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R = HZB/2

(1)

where R = recruitment rate, H = hen success rate, Z = the probability that at least one brood member will survive, and B = average brood size at fledging. An equal sex ratio at hatching is assumed. Hen success can be expressed in terms of nest success:

(2)

where P = nest success and alpha is a measure of nesting intensity that equals 1 in wet years when all hens attempt at least one nest. Alpha ranged from about 0.6 in a dry year to 1 in a wet year for Mallards in central North Dakota (Cowardin et al. 1985).

Cowardin and Johnson (1979) defined nest success as the probability that an individual nest will be successful. This is basically the same definition proposed by Kalmbach (1939). Stoudt (1982) used the terms nest success and adjusted nest success. His adjusted nest success is equivalent to hen success as defined in this chapter. Nest success is one of the most commonly measured components of recruitment. Mayfield (1961, 1975) demonstrated that the usual estimator employed, the apparent success rate, or the ratio of observed hatched nests to total observed nests, was biased because nests of different ages are found at different rates (see chapter 12 of this volume). Mayfield's method or refinements of it (Johnson 1979, Johnson and Klett 1985) are now used by most waterfowl biologists.

Hen success, the probability that a hen will be successful in one or more nesting attempts, is a function of nest success and the number of renesting attempts. If all hens attempt at least one nest (α = 1) and nest success does not equal 0 or 1, then hen success must be larger than nest success rate (equation 2). Also, the average number of nests per hen equals hen success rate divided by nest success rate. Direct measurement of hen success requires the use of marked birds and the assumption that all successful nests are found. Direct measurement of renesting is not practical because even with the use of radio-equipped hens, all destroyed nests cannot be found.

Average brood size at fledging--the average size of all broods with at least one member--appears simple to measure but is subject to important biases (see chapter 12 of this volume). Early-hatched broods are generally larger than late-hatched broods because clutch size declines as the nesting season progresses (Sowls 1955, Batt and Prince 1979, Krapu and Dory 1979, Toft et al. 1984). Brood surveys are normally conducted during a brief period, not throughout the nesting season. Older observed broods come from earlier-hatched nests than younger observed broods and, therefore, their average size tends to be larger. Cowardin and Johnson (1979) discussed the problem and presented a means of correcting for the bias based on unpublished Mallard data of M. C. Hammond. In addition, some hens lose ducklings to or gain brood members from other hens, a behavioral characteristic that may also cause bias of unknown magnitude.

The survival of entire broods to the time of census is an important, though often overlooked, component of recruitment. Cowardin and Johnson (1979) assumed that broods are usually censused at approximately age class II (Gollop and Marshall 1954; see also Pirkola and Hogmander 1974). Ignoring the loss of entire broods can lead to seriously inflated recruitment estimates (Ball et al. 1975, Reed 1975, chapter 12 of this volume). Measurement of brood survival is exceedingly difficult and requires the use of marked birds, preferably radio-marked. Because of the difficulty of marking and following ducklings, survival of broods remains one of the most poorly measured components of recruitment rate.