Statistical Issues in the Estimation of Functional Responses

2021 ◽  
pp. 115-132
Author(s):  
John P. DeLong
Keyword(s):  
Functional Response ◽  
Individual Variation ◽  
Handling Time ◽  
Trial Data ◽  
Data Sets ◽  
Functional Responses ◽  
Key Issues ◽  
Statistical Issues ◽  
Functional Response Models

In this chapter I cover some key issues in fitting functional response models to data and determining the values of parameters. Because some of these issues have been covered elsewhere, here I focus on the nature of foraging trial data and why noise, stochasticity, and individual variation pose particular challenges for understanding functional responses. I examine several data sets to illustrate methods of determining differences in functional response parameters and types. I also show through simulations that individual variation in functional response parameters may account for the noisiness of foraging data and also lead to underestimates of both space clearance rate and handling time in curve-fitting approaches.

Use of Functional Response Modeling to Evaluate the Effect of Temperature on Predation of Amblyseius swirskii (Acari: Phytoseiidae) Adults Preying on Tetranychus urticae (Acari: Tetranychidae) Nymphs

2021 ◽  
Author(s):  
Azadeh Farazmand ◽  
Masood Amir-Maafi
Keyword(s):  
Functional Response ◽  
Tetranychus Urticae ◽  
Attack Rate ◽  
Handling Time ◽  
Effect Of Temperature ◽  
Coefficient Of Determination ◽  
Temperature Threshold ◽  
Amblyseius Swirskii ◽  
Functional Responses ◽  
Wide Range

Abstract In this research, functional responses of Amblyseius swirskii Athias-Henriot preying on different Tetranychus urticae Koch nymphal densities (2, 4, 8, 16, 32, 64, and 128) were studied at eight constant temperatures (15, 20, 25, 27.5, 30, 32.5, 35 and 37.5°C) in a circular Petri dish (3-cm diameter × 1-cm height) under lab conditions. At all temperatures, the logistic regression showed a type II functional response. A nonlinear relationship was found between temperature and attack rate and the reciprocal of handling time. The reciprocal of handling time decreased exponentially with increasing temperature. In contrast, the attack rate grew rapidly with increasing temperatures up to an optimum, showing a decreasing trend at higher temperatures. In order to quantify the functional response of A. swirskii over a broad range of temperatures and to gain a better estimation of attack rate and handling time, a temperature-settled functional response equation was suited to our data. Our model showed that the number of prey consumed increased with rising prey density. Also, the predation rates increased with increasing temperatures but decreased at extremely high temperatures. Based on our model, the predation rate begins at the lower temperature threshold (11.73°C) and reaches its peak at upper temperature threshold (29.43°C). The coefficient of determination (R2) of the random predator model was 0.99 for all temperatures. The capability of A. swirskii to search and consume T. urticae over a wide range of temperatures makes it a good agent for natural control of T. urticae in greenhouses.

scholarly journals Fitting functional responses: Direct parameter estimation by simulating differential equations

2017 ◽  
Author(s):  
Benjamin Rosenbaum ◽  
Bjoern C. Rall
Keyword(s):  
Parameter Estimation ◽  
Functional Response ◽  
Marine Biology ◽  
Prediction Models ◽  
Functional Responses ◽  
Food Web Structure ◽  
Ode Models ◽  
Background Mortality ◽  
Functional Response Models ◽  
Scientific Fields

The feeding functional response is one of the most widespread mathematical frameworks in Ecology, Marine Biology, Freshwater Biology, Microbiology and related scientific fields describing the resource-dependent uptake of a consumer. Since the exact knowledge of its parameters is crucial in order to predict, for example, the efficiency of biocontrol agents, population dynamics, food web structure and subsequently biodiversity, a trustful parameter estimation is of utmost importance for scientists using this framework. Classical approaches for estimating functional response parameters lack flexibility and can often only serve as approximation for a correct parameter estimation. Moreover, they do not allow to incorporate side effects such as resource growth or background mortality. Both call for a new method to be established solving these problems. Here, we combined ordinary differential equation models (ODE models), that were numerically solved using computer simulations, with an iterative maximum likelihood fitting approach. We compared our method to classical approaches of fitting functional responses, using data both with and without additional resource growth and mortality. We found that for classical functional response models, like the often used type II and type III functional response, the established fitting methods are reliable. However, using more complex and flexible functional responses, our new established method outperforms the traditional methods. Additionally, only our method allows to analyze experiments correctly when resources experience growth or background mortality. Our method will enable researchers from different scientific fields that are measuring functional responses to estimate parameters correctly. These estimates will enable community ecologists to parameterize their models more precisely, allowing for a deeper understanding of complex ecological systems, and will increase the quality of ecological prediction models.

scholarly journals The Influence of Food Density, Flock Size, and Disturbance on the Functional Response of Bewick’s Swans (Cygnus columbianus bewickii) in Wintering Habitats

Animals ◽  
2019 ◽  
Vol 9 (11) ◽  
pp. 946 ◽  
Author(s):  
Chao Yu ◽  
Lizhi Zhou ◽  
Nazia Mahtab ◽  
Shaojun Fan ◽  
Yunwei Song
Keyword(s):  
Feeding Behavior ◽  
Functional Response ◽  
Habitat Management ◽  
Feeding Rate ◽  
Handling Time ◽  
Foraging Strategies ◽  
Food Density ◽  
Flock Size ◽  
Functional Responses ◽  
Cygnus Columbianus

Perceiving how animals adjust their feeding rate under a variety of environmental conditions and understanding the tradeoffs in their foraging strategies are necessary for conservation. The Holling functional response, which describes the relationship of feeding rate and food density to searching rate and handling time, has been applied to a range of waterbirds, especially with regard to Type II functional responses that describe an increasing feeding rate with food density but at a decelerating rate as the curve approaches the asymptote. However, feeding behavior components (feeding rate, searching rate, and handling time) are influenced by factors besides prey density, such as vigilance and flock size. In this study, we aim to elucidate how Bewick’s swans (Cygnus columbianus bewickii) adopt flexible foraging strategies and vary their feeding behavior components in response to disturbance, flock size, and food density. We collected focal sampling data on the foraging behavior of swans that foraged rice grains, foxnut seeds, and tubers in paddy field, foxnut pond, and lake habitats, respectively, in Shengjin and Huangpi lakes during winter from 2016 to 2018. The observed feeding rate was not correlated with food density and displayed a positive relationship with searching rate but negative relationships with handling time, flock size, overall vigilance time, and disturbance time. Handling time was negatively correlated with food density and flock size, yet it increased with disturbance, overall vigilance time, and normal vigilance time. Searching rate was negatively correlated with food density, flock size, and disturbance time. Feeding rate was affected by the combined effects of handling time and searching rate, as well as food density and searching rate. The shape of the observed functional response could not be fitted to Holling’s disc equation. However, the disc equation of the predicted feeding rate of wintering swans was found to be driven by food density. This provides insight into how wintering waterbirds adopt appropriate foraging strategies in response to complicated environmental factors, which has implications for wildlife conservation and habitat management.

scholarly journals Space race functional responses

2015 ◽  
Vol 282 (1801) ◽  
pp. 20142121 ◽  
Author(s):  
Henrik Sjödin ◽  
Åke Brännström ◽  
Göran Englund
Keyword(s):  
Functional Response ◽  
Community Dynamics ◽  
Simple Structure ◽  
Functional Responses ◽  
Response Models ◽  
Predator Prey ◽  
Prey System ◽  
Space Race ◽  
Functional Response Models ◽  
The Relationship

We derive functional responses under the assumption that predators and prey are engaged in a space race in which prey avoid patches with many predators and predators avoid patches with few or no prey. The resulting functional response models have a simple structure and include functions describing how the emigration of prey and predators depend on interspecific densities. As such, they provide a link between dispersal behaviours and community dynamics. The derived functional response is general but is here modelled in accordance with empirically documented emigration responses. We find that the prey emigration response to predators has stabilizing effects similar to that of the DeAngelis–Beddington functional response, and that the predator emigration response to prey has destabilizing effects similar to that of the Holling type II response. A stability criterion describing the net effect of the two emigration responses on a Lotka–Volterra predator–prey system is presented. The winner of the space race (i.e. whether predators or prey are favoured) is determined by the relationship between the slopes of the species' emigration responses. It is predicted that predators win the space race in poor habitats, where predator and prey densities are low, and that prey are more successful in richer habitats.

scholarly journals Functional response of the predatory mite Amblyseius swirskii (Acari: Phytoseiidae) to Eotetranychus frosti (Tetranychidae) and Cenopalpus irani (Tenuipalpidae)

Acarologia ◽  
2020 ◽  
Vol 60 (1) ◽  
pp. 30-39
Author(s):  
Fereshteh Bazgir ◽  
Jahanshir Shakarami ◽  
Shahriar Jafari
Keyword(s):  
Biological Control ◽  
Functional Response ◽  
Attack Rate ◽  
Biological Control Agent ◽  
Handling Time ◽  
Rate Coefficients ◽  
Immature Stages ◽  
Amblyseius Swirskii ◽  
Functional Responses ◽  
Phytoseiid Mites

Eotetranychus frosti and Cenopalpus irani Dosse are pests of apple trees that are widely distributed in apple orchards in Iran. The functional responses and predation rates of Amblyseius swirskii, one of the most commonly utilized phytoseiid mites for biological control, on these two pests were evaluated at 25 ± 1 °C, with 16:8 h L: D, and a relative humidity of 60 ± 10 % on apple leaves. The results of predation rate experiments on the two prey species indicated that the predator consumed significantly more eggs than larvae and protonymphs whereas consumption of deutonymphs were very rare. Likewise, the results of logistic regression analysis showed that A. swirskii exhibited a Type II functional response on all immature stages of E. frosti and C. irani. Handling time (Th) increased as prey size enlarged; the lowest handling times were determined as 0.4858 and 0.3819 h on eggs of E. frosti and C. irani, respectively, whereas the highest were found to be 1.4007 and 1.0190 h on deutonymphs, respectively. Amblyseius swirskii had the higher attack rate coefficient (α) on immature stages of C. irani than E. frosti. Attack rate coefficients (α) varied significantly between life stages of both pests with the highest attack rate obtained on eggs, followed by larvae, protonymphs, and deutonymphs. Results of this study suggest that A. swirskii could be a highly efficient biological control agent of E. frosti and C. irani at least at low prey densities.

scholarly journals Uji Pemangsaan dan Tanggap Fungsional Predator Chysoperla carnea Stephens (Neuroptera: Crysopidae) Terhadap Phenacoccus manihoti Matile-Ferrero (Hemiptera: Pseudococcidae)

2021 ◽  
Vol 11 (1) ◽  
pp. 76
Author(s):  
I WAYAN DIRGAYANA ◽  
I WAYAN SUPARTHA ◽  
I NYOMAN WIJAYA
Keyword(s):  
Functional Response ◽  
Block Design ◽  
Handling Time ◽  
Control Agent ◽  
Phenacoccus Manihoti ◽  
Functional Responses ◽  
Randomized Block Design ◽  
Predatory Capacity ◽  
Short Time ◽  
Prey Searching

Predation and Functional Response Test of Predator Chysoperla carnea Stephens (Neuroptera: Crysopidae) Against Phenacoccus manihoti Matile-Ferrero (Hemiptera: Pseudococcidae). This study aims to evaluate the predatory capacity of C. carnea by measuring the rate of searching capacity and handling-time of one prey and its functional response to the population density of P. manihoti. The research was conducted at the Integrated Pest Management Laboratory (IPMLab), Faculty of Agriculture, Udayana University. The study was conducted from February to May 2019. Testing of functional responses used a randomized block design with 5 treatments (3, 6, 9, 12, 15 nymphs-3) each of which was repeated 10 times. The results showed that the prey searching-capacity when the population was low (3 nymphs-3) took longer (10.37 minutes), while when the population was high it took a short time (6.23 minutes). The length of time for handling one prey in the low population was 6.08 minutes, while in the high population it was 5.48 minutes. Predator C. carnea has a tpe-2 functional response to an increase in the population of P. manihoti nymphs with the equation Y = 4.32x / 1 + 1.973x (R2 = 0.980). The rate of predation increases sharply when the population of low increases, and decreases when the increase of prey population increases. C. carnea has the potential to be developed as a control agent for P. manihoti.

scholarly journals Microzooplankton functional responses in the lab and in the field

2014 ◽  
Vol 7 (1) ◽  
pp. 149-167 ◽  
Author(s):  
S. F. Sailley ◽  
E. T. Buitenhuis
Keyword(s):  
Growth Rate ◽  
Functional Response ◽  
Laboratory Experiments ◽  
Nutrient Content ◽  
Growth Efficiency ◽  
External Factors ◽  
Data Sets ◽  
Functional Responses ◽  
Prey Concentration ◽  
Gross Growth Efficiency

Abstract. We present a collection of data relating to microzooplankton physiological traits collected from the literature. We define microzooplankton as unicellular zooplankton (protozoans). The collected data mostly relates to grazing rates collected either in the field or through laboratory experiments. There is an equal number of grazing and growth rate measured through laboratory experiments and a smaller number of Gross Growth Efficiency (GGE), respiration and egestion values. Although the collected data showed inconsistencies in units, or gaps in knowledge of microzooplankton (e.g. effect of prey nutrient content, combined measurement of grazing and growth), they also contained information on microzooplankton functional response, and how some external factors affect them (e.g. prey concentration, prey offered, temperature). Link to the repository: doi:10.1594/PANGAEA.820368 and doi:10.1594/PANGAEA.826106. Note that the sum of all data sets differs from the present data compilations which provides harmonized units and temperature adjusted metabolic. Within the repository there is a link to the "raw" dataset.

scholarly journals Predator type influences the frequency of functional responses to prey in marine habitats

2020 ◽  
Vol 16 (1) ◽  
pp. 20190758 ◽  
Author(s):  
Robert P. Dunn ◽  
Kevin A. Hovel
Keyword(s):  
Functional Response ◽  
Handling Time ◽  
Type Ii ◽  
Population Stability ◽  
Functional Responses ◽  
Type Iii ◽  
Marine Habitats ◽  
Per Capita ◽  
Predatory Fishes ◽  
Parameter Values

The functional response of a consumer to a gradient of resource density is a widespread and consistent framework used to quantify the importance of consumption to population dynamics and stability. Within benthic marine ecosystems, both crustaceans and fishes can provide strong top-down pressure on prey populations. Taxon-specific differences in biomechanics or habitat use, among other factors, may lead to variable functional response forms or parameter values (attack rate, handling time). Based on a review of 189 individual functional response fits, we find that these predator guilds differ in their frequency distribution of functional response types, with crustaceans exhibiting nearly double the proportion of sigmoidal, density-dependent functional responses (Holling type III) as predatory fishes. The implications of this finding for prey population stability are significant because type III responses allow prey persistence while type II responses are de-stabilizing and can lead to extinction. Comparing per capita predation rates across diverse taxa can provide integrative insights into predatory effects and the ability of predation to drive community structure.

scholarly journals Building a mechanistic understanding of predation with GPS-based movement data

2010 ◽  
Vol 365 (1550) ◽  
pp. 2279-2288 ◽  
Author(s):  
Evelyn Merrill ◽  
Håkan Sand ◽  
Barbara Zimmermann ◽  
Heather McPhee ◽  
Nathan Webb ◽  
...  
Keyword(s):  
Functional Response ◽  
Handling Time ◽  
Response Models ◽  
Movement Data ◽  
Global Positioning ◽  
Important Challenge ◽  
Sources Of Variation ◽  
Functional Response Models ◽  
Kill Site ◽  
The Right

Quantifying kill rates and sources of variation in kill rates remains an important challenge in linking predators to their prey. We address current approaches to using global positioning system (GPS)-based movement data for quantifying key predation components of large carnivores. We review approaches to identify kill sites from GPS movement data as a means to estimate kill rates and address advantages of using GPS-based data over past approaches. Despite considerable progress, modelling the probability that a cluster of GPS points is a kill site is no substitute for field visits, but can guide our field efforts. Once kill sites are identified, time spent at a kill site (handling time) and time between kills (killing time) can be determined. We show how statistical models can be used to investigate the influence of factors such as animal characteristics (e.g. age, sex, group size) and landscape features on either handling time or killing efficiency. If we know the prey densities along paths to a kill, we can quantify the ‘attack success’ parameter in functional response models directly. Problems remain in incorporating the behavioural complexity derived from GPS movement paths into functional response models, particularly in multi-prey systems, but we believe that exploring the details of GPS movement data has put us on the right path.

scholarly journals The functional response of, Chrysoperla carnea (Stephens) larvae on different nymphal instars of Dubas bug Ommatissus lybicus De Berg.

2014 ◽  
Vol 8 (2) ◽  
pp. 80-85
Author(s):  
Bassim. Sh. Hamad ◽  
Ryadh A. Okaily ◽  
George S. B. Yousif ◽  
Ahmed M. Abdullatif ◽  
Hussain F. Alrubeai
Keyword(s):  
Functional Response ◽  
Attack Rate ◽  
Larval Instar ◽  
Handling Time ◽  
Chrysoperla Carnea ◽  
Type Ii ◽  
Nymphal Instar ◽  
Functional Responses ◽  
Larval Instars ◽  
The Third

The functional response of second and third larval instars of Chrysoperla carnea (Stephens), against different nymphal instars of Dubas bug Ommatissus lybicus De Berg. was studied.The larval instars of the predator exhibited Type II functional responses against the prey. Based on disk equation the attack rate (a) of the second larval instars of the predator were estimated to 1.03± 0.043 , 0.94± 0.015 , 0.88± 0.009 and 0.77 ± 0.02 and the handling time (Th) were 0.0031, 0.0039, 0.0083, and 0.008 day for second, third, fourth and fifth nymphal instars respectively. The third instars larvae of the predator, the attack rate against these nymphal instars were 1.11± 0.01, 1.04 ± 0.29 , 0.97± 0.017 and 0.89 with handling time 0.0019, 0.0028, 0.0064, and 0.0067 day respectively. The theoretical maximum predation(T/Th) of the second larval instars were 322, 256, 120 and114 nymphs for second, third, fourth and fifth nymphal instar respectively; while they were 526, 357, 156, and 149 for the third larval instar. According to this study this predator have a good predation potential in preying on nymph of Dubas bug especially the small nymphs (second and third ).

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