Statistical analysis of fluctuations in red grouse bag data

Oikos, 2003

Are indirect measures of abundance a useful index of population density? The case of red grouse harvesting.-Oikos 100: 439-446. Indirect measures of population abundance, such as harvest data, are often used to make inference on long term population dynamics when direct data are either not available or are logistically difficult to obtain. However, when harvesting records are used, a common concern is that they may not reflect actual population abundance. We investigated the extent to which harvest data reflected changes in population density of the red grouse Lagopus lagopus scoticus in Great Britain. We used 92 independently managed populations over the period 1977-2000 and examined the temporal and spatial variability of the hunting records and independently obtained count data from each of these managed estates. Three different analyses support the conclusion that grouse hunting records are a reliable indicator of grouse abundance: 1) the number of red grouse shot in autumn showed a tendency to be linearly related to the density of individuals counted in the summer prior to the harvesting, 2) the relationships between the variance and the mean in the harvesting and corresponding count data, calculated over different populations at the same time, or the same locations at different times, were not statistically distinguishable, 3) similar direct and delayed density dependence patterns were observed in hunting records and count data. Our results suggest that red grouse hunting time series are a good proxy for population abundance.

Science of The Total Environment, 2014

Wildlife Biology

Forage quality is rarely the focus of studies on grouse performance. The plant stress hypothesis predicts that the protein digestibility of a focal food plant for grouse in Norway, the bilberry Vaccinium myrtillus should be highest after a peak in seed production. Protein digestibility may also be affected positively by cosmic ray (muon) fluxes, which fluctuate with the 9.3-year lunar nodal phase cycle, and negatively by high temperatures in the preceding summers. The annual change (first difference) in ln-transformed black grouse Tetrao tetrix and capercaillie T. urogallus hunting statistic indices from southern Norway 1999-2017 was positively related to the mean June temperature, which is assumed to have a direct positive impact on chick survival. In multiple regression models, there was also a positive relationship with the seed production of bilberry in the preceding year, the lunar nodal phase index with a two-year time lag, and a negative relationship with the combined mean June-September temperature of the two preceding years. Small rodent numbers did not contribute significantly in these models. In further monitoring of grouse populations, the seed production of bilberry or other important food plants should also be recorded.

Ibis, 2006

According to the alternative prey hypothesis, autumn populations of ground-nesting game birds fluctuate in synchrony with vole numbers because generalist predators that mainly eat voles switch to alternative prey, such as eggs and chicks, when vole numbers decline. In hunting statistics from Nord-Trøndelag, central Norway, 1901-24, annual fluctuations in the number of Willow Grouse Lagopus lagopus and Western Capercaillie Tetrao urogallus , but not of Woodcock Scolopax rusticola , were positively related to vole numbers in the current year. Both Woodcock and grouse indices were related to hunting indices of Goshawk Accipiter gentilis and to weather variables assumed to influence the birds' survival or reproduction, suggesting that the indices actually reflected local population levels. Synchronous vole and grouse fluctuations are consistent with the alternative prey hypothesis (although predator densities were low in the early 1900s), but the asynchronous Woodcock fluctuations refute the hypothesis. Rather, because the Woodcock does not feed on plants utilized by voles and grouse, I suggest that food quality is the ultimate factor for the synchrony in vole and grouse numbers in Norway.

Oikos, 2011

We study the dynamics of the capercaillie, black grouse, hazel grouse and willow grouse in Kainuu game management district in northeastern Finland in the years 1989 -2004. It appears that the 6 -7 year periodicity that prevailed in this region from 1960s up to 1980s has now vanished in all species. Th e grouse data are modelled using a linear autoregressive model with lag terms for population dynamics including grouse harvest as annual bag and an index of winter severity (winter-time area of Baltic Sea ice cover). We use the Akaike information criterion for selecting the best model for each species; fi rst order lag is forced to the models. It turns out that a term is needed for harvesting (with a negative coeffi cient) in models for all species. For the capercaillie and the hazel grouse second order lag was included, for the black grouse and the willow grouse fi rst order lag suffi ces. Th e willow grouse is the only species where the index of winter strength (with a negative coeffi cient) is needed in the model.

2003

Statistics is like a game: to find the best relationship between variables, the researcher tests different ways to improve a model. Here, we present new statistical results for a modelling approach to the climatic influence on the Black Grouse population dynamics in Belgium. The method, initially successfully developed for the Belgian population and then applied to several European Black Grouse populations, has been modified to refine more precisely the real time of the birds' breeding period during which climatic conditions are crucial. Statistical and biological values of the results with periods defined for 7 days rather than for 3 or 4 weeks are interpreted and discussed for three sub-populations of the Hautes-Fagnes plateau in Belgium.

Abstract We find multi− annual oscillations in the population size of seven Canadian species, based on century− long time− series of fur harvests. Our statistical analysis aims to ascertain the factors that influence the dynamics of the populations hunted. To do so, we use the advanced spectral methods of singular spectrum analysis and multi− tapering. The dynamics of the seven populations have several common features. First, they share periodic components with periods of 2.5, 3 and 10 years.

Cyclical behavior in wildlife populations, including northern bobwhite (Colinus virginianus), has long fascinated human observers. However, studies examining cyclicity of bobwhite abundance have yielded contradictory results. We reviewed evidence for periodic fluctuation in bobwhite abundance by studying 73 long-term time series. Our aim was to discern with time-series techniques whether cyclicity occurred in bobwhite abundance. We elucidated the frequency of occurrence, geographical distribution, and potential mechanisms responsible for cyclicity. Approximately one-half (n = 37) of the populations examined demonstrated cyclical behavior, with a period varying between 4 and 17 yrs. True cycles, consistent, significant fluctuations in abundance, were rare, occurring in only 3 time series. The predominant form of periodicity was of the phase-forgetting quasi-cycle type (n =
34). This phase-forgetting may have contributed to previous contradictory findings of cyclicity in this species. We reason cyclicity in bobwhite populations is caused by aperiodic environmental perturbations interacting with density-dependence. Cyclic bobwhite populations occupied the northern and western portion of the species’ range, where stochastic weather events regularly negatively influence bobwhite population dynamics. Bobwhite populations were non-cyclic in the relatively consistent climate of the southeastern United States, however, habitat fragmentation rather than climate may have contributed to the absence of cyclicity in this region.

Journal of Wildlife Management, 2005

Introduced brushtail possums (Trichosurus vulpecula) are a widespread pest of conservation and agriculture in New Zealand, and considerable effort has been expended controlling populations to low densities. A national protocol for monitoring the abundance of possums, termed trap catch index (TCI), was adopted in 1996. The TCI requires that lines of leghold traps set at 20-m spacing are randomly located in a management area. The traps are set for 3 fine nights and checked daily, and possums are killed and traps reset. The TCI is the mean percentage of trap nights that possums were caught, corrected for sprung traps and nontarget captures, with trap line as the sampling unit. We studied 1 forest and 1 farmland area in the North Island, New Zealand, to address concerns that TCI estimates may not be readily comparable because of seasonal changes in the capture probability of possums. We located blocks of 6 trap lines at each area and randomly trapped 1 line in each block in 3 seasons (summer, winter, and spring) in 2000 and 2001. We developed a model to allow for variation in local population size and nightly capture probability, and fitted the model using the Bayesian analysis software BUGS. Capture probability declined with increasing abundance of possums, generating a nonlinear TCI. Capture probability in farmland was lower during spring relative to winter and summer, and to forest during summer. In the absence of a proven and cost-effective alternative, our results support the continued use of the TCI for monitoring the abundance of possums in New Zealand. Seasonal biases in the TCI should be minimized by conducting repeat sampling in the same season.

Nature, 2005