Intrinsic Growth Rate Research Articles

Exploring ocean pH dynamics via a mathematical modeling with the Caputo fractional derivative

AbstractGlobal warming is a complex problem with far-reaching global implications. One of its notable repercussions is the escalation of $$CO_2$$ C O 2 levels in the atmosphere, resulting in the phenomenon known as Ocean Acidification (OA). In this research, we have established a correlation between four key factors: marine species, human population, $$CO_2$$ C O 2 levels, and ocean pH. By formulating a Caputo fractional differential equation, we investigated the dynamics of these variables to evaluate the significance of this climatic phenomenon. The model analysis reveals that the rise in anthropogenic $$CO_2$$ C O 2 emissions causes a reduction in the ocean’s pH level and increases OA. This process, in turn, decreases the ocean’s ability to absorb $$CO_2$$ C O 2 , making it less effective in mitigating climate change. In this study, it was demonstrated that elevated levels of $$CO_2$$ C O 2 result in a reduction in pH levels, which in turn causes a decrease in the population of marine species that play a critical role in numerous economic sectors such as tourism, aquaculture, and fisheries. Moreover, we conducted a comprehensive analysis of the influence exerted by the intrinsic growth rate of the human population. We examined various theoretical aspects, including the assessment of existence and uniqueness. Numerical simulations are carried out to illustrate the effect of key parameters on the dynamics of the system using the generalized Adams–Bashforth–Moulton method.

A stochastic hormesis Ricker model and its application to multiple fields

Random noise pervades ecosystems and has the potential for having major impacts on the growth processes of pest populations. In this paper, we aim to investigate the impact of random perturbations on the hormesis Ricker model by considering control measures applied within each generation which can generate hormetic effects, where randomness is characterized by a uniform discrete distribution and white noise, respectively. The main results indicate that the addition of discrete randomness will make the model appear with blurred orbits when the intrinsic growth rate is large enough. The position of the random variable, at the end of each generation or within each generation, cause the blurred orbits to exhibit various forms. Moreover, the effects of variances and expectations of the discrete uniform random variable on the dynamics are evaluated. Further, the introduction of randomness increases the hormetic zone and the maximum response, but can increase or decrease the monotonically increasing interval under different parameter values. In contrast, the stochastic model characterized by white noise, exhibits only a small effect on the bifurcation diagrams with respect to the intrinsic growth rate and the hormesis, which may be attributed to the mean of its noise being zero. Finally, we fit the stochastic model to experimental hormetic data sets observed in multiple fields, and our results demonstrate that the stochastic hormesis Ricker model can capture the characteristics of these data accurately. These findings could provide valuable insights into the understanding of the complexities of pest population dynamics, with implications for better pest control, resource management and for other complex biological systems such as toxicology and drug development.

Effect of Eucalyptus globulus and Ferula assafoetida essential oils and their nanoformulations on the life table parameters of Tetranychus urticae (Acari: Tetranychidae).

One of the most damaging pests of agricultural crops across the globe is the two-spotted spider mite, Tetranychus urticae Koch. A wide variety of arthropods and plant pathogens can be controlled by essential oils, which are secondary metabolites produced by plants. It is possible to enhance the stability as well as the anti-pest efficiency of plant essential oils by encapsulation. Water distillation was used to extract the essential oils from Eucalyptus globulus and Ferula assafoetida. The chitosan nanoparticles were used to load both essential oils into nanoformulations. Studies were conducted on T. urticae life table characteristics under experimental circumstances to determine the sublethal impacts of essential oils and their nanoformulations. Intrinsic growth rate (r) for population exposed to E. globulus, F. assafoetida essential oils, their nanoformulations and the control were 0.1, 0.069, 0.051, 0.018 and 0.21 per day, respectively. F. assafoetida and E. globulus nanoformulations resulted the lowest fecundity compared to the other treatments. According the result of the lethal and sublethal effects of purified essential oils and nanoformulations of F. assafoetida and E. globulus, they would be recommended for controlling the two-spotted spider mites, T. urticae.

On the deduction and quantification of irruptive dynamics in mountain pine beetle population and proxy data

AbstractIn attempting to develop a coherent description of the irruptive dynamics of mountain pine beetle (MPB) in North America, we examined a range of cases where authors described the dependency of intrinsic population growth rates on population attack levels. In some cases, detailed population data were used, but in most cases, investigators relied on operational aerial detection survey data. We found that study conclusions varied significantly depending on the type of data analysed and the spatial and temporal dimensions of the monitoring program. The ability to detect an intrinsic Allee effect (i.e., positive density‐dependent growth for low and rising population densities) depended on the type and the intensity of the sampling effort and the extent of sampling in space and time. Consequently, not all studies were able to quantify the irruption threshold (i.e., the population density at which endemic populations may transition towards the epidemic state). Notably, in every study where an Allee effect was demonstrated, investigators also identified at least one extrinsic environmental factor (e.g., winter weather, summer drought, microclimatic effect) that was regulating its strength. Our results suggest that population surveys conducted from the ground are a necessary complement to aerial survey data if the goal is to make inferences about the irruptive potential for MPB populations and the role of environmental factors in shaping that irruptive potential.

Acclimation to warmer temperatures can protect host populations from both further heat stress and the potential invasion of pathogens.

Thermal acclimation can provide an essential buffer against heat stress for host populations, while acting simultaneously on various life-history traits that determine population growth. In turn, the ability of a pathogen to invade a host population is intimately linked to these changes via the supply of new susceptible hosts, as well as the impact of warming on its immediate infection dynamics. Acclimation therefore has consequences for hosts and pathogens that extend beyond simply coping with heat stress-governing both population growth trajectories and, as a result, an inherent propensity for a disease outbreak to occur. The impact of thermal acclimation on heat tolerances, however, is rarely considered simultaneously with metrics of both host and pathogen population growth, and ultimately fitness. Using the host Daphnia magna and its bacterial pathogen, we investigated how thermal acclimation impacts host and pathogen performance at both the individual and population scales. We first tested the effect of maternal and direct thermal acclimation on the life-history traits of infected and uninfected individuals, such as heat tolerance, fecundity, and lifespan, as well as pathogen infection success and spore production. We then predicted the effects of each acclimation treatment on rates of host and pathogen population increase by deriving a host's intrinsic growth rate (rm) and a pathogen's basic reproductive number (R0). We found that direct acclimation to warming enhanced a host's heat tolerance and rate of population growth, despite a decline in life-history traits such as lifetime fecundity and lifespan. In contrast, pathogen performance was consistently worse under warming, with within-host pathogen success, and ultimately the potential for disease spread, severely hampered at higher temperatures. Our results suggest that hosts could benefit more from warming than their pathogens, but only by linking multiple individual traits to population processes can the full impact of higher temperatures on host and pathogen population dynamics be realised.

Effects of imidacloprid combined with validamycin on the population fitness and symbiotic of Nilaparvata lugens (Hemiptera: Delphacidae)

Using a high-efficiency insecticide in combination with fungicides that have different mechanisms of action is a conventional method in the current management of brown planthopper (BPH) resistance. In this study, we investigate the separate and combined effects of the low-toxicity fungicide validamycin and the non-cross-resistant insecticide imidacloprid on the fitness and symbiosis of BPH. These research results indicate that when the proportion of active ingredients in validamycin is combined with imidacloprid at a ratio of 1:30, the toxicity ratio and co-toxicity coefficient are 1.34 and 691.73, respectively, suggesting that the combination has a synergistic effect on the control of BPH. The number of yeast-like symbiotic (YLS) and dominant symbiotic (Noda) in the imidacloprid + validamycin groups were significantly lower than the other three treatment groups (validamycin, imidacloprid, and water). The results of the study on population fitness show that the lifespan of the BPH population in validamycin, imidacloprid, and imidacloprid + validamycin was shortened. Notably, the BPH populations in the imidacloprid + validamycin groups were significantly lower than other groups in terms of average generation cycle, intrinsic growth rate, net reproduction rate, finite rate of increase, and fitness. The Real-time quantitative PCR showed that validamycin and imidacloprid + validamycin can significantly inhibit the expression of the farnesyl diphosphate farnesyl transferase gene (EC2.5.1.21) and uricase gene (EC1.7.3.3), with imidacloprid + validamycin demonstrating the most pronounced inhibitory effect. Our research results can provide insights and approaches for delaying resistance and integrated management of BPH.

Impacts of Fulvic Acid on the Toxicity of the Herbicide Atrazine to Lemna minor.

Fulvic acids (FA) are environmentally prevalent components of dissolved organic carbon. Little research has evaluated their potential influence on the bioavailability of herbicides to non-target aquatic plants. This study evaluated the potential impacts of FA on the bioavailability of atrazine (ATZ) to the aquatic plant Lemna minor. Plants were exposed to 0, 15, 30, 60, 125, and 750µg/L ATZ in media containing three FA concentrations (0, 5, and 15mg/L) in a factorial study under static conditions. Fronds were counted after 7- and 14-days exposure and intrinsic growth rates (IGR) and total frond yields were calculated for analysis. Atrazine NOAECs and LOAECs within each FA treatment series (0, 5, or 15mg/L) were identified and EC50s were estimated. NOAEC/LOAECs for yield and IGR were 60/125 µg/L except for yield in the 0mg/L-FA series (30/60) and IGR in the 5mg/L-FA series (30/60). NOAEC/LOAECs were 30/60 µg/L for all treatments and both endpoints after 14 days exposure. EC50s ranged from 88.2 to 106.1µg/L (frond production 7 DAT), 158.0-186.0µg/L (IGR, 7 DAT), 74.7-86.3µg/L (frond production, 14 DAT), and 144.1-151.3µg/L (IGR, 14 DAT). FA concentrations did not influence the toxicity of ATZ.

Dynamics of a generalist predator–prey model in closed advective environments

In this paper, we consider a two‐species generalist predator–prey model in closed advective environments. Compared with the model in open advective environments to the generalist predator–prey model, the dynamics of our system are different. It is easy to verify that the generalist predator can always invade. Meanwhile, we provide the dynamical behaviors of the model in terms of the intrinsic growth rates, the carrying capacity of both species, the predation rate, and the trophic conversion efficiency. More precisely, we establish the local/global stability of the semi‐trivial steady states and a unique positive equilibrium for the model.

Methods for comparing theoretical models parameterized with field data using biological criteria and Sobol analysis

Prey–predator models are frequently developed to investigate trophic webs and to predict the population dynamics of prey and predators. However, the parameters of these models are often implemented without empirical data and may even be chosen arbitrarily. Commonly, only a few parameters are tested regarding their sensitivity and it is rare to read about the comparison between different prey–predator models (i.e. predation function structure). Here, we propose a method to compare four prey–predator models designed for two populations. We then apply this method to select the more biologically plausible one to model a simplified agricultural trophic system, including one predator compartment (the red fox Vulpes vulpes) and one prey group compartment (small mammals). These models are based on four Holling functional responses for the predation interaction and take the prey intrinsic growth rate into account through a Verhulst logistic function. Most parameters’ values (like attack rates or growth rates) were calculated from field data or based on literature review. We then used Sobol indices to conduct parameter exploration around mean parameter values to investigate and compare the model dynamics responses. Our first results showed that under our assumptions, the two most relevant models for our case study are the saturated Holling I and II models. We were also able to discriminate that among the 6 scaled parameters that vary, the model outputs are particularly sensitive to four of them (κ: saturation rate of the environment, Tr1: characteristic intrinsic decay time of the predators, Tc: characteristic growth time of the predator via the predation on the prey and λ: saturation rate of a predator’s stomach per time unit) and much less sensitive to two others (Tr2: characteristic intrinsic growth time of the prey and Ta: characteristic decay time of the prey due to the predation). These first encouraging results open the way for the next step, which will be to adapt this model construction to more complex prey–predator systems, with several predator and/or several prey compartments.

Can competitive effects and responses of alien and native species predict invasion outcomes?

The relative competitive ability of native and alien species, which consists of competitive effect (CE) and response (CR), has often been invoked as a key determinant of invasion success. Previous studies have reported that an alien species with a high CE and/or a low CR would successfully invade a native species. However, no studies have yet empirically examined the hypothesis or tested the consistency of invasion outcomes predicted by the CE-CR framework and modern species coexistence theory (MCT). To fill this research gap, we conducted a pairwise competition experiment between five alien and five native species, quantified CE and CR based on their biomass in the absence and presence of one competitor, and predicted invasion outcomes based on both CE-CR and MCT frameworks. We have demonstrated theoretically that the CE and CR frequently measured in previous work are only approximations of interspecific competitive coefficients, and thus could not completely predict the invasion outcomes. As we expected, the invasion outcomes predicted by the CE-CR framework were partially consistent with the predictions by the MCT framework. Specifically, aliens with low CR and high CE tended to exclude natives, while aliens with high CR and low CE tended to be excluded by natives according to MCT. In contrast, pairs of stable coexistence and priority effects did not conform to the theoretical expectation. Despite the theoretical defects of the CE-CR framework, it can provide some useful value in predicting the invasion outcomes, especially when intrinsic growth rate and intraspecific competition coefficients are not available. Our study is the first to compare invasion outcomes separately derived from qualitative (the CE-CR framework) and quantitative (the MCT framework) methods. We recommend that future research should adopt quantitative approaches such as MCT as far as possible, to more comprehensively understand and predict the biotic outcomes of interacting species.

Evolution of dispersal and the analysis of a resource flourished population model with harvesting

This study explores a spatially distributed harvesting model that signifies the outcome of the competition of two species in a heterogeneous environment. The model is controlled by reaction-diffusion equations with resource-based diffusion strategies. Two different situations are maintained by the harvesting effects: when the harvesting rates are independent in space and do not exceed the intrinsic growth rate; and when they are proportional to the time-independent intrinsic growth rate. In particular, the competition between both species differs only by their corresponding migration strategy and harvesting intensity. We have computed the main results for the global existence of solutions that represent either coexistence or competitive exclusion of two competing species depending on the harvesting levels and different imposed diffusion strategies. We also established some estimates on harvesting efforts for which coexistence is apparent. Also, some numerical results are exhibited in one and two spatial dimensions, which shed some light on the ecological implementation of the model.

Optimal Rotation Age in Fast Growing Plantations: A Dynamical Optimization Problem.

Forest plantations are economically and environmentally relevant, as they play a key role in timber production and carbon capture. It is expected that the future climate change scenario affects forest growth and modify the rotation age for timber production. However, mathematical models on the effect of climate change on the rotation age for timber production remain still limited. We aim to determine the optimal rotation age that maximizes the net economic benefit of timber volume in a negative scenario from the climatic point of view. For this purpose, a bioeconomic optimal control problem was formulated from a system of Ordinary Differential Equations (ODEs) governed by the state variables live biomass volume, intrinsic growth rate, and area affected by fire. Then, four control variables were associated to the system, representing forest management activities, which are felling, thinning, reforestation, and fire prevention. The existence of optimal control solutions was demonstrated, and the solutions of the optimal control problem were also characterized using Pontryagin's Maximum Principle. The solutions of the model were approximated numerically by the Forward-Backward Sweep method. To validate the model, two scenarios were considered: a realistic scenario that represents current forestry activities for the exotic species Pinus radiata D. Don, and a pessimistic scenario, which considers environmental conditions conducive to a higher occurrence of forest fires. The optimal solution that maximizes the net benefit of timber volume consists of a strategy that considers all four control variables simultaneously. For felling and thinning, regardless of the scenario considered, the optimal strategy is to spend on both activities depending on the amount of biomass in the field. Similarly, for reforestation, the optimal strategy is to spend as the forest is harvested. In the case of fire prevention, in the realistic scenario, the optimal strategy consists of reducing the expenses in fire prevention because the incidence of fires is lower, whereas in the pessimistic scenario, the opposite is true. It is concluded that the optimal rotation age that maximizes the net economic benefit of timber volume in P. radiata plantations is 24 and 19 years for the realistic and pessimistic scenarios, respectively. This corroborates that the presence of fires influences the determination of the optimal rotation age, and as a consequence, the net economic benefit.

ADDRESSING THE INTENSITY OF CHANGES IN THE PREHISTORIC POPULATION DYNAMICS: POPULATION GROWTH RATE ESTIMATIONS IN THE CENTRAL BALKANS EARLY NEOLITHIC

ABSTRACTThe intensity of changes in the population dynamics of the Early Neolithic (ca. 6250–5300 cal BC) communities in the Central Balkans was addressed by estimating the growth rate values. The Bayesian approach (Crema and Shoda 2021) of estimating intrinsic growth rates by fitting different models of population growth was applied to radiocarbon dates from the Early Neolithic sites in Serbia. We explored two possible episodes of population growth based on the results of the population dynamics reconstruction using the summed calibrated radiocarbon probability distributions (SPD) method. The results have shown that, within the first episode of growth, the intrinsic growth rate mean values are higher than the estimated continental average (between 1% and 2%). The results indicate a sudden and fast rise in population size, possibly due to the influx of the new population settling in the region at the beginning of the Neolithic. Lower values for the second episode could indicate more gradual population growth due to the mechanisms associated with the Neolithic Demographic Transition and the rise in fertility.

Greater capacity for division of labor brings greater benefits to an invasive clonal plant than its native partners

The majority of problematic invasive plants exhibit clonal growth, and the clonal traits are widely recognized as critical determinants contributing to their invasiveness. Division of labor represents a crucial advantage associated with clonal growth; therefore, it is reasonable to anticipate that this particular trait may confer a growth advantage upon invasive clonal species in comparison to native ones. To test this hypothesis, we conducted a comparative experiment in the greenhouse involving the highly invasive plant Alternanthera philoxeroides, its native congener A. sessilis, and its native co-occurring Jussiaea repens. We grew clonal fragments of these three stoloniferous plants under negative spatial covariance of light and soil nutrients while either preventing or allowing division of labor through severing or keeping intact their stolon connections. The results showed that stolon connection significantly increased the root mass to shoot mass ratio of basal ramets under low light and high soil nutrient conditions, but greatly decreased it in the apical ramets under high light and low soil nutrient conditions, suggesting induced division of labor in all studied plants. Moreover, the invasive plant A. philoxeroides demonstrated a greater capacity for division of labor than its co-genus and co-occurring native partners, which conferred it with greater growth performance at the whole clonal fragment level. Given that the commonly observed competitive superiority of invasive clonal plants over co-occurring native species due to their high intrinsic growth rates, these findings suggest that the division of labor may confer a competitive advantage upon some invasive clonal plants, thereby facilitating their successful invasion in heterogeneous habitats characterized by a strong negative correlation between light availability and soil nutrient levels.

Predicting the dispersal and invasion dynamics of ambrosia beetles through demographic reconstruction and process-explicit modeling.

Evaluating potential routes of invasion of pathogens and vectors of sanitary importance is essential for planning and decision-making at multiple scales. An effective tool are process-explicit models that allow coupling environmental, demographic and dispersal information to evaluate population growth and range dynamics as a function of the abiotic conditions in a region. In this work we simulate multiple dispersal/invasion routes in Mexico that could be taken by ambrosia beetles and a specific symbiont, Harringtonia lauricola, responsible for a severe epiphytic of Lauraceae in North America. We used Xyleborus bispinatus Eichhoff 1868 as a study subject and estimated its demography in the laboratory in a temperature gradient (17, 20, 26, 29, 35°C), which we then used to parameterize a process-based model to estimate its metapopulation dynamics. The maximum intrinsic growth rate of X. bispinatus is 0.13 with a thermal optimum of 26.2°C. The models suggest important regions for the establishment and dispersal the states of Veracruz, Chiapas and Oaxaca (high host and secondary vectors diversity), the Isthmus of Tehuantepec (connectivity region), and Michoacán and Jalisco (important avocado plantations). The use of hybridprocess-based models is a promising tool to refine the predictions applied to the study of biological invasions and species distributions.

On the slow–fast dynamics of a tri‐trophic food chain model with fear and Allee effects

A three‐species food chain model with Allee and fear effects on both prey and predator is investigated in this work. The model consists of ODEs describing the evolution and interaction of prey, predator, and top predator populations in a biological system. We assume that the intrinsic growth rate of the prey is much smaller than a threshold value determined by other biological parameters of the model. Consequently, the model is transformed into a singularly perturbed system that acts on two different time scales, ranging from slow for both prey and predator to fast for the top predator. Positivity and boundedness of the solutions of the model along with the stability for its equilibria are investigated. The model possesses the exact invariant manifold with changing stability (black swan) and exhibits the canard phenomenon. Some numerical simulations are performed to validate our analysis.

Examining Innovative Technologies: Nano-Chelated Fertilizers for Management of Wheat Aphid (Schizaphis graminum Rondani).

The use of nanofertilizers has both advantages and concerns. One benefit is that nano-fertilizers can enhance plant resistance against insect pests, making them a valuable strategy in integrated pest management (IPM). This study focused on the effect of wheat leaves treated with nano-chelated fertilizers and nitrogen (N) fertilizer on the wheat aphid (Schizaphis graminum Rondani), a harmful pest of wheat plants that transmits dangerous viruses. The nano-Cu treatment showed the longest pre-adult longevity. Additionally, the nano-Cu treatment resulted in the lowest adult longevity, fecundity, nymphoposition day number, intrinsic rate of population growth (r), finite rate of population increase (λ), and net reproductive rate (R0) and gross reproductive rate (GRR). Also, nano-Cu treatment led to the highest amount of (T). The N treatment led to the highest levels of fecundity, nymphoposition days, r, λ, and R0. Nano-Fe and nano-Zn demonstrated fewer negative effects on S. graminum life table parameters than nano-Cu. Our results indicate that N treatment yielded numerous advantageous effects on the wheat aphid while simultaneously impeding the efficacy of the aphid control program. Conversely, nano-Cu treatment exhibited a detrimental influence on various parameters of the aphid's life table, resulting in a reduction in the pest's fitness. Consequently, the integration of nano-Cu should be seriously considered as a viable option in the IPM of the wheat aphid.

Noise propagation and amplification in microbial communities with different resistance mechanisms

Antimicrobial resistance is a growing concern in the field of microbiology. In a microbial community, the Susceptible Subpopulations (SSs) and the Non-genetically Resistant Subpopulations (NRSs) can switch between each other, and NRSs can mutate to Genetically Resistant Subpopulations (GRSs). In order to quantitatively describe the relationship between noise and signal amplification in the subpopulations, a mathematical model for three subpopulations is proposed in this paper. The gain fluctuation relation is obtained by linear noise approximation of the master equation. Then, through the simulation of these theoretical results, the following conclusions are found. First, the indirect effects of the interaction between subpopulations are much greater than the direct effects, which may be one of the reasons that the infection is difficult to cure. This is consistent with the findings of Zhou et al. and indicates the reliability of our new model. Second, the intrinsic net growth rate of SSs can be chosen as the adjustment parameter, which can effectively exploit or avoid the strong correlation between SSs and the two resistant subpopulations, including NRSs and GRSs. Third, unlike unidirectional cascades, additional intrinsic noise in GRSs can propagate to NRSs. Similarly, although there is no direct interaction between SSs and GRSs, additional intrinsic noise in GRSs can propagate to SSs, and vice versa. Finally, both total noise and adjusted noise exhibit similar amplification properties in this population. It is worth noting that the noise is consistently amplified from NRSs to GRSs. These findings may provide new insights into antimicrobial therapy.

Mathematical modeling of cholera dynamics with intrinsic growth considering constant interventions

A mathematical model that describes the dynamics of bacterium vibrio cholera within a fixed population considering intrinsic bacteria growth, therapeutic treatment, sanitation and vaccination rates is developed. The developed mathematical model is validated against real cholera data. A sensitivity analysis of some of the model parameters is also conducted. The intervention rates are found to be very important parameters in reducing the values of the basic reproduction number. The existence and stability of equilibrium solutions to the mathematical model are also carried out using analytical methods. The effect of some model parameters on the stability of equilibrium solutions, number of infected individuals, number of susceptible individuals and bacteria density is rigorously analyzed. One very important finding of this research work is that keeping the vaccination rate fixed and varying the treatment and sanitation rates provide a rapid decline of infection. The fourth order Runge–Kutta numerical scheme is implemented in MATLAB to generate the numerical solutions.

Intrinsic growth rate and evolution of the Premnotrypes Vorax population using fuzzy information

The white potato worm (Premnotrypes Vorax (Hustache)) is one of the pests that causes the greatest damage to the potato crop and the greatest economic losses to the grower; therefore, knowing its life cycle and estimating its intrinsic growth rate is crucial for selecting an appropriate chemical control method, in order to reduce the environmental impact and ensure a profitable production suitable for consumption. In this article, we present a fuzzy Malthusian model describing the evolution of the white potato worm in the crop, considering that the intrinsic growth rate and the reported initial data on the problem are of fuzzy nature. The main contributions and novelty of this paper are summarized in the following two aspects: first, the estimation of the intrinsic growth rate of the white potato worm, in function of the temperature, by using a Takagi–Sugeno–Kang type fuzzy rule-based model; and second, since in practice the initial white potato worm population in a crop is subjective, imprecise and vague, knowing the intrinsic growth rate, we propose and solve a fuzzy initial value problem to determine the evolution in time of the white potato worm population. In conclusion, given a weekly average temperature, it is possible to know the white potato worm population per unit area oscillating in an interval whose length depends on the degree of inaccuracy of the initial population and the intrinsic growth rate. This study can be relevant for grower decision making in terms of the type and frequency of pest control on his crop.