- 1995) Bayesian Data Analysis. Chapman & Hall, London. , , , (
- 1986) Minimum viable populations: processes of species extinction. Conservation Biology: the science of scarcity and diversity (ed. M.E.Soulé), pp. 19 – 34. Sinauer Associates, Sunderland, Massachusetts. & (
- 1996) Long-term viability of the re-introduced population of the white-tailed eagle Haliaeetus albicilla in Scotland. Journal of Applied Ecology, 33, 357 – 368. , , (
- 2000) Conservation biology: ‘ghost’ alleles of the Mauritius kestrel. Nature, 403, 616. , , , (
- 1974) Statistical Distributions. Butterworths, London. & (
- 1996) A demographic model for a population of the endangered lesser kestrel in southern Spain. Journal of Applied Ecology, 33, 1085 – 1093. , , , (
- 1987) The larger land-birds of Mauritius. Studies of Mascarene Island Birds (ed. A.W.Diamond), pp. 208 – 300. Cambridge University Press, Cambridge. (
- 1991) A summary of the conservation management of the Mauritius Kestrel Falco punctatus 1973–91. Dodo, Journal of the Jersey Wildlife Preservation Trust, 27, 81 – 99. , , , , (
- 1995) The restoration of the Mauritius kestrel Falco punctatus population. Ibis, 137, 173 – 180. , , , , , (
- 1985) The status, ecology and conservation of the Mauritius kestrel. Conservation Studies on Raptors (eds I.Newton & R.D.Chancellor), pp. 211 – 222. International Council for Bird Preservation, Cambridge. & (
- 1999) Demographic estimates from radio-tagging: models of age-specific survival and breeding in the goshawk. Journal of Animal Ecology, 68, 1020 – 1033. , , (
- 1987) Effective population size, genetic variation, and their use in population management. Viable Populations for Conservation (ed. M.E.Soulé), pp. 87 – 123. Cambridge University Press, Cambridge. & (
- 1992) Modelling survival and testing biological hypotheses using marked animals: a unified approach with case studies. Ecological Monographs, 62, 67 – 118. , , , (
- 1997) Estimation of population trajectories from count data. Biometrics, 53, 488 – 497. & (
- 1998) Estimating population change from count data; application to the North American Breeding Bird Survey. Ecological Applications, 8, 258 – 268. & (
- 1977) The Mauritius Kestrel, some notes on its breeding biology, behaviour and survival potential. Hawk Trust Annual Report, 8, 19 – 21. (
- 1953) Equation of state calcuations by fast computing machines. Journal of Chemical Physics, 21, 1087. , , , (
- 1975) The bottleneck effect and genetic variability in populations. Evolution, 29, 1 – 9. , , (
- 1979) Population Ecology of Raptors. A.D. & T. Poyser, Berkhamstead. (
- 1988) Age and reproduction in the sparrowhawk. Reproductive Success (ed. T.Clutton Brock), pp. 201 – 219. University of Chicago Press, Chicago. (
- 1989) Sparrowhawk. Lifetime Reproduction in Birds (ed. I.Newton), pp. 279 – 296. Academic Press, London. (
- 1995) The contribution of some recent research on birds to ecological understanding. Journal of Animal Ecology, 64, 675 – 696. (
- 1999) Trends in the numbers and mortality patterns of sparrowhawks (Accipiter nisus) and kestrels (Falco tinnunculus) in Britain, as revealed by carcass analyses. Journal of Zoology, London, 248, 139 – 147. , , (
- 1993) Assessing minimum viable population size: demography meets population genetics. Trends in Ecology and Evolution, 8, 234 – 239. & (
- 1975) Pesticide use and hazards in Mauritian agriculture. Revue Agriculture Sucre Ile Maurice, 54, 143 – 148. (
- 1986) The Breeding Bird Survey: its first fifteen years, 1965–79. US Fish and Wildlife Service, Resource Publication, 157. , , (
- 1994) Recovery of the Kakerori: an endangered forest bird of the Cook Islands. Conservation Biology, 8, 1078 – 1086. , , , (
- 1997) Did organochlorine pesticide use cause declines in Mauritian forest birds. Biological Conservation, 6, 1445 – 1451. & (
- 1999) Population size and trends within the two populations of Southern Buller’s albatross. Diomedea Bulleri Bulleri. Biological Conservation, 89, 11 – 19. , , , , (
- 1983) Genetics and Conservation. Benjamin/Cummings Publishing Company, Menlo Park, California. , , , (
- 1971) Actual situation of the Mauritius birds. International Council of Bird Preservation Bulletin, 11, 226 – 227. (
- 1974) Wildlife in Mauritius today. Oryx, 13, 584 – 591. (
- 1977) Status and conservation of endemic kestrels on Indian Ocean islands. World Conference on Birds of Prey, Vienna, 1–3 October 1975 (ed. R.D.Chancellor), pp. 74 – 81. International Council for Bird Preservation, London. (
- 1978) Endangered Birds, Management Techniques for Preserving Threatened Species. University of Wisconsin Press, Madison, Wisconsin. (
- 1978a) The life histories of the indigenous landbirds of Mauritius (Kestrel, Pink Pigeon, Parakeet). Msc Thesis. Edward Grey Institute, Oxford. (
- 1986) Recovery of the endangered Mauritius kestrel from an extreme population bottleneck. Auk, 103, 632 – 633. (
- 1985) Turnover, age and sex ratios of kestrels in south Scotland. Journal of Zoology, London, 206, 175 – 189. (
Received 14 December 1999; revision received 3 October 2000