Sergio A. Estay (corresponding author), Center for Advanced Studies in Ecology and Biodiversity, Pontificia Universidad Católica de Chile, Casilla 114-D, Santiago, CP 6513677, Chile. E-mail: email@example.com
Climate change could profoundly affect the status of agricultural insect pests. Several approaches have been used to predict how the temperature and precipitation changes could modify the abundances, distributions or status of insect pests. In this article it is demonstrated how the use of simple models, such as Ricker’s classic equation, including a mechanistic representation of the influence of exogenous forces may improve our predictive capacity of the dynamic behaviour of insect populations. Using data from classical experiments in population ecology, we evaluate how temperature and humidity influence the density of two stored grain insect pest, Tribolium confusum and Callosobruchus chinensis, and then, using the A2 and B2 scenarios proposed by the Intergovernmental Panel on Climate Change and the previous modelling, we develop predictions over the future pest status of T. confusum along South America austral region, and specifically for eight cities in the continental Chilean territory. Tribolium confusum and C. chinensis show qualitatively different responses to the exogenous forcing of temperature and humidity, respectively. Our simulations predict a change in the equilibrium density of T. confusum from 10 to 14% under the moderate B2 scenario and 12 to 22% under the extreme A2 scenario to the period, 2071–2100. Both results imply a severe change in the pest status of this species in the southern region. This study illustrates how the use of theoretically based models may improve our predictive capacity. This approach provides an opportunity to examine the link between invasive species and climate change and how new suitable habitat may become available for species whose niche space is limited in some degree by climatic conditions. The use of different scenarios allows us to examine the sensitivity of the predictions, and to improve the communication with the general public and decision-makers; a key aspect in integrated pest management.
In temperate regions, most insects have their growth period during the warmer part of the year (Bale et al. 2002). Due to this, species whose niche space is defined by climatic regime will respond more predictably to climate change (Bale et al. 2002) while those in which the niche is limited by other abiotic or biotic factors will be less predictable (Jenkinson et al. 1996; Bale et al. 2002). In the first case, the general prediction is that if global temperatures increase, the species will shift their geographical ranges closer to the poles or to higher elevations, and increase their population size (Cammell and Knight 1992; Jenkinson et al. 1996; Woiwod 1997; Sutherst 2000; Harrington et al. 2001; Bale et al. 2002; Samways 2005). In agreement with this prediction, many examples may be found in the literature (e.g. Birch 1953; Woiwod 1997; Gordo and Sanz 2006; Olfert and Weiss 2006; Musolin 2007). In this regard, Chile offers an unique opportunity to test this hypothesis, because its territory has a clear cut gradient in climatic conditions experienced along the latitudinal extent of the country, ranging from 17°S to 55°S latitude. This allows the assessment of different hypotheses regarding the effect of current climate on animal populations and the potential effects of climate change on the distribution and abundance of animals at different latitudes.
The role of climate as an exogenous factor determining abundance and distribution has attracted the attention of ecologists since the very origin of the discipline (Elton 1924; Gause 1931; Davidson and Andrewartha 1948; Birch 1953), but even today, few solid and parsimonious theoretical frameworks are available to examine the effect of climate on population dynamics. Because of this, the quest for generalizations and for developing adequate predictive process-based models of change (Harrington et al. 2001) remains difficult.
Royama (1992) provides a simple and complete theoretical framework to evaluate the influence of exogenous factors on population dynamics. Briefly, this framework shows that the dynamics of a population may be described by studying the reproductive function (R-function). This is a mathematical function relating the changes in a populations realized per capita growth rate (R, plotted on the y axis) to the changes in population density at a given time lag (Nt−1, plotted on the x axis). The R-function may include responses to other biotic or abiotic variables on the population growth rate, as well as the effect of two or more time lags, making it a simple but comprehensive and powerful way to summarize the factors determining a species population dynamics. Royama then identifies three classes of modifications to the reproductive function (R-function) due to exogenous forces. The first two are called linear transformations. In the first, called vertical perturbation, the R-function completely displaces through the y-axis, which shifts both intercepts on the x and y axis. These changes mean that the maximum reproductive capacity and the equilibrium density (ED) are modified by the action of the exogenous factor. In the second class, called lateral perturbation, the R-function is displaced through the x-axis, changing only the intercept on this axis, in other words the ED is modified, but the maximum reproductive capacity remains unchanged. The last type of effect corresponds to non-linear transformations where the relative form of the R-function changes and it can modify both intercepts in a non-linear way. A complete description of the Royama’s classification is in Royama (1992, pp. 35–40). The use of this theoretical framework on data of several organisms has showed its utility and predictive capacity (see Lima and Berryman 2006; Lima et al. 2006; Lima and Berryman 2006; Lima et al. 2008a,b).
In this article, we use Royama’s classification to explore the effect of temperature and humidity on two stored-grains insect pest and to make predictions about the change in population dynamics, which is usually thought to be more difficult than predicting changes in geographic distributions (Bale et al. 2002). We use data from two classical experiments in population biology to parameterize and select the best population dynamics model according to the type of exogenous factor effect. We then use the selected models to evaluate the expected change in the ED under the climate change scenario in the Southern Cone of South America and especially along the Chilean territory.
Materials and Methods
Experimental data on the population fluctuations of Callosobruchus chinensis (L.) from Utida (1941), also in Royama (1992) and Tribolium confusum Duval from Park (1954) were used to evaluate different models of population dynamics. For the data from Utida’s experiments, we used the progeny produced per pair at different densities of C. chinensis under three different humidities (76, 52 and 32% HR) and one temperature (30.4°C) in the analysis. The data correspond to the density of individuals per 20 g of beans. Callosobruchus chinensis is originally from China, but now has a worldwide distribution, although it has not been reported in Chile. This species infests seeds of leguminous plants where it can complete its life cycle entirely (Royama 1992). From Park’s experiment, the time series of the density of experimental populations of T. confusum under three temperatures (34, 29, 24°C) and one humidity (70% RH) were used. We did not use time series with variable humidity because the variability in the experimental conditions was too high. In this case, the data studied correspond to the number of individuals per gram of flour (density). Tribolium confusum is another widespread pest of stored grains and flour commonly found in flour stored for a long time in houses and stores. Its present distribution in Chile ranges from latitude 17°S to 42°S approximately (Klein-Koch and Waterhouse 2000).
Population dynamics modelling
Given that these were experimental populations with a continuous supply of food and without natural enemies, their population dynamics are expected to be dominated by a first order density-dependent feedback (Berryman 1999). Hence we used a simple model of intra-specific competition, Ricker’s equation (Ricker 1954), to model the basic structure of the influence of endogenous and exogenous forces.
Ricker’s equation is:
Where Nt−1 is the abundance at time t−1; R is the realized per capita growth rate Rt = log(Nt/Nt-1); Rmax is the maximum per capita growth rate estimated for the species; K is the ED and Q is a non-linearity factor (Berryman 1999).
If the exogenous variable is symbolized by Vi, then the model representing the vertical perturbation is:
where C is a coefficient of scale.
The model representing the lateral perturbation is:
where f (Vi) is the function that represents how the ED change with the variable Vi.
These three models were evaluated using both sets of data, where the variable Vi is humidity for the Utida’s dataset and temperature for the Park’s dataset and for simplicity f (Vi) was assumed a linear function. Models were fitted by non-linear regression using the nls library in the r program (Bates and Watts 1988; R Development Core Team, 2004, available at http://www.r-project.org) and ranked according to the Bayesian Information Criterion (BIC or Schwarz Criterion; Schwarz 1978), and the minimum BIC values were selected to determine the best model.
Tribolium confusum is present and widely distributed in Chile (Klein-Koch and Waterhouse 2000), with a widely available developmental substrate (flour) and without potential natural enemies in Chile (Prado 1991). These facts support the idea that its distribution and abundance may be restricted primarily by climate. We calculated its expected ED under both current and predicted climatic conditions. To do this, we used the parameter values obtained for the best model selected for Park’s dataset, and estimated the current and expected ED of T. confusum under different scenarios of climate change in the Southern Cone and specifically in eight cities along a latitudinal gradient in Chile.
Current climatic data through Chile was obtained from Luebert and Pliscoff (2006) and Department of Geophysics, University of Chile (DGF in spanish, 2007). The mean January temperature was used in the estimation (summer seasons in the southern hemisphere, when the rate of degree days accumulation is maximum). The estimated increase in temperature for the interval, 2071–2100 through Chile was obtained from data generated by the DGF (2007) as part of the research study ‘Estudio de Variabilidad Climática en Chile para el Siglo XXI’ funded by the Chilean Comisión Nacional de Medio Ambiente (CONAMA). This study used the regional model PRECIS coupled to a global model to predict changes in temperature and precipitation along Chile with a spatial resolution of 25 km (DGF, 2007). The climatic predictions were made under two scenarios defined by the IPCC (Meehl et al. 2007), the moderate B2 scenario and the severe scenario A2. The locations of cities, current temperatures and estimated temperature increment for the interval, 2071–2100 are shown in Table 1. We used the predicted January average temperature in our estimation of ED. It must be noted that in this region, the flour is stored without climatic control facilities. This will result in high correlations between environmental temperatures and temperatures within flour storage facilities, especially in the abundant local bakeries.
Table 1. Selected cities, geographical location and current temperatures and predicted increments (from DGF, 2007) under two climate change scenarios
Current January average temperature (°C)
Estimated 2071–2100 temperature (°C)
Figures 1 and 2 show the distribution of the experimental data from Utida and Park, respectively. Each figure represents the per capita growth rate (R-function) of the species in function of the density in the previous time step (Nt-1). The intercepts with the x and y-axis are the ED and maximum per capita growth rate, respectively.
The results show that the lateral perturbation model is the best for C. chinesis according to BIC ranking (Table 2), which means that humidity modifies the equilibrium density (K) of the system. It is interesting to note that all treatments have the same intercept with y-axis (maximum per capita growth rate) but the equilibrium densities differ. Thus, C. chinesis response to humidity will be noted in equilibrium densities, but not in the population dynamics.
Table 2. Estimated parameters for each model and data set. Bayesian Information Criterion are shown, the best model selected is in bold face
R = Rmax*(1− (Nt-1/K)Q)
R = Rmax*(1− (Nt-1/K)Q + C*T)
R = Rmax*(1− (Nt-1/(A + B*T)Q)
R = Rmax*(1− (Nt-1/K)Q)
R = Rmax*(1− (Nt-1/K)Q + C*HR)
R = Rmax*(1− (Nt-1/(A + B*HR)Q)
In the case of Park’s experiment, given the strong concave form of the T. confusum data (fig. 2), we estimated the Rmax parameter using cubic splines and bootstrap to avoid convergence problems. This technique allowed us to obtain a realistic value for the parameter, which was used to fit the models. Table 2 shows the results of the fitted models.
In this case, the vertical perturbation model is the best according to BIC (Table 2). This means that temperature modifies both maximum reproductive capacity (Rmax) and equilibrium density (K) as is shown in fig. 2.
In order to estimate the expected ED along the western region of the Southern Cone, we set the value of R = 0 and Vi = Summer average temperature (temp) in equation (2) (the selected model) and then re-arrange it to solve for the value of Nt-1. ED is then expressed as:
Equation (4) allows us to obtain the expected ED given the temperature and the parameter estimates of the best model estimated in the previous step. Using this equation, ED is then expressed in the same units as in Park’s experiment (individuals/gram of flour).
Table 3 shows the result of the prediction for eight cities along Chile. Under the moderate B2 IPCC scenario, it is expected that ED of T. confusum will show an increase ranging from 10% (Concepción) to 14% (La Serena and Coyhaique). The same cities represent the extremes under the A2 IPCC scenario but with a larger increase in predicted ED (12% and 22%, respectively). Figure 3 shows the expected ED of T. confusum in all the South America’s Southern Cone.
Table 3. Predicted equilibrium densities of Tribolium confusum for eight cities along Chile (Ind/gram). Current estimations, and predictions under two climate change scenarios. Percentage of change in relation to current estimation is shown in parenthesis
B2 Scenario estimation
A2 Scenario estimation
In our results, the lateral perturbation model is shown to be the best one to represent the influence of humidity on the dynamics of C. chinensis. Previous research has shown that humidity has no influence in the oviposition rate and developmental time in the sister species C. maculatus and C. subinnotatus (Lale and Vidal 2003), which suggests that Rmax is probably not affected by humidity. Other stored products pest like Tribolium castaneum and T. confusum show similar behaviour (Howe 1956, 1960). A tentative hypothesis to explain the change in the ED is that relative humidity influences the availability of water, and insects need a larger volume of medium to satisfy their water needs when humidity decreases, which may then modify the ED in a closed system (Holdaway 1932).
In the case of T. confusum, a vertical perturbation model was found to be the best. The R-function is completely displaced vertically at each level of temperature, which implies that both Rmax and K change. It is known from previous research that temperature is inversely correlated with mortality and developmental time (Howe 1960; Cammell and Knight 1992), and positively correlated with fecundity (Park and Frank 1948). These relationships provide us with potential biological mechanisms to explain the selected vertical perturbation model: higher fecundity and shorter developmental time may both affect Rmax directly and the greater difference between birth and death rates may then displace the ED to the right when temperature increases. Given the degree of uncertainty associated to the current climate change scenario, we discuss the predicted equilibrium densities in terms of the relative changes, rather than focusing on the exact predicted values.
The predicted equilibrium densities show that in spite of the relatively similar temperature increment in the eight cities (in °C), the larger effects in population density would be at higher latitudes, due to the relative change (% change) is larger at the southern cities which implies a larger effect on the ED. These changes in densities would have two important consequences: A change in the status of the pest and an expansion of the distribution to southern latitudes. According to Klein-Koch and Waterhouse (2000), in the northern region of Chile (17°S–20°S), T. confusum is classified as an important and widespread pest, whereas in central Chile (30°S–35°S) it is considered as a locally important pest and at southern Chile as a non-pest species. Comparing our prediction for years 2071–2100 with the current estimation, it is possible to see that under the moderate B2 scenario, Temuco (38°S) would show densities similar to the current level of the northern region, (Arica, 18°S) which implies greater damages and losses and, therefore, a predicted change in the pest status from locally important to important and widespread. Under the severe A2 scenario this situation might expand to latitude 40°S. Finally, our predictions show that in Coyhaique (45°S), where T. confusum is rarely detected (Klein-Koch and Waterhouse 2000), the predicted densities might be similar to the current density in Pto. Montt (41°S) under the B2 and A2 scenario. This means that the model predicts a geographic range expansion of approximately 400 km to the south. Across South America, the highest densities could be observed in the central region of Argentina, where the expected values are around 35 to 40 individuals per gram. This would pose a serious menace to a region which concentrates on the wheat production of Argentina, a country that produces near to 14 million tons of wheat (SAGPyA, 2007).
Current predictions of insect responses to elevated temperatures is largely based on field and laboratory studies carried out over a limited range of temperatures (Bale et al. 2002), but usually this approximation is just phenomenological and the underlying mechanisms are ignored. This is the most important value of Royama’s classification of the effect of exogenous perturbation forces, for it provides a mechanistic approach to examine and decipher the effects of climatic factors on population dynamics. Moreover, this approach fits perfectly with the multimodel based inference approach, which is guided by three essential principles in science: parsimony, the use of multiple working hypotheses and the strength of evidence (Chamberlin 1890; Burnham and Anderson 2004).
Scientists now face the challenge of explaining and predicting the consequences of global climate change. This study provides an example of how the use of simple theoretically based models including exogenous perturbations may improve our predictive capacity. Moreover, this approach provides an opportunity to examine the link between invasive species and climate change (Ward and Masters 2007) and how new suitable habitat may become available for species whose niche space is limited in some degree by climatic conditions. Finally, the use of different scenarios is absolutely necessary when the reliability of the predictions is not clear, which is the case of the predicted future climate change (Cammell and Knight 1992). The use of different scenarios may allow us to examine the sensitivity of the predictions and to improve the communication of our researches to the general public and decision-makers, a key topic in pest management.
S.E. acknowledges the financial support of the CONICYT Doctoral scholarship. S.E. and M.L. acknowledge financial support from FONDAP-FONDECYT grant 1501-0001 (Program 2). F.A.L. was supported by Iniciativa Científica Milenio Grant ICM P05-002.