Stochastic modeling of aphid population growth with nonlinear, power-law dynamics

This paper develops a deterministic and a stochastic population size model based on power-law kinetics for the black-margined pecan aphid. The deterministic model in current use incorporates cumulative-size dependency, but its solution is symmetric. The analogous stochastic model incorporates the prolific reproductive capacity of the aphid. These models are generalized in this paper to include a delayed feedback mechanism for aphid death. Whereas the per capita aphid death rate in the current model is proportional to cumulative size, delayed feedback is implemented by assuming that the per capita rate is proportional to some power of cumulative size, leading to so-called power-law dynamics. The solution to the resulting differential equations model is a left-skewed abundance curve. Such skewness is characteristic of observed aphid data, and the generalized model fits data well. The assumed stochastic model is solved using Kolmogrov equations, and differential equations are given for low order cumulants. Moment closure approximations, which are simple to apply, are shown to give accurate predictions of the two endpoints of practical interest, namely (1) a point estimate of peak aphid count and (2) an interval estimate of final cumulative aphid count. The new models should be widely applicable to other aphid species, as they are based on three fundamental properties of aphid population biology.     

Forecasting migration of cereal aphids (Hemiptera: Aphididae) in autumn and spring

The migration of cereal aphids and the time of their arrival on winter cereal crops in autumn and spring are of particular importance for plant disease (e.g. barley yellow dwarf virus infection) and related yield losses. In order to identify days with migration potentials in autumn and spring, suction trap data from 29 and 45 case studies (locations and years), respectively, were set‐off against meteorological parameters, focusing on the early immigration periods in autumn (22 September to 1 November) and spring (1 May to 9 June). The number of cereal aphids caught in a suction trap increased with increasing temperature, global radiation and duration of sunshine and decreased with increasing precipitation, relative humidity and wind speed. According to linear regression analyses, the temperature, global radiation and wind speed were most frequently and significantly associated with migration, suggesting that they have a major impact on flight activity. For subsequent model development, suction trap catches from different case studies were pooled and binarily classified as days with or without migration as defined by a certain number of migrating cereal aphids. Linear discriminant analyses of several predictor variables (assessed during light hours of a given day) were then performed based on the binary response variables. Three models were used to predict days with suction trap catches ≥1, ≥4 or ≥10 migrating cereal aphids in autumn. Due to the predominance of Rhopalosiphum padi individuals (99.3% of total cereal aphid catch), no distinction between species (R. padi and Sitobion avenae) was made in autumn. As the suction trap catches were lower and species dominance changed in spring, three further models were developed for analysis of all cereal aphid species, R. padi only, and Metopolophium dirhodum and S. avenae combined in spring. The empirical, cross‐classification and receiver operating characteristic analyses performed for model validation showed different levels of prediction accuracy. Additional datasets selected at random before model construction and parameterization showed that predictions by the six migration models were 33–81% correct. The models are useful for determining when to start field evaluations. Furthermore, they provide information on the size of the migrating aphid population and, thus, on the importance of immigration for early aphid population development in cereal crops in a given season.     

Alate immigration disrupts soybean aphid suppression by predators

Natural enemies suppress many aphid populations, and yet, population outbreaks sometimes occur. The reasons predation fails to suppress such outbreaks are not clearly understood. While manipulating predators to examine their role in soybean aphid population growth, a natural immigration of soybean aphids occurred that enabled us to compare the roles immigration and predation played in population growth. Using predator exclusion cages, we found that predation on the top of the plant accounted for 42.3 ± 11.4% (mean ± SE) reduction in aphid population growth rates. When 90–100% of the canopy was exposed, predation failed to reduce aphid population growth because winged immigrants colonized plants, with an observed 6‐fold increase in alates compared to plants completely covered or exposing only the top nodes (approximately 10% of the total canopy). We conclude that reproduction by immigrants contributed to population growth rates sufficiently to compensate for predation. These results demonstrate that immigration can counteract high levels of predation and lead to aphid population growth rates that could result in outbreak population densities.     

Coccinellid immigration to infested host patches influences suppression of Aphis glycines in soybean

Generalist natural enemies may be well adapted to annual crop systems in which pests and natural enemies re-colonize fields each year. In addition, for patchily-distributed pests, a natural enemy must disperse within a crop field to arrive at infested host patches. As they typically have longer generation times than their prey, theory suggests that generalist natural enemies need high immigration rates to and within fields to effectively suppress pest populations. The soybean aphid, Aphis glycines Matsumura, is a pest of an annual crop and is predominantly controlled by coccinellids. To test if rates of coccinellid arrival at aphid-infested patches are crucial for soybean aphid control, we experimentally varied coccinellid immigration to 1 m² soybean patches using selective barriers and measured effects on A. glycines populations. In a year with low ambient aphid pressure, naturally-occurring levels of coccinellid immigration to host patches were sufficient to suppress aphid populations, while decreasing coccinellid immigration rates resulted in large increases in soybean aphid populations within infested patches. Activity of other predators was low in this year, suggesting that most of the differences in aphid population growth were due to changes in coccinellid immigration. Alternatively, in a year in which alate aphids continually colonized plots, aphid suppression was incomplete and increased activity of other predatory taxa contributed to adult coccinellid predation of A. glycines. Our results suggest that in a system in which natural enemy populations cannot track pest populations through reproduction, immigration of natural enemies to infested patches can compensate and result in pest control.     

Variation in and correlation between intrinsic rate of increase and carrying capacity

Intrinsic population growth rate and density dependence are fundamental components of population dynamics. Theory suggests that variation in and correlations between these parameters among patches within a population can influence overall population size, but data on the degree of variation and correlation are rare. Replicate populations of a specialist aphid (Chaetosiphon fragaefolii) were followed on 11 genotypes of host plant (Fragaria chiloensis) in the greenhouse. Population models fit to these census data provide estimates of intrinsic growth rate and carrying capacity for aphid populations on each plant genotype. Growth rate and carrying capacity varied substantially among plant genotypes, and these two parameters were not significantly correlated. These results support the existence of spatial variation in population dynamic parameters; data on frequency distributions and correlations of these parameters in natural populations are needed for evaluation of the importance of variation in growth rate and density dependence for population dynamics in the field.     

Effect of the timing of insecticide applications on infestation by Cavariella aegopodii Scop,on carrots*

The residual effectiveness of demeton-methyl and menazon sprays applied to carrot plants was compared in the laboratory using Cavariella aegopodii Scop, and more observations were made in the field, where applications of both insecticides were timed in relation to the observed immigration period of the aphid. The relative field performances confirmed those found in the laboratory and, as the aphid population control exercised was inversely proportional to the amount of alate immigration occurring after the sprays had become ineffective, the more persistent menazon was progressively superior to demeton-methyl the nearer they were applied to the beginning of immigration. A single spray application of either material towards the end of immigration gave a similar overall control of aphid numbers to that given by disulfoton granules applied at sowing time. To minimize colonization, two spray applications spanning the immigration peak were required and, with 2 weeks between the demeton-methyl sprays and 3 between those of menazon, the highest degree of control was obtained when the first application was made 7–10 days after the beginning of immigration.     

Response of Insect Relative Growth Rate to Temperature and Host-Plant Phenology: Estimation and Validation from Field Data

Between 1975 to 2011, aphid Relative Growth Rates (RGR) were modelled as a function of mean outdoor temperature and host plant phenology. The model was applied to the grain aphid Sitobion avenae using data on aphid counts in winter wheat at two different climate regions in France (oceanic climate, Rennes (western France); continental climate, Paris). Mean observed aphid RGR was higher in Paris compared to the Rennes region. RGR increased with mean temperature, which is explained by aphid reproduction, growth and development being dependent on ambient temperature. From the stem extension to the heading stage in wheat, there was either a plateau in RGR values (Rennes) or an increase with a maximum at heading (Paris) due to high intrinsic rates of increase in aphids and also to aphid immigration. From the wheat flowering to the ripening stage, RGR decreased in both regions due to the low intrinsic rate of increase in aphids and high emigration rate linked to reduced nutrient quality in maturing wheat. The model validation process showed that the fitted models have more predictive power in the Paris region than in the Rennes region.     

Nonlinear stochastic modeling of aphid population growth

This paper develops a stochastic population size model for the black-margined pecan aphid. Prajneshu [Prajneshu, A nonlinear statistical model for aphid population growth. J. Indian Soc. Agric. Statist. 51 (1998), p. 73] proposes a novel nonlinear deterministic model for aphid abundance. The per capita death rate in his model is proportional to the cumulative population size, and the solution is a symmetric analytical function. This paper fits Prajneshu's deterministic model to data. An analogous stochastic model, in which both the current and the cumulative aphid counts are state variables, is then proposed. The bivariate solution of the model, with parameter values suggested by the data, is obtained by solving a large system of Kolmogorov equations. Differential equations are derived for the first and second order cumulants, and moment closure approximations are obtained for the means and variances by solving the set of only five equations. These approximations, which are simple for ecologists to calculate, are shown to give accurate predictions of the two endpoints of applied interest, namely (1) the peak aphid count and (2) the final cumulative aphid count.     

Immigration can destabilize tri-trophic interactions: implications for conservation of top predators

Top predators often have large home ranges and thus are especially vulnerable to habitat loss and fragmentation. Increasing connectance among habitat patches is therefore a common conservation strategy, based in part on models showing that increased migration between subpopulations can reduce vulnerability arising from population isolation. Although three-dimensional models are appropriate for exploring consequences to top predators, the effects of immigration on tri-trophic interactions have rarely been considered. To explore the effects of immigration on the equilibrium abundances of top predators, we studied the effects of immigration in the three-dimensional Rosenzweig-MacArthur model. To investigate the stability of the top predator equilibrium, we used MATCONT to perform a bifurcation analysis. For some combinations of model parameters with low rates of top predator immigration, population trajectories spiral towards a stable focus. Holding other parameters constant, as immigration rate is increased, a supercritical Hopf bifurcation results in a stable limit cycle and thus top predator populations that cycle between high and low abundances. Furthermore, bistability arises as immigration of the intermediate predator is increased. In this case, top predators may exist at relatively low abundances while prey become extinct, or for other initial conditions, the relatively higher top predator abundance controls intermediate predators allowing for non-zero prey population abundance and increased diversity. Thus, our results reveal one of two outcomes when immigration is added to the model. First, over some range of top predator immigration rates, population abundance cycles between high and low values, making extinction from the trough of such cycles more likely than otherwise. Second, for relatively higher intermediate predator migration rates, top predators may exist at low values in a truncated system with impoverished diversity, again with extinction more likely.     

Structured models of metapopulation dynamics

I develop models of metapopulation dynamics that describe changes in the numbers of individuals within patches. These models are analogous to structured population models, with patches playing the role of individuals. Single species models which do not include the effect of immigration on local population dynamics of occupied patches typically lead to a unique equilibrium. The models can be used to study the distributions of numbers of individuals among patches, showing that both metapopulations with local outbreaks and metapopulations without outbreaks can occur in systems with no underlying environmental variability. Distributions of local population sizes (in occupied patches) can vary independently of the total population size, so both patterns of distributions of local population sizes are compatible with either rare or common species. Models which include the effect of immigration on local population dynamics can lead to two positive equilibria, one stable and one unstable, the latter representing a threshold between regional extinction and persistence.     

Aphid colony turn‐over influences the spatial distribution of the grain aphid Sitobion avenae over the wheat growing season

1 Temporary habitats are characterized by the appearance and disappearance of patches in which resources are available for a limited period only. Organisms living in those environments usually exhibit adaptive traits, such as a high ability to find and exploit new patches. Among them are phytophagous insects, such as crop pests living in agroecosystems. Understanding how phytophagous insects invade a new patch is of great agricultural importance. 2 Here, we investigated how aphids colonize a wheat field by studying the spatial and temporal dynamics of their populations at large (field) and fine (group of host plants) scales. 3 The sampling design consisted of counting and locating aphid colonies within 30 0.25 m² squares randomly spaced in a 1.5‐ha winter wheat field over 2 months. All colonies were precisely located within the squares and their composition in terms of morphs was determined. 4 We show that: (i) immigration of winged aphids was a major factor driving the aphid population dynamics during a large part of the season and (ii) within the field, populations established late in the growing season. Aggregated, populations of aphids became progressively homogeneously distributed at the field scale. At the scale of a 0.25 m² square, infested plants were clustered in randomly distributed small patches, and aphid colonies experienced high extinction rates, suggesting failure in population establishment. 5 Because immigration may considerably influence both population dynamics and spatial distribution, our study suggests that future predictive models should give a greater weight to spring immigrants.     

Influential factors for natal dispersal in an avian island metapopulation

Dispersal is a key parameter in evolutionary, demographic and conservation theory, but the factors influencing dispersal between populations are rarely known, and the contribution of immigrants to population stability remains uncertain. Using dispersal data from nine island populations of song sparrows, we show that female and male immigrants responded differently to population structure: in females, immigration varied with adult sex ratio; whereas immigration by males was more influenced by population density. These patterns are consistent with the hypothesis that intra-sexual competition for breeding resources influenced recruitment patterns. Immigrants often constituted a substantial fraction of local population size, and in six cases immigration by females prevented the extirpation of that sex from the island. Breeding vacancies and extirpations may have been more likely in females because their apparent survival was lower than in males. Local recruitment and immigration varied markedly among islands, perhaps as consequence of island size and isolation. Overall, our results suggest that immigration varied with local demography in a sex-specific way, stabilized population numbers and reduced extinction rates in the smallest populations.     

Non-linear feedback processes and a latitudinal gradient in the climatic effects determine green spruce aphid outbreaks in the UK

The role of climatic fluctuations in determining the dynamics of insect populations has been a classical problem in population ecology. Here, we use long-term annual data on green spruce aphid populations at nine localities in the UK for determining the importance of endogenous processes, local weather and large-scale climatic factors. We rely on diagnostic and modelling tools from population dynamic theory to analyse these long-term data and to determine the role of the North Atlantic Oscillation (NAO) and local weather as exogenous factors influencing aphid dynamics. Our modelling suggests that the key elements determining population fluctuations in green spruce aphid populations in the UK are the strong non-linear feedback structure, the high potential for population growth and the effects of winter and spring weather. The results indicate that the main effect of the NAO on green spruce aphid populations is operating through the effect of winter temperatures on the maximum per capita growth rate (R_m). In particular, we can predict quite accurately the occurrence of an outbreak by using a simple logistic model with weather as a perturbation effect. However, model predictions using different climatic variables showed a clear geographical signature. The NAO and winter temperature were best for predicting observed dynamics toward the southern localities, while spring temperature was a much better predictor of aphid dynamics at northern localities. Although aphid species are characterized by complex life-cycles, we emphasize the value of simple and general population dynamic models in predicting their dynamics.     

Population responses of a conifer-dwelling aphid to seasonal changes in its host

Abstract.  1. Current evidence suggests that seasonal changes in spruce needle sap nutrients have a decisive influence on green spruce aphid ( Elatobium abietinum ) population density, but the mechanisms of population change, the roles of development rate, fertility and mortality, and the existence of density-dependent processes, are not clearly understood.
2. Experimental studies of aphid populations were conducted in controlled environments to estimate seasonal patterns in aphid mean relative growth rate, prenatal development, fertility, and mortality. Studies were also made of the effect of aphid crowding on vital rates.
3. Independent of the degree of aphid crowding, seasonal changes in the amino acid concentration of needle sap were tracked by aphid growth rate, fertility (and adult size), but not by rates of aphid mortality. The most pronounced change in vital rates, and the one most likely to drive seasonal population change, was in fertility. Prenatal development time actually became shorter in periods when nutrients were scarce, but the resulting adult aphids were smaller and less fertile than during periods of improved nutrition.
4. Density dependence of vital rates was only observed during mid-summer when nutrients were least available. Mortality, growth rate, and prenatal development were the most strongly density-dependent processes. In contrast, there was no evidence that fertility rates were likely to respond to crowding.
5. There were no important differences between populations reared on small, potted spruce trees and those on plantation trees aged 25 years. This gives confidence that demographic data from a variety of field and laboratory sources could be used to compile data appropriate for population models.     

Sublethal effects of insecticides on the intrinsic rate of increase of cotton aphid

Insecticides are often implicated in causing outbreaks of the cotton aphid, Aphis gossypii (Glover) (Homoptera: Aphididae), through stimulation of reproduction. In this study we report the sublethal effects of dosages of bifenthrin, acephate, carbofuran or pyriproxifen on cotton aphid reproduction. We could not detect any increase or decrease in the intrinsic rate of increase of cotton aphids exposed to bifenthrin, acephate or carbofuran. However, we did detect some increases in the net reproductive rate of aphids treated with bifenthrin justifying further investigation of the effect on reproduction by this insecticide. Trends based on simple linear regression models suggest that sublethal dosages of bifenthrin or carbofuran have a negative impact on aphid population growth as dosages increase. These data suggest that stimulation of reproduction by these insecticides probably does not play a major role in cotton aphid outbreaks or resurgence. Pyriproxyfen is a juvenoid currently used for control of whiteflies in cotton. It demonstrated significant activity towards cotton aphid reared on treated cotton in our bioassays. Pyriproxyfen caused sterility in most aphids exposed to dosages exceeding 1 ppm, and reduced aphid longevity by approximately 50%. However, it did not appear to greatly influence the reproductive potential or longevity of reproductively mature aphids. A field study indicates that pyriproxyfen affects cotton aphid population structure and may have potential in managing cotton aphid outbreaks. Modifying aphid population structure and growth through the use of juvenoids such as pyriproxifen may prove to be an effective proactive approach to pest control without adversely impacting beneficial organisms or causing pest resurgence.     

The demographic drivers of local population dynamics in two rare migratory birds

The exchange of individuals among populations can have strong effects on the dynamics and persistence of a given population. Yet, estimation of immigration rates remains one of the greatest challenges for animal demographers. Little empirical knowledge exists about the effects of immigration on population dynamics. New integrated population models fitted using Bayesian methods enable simultaneous estimation of fecundity, survival and immigration, as well as the growth rate of a population of interest. We applied this novel analytical framework to the demography of two populations of long-distance migratory birds, hoopoe Upupa epops and wryneck Jynx torquilla, in a study area in south-western Switzerland. During 2002–2010, the hoopoe population increased annually by 11%, while the wryneck population remained fairly stable. Apparent juvenile and adult survival probability was nearly identical in both species, but fecundity and immigration were slightly higher in the hoopoe. Hoopoe population growth rate was strongly correlated with juvenile survival, fecundity and immigration, while that of wrynecks strongly correlated only with immigration. This indicates that demographic components impacting the arrival of new individuals into the populations were more important for their dynamics than demographic components affecting the loss of individuals. The finding that immigration plays a crucial role in the population growth rates of these two rare species emphasizes the need for a broad rather than local perspective for population studies, and the development of wide-scale conservation actions.     

Nestboxes and immigration drive the growth of an urban Peregrine Falcon Falco peregrinus population

Drivers of wildlife population dynamics are generally numerous and interacting. Some of these drivers may impact demographic processes that are difficult to estimate, such as immigration into the focal population. Populations may furthermore be small and subject to demographic stochasticity. All of these factors contribute to blur the causal relationship between past management action and current population trends. The urban Peregrine Falcon Falco peregrinus population in Cape Town, South Africa, increased from three pairs in 1997 to 18 pairs in 2010. Nestboxes were installed over this period to manage the interface between new urban pairs of Falcons and the human users of colonized buildings, and incidentally to improve breeding success. We used integrated population models (IPMs) formally to combine information from a capture–mark–recapture study, monitoring of reproductive success and counts of population size. As all local demographic processes were directly observed, the IPM approach also allowed us to estimate immigration by difference. The provision of nestboxes, as a possible stimulant of population growth, improved breeding success and accounted for an estimated 3–26% of the population increase. The most important driver of growth, however, was immigration. Despite low sample sizes, the IPM approach allowed us to obtain relatively precise estimates of the population‐level impact of nestbox deployment. The goal of conservation interventions is often to increase population size, so the effectiveness of such interventions should ideally be assessed at the population level. IPMs are powerful tools in this context for combining demographic information that may be limited due to small population size or practical constraints on monitoring. Our study quantitatively documented both the immigration process that led to growth of a small population and the effect of a management action that helped the process.     

The susceptibility of verieties of carrot to attack by the aphid, Cavariella aegopodii (Scop.)

Representative varieties from the carrot groups, Chantenay, Nantes, Berlikum and Autumn King, together with three Australian varieties, were tested for susceptibility to attack by Cavariella aegopodii (Scop.). Tests were done at different average temperatures in cages in the insectary by inoculating plants with apterous forms of the aphid and frequently checking the extent of colonization over the next 20 or so days. Field sowings of the varieties were also made in each of 3 years, and over the immigration period and the subsequent population development and decline of the aphid, regular counts were made of the alates settling on a standard number of plants of each variety, and of the progeny produced. Some differences in susceptibility to attack were noted but, because the main development of C. aegopodii on field carrots is limited to two generations, these were too small to be of practical value in terms of plant resistance, and on all varieties large numbers of aphids could be found. Although the Australian variety Osborne Park was thought to have some resistance to C. aegopodii in New Zealand, it proved to be of average susceptibility. Autumn King appeared to be the most aphidsusceptible variety but could be tolerant to motley dwarf virus. Nantes was not as tolerant to aphid attack as the other varieties and as it is also intolerant to motley dwarf virus, might suffer much damage in years favouring aphid expansion. Berlikum seemed to be the least susceptible to aphid attack. Temperature differences affected expressions of varietal susceptibility less than they affected aphid fecundity and a few degrees increase in temperature more than halved the number of young born in a generation.     

Population dynamics of the bird cherry‐oat aphid,Rhopalosiphum padi (L.), during the autumn and winter: a modelling approach

1 A simulation model was developed to investigate the inter‐relationship of factors influencing the population dynamics of the bird cherry‐oat aphid (Rhopalosiphum padi (L.)) in barley crops during the autumn and winter. 2 The model incorporated algorithms describing alate immigration, development and survival of adults and nymphs, fecundity and morph determination in newly born nymphs. 3 The model was validated against pest outbreaks in barley fields in south‐east England. 4 It simulated accurately the size of the outbreaks with predictions of peak aphid populations within 20% of the observed in all but one case. Similarly, all but one of the year‐sowing date combination predictions of timing of peak abundance fell within 14 days of the observed. 5 A sensitivity analysis of the model highlighted the relative importance of various population processes in determining simulated aphid population dynamics; decreasing mortality rates of apterous nymphs by as little as 5% over the autumn and winter increased peak densities by as much as 60‐fold, whereas increasing daily temperatures by only 1 °C more than doubled peak aphid abundance. 6 The model identified our understanding of the mechanisms of aphid mortality as a limiting factor in the accurate prediction of R. padi outbreaks in the field.     

Population Dynamics of Aphids on Cereals: Digging in the Time-Series Data to Reveal Population Regulation Caused by Temperature

Aphid populations show periodic fluctuations and many causes are attributed to their dynamic. We investigated the regulation by temperature of the aphid populations composed of Metopolophium dirhodum, Sitobion avenae, and Rhopalosiphum padi on winter wheat using a 24 years long time series data. We computed the sum of daily temperatures above 5°C, the threshold temperature for aphid development, and the sum of daily temperatures within the [0(threshold for wheat development),5] °C interval. Applying Generalised Additive Model framework we tested influences of temperature history expressed via degree days before the start of the aphid immigration on the length of their occurrence. We aimed to estimate the magnitude and direction of this influence, and how far to the past before the start of the aphid season the temperature effect goes and then identify processes responsible for the effect. We fitted four models that differed in the way of correcting for abundance in the previous year and in specification of temperature effects. Abundance in the previous year did not affect the length of period of aphid population growth on wheat. The temperature effect on the period length increased up to 123 days before the start of the current season, i.e. when wheat completed vernalization. Increased sum of daily temperatures above 5°C and the sum of daily temperatures within the [0,5] °C interval both shortened the length of period of aphid population growth. Stronger effect of the latter suggests that wheat can escape from aphid attacks if during winter temperatures range from 0 to 5°C. The temperature influence was not homogeneous in time. The strongest effect of past temperature was about 50 to 80 and 90 to 110 days before the beginning of the current aphid season indicating important role of termination of aphid egg dormancy and egg hatching.