Lecture 6: Dynamics of Consumer-Resource Interactions

Lecture 6: Dynamics of Consumer-Resource Interactions

Huang He

Phone: 18972127775 QQ:105367750 E-mail: hn.huanghe@163.com

PPT 模板下载： www.1ppt.com/moban/ 行业 PPT 模板： www.1ppt.com/hangye/ 节日 PPT 模板： www.1ppt.com/jieri/ PPT 素材下载： www.1ppt.com/sucai/PPT 背景图片： www.1ppt.com/beijing/ PPT 图表下载： www.1ppt.com/tubiao/ 优秀 PPT 下载： www.1ppt.com/xiazai/ PPT 教程： www.1ppt.com/powerpoint/ Word 教程： www.1ppt.com/word/ Excel 教程： www.1ppt.com/excel/ 资料下载： www.1ppt.com/ziliao/ PPT 课件下载： www.1ppt.com/kejian/ 范文下载： www.1ppt.com/fanwen/ 试卷下载： www.1ppt.com/shiti/ 教案下载： www.1ppt.com/jiaoan/

23/4/21 1

Population cycles of predators and their prey

Data from records of purchase by Hudson’s Bay Company, Canada

MacLuich 1937

2

Topics

6..1 Consumers can limit resource populations6.2 Many predator and prey populations increase and

decrease in regular cycles6.3 Mathematic models for predator-prey interaction6.4 Pathogen-host dynamics can be described by the S-I-R

model6.5 Lotka-Volterra model can be stabilized by predator

satiation6.6 Factors can reduce oscillation of predator-prey models6.7 Consumer-Resource system can have more than one

stable state

3

6.1 Consumers can limit resource populations

Populations of consumers are self-regulatedbecause of their effects on their resources

Consumers contribute to the regulation of resource population.

Thus, populations are regulated from above and below.

Questions: how large is the rule of consumers?

4

Predation on cyclamen 【植】仙客来 ( 属 ) mites

Cyclamen mite is a pest of strawberry in CA

Typhlodromus 盲走螨属 mite is a predatory mite

Greenhouse Experiment

One with predatory mite and one without by applying parathion

5

Herbivores and Plant Populations

Herbivores can control plant populations

Klamath 克拉马斯人 weed, or St. John’s wort麦芽汁 , 植物 , became a widely spread pest following its introduction.

When Chrysolina beetle 甲虫 was introduced, the Klamath weed was finally under control.

6

Effects of herbivores on plant production can be measured using exclosure experiments

7

6.2 Many Predator and Prey populations increase and decrease in regular cycles

Cycles of predator and prey populations are common The periods of cycles vary from species to species

Large herbivores (snowshoe hare, muskrat[ 动 ]麝鼠 , ruffed grouse 环毛松鸡 ) 9-10 year

Small ones (vole, mice, lemming [ 动 ] 旅鼠 ) 4 years cycle Predators feed on large prey have long cycle (red foxes, lynx 猞猁 ,

marten 貂鼠 , mink [ 动 ] 貂 (尤指水貂 ), 貂皮衣 ) Predators feed on small prey have short cycle (Artic fox,

hawks, snowy owls) Cycles (oscillations 摆动 , 振动 ) are caused by predator and

prey interaction (predator – prey).

8

Time delays and population cyclesTime delays and population cycles

Time delays in birth and death caused oscillation in population

Time delays also occur in predation

Period of population cycle should be 4 ~ 5 times the time delay

Hare populations fluctuated less on an island with few predators than on the surrounding mainland.

9

Physical conditions may change the period of cyclesPhysical conditions may change the period of cycles

4-year cycle in northern Scandinavia 斯堪的纳维亚 ( 半岛 )( 瑞典、挪威、丹麦、冰岛的泛称 ), but annually in southern Sweden. Winter delay in north maintain a long cycle. In the south, owls hunt voles whole year, create a short cycle. Climate warming may cause the shift from 4-yr to annual shown in this figure (or multiple prey). 10

Development of host immunityDevelopment of host immunity 免疫性免疫性 influences host populationsinfluences host populations

Cases of measles [ 医 ] 麻疹reported in London (before vaccine 疫苗 had been developed)

Peaked about every two years

Periodicity in pathogen-host relationshipsPeriodicity in pathogen-host relationships

11

Habitat structure can affect population cycles

Disease outbreak is density dependent

Forest tent caterpillar 毛虫 as host

Nuclear 细胞核的 polyhedrosis [ 昆 ]( 幼虫的 ) 多面体病 virus as pathogen

In many regions, tent caterpillars infestations 横行 last about 2 years before the virus brings its host population under control. In other regions, it may last 9 yearsForest fragmentation plays a role.Forest edges with more light, inactivate the virus.Habitats has second effects on population

12

Creating predator-prey cycles in the laboratoryCreating predator-prey cycles in the laboratory

Modeling and lab experiments Studies by GF Gause on protists [ 生 ]原生生物

Predator: Ciliated有纤毛的 protist, Didnium Prey: Protist, Paramecium [ 动 ]草履虫 Culture medium: test tube

Difficult to demonstrate the oscillations Predators eat all prey, then die Add refuge, predators would die and left some prey to survive Add small number of predators periodically oscillations.

13

Huffaker’s mite experimentHuffaker’s mite experimentC.B. Huffaker, UC Berkeley (1958)

Predator: mite螨 ,Typhlodromus. 盲走螨 Prey: six-potted mite (Eotetranychus 叶螨 ), pest of citrus fruits 柑橘类的水果Reproduction: parthenogenesis单性生殖 , 孤雌生殖

Control food resources: number and dispersion

First study: 40 positions, 4 fruits, 20 prey, after 11 days, add 2 predators 14

A spatial mosaic 【生】嵌合体 of habitats allows predators and prey to coexist

15

6.3 Mathematical model for predation

Lotka and Volterra equation for predation Prey

Where cNpredNprey is mortality of prey due to predator. c is per capita capture rate, and Npred, Nprey are the number of predators and prey, respectively.

Predator

Where b is efficiency of conversion of prey consumed (cNpredNprey) and d is death rate of predators

predpreypreyprey NcNrNdt

dN

predpredpreypred dNNcNbdt

dN )(

16

Solving the equations

For prey growth (dN_Prey/dt=0) Npred = r/c

Growth rate of prey population is zero when density of predators equals per capita growth rate of prey divided by per capita capture rate of predators.

Any increase in predator density will result in negative growth in prey population

For predator growth (dN_Pred/dt=0) Nprey = d/bc

Growth rate of predator population is zero when rate of increase of prey is equal to rate of mortality divided by the product乘积 of b and c.

Thus the two equations interact and this can be done graphically

17

18

There is a cyclical rise and fall in both the predator and prey populations with time

Density of predators lags behind density of prey

Feast and Famine scenario 盛宴和饥荒的情况Prey and predators are never quite driven to extinction

Mutual population regulation

Pred

19

Trajectories[ 物 ]( 射线的 ) 轨道 , 弹道 , 轨线 of predator and prey populations and their joint

equilibrium point

dP/dt=0 or dv/dt=0

Equilibrium isocline or more common, zero growth isocline

The change in predator and prey populations together follows a closed cycle that combines the individual changes in the predator and prey population, called joint population trajectory.

20

Another chart to show that Lotka-Volterra model predicts a regular cycling of predator and prey populations

Joint equilibrium point

This point is not stable, or neutral stable (exhibits neutral stability), as slightly change in either population will move to next cycle, rather than return

Period of oscillation:T=2Pi/sqrt(rd)

If r=2 (200%) and d=0.5 per year, then T=6.3

21

Influence of growth rate on predator and prey populations

Nprey or V=d/ac is the minimum requirement to sustain the growth of predator populations

Npredator or P=r/c is the largest number of predators that the prey population can sustain.

A surprising prediction of the model is that increase in r of prey growth leads to an increase in predator population, not the prey

22

An increase in the birth rate of prey increases the predator population, but no the prey population

Bohannan and Lenski, Michigan State University

Prey: E. coliPredator: bacteriphage T4

Prey food source: limited by glucose

Tow levels: 0.1 or 0.5 mg per litter

Add food supply only increased predator population.

23

6.4 Pathogen-host dynamics can 6.4 Pathogen-host dynamics can be described by the S-I-R modelbe described by the S-I-R model

Parasites do not remove host from population, but can develop time delays that lead to population cycling

Course of epidemic depends on Rate of transmission (b) and rate of recovery (g): Reproduction ratio: number of secondary cases produced by a primary case during its period of infectiousness, R0=(b/g)SR0>1, an epidemic will occur, each infected individual will infect more than one before it recoversR0<1, fails to take hold in the populationR0: 5-18 for measles, chicken pox etc. HIV: 2-5; malaria: >100.

24

The S-I-R model can predict the spread on epidemic through a host population

Total =100b=1, g=0.2, duration of infectiousness 1/g=5Beginning, S=1, R0=b/g*S=5

Assume no births of S, and no loss of resistance among previously infected individuals.

Influenza virusVaccination: remove individuals from S, reduce R0.

25

Case study: The chytrid fungus and the global decline of amphibians

Pathogenic fungus: Batrachochytrium dendrobatisdisIt kills hosts and persists by infecting alternative species.

Karan Lips, Southern Illinois University, 2006El Cope: first found in July 2004, rapid spread and caused abrupt drop. 26

The Lotka–Volterra model is criticized for overemphasizing the mutual regulation of predator and prey populations Differential equations, no time delay(Difference equations, add time delay) No internal forces act to restore the populations to the

joint equilibrium point, random perturbations could increase oscillations to a point that V=0 or P=0

cNpreyNpredator: at a given Npred, the rate at wich prey are captured increases with Nprey. This is not true. There is predator satiation.

6.5 Lokta-Volterra model can be stabilized by predator satiation

27

Functional and numerical responses

cN_preyN_pred (cVP): For prey population, this term serves to regulate

population growth through mortality For predator population, it serves to regulate population

growth through two distinct responses:

Predator’s Functional responses: the great the number of prey, the more the predator eats. The relationship between per capita rate of consumption and the number of prey (cNpreyNpred).

Predator’s Numerical response: an increase in consumption of prey results in an increase in predator reproduction (b(cNpreyNpred).

28

The functional response is the relationship between the per capita predation rate (number of prey consumed per unit time) and prey population size This idea was introduced by M.E. Solomon in 1949

Three types of functional response (I, II, and III) Developed by C.S. Holling

Functional Responses Relate Prey Consumed to Prey Density

29

Functional responseNe: per capita rate of predation, i.e., # of prey eaten

during a given period of search time.

Type I functional response Ne=c Nprey Passive predator such as spider or the prey is less

sufficiently abundant (e.g., kestrels and voles) All time allocated to feeding is searching.

30

Type II response Ne increase with Nprey rapidly, but level off at high prey

density.

31

Type III functional response

Sigmoid (S-shaped) response At high prey density, the response is the same as type II

response; however, the rate of prey consumed is low when the prey density is low at first, increasing in a S-shaped fashion.

Factors caused the S-shape response 1. availability of cover to escape the predators 2. predator’s search image 3. Prey switching. Switch to other preys (more abundant)

32

Functional response As prey increases, predators

take more prey But how

Linear– Rate of predation is constant

Decreasing rate to maximum– Rate of predation decline

Sigmoidal– Reaches maximum then declines

Functional responses related prey consumed to prey density

(Right panel is expressed as proportion of prey density, # prey consumed divided by prey density)

33

34

Linear Type 1 (European kestrel to vole)Mortality of prey simply density dependentNo limits on system

Decreasing Type 2 (weasel on rodent)Predators can only eat so much – satiationTime needed to kill and eat prey becomes

limiting Sigmoid Type 3 (warbler on budworm larvae)

Capture rate is density dependentAvailability of coverAlternative prey when preferred is rare

(prey switching)Prey not part of predators search image,

not a desirable food source

35

Prey switching Palatable versus less palatable Better return per kill Less energy needed to find and kill

an abundant prey

Model of prey switching

36

Numerical response Predators reproduce more

However reproduction usually slower than prey

Movement into high prey density areas

This aggregative response is very important as it rapidly increases predator density

Predators respond numerically to changing prey density

Aggregative response in the redshank

37

Other numerical response as increased reproductive effort Weasels as predators Rodents as prey Predators followed prey in reproduction Increase of rodent was due to good harvest in 1990

38

Predator population exhibits a numerical response to change in prey density

Most of the increase was due to local population growth rather than immigration from else where

After hare density fell to a low level, red squirrels and other small mammals were eaten by lynx.

39

Numerical response of a predator population lags behind changes in prey density following counterclockwise joint population trajectory

predicted by the Lotka-Volterra model

40

Stability: achievement of an unvarying equilibrium size, often the carrying capacity

Predator-prey: oscillations, but several factors could stabilizing: Predator inefficiency Density-dependent limitations of prey or predator by

other external factors Alternative food resource for predator Refuges for prey at low prey density Reduced time delays in predator responses to changes in

prey abundance

6.6 Factors that reduce oscillations in predator-prey models

41

Population size is determined by: abundance of its resources and of its consumers

One Extreme: resource population is only limited by its own food supply

Another: resource population is depressed below its carrying capacity

Balance between these factors create multiple equilibrium points: alternative state states

6.7 Consumer-resource system can have more than one stable state

42

Consumer-imposed equilibrium:At low density, prey can seek refuge, avoid predatorsAt low density, prey grows faster than predators

Low stable equilibrium point well below its carrying capacityResource-imposed equilibrium

in some cases, prey population can move up from the consumer-imposed equilibrium, due to the limited number of predators, predator satiation, or other factors that keep predators in check (nest limitation), reach equilibrium set by its carrying capacity.

Population could have two stable states and sometime move between these two (crop and forest pests, diseases).

43

23/4/21 44