scholarly journals Stochasticity in host-parasitoid models informs mechanisms regulating population dynamics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Abhyudai Singh
Keyword(s):  
Population Dynamics ◽  
Population Density ◽  
Functional Response ◽  
Discrete Time ◽  
Host Population ◽  
Reproduction Rate ◽  
Population Densities ◽  
Type Iii ◽  
Time Formalism ◽  
Large Fluctuations

AbstractPopulation dynamics of host-parasitoid interactions have been traditionally studied using a discrete-time formalism starting from the classical work of Nicholson and Bailey. It is well known that differences in parasitism risk among individual hosts can stabilize the otherwise unstable equilibrium of the Nicholson-Bailey model. Here, we consider a stochastic formulation of these discrete-time models, where the host reproduction is a random variable that varies from year to year and drives fluctuations in population densities. Interestingly, our analysis reveals that there exists an optimal level of heterogeneity in parasitism risk that minimizes the extent of fluctuations in the host population density. Intuitively, low variation in parasitism risk drives large fluctuations in the host population density as the system is on the edge of stability. In contrast, high variation in parasitism risk makes the host equilibrium sensitive to the host reproduction rate, also leading to large fluctuations in the population density. Further results show that the correlation between the adult host and parasitoid densities is high for the same year, and gradually decays to zero as one considers cross-species correlations across different years. We next consider an alternative mechanism of stabilizing host-parasitoid population dynamics based on a Type III functional response, where the parasitoid attack rate accelerates with increasing host density. Intriguingly, this nonlinear functional response makes qualitatively different correlation signatures than those seen with heterogeneity in parasitism risk. In particular, a Type III functional response leads to uncorrelated adult and parasitoid densities in the same year, but high cross-species correlation across successive years. In summary, these results argue that the cross-correlation function between population densities contains signatures for uncovering mechanisms that stabilize consumer-resource population dynamics.

scholarly journals Fluctuations in population densities inform stability mechanisms in host-parasitoid interactions

2021 ◽  
Author(s):  
Abhyudai Singh
Keyword(s):  
Population Dynamics ◽  
Population Density ◽  
Functional Response ◽  
Discrete Time ◽  
Host Population ◽  
Reproduction Rate ◽  
Population Densities ◽  
Type Iii ◽  
Time Formalism ◽  
Large Fluctuations

AbstractPopulation dynamics of host-parasitoid interactions has been traditionally studied using a discrete-time formalism starting from the classical work of Nicholson and Bailey. It is well known that differences in parasitism risk among individual hosts can stabilize the otherwise unstable equilibrium of the Nicholson-Bailey model. Here, we consider a stochastic formulation of these discrete-time models, where the host reproduction is a random variable that varies from year to year and drives fluctuations in population densities. Interestingly, our analysis reveals that there exists an optimal level of heterogeneity in parasitism risk that minimizes the extent of fluctuations in the host population density. Intuitively, low variation in parasitism risk drives large fluctuations in the host population density as the system is on the edge of stability. In contrast, high variation in parasitism risk makes the host equilibrium sensitive to the host reproduction rate, also leading to large fluctuations in the population density. Further results show that the correlation between the adult host and parasitoid densities is high for the same year, and gradually decays to zero as one considers cross-species correlations across different years. We next consider an alternative mechanism of stabilizing host-parasitoid population dynamics based on a Type III functional response, where the parasitoid attack rate accelerates with increasing host density. Intriguingly, this nonlinear functional response makes qualitatively different correlation signatures than those seen with heterogeneity in parasitism risk. In particular, a Type III functional response leads to uncorrelated adult and parasitoid densities in the same year, but high cross-species correlation across successive years. In summary, these results argue that the cross-correlation function between population densities contains signatures for uncovering mechanisms that stabilize consumer-resource population dynamics.

scholarly journals Population dynamics of multi-host communities attacked by a common parasitoid

2021 ◽  
Author(s):  
Abhyudai Singh
Keyword(s):  
Population Dynamics ◽  
Functional Response ◽  
Host Species ◽  
Attack Rate ◽  
Host Density ◽  
Apparent Competition ◽  
Species Interaction ◽  
Type I ◽  
Type Iii ◽  
Time Formalism

AbstractWe model population dynamics of two host species attacked by a common parasitoid using a discrete-time formalism that captures their population densities from year to year. It is well known starting from the seminal work of Nicholson and Bailey that a constant parasitoid attack rate leads to an unstable host-parasitoid interaction. However, a Type III functional response, where the parasitoid attack rate accelerates with increasing host density stabilizes the population dynamics. We first consider a scenario where both host species are attacked by a parasitoid with the same Type III functional response. Our results show that sufficient fast acceleration of the parasitoid attack rate stabilizes the population dynamics of all three species. For two symmetric host species, the extent of acceleration needed to stabilize the three-species equilibrium is exactly the same as that needed for a single host-parasitoid interaction. However, asymmetry can lead to scenarios where the removal of a host species from a stable interaction destabilizes the interaction between the remaining host species and the parasitoid. Next, we consider a situation where one of the host species is attacked at a constant rate (i.e., Type I functional response), and the other species is attacked via a Type III functional response. We identify parameter regimes where a Type III functional response to just one of the host species stabilizes the three species interaction. In summary, our results show that a generalist parasitoid with a Type III functional response to one or many host species can play a key role in stabilizing population dynamics of host-parasitoid communities in apparent competition.

scholarly journals Hybrid systems modeling of ecological population dynamics

2020 ◽  
Author(s):  
Abhyudai Singh ◽  
Brooks Emerick
Keyword(s):  
Population Dynamics ◽  
Discrete Time ◽  
Traditional Approach ◽  
Hybrid Approach ◽  
Host Density ◽  
Parasitoid Wasp ◽  
Host Population ◽  
Equilibrium Density ◽  
Reproduction Rate ◽  
Discrete Time Models

AbstractDiscrete-time models are the traditional approach for capturing population dynamics of insects living in the temperate regions of the world. These models are characterized by an update function that connects the population densities from one year to the next. We revisit classical discrete-time models used for modeling interactions between two insect species (a host and a parasitoid), and provide novel result on the stability of the population dynamics. In particular, for a class of models we show that the fixed point is stable, if and only if, the host equilibrium density is an increasing function of the host’s reproduction rate. We also introduce a hybrid approach for obtaining the update functions by solving ordinary differential equations that mechanistically capture the ecological interactions between the host and the parasitoid. This hybrid approach is used to study the suppression of host density by a parasitoid. Our analysis shows that when the parasitoid attacks the host at a constant rate, then the host density cannot by suppressed beyond a certain point without making the population dynamics unstable. In contrast, when the parasitoid’s attack rate increases with increasing host density, then the host population density can be suppressed to arbitrarily low levels. These results have important implications for biological control where a natural enemy, such as a parasitoid wasp, is introduced to eliminate a pest that is the host species for the parasitoid.

Effects of crop sequence and rainfall on population dynamics of Fusarium solani f.sp. phaseoli in soil

1992 ◽  
Vol 70 (10) ◽  
pp. 2005-2008 ◽  
Author(s):  
Robert Hall ◽  
Lana Gay Phillips
Keyword(s):  
Population Dynamics ◽  
Phaseolus Vulgaris ◽  
Population Density ◽  
Fusarium Solani ◽  
Population Densities ◽  
Total Rainfall ◽  
Colony Forming Units ◽  
Bean Crop ◽  
Previous Summer ◽  
Crop Sequence

Evidence is presented that population dynamics of Fusarium solani f.sp. phaseoli in soil depend on the effects of crop sequence and rainfall on parasitic activities of the pathogen. In a rotation trial started in 1978 and conducted over 14 years, population densities (colony-forming units/g) of the fungus in soil remained below 50 in treatments (fallow, repeated corn, repeated soybean) where the preferred host plant (common bean, Phaseolus vulgaris) was not grown. Where bean was grown every 3rd year or every year, population densities reached 475 and 660, respectively, by 1984. Thereafter, population densities of the fungus fluctuated widely from year to year in both rotation and repeated bean treatments. In the rotation treatment, peaks in population density of the pathogen coincided with the years of bean production. In repeated bean plots between 1985 and 1991, population density of the fungus in June was significantly correlated (r = 0.77, p = 0.04) with total rainfall received during the previous summer (June–August). It is postulated that higher rainfall during the growing season of the bean crop stimulated root growth and root infection, leading to the accumulation of higher levels of potential inoculum in infected tissue and the release of higher levels of inoculum into the soil by the following June. Key words: Fusarium solani f.sp. phaseoli, bean, Phaseolus vulgaris, rainfall, crop rotation.

scholarly journals Generalized conditions for coexistence of competing parasitoids on a shared host

2020 ◽  
Author(s):  
Abhyudai Singh
Keyword(s):  
Discrete Time ◽  
Life Histories ◽  
Host Density ◽  
Host Community ◽  
Reproduction Rate ◽  
Parasitoid Species ◽  
Slow Increase ◽  
Time Formalism ◽  
Adult Parasitoid ◽  
The Stability

AbstractMotivated by the univoltine life histories of insects residing in the temperate-regions of the world, there is a rich tradition of modeling arthropod host-parasitoid interactions using a discrete-time formalism. We introduce a general class of discrete-time models for capturing the population dynamics of two competing parasitoid species that attack the same vulnerable stage of the host species. These models are characterized by two density-dependent functions: an escape response defined by the fraction of hosts escaping parasitism; and a competition response defined by the fraction of parasitized hosts that develop into adult parasitoids of either species. Model analysis reveals remarkably simple stability conditions for the coexistence of competing parasitoids. More specifically, coexistence occurs, if and only if, the adult host density increases with host reproduction rate, and the log sensitivity of the competition response is less than half. The latter condition implies that any increase in the adult parasitoid density will result in a sufficiently slow increase in the fraction of parasitized hosts that develop into parasitoids of that type. We next consider a model motivated by differences in parasitism risk among individual hosts with risk from the two parasitoid species assumed to be independently distributed as per a Gamma distribution. In such models, the heterogeneity in host risk to each parasitoid is quantified by the corresponding Coefficient of Variation (CV). Our results show that parasitoid coexistence occurs for sufficiently large reproduction rate, if and only if, the sum of the inverse of the two CV squares is less than one. This result generalizes the “CV greater than one” rule that defined the stability for a single parasitoid-host system to a multi parasitoid-host community.

Population dynamics and production of a brine shrimp, Parartemia zietziana Sayce (Crustacea : Anostraca), in two salt lakes in westren Victoria, Australia

1977 ◽  
Vol 28 (4) ◽  
pp. 417 ◽  
Author(s):  
R Marchant ◽  
WD Williams
Keyword(s):  
Population Dynamics ◽  
Population Density ◽  
Temperature Stress ◽  
Brine Shrimp ◽  
Dry Weight ◽  
Salt Lakes ◽  
Confidence Limits ◽  
Length Frequency ◽  
Population Densities ◽  
The Mean

Quantitative samples of P. zietziana were taken monthly for two years from Pink Lake and Lake Cundare. Shrimps were usually contagiously distributed. To reduce error, samples were stratified resulting in confidence limits of 40-50% for the mean population density. Despite this variability, stable trends emerged, and variation was not so great as to mask significant differences. Length-frequency analyses distinguished cohorts; a regression was established between length and dry weight, enabling growth to be estimated from samples. By combining growth with population densities in Allen curves, production was computed. In Pink Lake and Lake Cundare mean pro- duction was 11.3 and 1.0 g dry weight m-2 year-1 respectively. Generally there were two or three generations per year, but time and extent of recruitment were not predictable. Each generation suffered continuous mortality, the death of young shrimps accounting for most of the production. This mortality remains unexplained; there are no significant predators and salinity and temperature stress would occur only during summer.

scholarly journals Population Dynamics of the Sting Nematode in California Turfgrass

Plant Disease ◽  
2000 ◽  
Vol 84 (10) ◽  
pp. 1081-1084 ◽  
Author(s):  
Sadia Bekal ◽  
J. Ole Becker
Keyword(s):  
Population Dynamics ◽  
Population Density ◽  
Golf Course ◽  
Golf Courses ◽  
Population Densities ◽  
Sampling Area ◽  
Coachella Valley ◽  
Belonolaimus Longicaudatus ◽  
Country Club ◽  
Desert Island

Population densities of Belonolaimus longicaudatus were monitored at monthly intervals at the Tamarisk country club golf course (1993 to 1994) and at the Annenburg Estates and Desert Island golf courses (1998). All three courses are located at Rancho Mirage, Coachella Valley, CA. The bermuda grass in the sampling area typically exhibited chlorosis at the beginning of April when the sting nematode populations began to increase. At the Tamarisk golf course, population density peaked in October, with 1,000 nematodes per 100 cm3 of soil, but declined rapidly, with the lowest population density occurring in December with approximately 50 nematodes per 100 cm3 of soil. At the Annenburg Estates and Desert Island golf courses, the nematode population densities peaked in June and July but declined rapidly to less than half of that density, presumably because of B. longicaudatus-caused host decline. Soil temperature and fluctuation of nematode densities were significantly correlated at all locations. Nematode distribution was greatest in the top 15 cm of soil except during the hottest summer months, when the population was higher at depths of 15 to 30 cm.

scholarly journals Warming can destabilise predator-prey interactions by shifting the functional response from Type III to Type II

2018 ◽  
Author(s):  
Uriah Daugaard ◽  
Owen Petchey ◽  
Frank Pennekamp
Keyword(s):  
Population Dynamics ◽  
Functional Response ◽  
Conversion Efficiency ◽  
Trophic Interactions ◽  
Clearance Rate ◽  
Temperature Effects ◽  
Type Ii ◽  
Predator Prey ◽  
Type Iii ◽  
Population Dynamic Model

The potential for climate change and temperature shifts to affect community stability remains relatively unknown. One mechanism by which temperature may affect stability is by altering trophic interactions. The functional response quantifies the per capita resource consumption by the consumer as a function of resource abundance and is a suitable framework for the description of nonlinear trophic interactions. We studied the effect of temperature on a ciliate predator-prey pair (Spathidium sp. and Dexiostoma campylum) by estimating warming effects on the functional response and on the associated conversion efficiency of the predator. We recorded prey and predator dynamics over 24 hours and at three temperature levels (15, 20 and 25 C). To these data we fitted a population dynamic model including the predator functional response, such that the functional response parameters (space clearance rate, handling time, and density dependence of space clearance rate) were estimated for each temperature separately. To evaluate the ecological significance of temperature effects on the functional response parameters we simulated predator-prey population dynamics. We considered the predator-prey system to be destabilised, if the prey was driven extinct by the predator. Effects of increased temperature included a transition of the functional response from a Type III to a Type II and an increase of the conversion efficiency of the predator. The simulated population dynamics showed a destabilisation of the system with warming, with greater risk of prey extinction at higher temperatures likely caused by the transition from a Type III to a Type II functional response. Warming-induced shifts from a Type III to II are not commonly considered in modelling studies that investigate how population dynamics respond to warming. Future studies should investigate the mechanism and generality of the effect we observed and simulate temperature effects in complex food webs including shifts in the type of the functional response as well as consider the possibility of a temperature dependent conversion efficiency.

scholarly journals The evolution of covert, silent infection as a parasite strategy

2009 ◽  
Vol 276 (1665) ◽  
pp. 2217-2226 ◽  
Author(s):  
Ian Sorrell ◽  
Andrew White ◽  
Amy B. Pedersen ◽  
Rosemary S. Hails ◽  
Mike Boots
Keyword(s):  
Infectious Disease ◽  
Population Dynamics ◽  
Seasonal Variation ◽  
Population Density ◽  
Host Population ◽  
Direct Link ◽  
Birth Rates ◽  
Transmission Rates ◽  
Transmission Success ◽  
Covert Infection

Many parasites and pathogens cause silent/covert infections in addition to the more obvious infectious disease-causing pathology. Here, we consider how assumptions concerning superinfection, protection and seasonal host birth and transmission rates affect the evolution of such covert infections as a parasite strategy. Regardless of whether there is vertical infection or effects on sterility, overt infection is always disadvantageous in relatively constant host populations unless it provides protection from superinfection. If covert infections are protective, all individuals will enter the covert stage if there is enough vertical transmission, and revert to overt infections after a ‘latent’ period (susceptible, exposed, infected epidemiology). Seasonal variation in transmission rates selects for non-protective covert infections in relatively long-lived hosts with low birth rates typical of many mammals. Variable host population density caused by seasonal birth rates may also select for covert transmission, but in this case it is most likely in short-lived fecund hosts. The covert infections of some insects may therefore be explained by their outbreak population dynamics. However, our models consistently predict proportions of covert infection, which are lower than some of those observed in nature. Higher proportions of covert infection may occur if there is a direct link between covert infection and overt transmission success, the covert infection is protective or the covert state is the result of suppression by the host. Relatively low proportions of covert transmission may, however, be explained as a parasite strategy when transmission opportunities vary.

scholarly journals Global redistribution and local migration in semi-discrete host-parasitoid population dynamic models

2019 ◽  
Author(s):  
Brooks Emerick ◽  
Abhyudai Singh
Keyword(s):  
Population Dynamics ◽  
Functional Response ◽  
Dynamic Models ◽  
Constant Density ◽  
Spatial Effects ◽  
Modeling Framework ◽  
Type Iii ◽  
Stable Coexistence ◽  
Vulnerable Period ◽  
Parasitoid Population

ABSTRACTHost-parasitoid population dynamics is often probed using a semi-discrete/hybrid modeling framework. Here, the update functions in the discrete-time model connecting year-to-year changes in the population densities are obtained by solving ordinary differential equations that mechanistically describe interactions when hosts become vulnerable to parasitoid attacks. We use this semi-discrete formalism to study two key spatial effects: local movement (migration) of parasitoids between patches during the vulnerable period; and yearly redistribution of populations across patches outside the vulnerable period. Our results show that in the absence of any redistribution, constant density-independent migration and parasitoid attack rates are unable to stabilize an otherwise unstable host-parasitoid population dynamics. Interestingly, inclusion of host redistribution (but not parasitoid redistribution) before the start of the vulnerable period can lead to stable coexistence of both species. Next, we consider a Type-III functional response (parasitoid attack rate increases with host density), where the absence of any spatial effects leads to a neutrally stable host-parasitoid equilibrium. As before, density-independent parasitoid migration by itself is again insufficient to stabilize the population dynamics and host redistribution provides a stabilizing influence. Finally, we show that a Type-III functional response combined with density-dependent parasitoid migration leads to stable coexistence, even in the absence of population redistributions. In summary, we have systematically characterized parameter regimes leading to stable/unstable population dynamics with different forms of spatial heterogeneity coupled to the parasitoid’s functional response using mechanistically formulated semi-discrete models.

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