prey size of single-prey loaders as an indicator of prey abundance

Prey size of single-prey loaders as an indicator of prey abundance Abstract In this paper I am concerned with the behaviour of seabirds that bring back just one prey item at a time to their young. I use a simple model from central place foraging theory to show that the size of fish that a parent bird brings back may increase or decrease with an increase in the abundance of fish. This means that it may not be possible to use the size of fish that is fed to the young as an indicator of prey abundance. Keywords Central place foraging, indicators, seabirds, single-prey loaders Ecology Letters (2000) 3 : 5±6 There is considerable interest in the possibility of using various aspects of the behaviour of seabirds as indicators of the abundance of fish (see, for example, Cairns 1992; Bost & Le Maho 1993; Monaghan 1996; and references therein). In this paper I use a simple model to show that the size of fish that a parent bird brings back to its young may increase or decrease with an increase in the abundance of fish. A parent bird delivering food to its young is what Orians & Pearson (1979) call a central place forager. In this paper I will be concerned with birds that bring back just one prey item at a time ± these are what Orians & Pearson call single-prey loaders. Several species of seabirds are single-prey loaders. For example, terns typically bring a single item to their chicks (e.g. Hays et al. 1973), as do some auks (e.g. Monaghan et al. 1994). The foraging cycle for a parent consists of flying from the nest to a foraging area, catching a prey item, and returning with it to the nest. Flying to and from the foraging area takes a time t. Once in the foraging area, possible prey items are found at a rate r. Both t and r are likely to depend on the abundance of prey. For simplicity I ignore the time taken by the parent to handle prey. If the parent is maximizing the gross rate at which it delivers energy to its young, then it is optimal to follow a rule of the form: accept the first prey item with an energy content greater than or equal to a and return with it to the young. Under such a rule, the expected energy delivered is the mean energy content of an item, given that the energy content is greater than a. If the distribution of energy content follows a negative exponential distribution with mean 1/m, then the expected amount of energy obtained from a cycle is G(a)= a + 1/m. If the parent is not selective, a = 0 and the expected energy delivered is simply the mean value. The expected time taken for a cycle, T(a), consists of two components, the round trip travel time and the expected time to find an acceptable item. The rate of encountering items is r and the probability that an item is acceptable is exp(±ma). Thus the rate at which acceptable items are encountered is rexp(±ma). The expected time to find an acceptable item is the reciprocal of this rate, and so T(a)= t + [exp(ma)]/r. The resulting gross rate of energy delivery is R(a)= G(a)/T(a). For further discussion, see Lessells & Stephens (1983), Houston & McNamara (1985) and Houston (1987). The value a* of a that maximizes R(a) can be found from the condition that dR(a*)/da = 0. It follows from this condition and the above equations that a* satisfies the equation ma*exp(ma*) = tr. (1) Equation (1) means that for given m the optimal acceptance threshold a* is determined by tr. Assume that the distribution of energy content does not change from year to year and that energy content always increases with size. Various changes in t and r between years can constitute an increase in abundance of prey. At one extreme, t may decrease while r remains constant. This #2000 Blackwell Science Ltd/CNRS Alasdair I. Houston School of Biological Sciences, University of Bristol, Woodland Road, Bristol BS8 1UG, UK. E-mail: [email protected] Ecology Letters, (2000) 3 : 5±6 IDEA Ahed Bhed Ched Dhed Ref marker Fig marker Table marker Ref end Ref start Paper 110 Disc

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