Multi-year Cycles Research Articles

A comparison of the dynamical impact of seasonal mechanisms in a herbivore–plant defence system

Plant defences can reduce herbivore fitness and may promote cycles in some herbivore populations. In this study, we model the interaction between plant defences and herbivores and include seasonal forcing, a ubiquitous environmental influence in natural systems. We compare the impacts of two different seasonal mechanisms on the dynamics of the herbivore–plant defence system. The first mechanism involves a fixed breeding season length and a variable birth rate within the breeding season; the second involves a variable breeding season length and a fixed birth rate within the breeding season. When parameterised for a specific cyclic system, namely field voles and silica, our model predicts that a variable season length gives multi-year cycles for a larger region in parameter space than a variable birth rate. Our results highlight the complexity of the dynamical effects of seasonal forcing and that these effects are strongly dependent on the type of seasonal mechanism.

Successional Dynamics in the Seasonally Forced Diamond Food Web

Plankton seasonal succession is a classic example of nonequilibrium community dynamics. Despite the fact that it has been well studied empirically, it lacks a general quantitative theory. Here we investigate a food web model that includes a resource, two phytoplankton, and a shared grazer-the diamond food web-in a seasonal environment. The model produces a number of successional trajectories that have been widely discussed in the context of the verbal Plankton Ecology Group model of succession, such as a spring bloom of a good competitor followed by a grazer-induced clear-water phase, setting the stage for the late-season dominance of a grazer-resistant species. It also predicts a novel, counterintuitive trajectory where the grazer-resistant species has both early- and late-season blooms. The model often generates regular annual cycles but sometimes produces multiyear cycles or chaos, even with identical forcing each year. Parameterizing the model, we show how the successional trajectory depends on nutrient supply and the length of the growing season, two key parameters that vary among water bodies. This model extends nonequilibrium theory to food webs and is a first step toward a quantitative theory of plankton seasonal succession.

Physicochemical simulation of the evolution of small lakes in a cold climate

The paper presents a generalized algorithm for the simulation of multiyear cycles in variations of the chemical composition of lake waters with regard for the seasonal specifics of hydrogeochemical processes. Data were obtained on the behavior of the hydrogeological system during a time span of 500–1000 years. Each of the simulated model cycles involved a successively alternating “summer-winter” time periods. Terrestrial exchange fluxes between reservoirs, groundwater inflow, falls of atmospheric precipitate, and the evaporation of lake water were taken into account for summer periods, whereas winter conditions were simulated as corresponding to the development of the ice phase, the absence of water exchange fluxes, a change from oxidizing to reducing conditions, and the burial of solid phases in the sediments. The results of our physicochemical simulations with the use of data on the composition of natural hydrogeological systems are in good agreement with natural observations and make it possible to realistically predict the evolution of small lakes in the Ol’khon area.

The hydrodynamics and salinity regime of a coastal lagoon – The Coorong, Australia – Seasonal to multi-decadal timescales

The Coorong is a choked coastal lagoon in South Australia that forms part of the terminal lake system at the end of the River Murray, Australia’s major river. It is an inverse estuary with a constricted channel connection to the sea at one end and extends parallel to the coast for more than 100 km away from this inlet. The present paper considers the physical dynamics of the Coorong, particularly its ecologically important salinity and water level regimes, and how these respond to connectedness with the ocean, barrage flows and meteorological conditions. The approach combines hydrodynamic modelling with measurements and considers temporal variation in the system ranging from seasonal to multi-decadal timescales. The Coorong is relatively unusual in that the major freshwater input occurs through barrages much closer to the estuary mouth than to its head. Thus, the barrage flows only ‘flush’ the Coorong between the barrages and the sea. Over most of its length, salt accumulating through evapo-concentration mixes back out of the system by fluctuating water motions caused by sea level variations propagating through the inlet channel and by wind. By scouring the inlet channel on a seasonal basis, barrage flows facilitate the penetration of sea level variations into the Coorong leading to enhanced along-lagoon mixing. Further, barrage flows freshen the waters near the seaward end of the system causing water of lower salt content than sea water to replace evaporative losses in its interior. By increasing the water depth in the system, barrage flows facilitate the exchange between the North and South Lagoons of the Coorong which are its two major basins. The modelling supported by measurements shows how the salinity regime in the Coorong appears to have responded to multi-year cycles of variation in discharge of the River Murray over the last 50 years. Even before the present drought, which has seen salinity in the South Lagoon exceed four times sea water, the lagoon was dominantly hypersaline. The modelling suggests that the significant reductions in freshwater inflows to the Coorong due to water resource development would have caused the South Lagoon to evolve from a state of being usually brackish to marine into its present hypersaline state. The conceptual understanding of the Coorong’s physical dynamics and their encapsulation in a hydrodynamic model are enabling strategies to be evaluated for alleviation of its present degraded condition, and for its improved future management.

Island fever: the historical determinants of malaria in the Andaman Islands

Malaria was the major cause of morbidity and a leading cause of mortality in the Andaman Islands Penal Colony from 1858 to 1945. Besides annual malaria incidence peaks coinciding with the arrival of the monsoon, multi-year cycles (administrative in nature) of 10-15 years are also discernable. The size of the previous year's prisoner intake was associated (r(2)=0.21, n=57) with increased malaria. The positive relationship (r(2)=0.33, n=47) between the total number of Buddhist prisoners and malaria may have been due to prisoners of Burmese ethnicity introducing new malaria strains to the otherwise isolated islands. Well-meaning but ultimately disastrous attempts were made to drain the mangrove swamps around the penal colony. Because of the brackish-water breeding habits of the main vector, Anopheles sundaicus, engineering works along the shoreline often increased malaria. Malaria morbidity approximately trebled from 1928 to 1929 and doubled again in the next year with increases in all-cause mortality from 20/1000 in 1929 to 51/1000 in 1930, coincident with a major dredging operation for a new port. The history of malaria control in the Andaman Islands Penal Colony is a cautionary tale that well-meaning and well-funded efforts can fail spectacularly if local epidemiological reality is not well understood.

Multi-year cycles observed in air temperature data and proxy series

First, palaeoclimatic time series are analyzed under the lens of the continuous wavelet transform. Two cycles, of period 30 and 43 months respectively, are detected in millennial temperature reconstructions. These rhythms correspond to the ones detected in weather station temperature records in a previous study of the authors. It is then showed that most parts of the globe are affected by at least one of the two cycles. Their relationship with the main climatic indices is also investigated, as well as the statistical significance of the observations.

The effects of density-dependent dispersal on the spatiotemporal dynamics of cyclic populations

Density-dependent dispersal occurs throughout the animal kingdom, and has been shown to occur in some taxa whose populations exhibit multi-year population cycles. However, the importance of density-dependent dispersal for the spatiotemporal dynamics of cyclic populations is unknown. We investigated the potential effects of density-dependent dispersal on the properties of periodic travelling waves predicted by two coupled reaction–diffusion models: a commonly used predator–prey model, and a general model of cyclic trophic interactions. We compared the effects of varying the gradient of both positive and negative density-dependent dispersal rates, to varying the ratio of the (constant) dispersal rates of the two interacting populations. Our comparison focussed on the possible range of wave properties, and on the waves generated by landscape obstacles and invasions. In all scenarios that we studied, varying the gradient of density-dependent dispersal has small quantitative effects on the travelling wave properties, relative to the effects of varying the ratio of the diffusion coefficients.

Periodic travelling waves in cyclic populations: field studies and reaction-diffusion models.

Periodic travelling waves have been reported in a number of recent spatio-temporal field studies of populations undergoing multi-year cycles. Mathematical modelling has a major role to play in understanding these results and informing future empirical studies. We review the relevant field data and summarize the statistical methods used to detect periodic waves. We then discuss the mathematical theory of periodic travelling waves in oscillatory reaction-diffusion equations. We describe the notion of a wave family, and various ecologically relevant scenarios in which periodic travelling waves occur. We also discuss wave stability, including recent computational developments. Although we focus on oscillatory reaction-diffusion equations, a brief discussion of other types of model in which periodic travelling waves have been demonstrated is also included. We end by proposing 10 research challenges in this area, five mathematical and five empirical.

The effects of obstacle size on periodic travelling waves in oscillatory reaction–diffusion equations

Many natural populations undergo multi-year cycles, and field studies have shown that these can be organized into periodic travelling waves (PTWs). Mathematical studies have shown that large-scale landscape obstacles represent a natural mechanism for wave generation. Here, we investigate how the amplitude and wavelength of the selected waves depend on the obstacle size. We firstly consider a large circular obstacle in an infinite domain for a reaction–diffusion system of ‘ λ – ω ’ type. We use perturbation theory to derive a leading order approximation to the wave generated by the obstacle. This shows the dependence of the wave properties on both parameter values and obstacle size. We find that the limiting values of the amplitude and wavelength are approached algebraically with distance from the obstacle edge, rather than exponentially in the case of a flat boundary. We use our results to predict the properties of waves generated by a large circular obstacle for an oscillatory predator–prey system, via a reduction of the predator–prey model to normal form close to Hopf bifurcation. Our predictions compare well with numerical simulations. We also discuss the implications of these results for wave stability and briefly investigate the effects of obstacles with elliptical geometries.

Shifting patterns: malaria dynamics and rainfall variability in an African highland

The long-term patterns of malaria in the East African highlands typically involve not only a general upward trend in cases but also a dramatic increase in the size of epidemic outbreaks. The role of climate variability in driving epidemic cycles at interannual time scales remains controversial, in part because it has been seen as conflicting with the alternative explanation of purely endogenous cycles exclusively generated by the nonlinear dynamics of the disease. We analyse a long temporal record of monthly cases from 1970 to 2003 in a highland of western Kenya with both a time-series epidemiological model (time-series susceptible-infected-recovered) and a statistical approach specifically developed for non-stationary patterns. Results show that multiyear cycles of malaria outbreaks appear in the 1980s, concomitant with the timing of a regime shift in the dynamics of cases; the cycles become more pronounced in the 1990s, when the coupling between disease and rainfall is also stronger as the variance of rainfall increased at the frequencies of coupling. Disease dynamics and climate forcing play complementary and interacting roles at different temporal scales. Thus, these mechanisms should not be viewed as alternative and their interaction needs to be integrated in the development of future predictive models.

Disease effects on reproduction can cause population cycles in seasonal environments

Recent studies of rodent populations have demonstrated that certain parasites can cause juveniles to delay maturation until the next reproductive season. Furthermore, a variety of parasites may share the same host, and evidence is beginning to accumulate showing nonindependent effects of different infections.We investigated the consequences for host population dynamics of a disease-induced period of no reproduction, and a chronic reduction in fecundity following recovery from infection (such as may be induced by secondary infections) using a modified SIR (susceptible, infected, recovered) model. We also included a seasonally varying birth rate as recent studies have demonstrated that seasonally varying parameters can have important effects on long-term host–parasite dynamics. We investigated the model predictions using parameters derived from five different cyclic rodent populations.Delayed and reduced fecundity following recovery from infection have no effect on the ability of the disease to regulate the host population in the model as they have no effect on the basic reproductive rate. However, these factors can influence the long-term dynamics including whether or not they exhibit multiyear cycles.The model predicts disease-induced multiyear cycles for a wide range of realistic parameter values. Host populations that recover relatively slowly following a disease-induced population crash are more likely to show multiyear cycles. Diseases for which the period of infection is brief, but full recovery of reproductive function is relatively slow, could generate large amplitude multiyear cycles of several years in length. Chronically reduced fecundity following recovery can also induce multiyear cycles, in support of previous theoretical studies.When parameterized for cowpox virus in the cyclic field vole populations (Microtus agrestis) of Kielder Forest (northern England), the model predicts that the disease must chronically reduce host fecundity by more than 70%, following recovery from infection, for it to induce multiyear cycles. When the model predicts quasi-periodic multiyear cycles it also predicts that seroprevalence and the effective date of onset of the reproductive season are delayed density-dependent, two phenomena that have been recorded in the field.

Life-cycle and population dynamics of Rhincalanus gigas (Copepoda: Calanoida) in the Scotia Sea

A stage- and age-structured model was constructed to simulate stage-abundance patterns of Rhincalanus gigas in a data set consisting of over 80 yr of net-catch observations in the Scotia Sea. The model was initialised with the observed annual abundances of the Cl stage and the population developed according to pre-defined developmental stage durations, which varied according to life-cycle phenotype. Better fits to net-catch observations were achieved by models that allowed a number of different life-cycle phenotypes to co-exist in the population. In particular, a model in which 71 % of individuals reached adulthood in 2 yr (2 yr phenotype) and 29 % in 1 yr (1 yr phenotype) achieved the best fit. Of the 2 yr phenotypes, most individuals spent their 1st winter as a CIII, although a fraction passed this period as a CIV or CV. The 1 yr phenotypes entered their 1st winter as a CV but moulted through to adulthood before the following spring. During the productive period, the mortality rate of the early developmental stages was 0.1 d(-1), but this fell to 0.007 d(-1) as individuals developed beyond stage CIII. During the winter, the mortality rate fell further to 0.003 d(-1). Such rates meant that around 1.5 % of the copepodite population lived for 3 yr or more. Many of these spent 2 yr as an adult. Quantitative descriptions of development and mortality rates in the later stages of long-lived copepods are relatively few because of the difficulty in distinguishing the many generations in a typical population. As well as being the first to determine these rates in R. gigas, this study provides a methodological framework for determining such rates in other copepods with multi-year life cycles.

Epidemiological effects of seasonal oscillations in birth rates

Seasonal oscillations in birth rates are ubiquitous in human populations. These oscillations might play an important role in infectious disease dynamics because they induce seasonal variation in the number of susceptible individuals that enter populations. We incorporate seasonality of birth rate into the standard, deterministic susceptible–infectious–recovered (SIR) and susceptible–exposed–infectious–recovered (SEIR) epidemic models and identify parameter regions in which birth seasonality can be expected to have observable epidemiological effects. The SIR and SEIR models yield similar results if the infectious period in the SIR model is compared with the “infected period” (the sum of the latent and infectious periods) in the SEIR model. For extremely transmissible pathogens, large amplitude birth seasonality can induce resonant oscillations in disease incidence, bifurcations to stable multi-year epidemic cycles, and hysteresis. Typical childhood infectious diseases are not sufficiently transmissible for their asymptotic dynamics to be likely to exhibit such behaviour. However, we show that fold and period-doubling bifurcations generically occur within regions of parameter space where transients are phase-locked onto cycles resembling the limit cycles beyond the bifurcations, and that these phase-locking regions extend to arbitrarily small amplitude of seasonality of birth rates. Consequently, significant epidemiological effects of birth seasonality may occur in practice in the form of transient dynamics that are sustained by demographic stochasticity.

Alternative models for cyclic lemming dynamics

Many natural population growths and interactions are affected by seasonal changes, suggesting that these natural population dynamics should be modeled by nonautonomous differential equations instead of autonomous differential equations. Through a series of carefully derived models of the well documented high-amplitude, large-period fluctuations of lemming populations, we argue that when appropriately formulated, autonomous differential equations may capture much of the desirable rich dynamics, such as the existence of a periodic solution with period and amplitude close to that of approximately periodic solutions produced by the more natural but mathematically daunt ing nonautonomous models. We start this series of models from the Barrow model, a well formulated model for the dynamics of food-lemming interaction at Point Barrow (Alaska, USA) with sufficient experimental data. Our work suggests that an autonomous system can indeed be a good approximation to the moss-lemming dynamics at Point Barrow. This, together with our bifurcation analysis, indicates that neither seasonal factors (expressed by time dependent moss growth rate and lemming death rate in the Barrow model) nor the moss growth rate and lemming death rate are the main culprits of the observed multi-year lemming cycles. We suspect that the main culprits may include high lemming predation rate, high lemming birth rate, and low lemming self-limitation rate.

Nonlinear trends and multiyear cycles in sea level records

We analyze the Permanent Service for Mean Sea Level (PSMSL) database of sea level time series using a method based on Monte Carlo Singular Spectrum Analysis (MC‐SSA). We remove 2–30 year quasi‐periodic oscillations and determine the nonlinear long‐term trends for 12 large ocean regions. Our global sea level trend estimate of 2.4 ± 1.0 mm/yr for the period from 1993 to 2000 is comparable with the 2.6 ± 0.7 mm/yr sea level rise calculated from TOPEX/Poseidon altimeter measurements. However, we show that over the last 100 years the rate of 2.5 ± 1.0 mm/yr occurred between 1920 and 1945, is likely to be as large as the 1990s, and resulted in a mean sea level rise of 48 mm. We evaluate errors in sea level using two independent approaches, the robust bi‐weight mean and variance, and a novel “virtual station” approach that utilizes geographic locations of stations. Results suggest that a region cannot be adequately represented by a simple mean curve with standard error, assuming all stations are independent, as multiyear cycles within regions are very significant. Additionally, much of the between‐region mismatch errors are due to multiyear cycles in the global sea level that limit the ability of simple means to capture sea level accurately. We demonstrate that variability in sea level records over periods 2–30 years has increased during the past 50 years in most ocean basins.

Agricultural Practices Influence Flow Regimes of Headwater Streams in Western Iowa

Agricultural tillage influences runoff and infiltration, but consequent effects on watershed hydrology are poorly documented. This study evaluated 25 yr (1971-1995) hydrologic records from four first-order watersheds in Iowa's loess hills. Two watersheds were under conventional tillage and two were under conservation (ridge) tillage, one of which was terraced. All four watersheds grew corn (Zea mays L.) every year. Flow-frequency statistics and autoregressive modeling were used to determine how conservation treatments influenced stream hydrology. The autoregressive modeling characterized variations in discharge, baseflow, and runoff at multi-year, annual, and shorter time scales. The ridge-tilled watershed (nonterraced) had 47% less runoff and 36% more baseflow than the conventional watershed of similar landform and slope. Recovery of baseflow after drought was quicker in the conservation watersheds, as evidenced by 365-d moving average plots, and 67% greater baseflow during the driest 2 yr. The two conventional watersheds were similar, except the steeper watershed discharged more runoff and baseflow during short (<30 d), wet periods. Significant multi-year and annual cycles occurred in all variables. Under ridge-till, seasonal (annual-cycle) variations in baseflow had greater amplitude, showing the seasonality of subsurface contaminant movement could increase under conservation practices. However, deviations from the modeled cycles of baseflow were also more persistent under conservation practices, indicating baseflow was more stable. Indeed, flow-frequency curves showed wet-weather discharge decreased and dry-weather discharge increased under conservation practices. Although mean discharge increased in the conservation watersheds, variance and skewness of daily values were smaller. Ridge tillage with or without terraces increased stream discharge but reduced its variability.

Intrinsic and climatic factors in North-American animal population dynamics

BackgroundExtensive work has been done to identify and explain multi-year cycles in animal populations. Several attempts have been made to relate these to climatic cycles. We use advanced time series analysis methods to attribute cyclicities in several North-American mammal species to abiotic vs. biotic factors.ResultsWe study eleven century-long time series of fur-counts and three climatic records – the North Atlantic Oscillation (NAO), the El-Niño-Southern Oscillation (ENSO), and Northern Hemisphere (NH) temperatures – that extend over the same time interval. Several complementary methods of spectral analysis are applied to these 14 times series, singly or jointly. These spectral analyses were applied to the leading principal components (PCs) of the data sets. The use of both PC analysis and spectral analysis helps distinguish external from intrinsic factors that influence the dynamics of the mammal populations.ConclusionsOur results show that all three climatic indices influence the animal-population dynamics: they explain a substantial part of the variance in the fur-counts and share characteristic periods with the fur-count data set. In addition to the climate-related periods, the fur-count time series also contain a significant 3-year period that is, in all likelihood, caused by biological interactions.

The Limnology of Summer Camp Pit Lake: A Case Study

Surface water bodies are expected to form in several pits at the Getchell Open Pit Mine after mining has ceased due to inflowing surface and ground water. Predicting the long-term geochemical behavior of the pit water is important in assessing potential environmental effects. One of the pits, the Summer Camp Pit, began to develop a pit lake in 1991 when dewatering ceased and the pit was used to store water pumped from underground operations. This provided a field-scale opportunity to identify the controls on lake water chemistry and determine the effects of seasonal mixing events on long-term chemical behavior. During a five-year period (1996-2001), a number of physical, chemical and mineralogical characteristics of the lake were monitored with the intent of using this information as a basis for predicting long-term geochemical behavior of future lakes in the other pits. Seasonal and multiyear cycles were identified within the water column. These cycles were influenced by climatic changes and element and sediment loadings of inflow to the lake. Stratification occurred, with the metalimnion or active layer of the lake evolving from a low total dissolved solids (TDS), alkaline water to a high TDS, neutral to mildly acidic water, until turnover occurred due to density variations between the metalimnion and epilimnion, completely mixing the layers. A hypolimnion that formed has the potential to stabilize metals in the basal sediments as sulfide minerals below a chemolimnion in the lake. Longer-term events also appear to involve the hypolimnion. The monitoring program demonstrated the dynamic nature of a pit lake and how the complex limnology can affect seasonal water quality. Such considerations are important in interpreting water quality from pit lakes and in selecting monitoring data to use when constructing mathematical models for predicting changes in water quality.

Latitudinal Gradients of Trophics in Ural Macrolepidoptera: The Role of Food Quality

The Macrolepidoptera fauna of the Urals, from the southern to the northern boundary of the forest zone (i.e., from the forest–steppe of the Southern Urals to the forest–tundra of the Polar Urals) has been analyzed. It has been demonstrated that the proportion of Lepidoptera feeding on woody plants, including evergreens, increases in this direction. Among the Heterocera, the proportion of species feeding on graminoids decreases; in the Polar Urals, none of these species is specialized. The food spectrum is particularly variable in noctuids and almost invariable in geometrids and Rhopalocera. It is assumed that foods with a low nutrient value (grasses, mosses, lichens, plant debris, wood, and roots of various plants) prevent Macrolepidoptera species from spreading in the Subarctic region. In the Polar Urals, multiyear developmental cycles and wintering at the larval stage are related to feeding on these types of food.

Helminth parasites of the southern sea otter Enhydra lutris nereis in central California: abundance, distribution and pathology.

From October 1997 to May 2001, the gastrointestinal tracts from 162 beach-cast southern sea otters Enhydra lutris nereis were examined for helminth parasites and associated lesions. Carcasses were collected opportunistically in central California between Pt. San Pedro and Pt. Arguello. The primary goals of this study were to examine spatial and temporal variability in mortality due to parasite infection, identify factors associated with increased risk of infection, and illustrate the process of intestinal perforation by Profilicollis spp. Two genera and 4 species of acanthocephalans (Profilicollis altmani, P. kenti, P. major, Corynosoma enhydri) were found in 46.3% (Profilicollis spp.) and 94.4% (C. enhydri) of the carcasses examined. Three species of Digenea (Microphallus pirum, M. nicolli, Plenosoma minimum) were found in 47% of carcasses, at times in massive numbers (> 3000 per cm2). This is the first report of the latter 2 species from the sea otter. Mortality resulting from infection by Profilicollis spp. occurred in 13.0% (n = 21) of sampled carcasses, either directly, due to perforation of the intestinal wall and peritonitis (9.9%, n = 16), or indirectly, due to inhibition of host nutrient uptake or depletion of host energy reserves to fight chronic infections (3.1%, n = 5). The most massive infections (< 8760 parasites), and all cases of intestinal perforation occurred in carcasses infected by P. altmani and/or P. kenti. Mortality due to infection by Profilicollis spp. occurred more frequently among juvenile and old-adult females (chi2 = 17.479, df = 9, p = 0.045) from sand and mixed habitats in Monterey and Santa Cruz in the north of the sea otter range (chi2 = 9.84, df = 4, p = 0.045). Spatial differences in sea otter mortality coincided with the relative distributions of Profilicollis altmani, P. kenti, and P. major, and may reflect differences in sea otter diet, or differences in intensity of infection in intermediate hosts. Mortality rate due to infection by Profilicollis spp. decreased between 1998 and 2001, though differences were not significant (chi2 = 3.983, df = 3, p = 0.40), and may vary on multi-year cycles due to environmental factors such as density of definitive hosts (e.g. the surf scoter Melanitta perspicillata), or El Niño. Corynosoma enhydri did not cause significant damage to the intestine of the host, even when present in great numbers.