scholarly journals Comparison of stabilizing mechanisms between discrete- and continuous-time consumer-resource models

2021 ◽  
Author(s):  
Abhyudai Singh
Keyword(s):  
Population Dynamics ◽  
Functional Response ◽  
Discrete Time ◽  
Continuous Time ◽  
Overlapping Generations ◽  
Type Ii ◽  
Stability Regime ◽  
Discrete Time Models ◽  
Consumer Resource ◽  
Type Ii Functional Response

There is rich literature on using continuous-time and discrete-time models for studying population dynamics of consumer-resource interactions. The continuous-time framework is generally used to model populations with overlapping generations and all year-round reproduction. In contrast, discrete-time models are more suited for populations with non-overlapping generations that reproduce in a discrete pulse determined by season. Inspired by the Nicholson-Bailey/Lotka-Volterra modeling formalisms in discrete-time/continuous-time, respectively, we consider host-parasitoid interactions with an arbitrary parasitoid attack rate that is a function of  both the host and parasitoid population densities. We characterize and compare stability regimes in both modeling frameworks for analogous host reproduction and attack rates. Our analysis shows that a Type II functional response is stabilizing in both modeling frameworks only when combined with other mechanisms, such as mutual interference between parasitoids. This stability regime related to a Type II functional response  is smaller in the discrete-time framework compared to continuous-time, and shrinks with increasing host reproduction. A Type III functional response is by itself stabilizing, but the extent of attack-rate acceleration needed is much higher in the discrete-time framework, and its stability regime expands with increasing host reproduction. Finally, our results show that while mutual parasitoid interference can stabilize population dynamics, cooperation between parasitoids to handle hosts is destabilizing  in both frameworks. However, a combination of a Type III functional response together with parasitoid cooperation can create stability. In summary, our comparative analysis systematically characterizes diverse ecological processes driving stable population dynamics in discrete-time and continuous-time consumer-resource models.

scholarly journals Analytical Discrete-Time Models of Insect Population Dynamics

2020 ◽  
Author(s):  
Abhyudai Singh
Keyword(s):  
Population Dynamics ◽  
Discrete Time ◽  
Continuous Time ◽  
Overlapping Generations ◽  
Insect Population ◽  
Dynamical Behaviors ◽  
Insect Population Dynamics ◽  
Classical Models ◽  
Discrete Time Models ◽  
Simple Models

Insect population dynamics has been extensively studied using two different approaches: continuous-time and discrete-time models. The continuous-time framework is generally used to model populations with overlapping generations and all year-round reproduction. In contrast, discrete-time models are more suited for populations with non-overlapping generations that reproduce in a discrete pulse determined by season. We revisit simple models of host-parasitoid interactions and describe tools for elucidating their dynamical behaviors. One advantage of simple models is that they are often analytically tractable providing key insights into regulatory mechanisms and parameter regions that lead to stable, unstable or oscillatory population dynamics. While reviewing classical models introduced decades ago, we also highlight new modeling frameworks and results from recent literature.

Predator-dependent transmissible disease spreading in prey under Holling type-II functional response

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dipankar Ghosh ◽  
Prasun K. Santra ◽  
Abdelalim A. Elsadany ◽  
Ghanshaym S. Mahapatra
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Linearization Method ◽  
Logistic Growth ◽  
Type Ii ◽  
Disease Spreading ◽  
Predator Interactions ◽  
The Stability ◽  
Infected Prey ◽  
Type Ii Functional Response

Abstract This paper focusses on developing two species, where only prey species suffers by a contagious disease. We consider the logistic growth rate of the prey population. The interaction between susceptible prey and infected prey with predator is presumed to be ruled by Holling type II and I functional response, respectively. A healthy prey is infected when it comes in direct contact with infected prey, and we also assume that predator-dependent disease spreads within the system. This research reveals that the transmission of this predator-dependent disease can have critical repercussions for the shaping of prey–predator interactions. The solution of the model is examined in relation to survival, uniqueness and boundedness. The positivity, feasibility and the stability conditions of the fixed points of the system are analysed by applying the linearization method and the Jacobian matrix method.

scholarly journals Demography and feeding behavior of Stenostomum leucops (Dugés, 1828)

2016 ◽  
Vol 75 (s1) ◽  
Author(s):  
Alma R. Núñez-Ortiz ◽  
Sarma Nandini ◽  
S.S.S. Nandini
Keyword(s):  
Functional Response ◽  
Food Preference ◽  
Type Ii ◽  
Final Density ◽  
Two Temperatures ◽  
The Difference ◽  
Growth Experiments ◽  
Pelagic Communities ◽  
Type Ii Functional Response ◽  
Planktonic Communities

<p>Freshwater turbellarians, despite their mainly benthic habits, interact with pelagic communities of rotifers and cladocerans. However, very little is known about their demographic characteristics, food preference and functional response. To fill that gap we studied one of the most widely spread species, <em>Stenostomum leucops</em>.  We conducted population growth experiments using abundant food (several rotifer and cladocerans species). To evaluate possible impact of <em>S. leucops</em> on planktonic communities, we conducted prey preference experiments at two temperatures: 18 and 23°C. The number of rotifers and cladocerans consumed was calculated by the difference between the initial and final density. We found that diets supplemented with fresh algae achieved higher <em>S. leucops</em> densities than those with detritus supplements in their diets. In the case of animal diets, <em>Euchlanis dilatata</em> allowed <em>S. leucops</em> reach higher densities than the other zooplankton species; <em>E. dilatata</em> was positively selected for in the selectivity study at both 18 and 23°C.  <em>Stenostomum leucops</em> showed a type II functional response on rotifers and the cladoceran <em>Alona glabra</em>. Our results suggest that <em>S. leucops</em> select their prey according to their vulnerability using different mechanisms, which optimize their food intake.</p>

scholarly journals PREFERENSI DAN TANGGAP FUNGSIONAL PARASITOID HEMIPTARSENUS VARICORNIS (GIRAULT) (HYMENOPTERA: EULOPHIDAE) PADA LARVA LALAT PENGOROK DAUN KENTANG

2009 ◽  
Vol 9 (1) ◽  
pp. 15-21
Author(s):  
Hidrayani Hidrayani ◽  
Aunu Rauf ◽  
S. Sosromarsono ◽  
U. Kartosuwondo
Keyword(s):  
Regression Analysis ◽  
Functional Response ◽  
Preference Test ◽  
Handling Time ◽  
Equation Model ◽  
Type Ii ◽  
Female Parasitoid ◽  
Host Abundance ◽  
Liriomyza Huidobrensis ◽  
Type Ii Functional Response

The preference and functional response of Parasitoid Hemiptarsenus varicornis (Girault) (Hymenoptera:Eulophidae) on host larvae of potato leafminers. The preference of Hemiptarsenus varicornis (Girault) on host larvae of potato leafminers (Liriomyza huidobrensis) and their  functional response on host abundance were studied in laboratory. The preference test was conducted by releasing a female parasitoid in a cage containing two redbean leaves, one with 2nd instar and another one with 3rd instar.  The functional response test was conducted by providing 3rd instar  with density 1, 4, 6, 8, 10, and 13  larvae  per leaf. The result showed that  H. varicornis had the preference on 3rd instar  larvae compared to 2nd instar, either for parasitisation or paralysis. Based on logistic regression analysis it was found that the parasitoid showed type II functional response on the increase of host abundance. The searching rate (a) and handling time (Th) for paralysis were 0.038 and 1.473 based on disk equation model, and 0.076 and 2.060 on ramdom equation model.  For parasitisation activity, the value of  a and Th were  0.012 and 4.649 based on disk equation model, and 0.014 and 5.075 on random equation model.

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