Population Biology I: Population Growth

A population is agroup of organisms of a single species that live and reproduce in the same area.

Types of variables
State variable: ratio
Rate variable: how fast a state variable changes

Single species model
Starts out with continuous exponential growth.
Exponential growth is the first principle of population dynamics. A population will grow exponentially as long as the environment remains constant.
A continuous model implies rapid feedback, continuous births, and overlapping generations. Uses differential equations.
A discrete model implies births in specific periods, non-overlapping generations, and uses difference equations.

Nt = population size (number of individuals) at a certain time 't'.
N0 = initial population size (at time 0)
B = Total Births
D = Total Deaths
I = Immigration
E = Emigration

Nt = N0+B+I-D-E

Assuming a closed system, there will be no I nor E, thus Nt = N0+B-D
Nt - N0 = B - D
∆N = B-D

b = birth rate per capita
d = death rate per capita
r = intrinsic rate of increase; r is species-specific and can change within a species
r = b-d

∆N = B-D
∆N = bN-dN
∆N = (b-d)N
∂N/∂t = (b-d)N
∂N/∂t = rN

Nt = N0e^(rt)

Doubling time: time it takes to double the population

tdouble = ln(2)/r

Discrete exponential growth

lambda = Nt/N0 (N at a future time/initial population)
lambda = finite rate of increase
lambda > 1.0 population increases
lambda = 0 population constant
lambda < 1.0 population decreases

Best estimate of lambda occurs when the population reaches a Stable Age Distribution (SAD).
SAD: relative proportion of individuals in each class remains constant

Nt = lambdaN0

Two models converge when the time step (interval) in the discrete model becomes shorter. It allows conversion from one model to the other.

lambda = e^r
r = ln(lambda)

Probability of extinction
Pex can be seen as a function of N0
Pex=(d/b)^N0
A lower initial population increases the probability of extinction.
Highlights the importance of population size for persistence of populations.

Life Histories II: Allocation

Principle of Allocation
Organisms have a limited amount of energy to spend so they much allocate it to competing demands.
How are resources divided among life history stages or functions?

Energy Budget
C = P - R - (U + F)

C = energy consumed
P = production (excess energy)
R = respiration
U = urea
F = feces
(U+F = W; waste)

Growth/Reproduction Tradeoff
The excess energy must be used either for growth or reproduction. It is a dynamic situation and it is not characteristic of an organism's entire life history.
Examples:

• Douglas fir width of growth rings vs. number of cones per tree
• Goldenrod increased biomass dedicated to reproduction when found in sunny areas.

Parent/Offspring Conflict

There is an optimum energy expenditure from the parents in order to ensure offspring fitness. Beyond that point there is decreased return of energy expenditure.

Size/Number Tradeoff

The optimal number and size of eggs to produce occurs at intermediate clutch sizes. 

Observed in birds, mammals, lizards, amphibians

Mean fitness of offspring is inversely proportional to the total number of offspring produced.

Example: lizards fed to satiation still exhibited similar, albeit weaker, pattern.

An alternate hypothesis is that hatching mass is limited by maximum body capacity rather than by energy.

Effect of offspring survival as a function of size: Bryozoans; larger egg size, better survival

Size vs. Number in Varying Quality of Environment for Offspring

As environmental quality deteriorates, the organism should produce fewer and larger gametes.

Shell vs. Tissue Growth

Seen in Littorina snail preyed upon by crabs. 

Allocation to defense vs. maintenance

Crab chemicals cues influenced shell growth

Clonal, Modular, and Unitary Organisms

Clonal organisms can respond quickly to environmental conditions to take advantage of resources to reproduce.

Unitary/Aclonal

• Germ line separate from somatic cell line. (Germ line - reproductive)
• Fixed cell fates
• Body form is highly determinative

Clonal

• Cell fates are not fixed. Great deal of plasticity.
• Body form is indeterminate. There is an ability to change body type or body plan.

Within clonal organisms, there can be modular an non-modular organisms.

Modular

• Grow by repeated iteration of parts
• Bryozoans, corals, ascidians

Non-modular

• Do not grow by repeated iterations of parts
• Lizards, plants, aphids, daphnia

Clone: assemblage of individuals genetically identical by descent.

Genet: whole organism of one genotype

Ramet: clonally produced part of genet

Being clonal can sometimes yield a competitive advantage.

Clonal organisms can reproduce asexually by fission, fragmentation, budding, parthenogenesis.

Consequences of cloning

Advantages:

• Enables fit genotypes to be inherited intact
• Enables rapid colonization, particularly over short distances
• Reproductive output doesn't necessarily decrease with age.
• Rapid utilization of food resources
• Polymorphism: specialization of modules for different functions
• Can survive partial mortality
• Reduce risk of genotype mortality by replicating parts of clone

Disadvantages

• Mutational meltdown: accumulation of deleterious mutations
• Inability to respond quickly to environmental change via natural selection due to loss of genetic variation
• May have poor long distance colonizing ability
• Fission may divide organism into smaller than optimal body size

Life Histories and Dispersal

Life history refers to the schedule of reproduction, along with the allocation tradeoffs of reproduction and survival.
Dispersal is the spread of reproductive products (propagules, larvae, seeds) or individuals (juveniles or adults) from a single source. It is molded by natural selection.

Reproductive strategies: Frequency of reproduction during lifetime

1. Iteroparous: organisms reproduce more than once
• Benefits: Many chances to increase fitness
• Costs: Continued allocation of energy throughout lifetime
• Mast seeding: episodic, synchronous production of large seed crops by a population of plants. Masting is geographically disperse.
• Maple trees
• Fruit trees
• Lowland rainforest trees
• Conifers
• Oaks
• Beech
2. Semelparous: organisms reproduce only once
• Benefits: Delay the cost of reproduction and allocate energy to growth and maintenance.
• Advantages: Often associated with mortality (ultimate loss of fitness)
• The investment of reproduction is sometimes too great that the organism dies. 
• Bamboo
• Squid
• Yucca century plant

Three major hypothesis for the origin of masting

1. Predator satiation
• Reduce per capita seed mortality; swamp predator (especially specialists)
2. Wind pollination
• Increase chances of fertilization; no animals
3. Environmental facing (prediction)
• Species track weather
• Masting after El Niño rains
• Fires in Australia synced to masting
• New hypothesis: difference in temperatures between two and one years previous to masting

'r' vs. 'k' selection

Population growth curve for r-selected species is exponential.

r = intrinsic rate of increase

dN/dt = rN

Traits:

1. High reproductive investment
2. High dispersal
3. Poor competitor

Examples:

• Weedy species
• Invasive species
• zebra mussels
• cheat grass
• purple loofstrife

Population growth curve for k-selected species is logistic.

k = carrying capacity; limit to population size set by resources.

dN/dt = rN(1-N/k)

Traits:

1. Low/Moderate reproduction investment
2. Lower dispersal
3. Good competitors

Examples:

• Some tree species
• Some corals

Dispersal

All organisms can exhibit three subtypes of dispersal

1. Fragmentation: organisms break and disperse
2. Migration: adults and juveniles
3. Individuals of new generation

Why should organisms disperse?

• Disperse away from habitat with poor resources or low amounts
• Increase survival by reducing competition
• Spread genotypes in place where they'll have high fitness
• Prevent local extinction by maintaining connectivity among populations
• Dispersal can save species from extinction

Escape hypothesis

"Get away from parents". 

Survival increases with increased distance from parents.

Selective force for dispersal; escape high mortality close to parents

Sources of high mortality

1. High competition for resources; low light, low nutrients
2. High predation on seeds; seed shadow; predators aggregate near base of tree
3. Pathogens; high risk from molds or fungi

Janzen-Connel Model

Hobbel Model

Exact Compensation Model

Dispersal distances

Short distance dispersal

• Seeds (maple seeds); propagules
• Sea palms: drip zoospores
• Ascidians: asexual fragmentation

Long distance dispersal

• Pacific trade winds
• Dominance of passive dispersal

Dispersal vectors

• Animals: seeds ingested and defecated
• Wind
• Seed burrs: hooks attach to animals

Behavior can influence dispersal. Example: bellbirds drop seeds away from canopy when showing off for females

Behavioral Ecology I - Foraging

Foraging refers to a species eating habits - what to eat, when to eat, where to eat, and when to stop feeding in a certain area. Foraging is molded by natural selection. Essentially, energy gained by feeding affects reproduction and without food there is no survival.

Energy consumed either gets absorbed or is voided as feces. From the energy absorbed, some of it is lost through respiration, digestion, tissue maintenance and movement. The energy left is used for growth. The energy is divided into energy used for somatic growth and energy used for reproductive output. (There are allocation tradeoff, but more on that later.)

Consumer types

There are several consumer types. Although they can be grouped into specialists and generalists, these are not discrete categories, but rather a continuum.

• Monophagous: 1 prey type
• Oligophagous: few prey types
• Polyphagous: many prey types

However, for comparison purposes, we will classify consumer types into two broad categories.

1. Specialists: Feed on one/few type(s) of prey.
• Advantages include being adapted to one single prey, which means they can overcome prey defenses. There is less competition.
• Disadvantages include the risk of prey extinction, making them vulnerable. There may also be nutrition problems due to unmixed diet. In areas of low prey population density, there is an increased search time.
2. Generalists: Feed on multiple types of prey.
• Advantages include low search time and diffused effect of prey toxins.
• Disadvantages include a high or strong interspecific competition. Generalists are also vulnerable to prey defense due to lack of local adaptation.

Optimal Foraging Theory

Optimal Patch Use Model

This model describes the ideal pattern a species should follow to obtain the maximum energy gain. This model takes into account certain assumptions:

1. Food is found in discrete patches
2. No energy is gained when traveling from patch to patch
3. Consumers can assess food's energy value in a patch

The model is represented as an energy gain curve. There's an optimal time to remain in a given patch and an optimum energy gain described by the tangent (with the steepest slope) to the energy gain curve.

Marginal value theorem: Optimum time to reside is defined by the rate of energy gain at the time of leaving the patch.

[Foxglove flower example]

Optimal Diet Model

Maximum foraging is calculated by E/T where E is the energy content and T is the total time spent searching and handling prey. 

T = s + h (searching + handling)

Organisms can behave as time minimizers or energy maximizers.

1. Time minimizers
• Minimize time to gain specific amount of energy
• Mouse - high risk of predation
• Antelopes - males minimize foraging to defend females against other males.
• Snails feeding on barnacles - eat small barnacles quickly, whereas eating large barnacles takes longer
• Prefer small barnacles due to less risk of predation
• Large barnacles expose snails to predators
2. Energy maximizers
• Focus on increasing prey profitability
• Bison, deer, penguins, birds, sunfish

Prey profitability

The profitability of a specific prey can be obtained by dividing its energy content by its handling time (E/h). Handling time refers to the time it takes a predator to attack, kill, and consume a prey once it has encountered it. This is assuming a simple system where there are only two prey types.

Rules of thumb:

(assuming prey type 1 is more profitable than prey type 2)

• If a predator encounters prey type 1 eat it on the spot. Always eat.
• If predator encounters prey type 2, eat if the gain from eating it exceeds the gain from rejecting it and searching for prey type 1.
• if E2/h2 > E1/(s1+h1) where s1 is the additional search time.

Other important notes:

1. A predator will specialize on a prey type only if its search time is low
2. A predator will switch from a specialist to a generalist as average search time for prey 1 increases

Simplifying assumptions of OFT Models:

1. A predator can sense the energetic value of a prey
2. Foraging behaviors are heritable
3. The model only considers 2 prey types
4. Energy content is the only influence on prey choice. (Does not consider other factors such as salt, H2O, etc.)

It is a simplistic theory, but there is a great amount of evidence that supports it.

Scaling

Scaling means relating an organism's body size to an entity of process. It is usually done with power functions. Body size is important because it affects a variety of aspects:

1. Metabolisms
2. Growth and shape
3. Survival
4. Impact of predation and competition
5. Population density and growth
6. Territory area
7. Food acquisition
8. Species diversity
9. Reproduction

Some key aspects to consider:

1. There are general scaling rules that apply across organisms
2. Scaling relationships can be inter-related producing counterintuitive insights.

Power functions

Y= Yom^b

log(Y) = log(Yo)+ b*log(m)

m=mass

b= predictive of slope.

Log transformations allow a better appreciation of the slope of the function.

b = 1.0 means it is isometric, which indicates that the process/pattern to mass ratio is 1:1. (This is rare)

b ≠ 1.0 means it is allometric

b = 0 means there is a scale invariance

Scaling can also be geometric, this means shape doesn't change with body size:

b = 1/3 means the scaling process is in relation to length

b = 2/3 means the scaling process is in relation to area

Types of scaling:

1. Within organisms
• Tree cross-sectional area
• Geometric scaling with area M^0.66
• M^0.75 gives a greater slope. Extra scaling gives tree an advantage against buckling and fractures in high flow forces
• Mammalian heart rate
• M^-0.25
• Number of heart beats per lifetime does not vary with body size
2. Among individuals
• Standard metabolic rate
• Energy expenditure at rest; Kleiber's rule (1932)
• MR = M^0.75
3. Scaling at population-community levels
• Scaling of body mass and population density of mammalian herbivores
• (Population density)(Metabolic rate) = M^0 = scale invariance
• Energetic Equivalence Rule (EER) =  population energy flux of individuals is invariant with body size
• Species of different body sizes use approximately equal amounts of energy
• Plants: Population density related to mass; M^-0.75
• Metabolic resource use in plants; M^0.75
• EER applies to marine and terrestrial plants

Types of size-density relationships

1. Global size-density relations
2. Local size-density relations
• All population data taken from a single region

Biomechanics

There are many aspects of biomechanics that can be seen and studied in nature. However, this lecture focuses on how moving fluids affect organisms. In order to approach this topic it is necessary to first talk about the boundary layer. All life occurs in boundary layers, in the case of marine ecosystems, this can be seen as a flow gradient and the velocity you experience depends on where you are in the boundary layer. The following image explains better than I can what a boundary layer is.

(Image obtained from http://www.grc.nasa.gov/)

As it can be seen in the image above, the velocity increases as you move closer to the top. At the very bottom, the velocity is practically zero. This is known as the no slip condition. This means that fluid immediately in contact with the solid surface does not slip or move relative to the surface. 

With this knowledge, we can talk about the force that acts upon on organisms. Newton's third law states that an action produces an equal and opposite direction. This means that fluid exerts force on an object and an organism responds by exerting equal force on the fluid but in the opposite direction. The force exerted by a fluid is known as drag. Drag can be calculated using the following equation:

Fd=0.5*p(U^ß)AcCd

Fd = drag force

p = (Greek letter ro) = density of fluid

U = velocity of fluid

ß = usually 2

Ac = area perpendicular to flow, also known as characteristic area

Cd = drag coefficient

There are two types of drag: pressure drag and skin friction drag. Pressure drag is due to upstream/downstream differences in pressure. The pressure builds up on one side of the body. This is the most ecologically important type of drag. Skin friction drag refers to the fact that the more surface or 'skin' the organism has, the greater its drag will be. This type of drag is mostly relevant at low velocities.

Nature is smart and organisms have developed drag minimizing strategies. Some of them are:

• Increased flexibility
• This can be seen in sea fans, which bend over with the current. They become parallel to flow and manage to go down near the boundary layer. This is helpful because even though they have a great characteristic area, they are able to be near the low velocity zone of the boundary layer.
• Another example is the strategy seen in holly leaves, which bundle up and collapse as flow increases. 
• A sea anemone's tentacles collapse in high velocities.
• Intertidal and subtidal seaweed also exhibits great flexibility.
• Drag resistance
• This property is related to material strength, such as that seen in wood. Large tropical trees have wide bases (buttress), which gives them support. Having a great basal width offers drag resistance because the center of gravity is distributed over a large area. Basal width increases the distance from the rotation point. Trees also have a considerable weigh that would require great force in order to uproot them.
• Reduced drag coefficient
• A streamlined body shape results in a lower drag coefficient. This can be seen in animals such as dolphins, fish, sharks, among others. Streamlining affects fitness and is an example of convergent evolution.
• Another strategy is to transcend the air/water barrier, as seen in dolphins and flying fish. Since air is roughly 830 times less dense than water, moving temporarily out of the water is a valid strategy to reduce drag.

In order to study pressure-flow relations it is necessary to look at the principle of continuity and Bernoulli's principle. The principle of continuity states that velocity is inversely proportional to cross-sectional area. Bernoulli's principle states that velocity is inversely proportional to pressure.

The principle of continuity can be seen in sponges and their 'biological nozzle'. These organisms reduce the area of aperture to increase excurrent velocity. They expel water at great velocities to minimize the chance of refiltering the same water.

Bernoulli's principle allows us to compare velocities and pressure at different points in an ecosystem. At a point with high pressure, there will be low velocity and vice versa, at a point with low pressure there will be high velocity.  

Induced flow is the coupling of external to internal flow which results in the fluid being drawn passively through an object or organism. An example of this is the prairie dog burrow, in which a reduction in pressure between two points allows air to be passively drawn in through the structure. This is also seen in sponges, where a change in pressure passively draws food-laden water into sponge and augments filter feeding.

Other examples of pressure-flow relationships include fish experiencing pressure flow differentials across their bodies. This allows water to passively enter mouth and go through gills. It also offer advantages for respiration and visual acuity (there is zero pressure at the eyes).

Another force to be considered when taking about pressure is lift. Lift is concerned with pressure differences between the top and the bottom. There is also an equation that can be used to quantify the lift force experienced by an organism. 

Fl = 0.5p(U^2)AcCl

Fl = lift force

p = ro = density of fluid

U = velocity

Cl = lift coefficient

Ac = characteristic area (projected fluid perpendicular to flow)

As with drag, there are lift minimizing strategies (e.g. limpets), but unlike drag there are also lift maximizing strategies (e.g. flight)

Lift can be generated with an oncoming wind and a circulation. In stationary organisms, an adaptation is to have a body tapered in direction of lift so as to decrease the characteristic area and thus reduce the lift force.

However, it is important to consider that velocity is not always stationary. 

acceleration reaction = pCmVa

p = density of fluid

Cm = added mass coefficient (inertia)

V = volume of organism

a = acceleration

With these three equation, one can calculate the total (net) force on an organism, which is the sum of forces due to drag, lift, and acceleration. It is calculated by the Morrison equation.

Morrison equation:

Total net force = √[(Fd+Fa)^2 + Fl^2]

Biomechanics and the principles of drag and lift are also important because of the ecological consequences of high flow forces. Some ecological manifestations and effects are:

1. Hurricane impacts
• Hurricanes have restructured forests by reshaping species distribution and abundance. 
• Example: 1983 hurricane
• There have been species-specific effects, such as tallest trees experiencing the highest velocities.
• Landscape can be predictable as to how wind speed will impact it.
2. Wind speed effects
• Wind speed has had a negative effect on barn swallow fitness.
• Survival rate of birds depends on wind speed.
• Intertidal snails survived perfect storm because of smaller body size.
• smaller drag and lift forces
• High flow forces have selection of a population
3. Distribution of organisms
• Hypothesis: Sea urchins could not occupy shallow areas in exposed site because they get dislodged. 
• Conclusion: Sea urchins did not occupy shallow areas because they could not move and feed.
4. Size and reproduction of organisms
• Seaweed blade area reduced in high flow (lower area)

Conclusion -  High flow affects:

• Shape and performance
• Exchange processes
• Fitness and survival
• Distribution of organisms
• Transport processes
• dispersal
• recruitment
• nutrient transport

Ecology: Introduction

Ecology is the study of "home life of living organisms. It comes from the Greek word oikos, meaning house. It is the study of the interactions that determine the distribution and abundance of organisms. These interactions can be both physical and biological factors.

Studies in ecology deal with a variety of questions. These are some of them:

• Why do populations fluctuate?
• What is controlling population density?
• How do organisms allocate energy to competing life processes?
• Why do predators consume one prey and not another?
• Where do new organisms come from and how are they dispersed?
• How can a sustainable population be achieved?
• What is the effect of removing or adding species to a food web?
• Why do biodiversity hotspots occur? What processes enable it? Why do they occur where they occur?
• What triggers abrupt shifts in ecosystems and do they result in alternate states?
• How are human impacts damaging ecological systems?

Within an ecosystem, there are subtle, and sometimes indirect, interactions that are numerous because of the many different species and the wide variety of factors that play a role. It should also be said that ecological interactions are not static and are constantly evolving.

When talking about evolution, we should mention genetic change, natural selection and fitness. Genetic change consists of mutations and other processes that produce new and variant forms of genes. Natural selection is a process that operates on individuals with different combinations of these genes to endow the most fit a survival advantage. It occurs by differential reproduction and survival of genetically distinct individuals in the population, and involves death and limits to reproductions. Natural selection also ensures that existing species are suited to their environment. Fitness is the proportionate contribution of individuals to future generations. The fittest individual equals 1.0, while all the rest are <1.0. The individuals leaving the greatest number of descendants relative to others are the fittest of the population. There are ways to measure the correlates of fitness, such as reproduction and fertility, survival and mortality, and growth.

Endler (1986) offers ~140 demonstrations of natural selection in the wild. It is one of the best evidences demonstrating a) variability in a trait, b) that trait variation is heritable, and c) that a trait can confer a fitness advantage. These traits can also be observed in Grant and Grant (1993).

Rapid evolution is defined as the evolutionary changes occurring in a population in less than a hundred years. Four categories of rapid evolution affecting species' interaction are:

1. Evolution of trophic links via specialization
• During the 1982-1983 El Niño there was an especially high amount of rainfall which caused a change in seeds. This put selective pressure on finches, leading to a rapid evolution of beak sizes. This event favored granivorous finches. (Grant and Grant 1993)
2. Evolution of defense
• Cryptic coloration in moths responded to changes in color of habitat. By 1900, tree bark was darkened by pollution and the percentage of dark moths increased significantly. (Kettlewell 1995)
3. Rapid loss of traits in absence of interaction
• Guppies exhibited loss of defensive antipredator traits when predation diminished. These traits included cryptic coloration, body size, and specific behaviors. (Endler 1995)
4. Change in outcome of interaction
• The Myxoma virus was introduced in Australia to control the rabbit population, but soon rabbits evolved resistance while the virus evolved decreased virulence. This is an example of coevolution and reciprocal genetic change.

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Niche Theory

A niche is an organism's place in the environment. It is defined by both physiological tolerances and resource requirements and availability. A fundamental niche is a multidimensional space that is quantifiable. Also referred to as a 3D space called hypervolume. It is where a species could live. A realized niche is the space constrained by biological interactions among species. It is the "post-interactive" niche and it is where the species actually lives. The key question now is what determines the width of the realized niche?