31st Mar, 2018

University of Tennessee

Question

Asked 4th Apr, 2016

The Lotka Volterra model is the basic model for predator-prey interactions. Is it also used for herbivore-plant interactions or is there a different, equivalently standard model for herbivore-plant interactions? And has there been research on using the Lotka Volterra model with an additional carrying capacity for the prey?

Instead of the LV model, you can use the Nicholson-Bailey model which is originally a host-parasite model but that works well for a plant-herbivore system as well. See for example https://math.la.asu.edu/~dieter/papers/herbivore.pdf

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«Data analysis.—We tested for the effects of initial body-size varia-tion on the survival of grasshoppers with and without their spider predators, using a Cox proportional hazard model (Hosmer & Lemeshow 1999) with initial body-size variation (Low Variation = 0, Normal Variation = 1, and High Variation =2), predation treat-ment (Predator Absent = 0, and Predator Present = 1), and the respective interaction term as covariates. This is a commonly used survival analysis method, which allows evaluating effects of differ-ent predictors (i.e., covariates) on mortality rate, independent of the time-varying background mortality rate (Hosmer & Lemeshow 1999). To control for repeated measurements on a subject, which in our case, were individual cages that were repeatedly censused throughout the season, we used a robust jackknife variance estimator, grouped by observations per cage (Lin & Wei 1989).»

Filin, I., Schmitz, O. J., & Ovadia, O. (2008). Consequences of individual size variation for survival of an insect herbivore: an analytical model and experimental field testing using the red-legged grasshopper. Journal of Orthoptera Research, 17(2), 283–291. doi:10.1665/1082-6467-17.2.283

«The use of individual-based modeling (IBM)can facilitate understanding of a system and even decision making in resource management (Judson 1994, Grimm1999, Lomnicki1999), and the use of individual-based modeling has grown in ecology in the last 2 to 3 decades (Grimm 1999, Lomnicki 1999, DeAngelisetal, 2001).Individual-based models may explicitly include space, as may math-ematical or other models. Arguments for the inclusion of space are similar to those for the use of IBMs themselves: Such models may more closely simulate some aspects of the natural system being modeled, aspects that are important for the question being researched.» CHIVERS, W. J., GLADSTONE, W., & HERBERT, R. D. (2008). SPATIAL EFFECTS IN AN INDIVIDUAL-BASED MODEL OF PRODUCER-HERBIVORE INTERACTION. Natural Resource Modeling, 21(1), 72–92. doi:10.1111/j.1939-7445.2008.00013.x

«Individual-based models, also called agent-based models, are a population and community modeling approach that allows for a high degree of complexity of individuals and of interactions among individuals. Individual-based models simulate populations or systems of populations as being composed of discrete individual organisms. Each individual has a set of state variables or attributes and behaviors. State variables can include spatial location, physiological traits and behavioral traits. These attributes vary among the individuals and can change through time. Behaviors can include growth, reproduction, habitat selection, foraging, and dispersal. Unlike traditional differential equation population models, which are described in terms of imposed top-down population parameters (such as birth and death rates), individual-based models are bottom-up models in which population-level behaviors emerge from the interactions among autonomous individuals with each other and their abiotic environment. An advantage of individual-based models over traditional models is that they can incorporate any number of individual-level mechanisms. They are thus used whenever one or more of the following aspects, which are hard or impossible to represent in population-level differential equations, are considered essential for answering a research question or solving an applied problem: variation among individuals and of individuals during their life cycle; local interactions among individuals; and adaptive behavior, which includes physiology and energy budgets.» DeAngelis, D. L., & Grimm, V. (2014). Individual-based models in ecology after four decades. F1000Prime Reports, 6. doi:10.12703/p6-39

I hope this may help you

Regards

Jose Macedo

1 Recommendation

If you are going to include plant density dependence (as the Lotka-Volterra does) as well as herbivore effects on plants and plant effects on herbivores, be aware that there are better ways to model density-dependence among plants than the logistic/Lotka-Volterra. We (and many others) have found that found that the type of function described by Firbank and Watkinson 1985 (N2 = N1 * 1/(1 + constant*N1)) gives a much better fit (Fowler and Pease 2010) for density-dependence in plants than the logistic (the logistic is just the LV without other species). This consideration is relevant whether or not you are using an individual-based model.

There are a number of excellent studies that have modeled plant-herbivore interactions. For example, Buckley et al. 2005. Stable coexistence of an invasive plant and biocontrol agent: a parameterized coupled plant–herbivore model. Or Abbott and Dwyer 2007 (Food limitation and insect outbreaks: complex dynamics in plant–herbivore models) who, as we did, compared different algebraic functions

See also the review by Maron and Crone 2006 (Herbivory: effects on plant abundance, distribution and population growth).

A final note: if you use an individual-based model where each plant occupies a different cell in a cellular automata-type map, you will be including density-dependence implicitly and therefore probably do not need to worry about the shape of the density-dependent function.

Good luck!

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See: Alternatives to Lotka-Volterra competition: Models of intermediate complexity, http://dx.doi.org/10.1016/0040-5809(76)90022-8 for alternatives.

I hope this helps!

Andrew :-)

Instead of the LV model, you can use the Nicholson-Bailey model which is originally a host-parasite model but that works well for a plant-herbivore system as well. See for example https://math.la.asu.edu/~dieter/papers/herbivore.pdf

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Do these physical constant anomalies signify a mathematical relation between the units, and if so, would this suggest we in a simulation?

Question

29 answers

- Asked 13th Jul, 2022

- Malcolm J. Macleod

The physical constants (*G*, *h*, *c*, *e*, *me*, *kB*), can be considered fundamental only if the units they are measured in (*kg*, *m*, *s* ...) are independent. However there are anomalies which occur in certain combinations of these constants which suggest a mathematical (unit number) relationship. By assigning a unit number **θ** (*kg* -> **15**, *m* -> **-13**, *s* -> **-30**, *A* -> **3**, *K* -> **20**) to each unit we can define a relationship between the units.

The 2019 redefinition of SI base units resulted in 4 physical constants independently assigned exact values, and this confirmed the independence of their associated SI units, however these anomalies question this fundamental assumption. In every combination predicted by the model they give an answer consistent with CODATA precision. Statistically therefore, can these anomalies be dismissed as coincidence?

For convenience, the anomalies are listed on this wiki site (adapted from the article)

**https://en.wikiversity.org/wiki/Physical_constant_(anomaly) (https://www.youtube.com/watch?v=9HY5AgHn25g)****Are these physical constant anomalies evidence of a mathematical relation between the SI units?****https://en.wikiversity.org/wiki/Electron_(mathematical)**

The diagram shows how in certain combinations of the physical constants, the units and scalars cancel, the constants then default to the geometrical objects for mass, length, time and charge and so can be solved using 2 dimensionless constants, the fine structure constant alpha and Omega.

...

Some general background to the physical constants.

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