From pattern to process? Dual travelling waves, with contrasting propagation speeds, best describe a self-organised spatio-temporal pattern in population growth of a cyclic rodent.

The dynamics of cyclic populations distributed in space result from the relative strength of synchronising influences and the limited dispersal of destabilising factors (activators and inhibitors), known to cause multi-annual population cycles. However, while each of these have been well studied in isolation, there is limited empirical evidence of how the processes of synchronisation and activation-inhibition act together, largely owing to the scarcity of datasets with sufficient spatial and temporal scale and resolution. We assessed a variety of models that could be underlying the spatio-temporal pattern, designed to capture both theoretical and empirical understandings of travelling waves using large-scale (>35,000 km2 ), multi-year (2011-2017) field monitoring data on abundances of common vole (Microtus arvalis), a cyclic agricultural rodent pest. We found most support for a pattern formed from the summation of two radial travelling waves with contrasting speeds that together describe population growth rates across the region.

Biased estimation of trends in cohort effects: the problems with age-period-cohort models in ecology.

Environmental variation can generate life-long similarities among individuals born in the same breeding event, so-called cohort effects. Studies of cohort effects have to account for the potentially confounding effects of current conditions (observation year) and age of individuals. However, estimation of such models is hampered by inherent collinearity, as age is the difference between observation year (period) and cohort year. The difficulties of separating linear trends in any of the three variables in Age-Period-Cohort (APC) models are the subject of ongoing debate in social sciences and medicine but have remained unnoticed in ecology. After reviewing the use of APC models, we investigate the consequences of model specification on the estimation of cohort effects, using both simulated data and empirical data from a long-term individual-based study of reindeer in Svalbard. We demonstrate that APC models are highly sensitive to the model's treatment of age, period and cohort, which may generate spurious temporal trends in cohort effects. Avoiding grouping ages and using environmental covariates believed to be drivers of temporal variation reduces the APC identification problem. Nonetheless, ecologists should use caution, given that the specification issues in APC models may have substantial impacts on estimated effect sizes and therefore conclusions.

Europe-wide dampening of population cycles in keystone herbivores.

Suggestions of collapse in small herbivore cycles since the 1980s have raised concerns about the loss of essential ecosystem functions. Whether such phenomena are general and result from extrinsic environmental changes or from intrinsic process stochasticity is currently unknown. Using a large compilation of time series of vole abundances, we demonstrate consistent cycle amplitude dampening associated with a reduction in winter population growth, although regulatory processes responsible for cyclicity have not been lost. The underlying syndrome of change throughout Europe and grass-eating vole species suggests a common climatic driver. Increasing intervals of low-amplitude small herbivore population fluctuations are expected in the future, and these may have cascading impacts on trophic webs across ecosystems.

Multi-scale processes in metapopulations: contributions of stage structure, rescue effect, and correlated extinctions.

Metapopulations function and persist through a combination of processes acting at a variety of spatial scales. Although the contributions of stage structure, spatially correlated processes, and the rescue effect to metapopulation dynamics have been investigated in isolation, there is no empirical demonstration of all of these processes shaping dynamics in a single system. Dispersal and settlement differ according to the life stage involved; therefore, stage-specific population size may outperform total population size when predicting colonization-extinction dynamics. Synchrony in patch dynamics can lead to accelerated metapopulation extinction, although empirical evidence of the interplay between correlated colonization events and correlated extinctions is lacking. Likewise, few empirical examples exist that provide compelling evidence of migration acting to reduce extinction risk (the rescue effect). We parameterized a hierarchy of metapopulation models to investigate these predictions using a seven-year study of a naturally occurring water vole (Arvicola amphibius) metapopulation. Specifically, we demonstrated the importance of local stage structure in predicting both colonization and extinction events using juvenile and adult population sizes, respectively. Using a novel approach for quantifying correlation in extinction events, we compared the scale of synchrony in colonization and extinction. Strikingly, the scale of dispersal acting to synchronize colonization was an order of magnitude larger than that of correlated extinctions (halving distance of the effect: 12.40 km and 0.89 km, respectively). Additionally, we found compelling evidence for the existence of a nontrivial rescue effect. Here we provide a novel empirical demonstration of a variety of metapopulation processes operating at multiple spatial scales, further emphasizing the need to consider stage structure and local synchrony in the dynamics of spatially dependent, stage-structured (meta) populations.

Long-term datasets in biodiversity research and monitoring: assessing change in ecological communities through time.

The growing need for baseline data against which efforts to reduce the rate of biodiversity loss can be judged highlights the importance of long-term datasets, some of which are as old as ecology itself. We review methods of evaluating change in biodiversity at the community level using these datasets, and contrast whole-community approaches with those that combine information from different species and habitats. As all communities experience temporal turnover, one of the biggest challenges is distinguishing change that can be attributed to external factors, such as anthropogenic activities, from underlying natural change. We also discuss methodological issues, such as false alerts and modifications in design, of which users of these data sets need to be aware.

Regression analysis of spatial data.

Many of the most interesting questions ecologists ask lead to analyses of spatial data. Yet, perhaps confused by the large number of statistical models and fitting methods available, many ecologists seem to believe this is best left to specialists. Here, we describe the issues that need consideration when analysing spatial data and illustrate these using simulation studies. Our comparative analysis involves using methods including generalized least squares, spatial filters, wavelet revised models, conditional autoregressive models and generalized additive mixed models to estimate regression coefficients from synthetic but realistic data sets, including some which violate standard regression assumptions. We assess the performance of each method using two measures and using statistical error rates for model selection. Methods that performed well included generalized least squares family of models and a Bayesian implementation of the conditional auto-regressive model. Ordinary least squares also performed adequately in the absence of model selection, but had poorly controlled Type I error rates and so did not show the improvements in performance under model selection when using the above methods. Removing large-scale spatial trends in the response led to poor performance. These are empirical results; hence extrapolation of these findings to other situations should be performed cautiously. Nevertheless, our simulation-based approach provides much stronger evidence for comparative analysis than assessments based on single or small numbers of data sets, and should be considered a necessary foundation for statements of this type in future.

Estimating the annual number of breeding attempts from breeding dates using mixture models.

Well-established statistical methods exist to estimate variation in a number of key demographic rates from field data, including life-history transition probabilities and reproductive success per attempt. However, our understanding of the processes underlying population change remains incomplete without knowing the number of reproductive attempts individuals make annually; this is a key demographic rate for which we have no satisfactory method of estimating. Using census data to estimate this parameter from requires disaggregating the overlying temporal distributions of first and subsequent breeding attempts. We describe a Bayesian mixture method to estimate the annual number of reproductive attempts from field data to provide a new tool for demographic inference. We validate our method using comprehensive data on individually-marked song sparrows Melospiza melodia, and then apply it to more typical nest record data collected over 45 years on yellowhammers Emberiza citrinella. We illustrate the utility of our method by testing, and rejecting, the hypothesis that declines in UK yellowhammer populations have occurred concurrently with declines in annual breeding frequency.

Increasing litter species richness reduces variability in a terrestrial decomposer system.

Debate on the relationship between diversity and stability has been driven by the recognition that species loss may influence ecosystem properties and processes. We conducted a litterbag experiment in the Scottish Highlands, United Kingdom, to examine the effects of altering plant litter diversity on decomposition, microbial biomass, and microfaunal abundance. The design of treatments was fully factorial and included five species from an upland plant community (silver birch, Betula pendula; Scots' pine, Pinus sylvestris; heather, Calluna vulgaris; bilberry, Vaccinium myrtillus; wavy-hair grass, Deschampsia flexuosa); species richness ranged from one to five species. We tested the effects of litter species richness and composition on variable means, whether increasing litter species richness reduced variability in the decomposer system, and whether any richness-variability relationships were maintained over time (196 vs. 564 days). While litter species composition effects controlled variable means, we revealed reductions in variability with increasing litter species richness, even after accounting for differences between litter types. These findings suggest that higher plant species richness per se may result in more stable ecosystem processes (e.g., decomposition) and decomposer communities. Negative richness-variation relationships generally relaxed over time, presumably because properties of litter mixtures became more homogeneous. However, given that plant litter inputs continue to enter the belowground system over time, we conclude that variation in ecosystem properties may be buffered by greater litter species richness.

Identifying when weather influences life-history traits of grazing herbivores.

1. There is increasing evidence that density-independent weather effects influence life-history traits and hence the dynamics of populations of animals. Here, we present a novel statistical approach to estimate when such influences are strongest. The method is demonstrated by analyses investigating the timing of the influence of weather on the birth weight of sheep and deer. 2. The statistical technique allowed for the pattern of temporal correlation in the weather data enabling the effects of weather in many fine-scale time intervals to be investigated simultaneously. Thus, while previous studies have typically considered weather averaged across a single broad time interval during pregnancy, our approach enabled examination simultaneously of the relationships with weekly and fortnightly averages throughout the whole of pregnancy. 3. We detected a positive effect of temperature on the birth weight of deer, which is strongest in late pregnancy (mid-March to mid-April), and a negative effect of rainfall on the birthweight of sheep, which is strongest during mid-pregnancy (late January to early February). The possible mechanisms underlying these weather-birth weight relationships are discussed. 4. This study enhances our insight into the pattern of the timing of influence of weather on early development. The method is of much more general application and could provide valuable insights in other areas of ecology in which sequences of intercorrelated explanatory variables have been collected in space or in time.

Low intensity, mixed livestock grazing improves the breeding abundance of a common insectivorous passerine.

Livestock grazing is a major driver of ecosystem change and has been associated with significant declines in various bird species in Britain and worldwide. However, there is little experimental evidence to show how grazing affects bird populations. We manipulated livestock densities in a replicated field experiment and found that mixed sheep and cattle grazing, at low intensity, improved the breeding abundance of a common upland passerine, the meadow pipit Anthus pratensis, after two years. Plots stocked with sheep alone (at high or low density) or not stocked at all held fewer pipit territories. Despite a year-on-year decline in pairs of meadow pipits in intensively grazed plots, we found no effect of sheep number on breeding abundance. Our results support the hypothesis that mixed species of herbivores generate greater heterogeneity in vegetation structure, which modifies prey availability, resulting in a greater abundance of birds. The results of our study should inform the management of grassland areas and enhance the abundance of some bird species, particularly in areas that have seen significant shifts from mixed livestock grazing to grazing dominated by single species of animals.

Determinants of quality in a long-lived colonial species.

1. In many animal populations a small proportion of individuals produce the majority of surviving offspring, but the underlying mechanisms are unclear. Behaviour may be an important determinant of variation in fitness: 'high-quality' individuals may have enhanced abilities in foraging or predator and parasite avoidance. 2. The role of behaviour in determining variation in quality was examined using the common guillemot Uria aalge, a monogamous seabird with biparental care. Using a novel mixed model approach, we analysed binary data on breeding success of each pair attempting to breed in each year with variables critical to breeding success (timing of breeding; inferred age; breeding experience and success; number of nest sites and partners) as fixed effects. Random effects for year, male, female and each distinct pairing of a male and a female were included in the model, allowing a quality estimate to be derived for each individual and pair. A range of behaviours associated with breeding were examined in relation to these quality estimates. 3. Breeding success declined with timing of breeding, and increased initially with age before declining in old age. It increased with previous successful experience, not breeding experience per se, until senescence effects became apparent. For males, breeding success declined with increasing numbers of mates. 4. The most important behavioural determinants of quality operated at the level of the pair, with the time mates spent together at the site and chick feeding rates both positively related to quality. At the individual level, trip durations and feeding rates were associated with female but not male quality, suggesting that pair quality was operating principally through the female. However, removal of laying date, the most important component in the binomial model, confirmed that the pair effect was much larger than the female effect. 5. This study demonstrates the potential of mixed modelling to determine quality estimates based on long-term breeding histories. The probability of a successful reproductive attempt was explained by the timing of breeding, age, successful breeding experience and number of mates. Behaviour was an important proximate mechanism underlying quality, in particular the foraging abilities of the pair, and the female's contribution to offspring provisioning. In species with biparental care, behavioural correlates of quality operate most strongly at the scale of the breeding pair, because contributions from both individuals are required for a successful outcome.

Changes over time in the spatiotemporal dynamics of cyclic populations of field voles (Microtus agrestis L.).

We demonstrate changes over time in the spatial and temporal dynamics of an herbivorous small rodent by analyzing time series of population densities obtained at 21 locations on clear cuts within a coniferous forest in Britain from 1984 to 2004. Changes had taken place in the amplitude, periodicity, and synchrony of cycles and density-dependent feedback on population growth rates. Evidence for the presence of a unidirectional traveling wave in rodent abundance was strong near the beginning of the study but had disappeared near the end. This study provides empirical support for the hypothesis that the temporal (such as delayed density dependence structure) and spatial (such as traveling waves) dynamics of cyclic populations are closely linked. The changes in dynamics were markedly season specific, and changes in overwintering dynamics were most pronounced. Climatic changes, resulting in a less seasonal environment with shorter winters near the end of the study, are likely to have caused the changes in vole dynamics. Similar changes in rodent dynamics and the climate as reported from Fennoscandia indicate the involvement of large-scale climatic variables.

Testing the role of parasites in driving the cyclic population dynamics of a gamebird.

The role of parasites in regulating populations has been the subject of debate. We tested whether parasites caused population cycles in red grouse by manipulating parasite intensities in four, paired 1 km(2) study areas during cyclic population declines over 4 years. Parasite reductions led to (1) larger grouse broods, (2) higher population densities in both autumn and spring, (3) reduced autumn population declines in one of two regions, and (4) reduced spring declines, but only in the first year. We infer that a single trophic interaction between a parasite and its host does not explain cyclic dynamics in spring breeding density in this species, although it contributed to the start of a cyclic decline. Another process was operating to drive the populations down. Together with our other results these findings emphasize that both trophic and intrinsic processes may act within populations to cause unstable dynamics.

Browse selection in response to simulated seasonal changes in diet quality through postingestive effects.

Browse species undergo seasonal changes in nutritional value and secondary plant compound concentrations. The capacity of herbivores to monitor such change through postingestive effects and to modify their food choice appropriately was investigated. Twenty-four goats were offered a different conifer species on four successive learning days per 7-d period for six periods. During conifer consumption on learning days, animals received either a positive or a negative digestive stimulus to simulate the nutritional rewards and toxic consequences of browse consumption. For each animal, a different postingestive stimulus treatment was associated with each conifer species. The treatments consisted of an increasing positive stimulus, a decreasing positive stimulus, an increasing negative stimulus, or a decreasing negative stimulus. The levels of the stimuli were adjusted in 20% increments in successive periods (from 0 to 100% for the increasing treatments and from 100 to 0% in the decreasing treatments) to simulate seasonal changes in browse characteristics. Diet preference was measured on d 5 of each period. Animals adjusted their diet choice in response to the changing intensity of the negative stimulus, but not the positive stimulus. Animals avoided foods associated with the negative stimulus to a greater extent when the stimulus was increasing each period compared to when it was decreasing. The results suggest that herbivores are adept at monitoring and responding to temporal change in secondary compound concentrations through assessing their changing postingestive effects and adjusting their food choice accordingly.

Livestock grazing affects the egg size of an insectivorous passerine.

Livestock grazing is a major driver of ecosystem change, and has been associated with significant declines in various bird species worldwide. In Britain, there is particular concern that severe grazing pressure is deleteriously affecting vegetation and birds in upland regions. However, the mechanism by which grazing affects birds is unclear. Here, we report for the first time, to our knowledge, that sheep grazing pressure affects the egg size of a common upland passerine: the meadow pipit Anthus pratensis. We manipulated sheep stocking densities in a replicated field experiment, and found that plots with the highest stocking density contained nests with the smallest eggs, and that plots with low stocking density contained nests with the largest eggs. However, eggs laid in ungrazed plots were also small, suggesting that either too many sheep or their removal from upland areas might have a detrimental effect on pipit egg size. We found no significant effect on fledging success but the reduced post-fledging survival of young from smaller eggs, as seen in other studies, could partly explain declines in upland birds.