Mayfield Method Research Articles

Chi-Square Tests for Intrabrood Independence When Using the Mayfield Method

I examined 3 variations of the Chi-square test to test the assumption that survival rates of individuals within a group are independent when using the Mayfield method. An example of each test is given using data on juvenile Canada geese (Branta canadensis moffitti) presented by Eberhardt et al. (1989). A test that uses a randomly selected subsample of groups to calculate expected values is more appropriate than a test that uses the brood-specific survival rate or one that uses the survival rate estimated from the entire sample

Estimating Nest Success: When Mayfield Wins

-The Apparent estimator of nest success may be severely biased because unsuccessful nests are less likely to be found than are successful nests. The Mayfield estimator is a preferred alternative. The situation is somewhat different for nests in colonies or on islands because of greater visibility of nests, higher synchrony of nesting, and often higher hatch rates than dispersed mainland nests. Also, destruction is more likely to occur catastrophically, which violates an assumption of the Mayfield method that the mortality rate is constant. By simulation we investigated the performance of the Apparent and Mayfield estimators under a variety of circumstances. We found that when mortality rate was constant, the Mayfield estimator generally performed well regardless of whether or not nesting was synchronous or whether mortality was high or low. The Apparent estimator required more searches and higher detectability of nests. When mortality was mostly catastrophic, the Mayfield method performed poorly. The Apparent method was better, but high levels of detectability were needed for accurate estimates. We reached similar conclusions for attempts to estimate the number of nests initiated. Received 31 July 1989, accepted 5 January 1990. ORNITHOLOGISTS have come to realize that the traditional estimate of nest success (the fraction of observed nests that are successful) may be severely biased. This unwelcome result exists because unsuccessful nests may be active only briefly and are less likely to be observed than are successful nests, which persist for the entire laying and incubation period. Although Snow (1955), Hammond and Forward (1956), and others alluded to the bias, it was not formally dealt with until Mayfield (1961, 1975) proposed a solution. Johnson (1979) provided the statistical underpinnings of the method, which is similar to estimating an exponential survival function with censoring (e.g. Gross and Clark 1975). Problems that require a Mayfield treatment are somewhat different for nests on islands or in nesting colonies for four reasons, some of which Ely and Raveling (1984) identified. First, nest success is often much higher on islands than on mainlands. This reduces the bias of the Apparent hatch rate, and minimizes the need for the Mayfield method. Second, nesting on islands or in colonies is often fairly synchronous, which facilitates nest finding in early stages, before many of them are destroyed. Third, mortality of clutches in island or colonial nests is more often catastrophic than in mainland or isolated nests. The Mayfield method assumes that a constant mortality rate applies. Fourth, the small size of the nesting area, and high density and high visibility of nests, often permit many destroyed clutches to be found, which reduces the bias in the Apparent hatch rate. Additionally, nests destroyed before discovery are not used in the Mayfield calculation. In island or colonial situations these may be numerous, and biologists are tempted to include them to enhance sample sizes.

A distribution-free nest survival model

In many nest survival studies, nests are not found until after incubation has begun and nests that fail are of unknown age while nests that succeed can be aged afterwards. Typically ornithologists have considered the survival time to be from first encounter and have used the Mayfield method (Mayfield, 1961, Wilson Bulletin 73, 255-261; Mayfield, 1975, Wilson Bulletin 87, 456-466) or variations of it. Here we consider a new discrete survival model that allows estimation of the survival distribution from the time of nest initiation. Nests that succeed are used to estimate the proportions of nests being found (encountered) in each time interval. Assuming that these encounter probabilities also apply to the nests that fail, it is possible to estimate a series of discrete failure time probabilities for all the nests. We present maximum likelihood estimators and computer programs to calculate them. Our methodology is illustrated and compared to other approaches using real data on mourning dove nests.

Breeding performance of the red‐throated diver Gavia stellata in Shetland

Breeding red‐throated divers Gavia stellata were studied in Shetland during 1981‐1983. The overall probabilities of nest success were 0.35 in 1981 and 0.25 in 1982, as calculated by the Mayfield method. Productivity was shown to be at least 0.51 chicks fledged per breeding pair in 1981 (n = 100) and 0.36 in 1982 (n = 91), and a review of all field studies for Shetland gave a mean value of 0.45 per year (n = 1104) with no detectable trends in productivity since 1918; this was considered probably sufficient to maintain a stable population. Nests at lochs smaller than one hectare experienced the greatest hatching success. The majority of known breeding lochs wore used in three consecutive years, with a significantly greater re‐use of lochs which had previously supported successful pairs. Breeding success declined with season in 1981 and 1982 largely due to reduced hatching success of late nesters, and a slight seasonal decline in egg volume was found in 1983.

Hatching Success of Caspian Terns Nesting in the Lower Laguna Madre, Texas, USA

-The average clutch size of Caspian Terns nesting in a colony in the Lower Laguna Madre near Laguna Vista, Texas, USA in 1984 was 1.9 eggs per nest. Using the Mayfield method for calculating success, one egg hatched in 84.1% of the nests, and 69.8% of the eggs laid hatched. These hatching estimates are as high or higher than estimates from colonies in other areas.

Environmental Contaminants in Eastern Cooper's Hawk Eggs

Survival of 101 radio-marked hen ring-necked pheasants (Phasianus colchicus) in wheatlands of northeastern Colorado was determined using the Mayfield method, during March-August, 1979-81. Lowest monthly survival (0.786/month) occurred in April, primarily as a result of avian predation. Predation declined after green wheat attained adequate height to conceal hens. Hen survival remained high (0.998/ day) through nesting and brood-rearing. The survival rate for the March-August (184-day) period averaged 0.561. The annual spring-to-spring survival rate was 0.517 during 1981-82 when relatively mild weather and above average cover conditions prevailed. Adult hens had higher weights and survival rates than yearlings during March-August intervals (P < 0.01). Analyses failed to discern the impact of the transmitter weight:body weight relationship on survival. J. WILDL. MANAGE. 49(4):1044-1050 The importance of survival to management of pheasants was illustrated by Jarvis and Simpson (1978), who showed that long-term population fluctuations (based on spring indices) resulted primarily because of changes in survival of hens and not from changes in reproductive performance. However, survival data for hen pheasants, in hunted or nonhunted populations, are relatively limited (Leopold et al. 1943, Buss 1946, McCabe 1949, Stokes 1954, Mallette and This content downloaded from 207.46.13.93 on Tue, 02 Aug 2016 05:40:11 UTC All use subject to http://about.jstor.org/terms

Habitat Comparisons and Productivity in Nesting Common Terns on the Mid-Atlantic Coast

-Nesting Common Terns (Sterna hirundo) were studied at a number of barrier beaches and small islands of tidal salt marsh in New Jersey and the Eastern Shore of Maryland-Virginia from 1980 through 1982. Data were collected on clutch sizes, nest spacing, and nesting success. The principal null hypothesis tested was that no difference in reproductive success exists between beach and marsh habitats. Nests were monitored from egg-laying in mid-May until mid-July when young fledged. Clutch sizes varied among colonies and across years but no systematic effect of year, habitat, or colony size on mean clutch size per colony was detected. Analyses of nest productivity (estimated using both the Mayfield method and using a colony average) failed to reveal significant effects of habitat or colony size but showed a strong year effect. Storm tide flooding and egg chick disappearance (presumably predation by Herring Gulls Larus argentatus and Laughing Gulls L. atricilla nesting nearby) accounted for most nest failures. Losses due to both these mortality factors were unpredictable from year to year. Nest spacing in salt marsh colonies was much closer than it was on barrier beaches. In mixedspecies colonies with Black Skimmers (Rynchops niger), distances between tern and skimmer nests were also much smaller in marsh colonies than they were on beaches. The limited amount of wrack (windrows of dead, matted vegetation) preferred by marsh-nesting terns probably explains these spacing differences. Several lines of evidence suggest that terns prefer beaches to marshes for nesting, however, the uncertainty of predation and flooding may often obscure any intrinsic differences in habitat quality. Long-term field studies are essential for testing hypotheses related to differential fitness of individuals among habitats.

Dynamics of a Local Population of the Willow Warbler Phylloscopus trochilus in Southern Finland

A local population (22-27 pairs) of the Willow Warbler Phylloscopus trochilus L., studied in 1972-1978, was almost stable (18-20 pairs, CV = 5%) in the deciduous part of the study area, but more variable (4-7 pairs, CV = 28%) in the spruce-dominated part. The annual survival rate of the highly site-tenacious adult males was about 41%, but only 17% of the breeding females returned in the subsequent year. Adult mortality was low during the breeding season. The mean clutch size decreased after y = -0.060x + 6.51 eggs during the season (x is the day of the first egg, x = 0 on 31 May). Timing differences of the breeding season explained almost all annual differences of the mean clutch size. Nesting mortality was higher when the nestlings were 0-7 d old than during other phases of the whole nesting period, but this was due to human disturbance increasing the vulnerability of some nests to predation. No significant differences in the nesting success between years, parts of the study area, stage of the breeding season, or broods of different sizes were found. Estimated with the Mayfield method, only about 34% of the eggs laid produced fledglings, but probably more than 50% if the effect of disturbance is corrected for.

Variability in Nest Survival Rates and Implications to Nesting Studies

-We used four reasonably large samples (83-213) of Mallard (Anas platyrhynchos) and Blue-winged Teal (A. discors) nests on an interstate highway right-of-way in southcentral North Dakota to evaluate potential biases in hatch-rate estimates. Twelve consecutive, weekly searches for nests were conducted with a cable-chain drag in 1976 and 1977. Nests were revisited at weekly intervals. Four methods were used to estimate hatch rates for the four data sets: the Traditional Method, the Mayfield Method, and two modifications of the Mayfield Method that are sometimes appropriate when daily mortality rates of nests are not constant. Hatch rates and the average age of nests at discovery declined as the interval between searches decreased, suggesting that mortality rates were not constant in our samples. An analysis of variance indicated that daily mortality rates varied with the age of nests in all four samples. Mortality was generally highest during the early laying period, moderately high during the late laying period, and lowest during incubation. We speculate that this relationship of mortality to nest age might be due to the presence of hens at nests or to differences in the vulnerability of nest sites to predation. A modification of the Mayfield Method that accounts for age-related variation in nest mortality was most appropriate for our samples. We suggest methods for conducting nesting studies and estimating nest success for species possessing similar nesting habits. Received 21 January 1981, accepted 1 July 1981. INVESTIGATORS have attempted to determine the nesting success of birds for many purposes and have used diverse methods as they studied species with different breeding strategies in a wide range of habitats. One characteristic common to most studies is the method used to calculate hatch rates: the percentage of nests in an observed sample in which at least one egg hatched (referred to as the Traditional Method in this paper). Several investigators (Lack 1954: 74, Coulson 1956, Hammond and Forward 1956, Peakall 1960) recognized that hatch rates calculated in this way were biased. Hammond and Forward (1956) warned, Neglect of consideration for the length of time nests are under observation as compared to the total period they are exposed to predation would lead to a recorded success higher than that actually occurring. Eggs found in older nests are more likely to hatch than those found in younger nests, because they have already survived a period of risk to which the latter have yet to be exposed. By following this reasoning to the ultimate, it is clear that only samples of nests found on the day they are initiated will yield an unbiased hatch rate. The bias will increase with the average age of nests at discovery. Mayfield (1961) proposed a method that accounts for bias related to the age of nests at discovery by introducing into the calculations the period of time nests are under observation. Mayfield's Method will greatly reduce the bias inherent in the hatch rate calculated by the Traditional Method if daily mortality rates are reasonably constant for all nests in the sampled population. Some progress has also been made in analyzing nesting data for which daily mortality rates are not constant. Mayfield (1961, 1975) and Johnson (1979) described a method of calculating nest success when daily mortality varies among laying, incubation, and nestling stages. Johnson (1979) also proposed a method to use when the daily mortality of nests varies between population components such as yearling and older nesters. These methods will be described later in this paper. The researchers who developed these methods often depended upon hypothetical population models or pooled samples from studies conducted over a period of years and sometimes in different areas. Our study is an attempt to evaluate these methods by applying them to four reasonably large samples of nests 77 The Auk 99: 77-87. January 1982 This content downloaded from 207.46.13.189 on Thu, 04 Aug 2016 04:31:18 UTC All use subject to http://about.jstor.org/terms 78 KLETT AND JOHNSON [Auk, Vol. 99 of two species, Mallard (Anas platyrhynchos) and Blue-winged Teal (A. discors), that were observed during 2 yr on a single study area. The specific purposes of this paper are (1) to evaluate the variation in daily mortality rates in four samples of nests, (2) to determine the importance of variation in estimating hatch rates by the methods listed above, (3) to discuss the appropriate methodologies for evaluating our data, and (4) to recommend methods to researchers studying species with similar characteristics.

Estimating Reproductive Success in Colonial Waterbirds: An Evaluation

-To estimate reproductive success in a population one ideally would like to determine the number of young fledged per nesting female. However, this is difficult because often (1) the adults are not individually marked, (2) the colony is not visited daily, and (3) the investigator is unable to monitor all young until they fledge. If adults are unmarked and successful renesting occurs, reproductive success will be underestimated. If a colony is not visited daily and nests are initiated and lost between visits, reproductive success will be overestimated. The Mayfield method is one approach to overcoming this latter problem. Finally, nestling colonial birds are often able to move away from the nest site well before fledging and thus avoid being detected. To overcome this problem capture-recapture methods and enclosures have been used. In this paper we discuss these limitations and evaluate methods of dealing with them.

Interpreting the Results of Nesting Studies

Nesting studies are used to assess the production of birds and to evaluate nesting habitats. Most such studies involve finding nests in a given area and subsequently determining the proportion that hatched. Unfortunately, the results are often biased by unrecognized differences in the probabilities of finding successful and unsuccessful nests. The observed hatch rates of 1,900 nests of blue-winged teal (Anas discors) are presented to illustrate the relationship of hatch rates to time remaining until the nests should hatch. The Mayfield method of correcting for these biases is illustrated. Other examples demonstrate the possible effects of sampling procedures on observed hatch rates and nest density. J. WILDL. MANAGE. 42(3):471-476 Nesting studies are common in investigations of waterfowl and other birds. Most are undertaken to assess the production of breeding birds and to evaluate nesting habitats and the techniques of managing such habitats. The objectives are to determine hatch rates and density of nests in selected habitats. The procedures commonly used are searching selected areas to find nests and subsequently checking those nests to ascertain whether or the eggs were hatched. Unfortunately, the nests of most species are initiated over periods of at least several days during which some of the nests may be destroyed. If nests are destroyed, many females will renest 1 or more times; consequently, it is common to find newly initiated nests after others of the same species have hatched. Continuous searches over such prolonged periods generally are impractical; hence, most studies involve periodic searches. If some nests were missed because they were initiated and destroyed between searches, the observed nest density clearly would be biased downward. Less obviously, but more importantly, the observed nesting success would be biased upward. We have restricted our discussion to these biases. These potential biases, among several commonly occurring in nesting studies, were recognized previously by Hammond and Forward (1956) and Mayfield (1960, 1961). Mayfield (1961) elaborated the method of estimating nesting success from nests observed during all or any portion of the period between initiation and hatch. The method has been widely adopted. Mayfield therefore published the method again 14 yr later and noted correctly (Mayfield 1975:456) that not every published report shows awareness of the problem. At least 2 other investigators (Townsend 1966, Reed 1975) acknowledged the problem in waterfowl studies; Townsend used Mayfield's method in his analysis. Our purpose is to bring the potential biases associated with periodic searching to the attention of investigators who may consider undertaking nesting studies. Our studies will exemplify the magnitude of these biases. We will also illustrate how the inconsistency of the biases invalidates many comparisons commonly made within and among nesting studies. We will demonstrate Mayfield's method for obtaining better estimates of the success and density of nests. ' Present address: U.S. Fish and Wildlife Service, 1978 South Garrison Street, Denver, Colorado 80227. J. Wildl. Manage. 42(3):1978 471 This content downloaded from 157.55.39.102 on Sat, 24 Dec 2016 05:19:18 UTC All use subject to http://about.jstor.org/terms 472 BIAS IN NESTING STUDIES Miller and Johnson We hereby acknowledge the support and guidance of H. K. Nelson, former Director, and W. R. Goforth, Director of the Northern Prairie Wildlife Research Center, in the studies which led to this paper. We are especially grateful for the use of the nest records provided by, and for the constructive comments of, H. F. Duebbert, K. F. Higgins, L. M. Kirsch, A. T. Klett, and J. T. Lokemoen. Our thanks to D. A. Davenport for assistance with computer programing, to C. W. Shaiffer for drafting the figures, and to H. F. Mayfield for reviewing an earlier draft of this report. Our special thanks to L. M. Cowardin for perceptive technical and editorial comments on the manuscript.