Analyzing population growth curves

Assessing animal population growth curves is an essential feature of field studies in ecology and wildlife management. We used five models to assess population growth rates with a number of sets of population growth rate data. A 'generalized' logistic curve provides a better model than do four other popular models. Use of difference equations for fitting was checked by a comparison of that method and direct fitting of the analytical (integrated) solution for three of the models. Fits to field data indicate that estimates of the asymptote, K, from the 'generalized logistic' and the ordinary logistic agree well enough to support use of estimates of K from the ordinary logistic on data that cannot be satisfactorily fitted with the generalized logistic. Akaike's information criterion is widely used, often with a small sample version AIC_c. Our study of five models indicated a bias in the AIC_c criterion, so we recommend checking results with estimates of variance about regression for fitted models. Fitting growth curves provides a valuable supplement to, and check on computer models of populations.     

IMPLICATIONS OF NON-LINEAR DENSITY DEPENDENCE

Abstract: Ranges of the ratio of maximum net productivity level (MNPL) to carrying capacity (K) are explored in general models for pinnipeds and odontocetes. MNPL/K is used in management of marine mammals but no empirical evidence exists to limit the range of values expected. Density dependent changes in age-specific birth and death rates have been used to infer MNPL/K. Non-linearities in these rates do not translate directly to population growth curves. The simple models demonstrate: (1) density dependence is likely to involve more than a single parameter (such as birth rate), (2) MNPL/K can be greatly reduced from that inferred from one strongly non-linear parameter when changes in other parameters are linear, (3) ranges of MNPL/K depend on biological limits on ranges of fecundity and survival rates, and (4) the magnitude and sign of bias incurred by inferring MNPL/K from functional forms of single parameters cannot be determined. Given current empirical evidence the range of MNPL/K for marine mammals as a group is large. Although MNPL/K should not be inferred from single parameter non-linearities, distributions of MNPL/K values can be generated through models which account for single species ranges for birth and death rates and maximum population growth rate.     

PROJECTING THE TREND OF STELLER SEA LION POPULATIONS IN WESTERN ALASKA

This paper attempts to project the trends of Steller sea lion ( Eumetopias jubatus ) populations in six subdivisions of the western Alaska population. The overall Western Alaska population has declined dramatically since the 1970s. Trends in half of the areas appear to have leveled-off and possibly to be on the increase. Bootstrapping has been used to provide confidence intervals on predictions for the 2004 counts. For the three areas in which we expect increases, the 95% confidence intervals on predictions were: Eastern Gulf (2,430–3,740), Central Gulf (3,260–3,660) and Central Aleutians (5,160–6,580). The Western Gulf counts have been somewhat erratic, with a gradual rate of decrease (about 2% per year) and wide confidence limits on a linear prediction (logarithmic scale) of 2,690–3,240. Trends in the Eastern Aleutians have been even more erratic, so that about all that can be inferred is that the population may be roughly stabilized. Only the Western Aleutians appear to be rapidly declining at about 10% per year, with a 95% confidence interval on a linear trend of 610–1,100. The predictions were made before the 2004 counts and are in reasonable accord with the 2004 counts. Age structure changes do not appeat to provide a viable explanation for the changing trends.     

SURVIVAL OF FIVE SPECIES OF CAPTIVE MARINE MAMMALS

Survival in captivity was calculated for 1,707 bottlenose dolphins (BD), 72 killer whales (KW), 73 white whales (WW), 3,090 California sea lions (CSL), and 47 Steller sea lions (SSL) based on data in the Marine Mammal Inventory Report (MMIR) of the NMFS. Mean annual survival rates (ASRs) between 1988 and 1992 were 0.951, 0.937, and 0.954 for BD, KW, and WW, respectively, and 0.952 and 0.969 for CSL and SSL, respectively. These estimates represent significant increases in survival for both BD and CSL over the last 5 yr. Using all of the MMIR data (1940–1992), the ASR of BD calves (< 1 yr of age) was significantly less than the ASR of non-calves (0.666 vs .948, 0.001). Similarly, the ASR of CSL pups (< 1 yr of age) was significantly less than survival of non-pups (0.858 vs .962, 0.001). Survival of captive-born CSL was significantly higher than those born in the wild (0.962 vs .945, 0.003), but the difference was not significantly different for BD (0.948 vs .944, 0.60). For non-calf BD and KW, captive animals survived at a slightly lower rate (BD 0.944 vs .961, = 0.07; KW 0.938 vs .976, 0,001) than animals in the wild (BD: Wells and Scott 1990, KW: Olesiuk 1990). Survival of captive non-pup SSL was slightly higher (0.968 vs .930) than animals in the wild (York 1994, life-table analyses). Survival rates were significantly different among institutions for BD calves and non-calves, CSL pups and non-pups, and SSL non-pups.     

AN ESTIMATION OF CARRYING CAPACITY FOR SEA OTTERS ALONG THE CALIFORNIA COAST

Carrying capacity (K) for the California sea otter ( Enhydra lutris nereis ) was estimated as a product of the density of sea otters at equilibrium within a portion of their existing range and the total area of available habitat. Equilibrium densities were determined using the number of sea otters observed during spring surveys in 1994, 1995, and 1996 in each of three habitat types where sea otters currently exist. Potential sea otter habitat was defined as from the California coastline to the 40-m isobath and classified as rocky, sandy, or mixed habitat according to the amount of kelp and rocky substrate in the area. The amount of habitat available to sea otters in California was estimated using a Geographic Information Systems (GIS) program. The estimated mean number of sea otters that could be supported by the marine environment to a depth of 40 m in California was 15,941 (95% CI 13,538–18,577). The GIS-based approach incorporated detailed bathymetric contours, produced repeatable and accurate estimates, and served as an innovative method of measuring sea otter habitat. We believe the approach described in this paper represents the best available information on how a sea otter population at equilibrium would be distributed along the California coast.     

ACCLIMATION TO CAPTIVITY: A QUANTITATIVE ESTIMATE BASED ON SURVIVAL OF BOTTLENOSE DOLPHINS AND CALIFORNIA SEA LIONS

An estimate of how long marine mammals need to acclimate to captivity would permit more precise comparisons of husbandry practices, yet no quantitative analysis of acclimation has been performed. Therefore, we estimated the duration of acclimation to captivity for bottlenose dolphins (BD) and California sea lions (CSL) by comparing 5-d survival rates during the first 90 d of captivity with a survival rate based on days 91-365 in captivity. Wild-born BD (n = 1,270) and CSL (n = 1,650) acclimate to captivity in approximately 35 and 40 d, respectively, whereas captive born BD (n = 332) and CSL (n = 992) acclimate in approximately 50 and 40 d, respectively. When transferred between two institutions, BD (n = 911) acclimated in the same amount of time (45 d) as when first transferred from the wild, whereas transferred CSL (n = 336) acclimated more rapidly (15 VJ. 40 d) than when first transferred from the wild. Based on results from these two species, a 60-d acclimation period is recognized as a distinct interval of relatively high mortality that should be treated separately from long-term survival estimates when evaluating husbandry practices of ocean-aria and zoos.