Population dynamics
How populations change over time
�Why study population dynamics and growth?
- prediction of future population growth
-helps manage population sizes
-saves populations from extinction
-helps control pest populations
Growth rate
intrinsic growth rate (r)
Growth rate- number of new individuals that are produced in given amount of time
�Ideal conditions-Populations can experience maximum growth rate called intrinsic growth rate (r)
�E.g., abundant resources allow white-tailed to have twins.
What are the 3 basic models of population growth
Exponential growth model
-Geometric growth model
-Logistic growth model
Exponential Growth Model
Exponential Growth Model�Continuous growth-Useful for populations that reproduce continuously-E.g., Humans, bacteria
�Assumptions: Unlimited resources
What is the Exponential Growth Model equation and explain each part
Nt = number of individuals at time t N0= number of individuals at time 0(initial population)
e= constant, base of Natural log (=2.72)
r = intrinsic growth rate
t= time period
Nt = N0ert
When conditions are ideal, the size of the pop in the future (Nt) dep
Solve this problem for exponential growth model
There are 100 mice with intrinsic growth rate of 0.4. What is the mice population in 5yrs?
Nt= N0ert
N5 = (100 x 2.72)0.4x5
N5= 739
Geometric growth Model
Discrete growth-Population is defined at discrete points in time (e.g. t1t2 t3 , generations)
-Useful when organisms have seasonal breeding�Assumptions :Unlimited environment
What is the equation for Geometric Growth Model
Nt = N0 ?t
Nt = number of individuals at time t
N0 = number of individuals at time 0(initial population)
? = growth rate
t = number of time intervals (generations)
What is Logistic growth
Growth limited by environment
�Growth slows as population reaches environmental limit-how many individuals the environment can sustain-Carrying capacity (K)
�Generates S shaped (sigmoid curve)
Explain what happens in a Logical growth model if
N half way to K
N far from K orN near K
N = K
N > K
Rapid Growth
low growth
No growth
Negative growth
What factors influence or sets K
climate
food
water
breeding sites
predators
competition
What are growth limits of populations?
1.Density-independent factors-Natural disasters-Changes in temperature and drought
2. Density-dependent factors - limited resources - higher levels of stress - disease transmission - predatorsa.Negative density-dependentb.Positive density-dependent
What is Negative and Positive density dependent factors
Positive density-dependent :
Occurs when population densities are low-Hard to find mates; especially uneven sex ratio�Leads to harmful effects of inbreeding�Leads to predation risk
Negative density:
Survivorship curves-
What are the three types
Survivorship curves- To understand survival of the different age classes:- Graph by plotting age class (x) by survivorship (lx)
Type 1- Very little mortality early in life high mortality at end of life
Type 2- relatively constant mortality throughout its
When looking at Life Tables what does X, nx, Sx and Bx mean
x = age class
nx = the number of individuals in each age class
sx= the survival rate from one age class to the next
bx= the fecundity of each age class
What are the three models of population growth?
Geometric:
Exponential: Equation tells us when the conditions are ideal what the size of the population in thr future (Nt) depends on the current size of the pouplation (N0) the population intristic growth rate (r) and the time it took to grow (t)
Logisti
Define the following
Predator
Parasite
Parasitoid
Herbivores
Predator - kills prey, consumes many prey over its lifetime
�Parasite - consumes part of a host, doesn't kill host, consumes few hosts over lifetime
�Parasitoid - species of wasps and flies, lay eggs within other insects -Larvae develop inside host, kill
Desrcibe the cycle between prey and predator
predators limit prey populations
The synchrony of population cycles between predators and their prey suggests that these oscillations are the result of interactions between them.
Example the lunx and rabbit.
Both populations cycle of 9-10 years, with lynx
Explain Carl Huffaker -biological control of pests. What was the main take away ?
-Tested the conditions that cause predator and prey populations to fluctuate-Prey - six spotted mite: feeds on oranges-Predator - westernpredatory mite
What caused the populations to cycle?-Predators dispersed more slowly than prey-Time needed for predato
Explain the Lotka-Volterra Models
Predator-prey equations-Demonstrate that simple models will produce predator-prey cycling
This model shows predator numbers lagging behind those of prey. It calculates the rate change in prey population and rate change in predator population
�Assumptions-
Lotka-Volterra Models Equation Growth rate for prey
dN/dt=rN-cNP
Growth rate of prey population depends on: - the rate of individuals being added to the prey population - minus - the rate of individuals being killed by predators
N = # of prey individuals
r = exponential growth rate of prey
c = capture efficiency
P = #
Lotka-Volterra Models Equation Growth rate for predators
dP/dt=acNP-mP
cNP = # consumed by predator
a = efficiency of converting food to offspring
m = mortality rate
P = # of predators
What is the equation to predict prey population is stable? What about predator?
Hence, a prey population is stable when the addition of prey is balanced by the consumption of prey
r/c=P
Hence, a predator population is stable when the addition of predators is balanced by the mortality of predators.
m/ac=N
equilibrium isocline
a line on a graph representing the sizes of a predator and a prey population, or of competing populations, designating points at which the growth rate of one of the populations is zero.
Where isoclines cross: Joint equilibrium: P and N stableWhen not at e
Example problem
Draw and label the growth isoclines for populations of lynx (P,predator) and snowshoe hare (N, prey)� r = 0.8, c = 0.02, m = 0.4, a = 0.1�Plot the 4 different starting points below and Draw the trajectories for the changes in the lynx and
Draw and label the growth isoclines for populations of lynx (P,predator) and snowshoe hare (N, prey)� r = 0.8, c = 0.02, m = 0.4, a = 0.1�Plot the 4 different starting points below and Draw the trajectories for the changes in the lynx and hare populations
What are some Adaptations to avoid predation
1. Behavioral defenses-Alarm calling - alert conspecifics to threat-In response to alarm or predator cues�spatial avoidance, reduced movement
Example Tadpoles: In order to avoid being caught, they become less active
2.Crypsis - blending in with their surr
Explain and give example of Mimicry
Batesian Mimicry-Harmless organism mimics a noxious species-Consumers are agents of selection�Predators less likely to consume a harmless mimic after experience with a toxic model
Mullerian mimicry-Many different noxious organisms have similar color patte
What is the cost of Defenses?
�Behavior defenses-Reduced feeding
�Structural defenses-Energetically costly
�Chemical defenses-Energetically costly
�All may reduce growth and development
How do predators adapat to their prey defenses?
Coevolution
Example:
�Porcupines & bobcats�Cane toads - toxic skin, introduced into Australia-Black snakes developed resistance to toxin-Tested resistance to toxin in various populations by measuring swimming speed
Structural � spines, seed coatsChemical�
What are the Cost of Herbivore Defenses
Example of Tobacco plants
Researches damanged tobacco plants to create the act of herbivory. They treated one plant with hormones and left the other alone. The plant treated with hormes didnt excrete danger chemicals instead had a higher seed life
Competition Interactions
Intra and Inter specific competitions
What is competed for?
CompetitionInteractions that negatively affect both organisms (-/-)
Intraspecific competition�competition between members of the SAME species�Limits pop. growth (density-dependant factor)
Interspecific competition�competition between members of DIFFERENT
What is "Liebig's law of the Minimum
Not all resources limit population growth�A single resource may be most scare relative to demand-"Liebig's law of the Minimum"�Example: food vs. O2 supply in terrestrial systems�Knowing the minimum amount of resource required for population to grow-Predic
Explain the Liebig's law of the Minimum" with teh silica, asterionella and syndera example
The two species have different demands of this limiting resource.�Asterionella populations reach carrying capacity when they draw silica down to 1?M.�Synedra populations reach carrying capacity when silica goes down to 0.4?M.
�When grown together, Synedra
Principle of Competitive Exclusion
How does natural selection balnce the playing field?
Principle of Competitive Exclusion
Two species with identical niches cannot coexist indefinitely.One will be a better competitor and thus have higher fitness and eventually exclude the other.
For species that compete strongly, natural selection should fav
What factors influence outcome of Competition
Abiotic Factors
�Monitored survival of both species in upper and lower intertidal zone�Rock barnacle: more susceptible to desiccation�Stellate barnacle: more tolerant to desiccation�Why is stellate restricted to upper intertidal zone?
desiccation- removal
What are mechanisms of competition
Exploitative, Interference (aggestive and allelopathy) and Apparent competition
Exploitative-Compete indirectly by depleting common resources-Most common
�Interference (Aggressive and Allelopathy)-Direct aggressive interactions defending a resource-Less common
�Apparent competition-Has the appearance of competition for shared resourc
Interference: Aggressive competition
Interference: Allelopathy
give example
Agressive: Long-legged ants and red harvester ants compete for seeds and insects-Long-legged ants plug harvester ant nests-Harvester ants take several hours to excavate before foraging
Allelopathy: Form of interference competition in plants�Production of
Apparent competition
Two species share a resource but have (-) effects on each other through a common enemy�Ex. Ring-necked pheasant & gray partridge share habits and resources-Allowed both birds to feed on soil infected with parasites (nematodes)�Partridge decline due to hea
Define these three types of Mutualism
Trophic�Both species gain energy and or nutrients
Defensive�One species defends the other and gets food and/or shelter in return
Dispersive�One species disperses seeds or pollen and is rewarded with food.
Define Facultative and Obligate mutualisms
Facultative mutualisms-species can live without mutualistic partner-beneficial but not required for survival-Ex. Ants and aphids, cleaner fish and hosts
Obligate mutualisms-Species can't survive without other species-mutualism required for survival-Ex. Ma
Give and example of Trophic Mutualism
Mycorrhizal fungi
�Endomycorrhizal-
�Ectomycorrhizal
Rhizobium bacteria
Trophic Mutualisms - Plants and fungi Mycorrhizal fungi
�Grow in and around plant roots
�Receive sugar
�Provide N, P, and water
�Endomycorrhizal-Lives inside plant cells
�Ectomycorrhizal-Around plant cel
Rhizobium bacteria live in root nodules of legumes-
Trophic Mutualisms - Animals, Protozoan & bacteria
Define Ruminants
Termites and protozoans�Protozoans digest cellulose in wood�Termites use protozoan waste products
Ruminants �Also have bacteria and protozoans to help digest cellulose
Define endophytic fungi
Some plants defend themselves with endophytic fungi-fungi that live inside a plant's tissue.
�Endophytic fungi produce chemicals that repel herbivores
Give an example of Defensive Mutualism
Bullhorn Acacia - tropical tree -Subject to many competitors and herbivores�"acacia-ants" (Pseudomyrmex) live in the thorns of acacia-Will attack, bite, sting all insects on home plant or herbivores that attempt to graze-Chew on nearby competing plants to
Defensive Mutualism - Cleaners
Cleaner wrasse fish - obtain food by consuming ectoparasites attached to larger fish; -the fish benefit by having fewer parasites
Oxpeckers - preferentially perch on mammals with higher tick abundances, - indicating that this relationship is primarily a m
Dispersal mutualisms - Pollinators
Plants reward pollinators with nectar and /or pollen
example: Some plants have evolved very specific mutualisms�Yucca and yucca moth-Most Yucca rely on only yucca moth -Lays eggs in flower ovaries-Pollinates flower to ensure seeds develop for larval food-
Dispersal mutualisms - seed dispersers
Nutritious fruit often surrounds seed-protein-rich packets on seeds of bloodroot�Hard seed coats helps withstand digestion-Ex. Omphalocarpum fruits - very large�Must be consumed by elephants to germinate�Fruits often green until seed is mature�Prevents pr