Detecting density dependence in recovering seal populations

Abstract

Time series of abundance estimates are commonly used for analyses of population trends and possible shifts in growth rate. We investigate if trends in age composition can be used as an alternative to abundance estimates for detection of decelerated population growth. Both methods were tested under two forms of density dependence and different levels of environmental variation in simulated time series of growth in Baltic gray seals. Under logistic growth, decelerating growth could be statistically confirmed after 16 years based on population counts and 14 years based on age composition. When density dependence sets in first at larger population sizes, the age composition method performed dramatically better than population counts, and a decline could be detected after 4 years (versus 10 years). Consequently, age composition analysis provides a complementary method to detect density dependence, particularly in populations where density dependence sets in late.

Fig. 1

General age-structured life cycle of a seal population, where m is the age at which a seal starts reproducing, and c is the maximum age

Fig. 2

a Pup survival (p_p) as a function of abundance for the Baltic grey seal population growing according to the logistic equation, i.e., p_p(t) = p_p(1 − (N_t/K_e)^θ), for linear density dependence, θ = 1 (solid line) and initially weak density dependence, θ = 4 (dashed line). b Abundance as a function of time for θ = 1 (solid line) and θ = 4 (dashed line)

Fig. 3

The probability to detect a significant trend in time series of abundance data (as given by the gray scale of the shaded area) for a population growing from low numbers at year 1 to carrying capacity in years 100–200 (as depicted in Fig. 2). During this time, population size is estimated from subsets of the data and analyzed for signs of density dependence. As the measurement window of the sub-sampled time series is increased (y-axis), the probability to detect a significant trend increases. a, b Illustrate the case when an ordinary “symmetric” logistic growth function is applied. c, d Illustrate a skewed, initially weak, density dependence. a, c Show cases of low environmental variability whereas b and d show cases of high environmental variability

Fig. 4

This figure is directly analogous to Fig. 3, but instead of trends in population size the data sampled here is age structure (adult proportion as a ratio to total population size excluding pups). Window size is the number of years over which the sub-sampling is performed (y-axis). The intensity of the gray scale represents the probability to detect a significant trend in a time series of age composition data during logistic growth (a, b), during initially weak density dependence (c, d) and for low (a, c) and high (b, d) environmental variability