VALIDATING THE ASSUMPTIONS OF THE MAYFIELD METHOD

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1 J. Field Ornithol., 71(4): VALIDATING THE ASSUMPTIONS OF THE MAYFIELD METHOD GEORGE L. FARNSWORTH 1,KENDRICK C. WEEKS, AND THEODORE R. SIMONS Cooperative Fish and Wildlife Research Unit, Department of Zoology North Carolina State University, Raleigh, North Carolina USA Abstract. We tested the assumptions of the Mayfield method (Mayfield 1975) using 416 Wood Thrush (Hylocichla mustelina) nests monitored from in the Great Smoky Mountains National Park. We tested for differences in nest survival throughout the breeding season and throughout the nesting cycle. We compared the Mayfield cumulative survival curve with a modified version of the Kaplan-Meier with staggered entry. In addition, we compared the group of nests found during nest initiation with those found later in the nesting cycle. There was no evidence nest survival varied through the breeding season or with different stages of the nesting cycle. Furthermore, the Kaplan-Meier survival curve agreed with the Mayfield calculation. We found no evidence of heterogeneity. Validation of Mayfield assumptions is important because the method is widely used, allows for statistical comparisons, and is critical for estimating seasonal fecundity in bird populations. VALIDANDO LAS PREMISAS DEL MÉTODO MAYFIELD Sinopsis. Pusimos a prueba las premisas del método Mayfield (Mayfield 1975) monitoreando del , 416 nidos de zorzal (Hylocichla mustelina). El estudio se llevó a cabo en el parque nacional Great Smoky Mountains. Pusimos a pruebas las diferencias de supervivencia del nido a través de la temporada reproductiva y del ciclo reproductivo. Comparamos la curva acumulativa de supervivencia de Mayfield con una versión modificada del Kaplan- Meier. Además comparamos el grupo de nidos encontrados durante la iniciación de los mismos con aquellos que encontramos más tarde en el ciclo de anidamiento. No encontramos evidencia que indique que la supervivencia del nido varía a través de la temporada reproductiva o en diferentes etapas del ciclo de anidamiento. Por otra parte, la curva de supervivencia del Kaplan-Meier está en armonía con calculas de método Mayfield. No encontramos evidencia de heterogeneidad. La validación de las premisas del método Mayfield es de gran importancia dado el caso de que el mismo ha sido de amplio uso, y permite comparasiones estadísticas y es crítico para estimar la fecundidad estacional en poblaciones de aves. An unbiased estimate of nesting success requires more information than the proportion of successful nests to observed nests. Coulson (1956) pointed out that nests discovered later in the nesting cycle are more likely to fledge because they are exposed to predation for less time. Mayfield (1975) proposed an alternative technique for measuring nesting success in which the number of days from discovery of the nest to fledging or failure (exposure days) is used to compute a daily nest survival rate (s) where: No. of failed nests s 1 (1) No. of exposure days This technique has gained widespread acceptance for comparing the nesting success of different areas (e.g., Hoover et al. 1995, Robinson et 1 Current address: Department of Natural Science, University of Houston Downtown, One Main St., Houston, Texas USA. 658

2 Vol. 71, No. 4 Validating Mayfield Assumptions [659 al. 1995) and for estimating seasonal fecundity (Donovan et al. 1995, Pease and Grzybowski 1995, Farnsworth 1998). The main assumption of this method is that every nest exposure day is independent. This assumption can be divided into at least three components: (1) nests are homogeneous (i.e., every nest has the same probability of fledging young), (2) nest survival rate is independent of the stage of the nesting cycle, and (3) survival is constant through the breeding season. If nesting success is heterogeneous (some nests having higher survival rates), we would expect the Mayfield daily survival rate to over-estimate the survival of nests because those nests most likely to fail would have a lower probability of being discovered by the investigator ( Johnson 1979, Bart and Robson 1982). This could occur, for example, if nests of young, inexperienced birds are more likely to fail than nests of older birds. The stage of the nesting cycle may also influence nest survival rates. The behavior of adult birds differs markedly between the incubation and chick-feeding stages. Frequent feeding trips by the adults may lead predators to the nest (Skutch 1940). Changes in the activity of predators during the season could also influence survival. For example, the density of active nests may fluctuate through the season, and increasing density may lead to higher rates of nest predation (Martin 1988). In this paper we test each of these assumptions with data from Wood Thrush (Hylocichla mustelina) nests. In addition, we compare the Mayfield technique with an alternative, the Kaplan-Meier survival estimator (Kaplan and Meier 1958) with staggered entry (Pollock et al. 1989). This method is commonly used to analyze survival with radio-elemetry data (e.g., Sorensen and Powell 1998, Pollock et al. 1995) but was adapted to nest survival by Cornelius (1993). The Kaplan-Meier estimator does not require constant survival for all nest stages, but rather predicts a cumulative survival curve. METHODS We located and monitored the survival of 416 Wood Thrush nests in Great Smoky Mountains National Park from 1993 to 1997 (for details of field methods see Farnsworth and Simons 1999). Briefly, we monitored each nest by visiting at 3-d intervals. Only complete nest failure was considered in this analysis, and nest failure was assigned to the halfway point between the last two checks (Mayfield 1975). If a nest survived to 10 d past hatching, we considered it successful. At this age, Wood Thrush chicks are usually capable of leaving the nest (Roth et al. 1996). For all statistical comparisons of daily survival rate we used the test statistic of Johnson (1979). To examine the survival rate throughout the breeding season, we divided the exposure days and nest failures into three intervals of 4 wk each. We compared the resulting Mayfield daily survival rate for each interval. To test if the daily survival rate of nests changed through the nesting cycle, we calculated the daily survival rate for each of three stages in the nesting cycle (egg-laying, incubation, and chick-feeding). We also

3 660] Farnsworth et al. J. Field Ornithol. Autumn 2000 compared the Mayfield cumulative survival curve with a Kaplan-Meier survival curve. The Kaplan-Meier model estimates the cumulative probability that a nest will survive to fledge chicks from daily conditional survival probabilities. Thus, this method does not assume the survival rate to be constant throughout the nesting cycle. We used the model with a staggered-entry design (Pollock et al. 1989, Cornelius 1993). For this comparison, we used only those nests found during egg-laying (group 1; see below) because the Kaplan-Meier method requires all nests to be of known age (Cornelius 1993). For simplicity, we adjusted the number of exposure days for each nest to a whole number. To test if nesting success was heterogeneous among nests, we divided the nests into two independent groups. We compared the survival rates of nests found during the egg-laying stage (group 1) with nests found later in the nesting cycle (group 2). We assumed all nests in group 1 represented an unbiased sample with respect to heterogeneity in survival rate because they were found so early in the nesting cycle. If nesting success were heterogeneous, the daily survival rate calculated from nests in group 1 should be lower than that calculated from nests in group 2. We also used the daily survival rate calculated from nests in group 2 to predict the number of nests that should have hatched and fledged young from those nests in group 1. This was calculated by assuming each nest found during egg-laying must survive 15 d to hatch (3 d to complete egglaying and 12 d of incubation), and another 11 d to fledge young. We used a chi-square test of differences between these observed and predicted values. RESULTS The overall Mayfield daily survival rate from was (SE 0.003). We monitored a total of 5407 exposure days and recorded 225 nest failures. These were divided into d (100 failures) during the first 4 wk, 2367 d (104 failures) during the middle 4 wk, and d (21 failures) during the last 4 wk. The survival rates of nests did not differ between 4-wk intervals through the breeding season (Fig. 1A). No two intervals were significantly different (all P 0.2). We observed nest exposure days (17 failures) during egg-laying, days (129 failures) during incubation, and 2056 days (79 failures) during chick-feeding. The resulting nest survival rates did not differ between stages of the nesting cycle (Fig. 1B; all P 0.10). A total of 161 nests (out of the 416) were found during the egg-laying stage and followed until they failed or fledged young. The daily survival rate calculated for these nests (group 1) was (2588 d with 106 failures). The daily survival rate for the remaining 256 nests (group 2), was (2819 nest days with 119 nest failures) and was not significantly different from that for group 1 (z 0.23, P 0.8). The cumulative survival estimated by the Kaplan-Meier (34.2%; for nests in group 1) was not different from that predicted by the Mayfield method (33.7%; for nests in group 1; Fig. 2).

4 Vol. 71, No. 4 Validating Mayfield Assumptions [661 FIGURE 1. Mayfield daily survival rates ( 1 SE) of Wood Thrush nests throughout the season (A) and between stages of the nesting cycle (B). If nesting success were homogeneous, and all nests had a probability of surviving from one day to the next (calculated above for nests in group 2), we would expect a nest from group 1 to have a (0.958) probability of hatching and a (0.958) probability of fledging young. From this we would predict that of the 161 nests in group 1, 84.3 should have hatched and 52.5 should have fledged young. The observed numbers of nests to hatch (82) and fledge young (55) were not different from the expected numbers ( , P 0.67). DISCUSSION The Mayfield method for estimating daily Wood Thrush nest survival rates appears to work well for this system. This is encouraging because the method is widely used, and because it allows comparisons of nest

5 662] Farnsworth et al. J. Field Ornithol. Autumn 2000 FIGURE 2. Cumulative survival probabilities of Wood Thrush nests as calculated by the Mayfield and Kaplan-Meier models. survival rates from different studies and locations. We found no evidence for heterogeneity in nest survival rates. In a more detailed analysis of the factors affecting the survival of nests with this database, Farnsworth and Simons (1999) also found no convincing evidence of different survival rates between nests. Overall, survival rates did not vary over the course of the breeding season or throughout the nesting cycle (Figs. 1 and 2; see also Farnsworth and Simons 1999). The divergence between the survival curves for the Kaplan-Meier and Mayfield models early in the nesting cycle (Fig. 2) probably represents an artifact of the sampling interval. Nests were visited only once every 3 d. If a nest failed before the next nest visit, the failure of that nest was assigned to one of the intervening days for the Kaplan-Meier method. Because nests were added to the Kaplan-Meier model only during the laying period (day 4 to day 0; Fig. 2), there was a delay before a nest could be considered failed. When we explicitly tested the Mayfield daily

6 Vol. 71, No. 4 Validating Mayfield Assumptions [663 survival rate, we did not detect a difference in the survival of nests in the egg-laying and incubation stages. However, it is possible our methodology prevented us from detecting such a difference with this test as well. A shorter sampling interval (e.g., visiting the nest every day) would probably provide a test with greater resolution. Unattended nests may experience lower predation rates due to the eggs being at ambient temperature or to the lack of adult activity. Although we found the Kaplan-Meier useful for examining the shape of the survival curve during the nesting cycle, this estimator can only be used when nest ages are known at the time of discovery. We found many nests during incubation, after egg-laying was completed. When these nests failed before their eggs hatched, we were unable to reliably determine nest age. We were able to determine the age of nests found after egglaying if those nests survived to hatching. However, we could not include these nests in the analysis post facto. Including these nests would insert a bias toward nests that reached hatching, causing the estimator to overestimate the cumulative survival. We were encouraged to find that the assumptions of the Mayfield method appeared to be valid in our study. Recent attempts to extend the calculations of the Mayfield method to estimate the seasonal fecundity of songbird populations rely on these assumptions (e.g., Donovan et al. 1995, Pease and Grzybowski 1995, Farnsworth 1998). Estimates of annual fecundity are critical when evaluating the significance of population sources or sinks (e.g., Donovan et al. 1995, Simons et al. 2000). ACKNOWLEDGMENTS We thank Ken Pollock for help with the Kaplan-Meier survival estimate. We also thank the many members of our field crews, without whose help we never would have found enough nests to make this analysis possible. Jaime Collazo, Martha Groom, and Jeremy Lichstein provided useful comments on earlier versions of this manuscript. LITERATURE CITED BART, J., AND D. S. ROBSON Estimating survivorship when subjects are visited periodically. Ecology 63: CORNELIUS, W. L An avian nest survival modeling scheme and comparisons of nest survival probability. Ph.D. dissertation. North Carolina State University, Raleigh, North Carolina. COULSON, J. C Mortality and egg production of the Meadow Pipit with special reference to altitude. Bird Study 3: DONOVAN, T. M., F. R. THOMPSON III, J. FAABORG, AND J. R. PROBST Reproductive success of migratory birds in habitat sources and sinks. Cons. Biol. 9: FARNSWORTH, G. L Nesting success and seasonal fecundity of the Wood Thrush, Hylocichla mustelina, in Great Smoky Mountains National Park. Ph.D. dissertation. North Carolina State University, Raleigh, North Carolina., AND T. R. SIMONS Factors affecting nesting success of Wood Thrushes in Great Smoky Mountains National Park. Auk 116: HOOVER, J. P., M. C. BRITTINGHAM, AND L. J. GOODRICH Effects of forest patch size on nesting success of Wood Thrushes. Auk 112: JOHNSON, D. H Estimating nesting success: the Mayfield method and an alternative. Auk 96:

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