-formal way of referring to the mean

-tells us where the middle of the measurements falls

denoted as an x with a line on top

-standard deviation tells us how far apart the individual measurements tend to fall

 -clustered = small SD

-all of an organism's physical and behavioral characeristics

-phenotypic variation is when individuals of the same species vary from one environment to the next

-geographical range - this is limited by tolerance, and is non adaptive

-acclimation - reversible physiological changes to function better under local conditions (i.e. producing more red blood cells @ higher elevation)

-genetic (ecotypes/)

-reaction norms... same genes but non reversible processes

ecotypes: different genetic strains of a species... adaptions to local conditions

 Org A -> phenotype A

Org B -> phenotype B

reaction norm: when organism's genes have a flexible developmental program that allows the organism to grow and develop differently in each environment

-i.e. genetically identical plants will grow taller in the shade and shorter in full sun

Org A -> phenotype AorB

-a population represents a group of organisms and also a measurement that wil be taken on them

** this is a statistician's definition (not a biological population)

-used to characterize a population, as n number of datum on their own aren't all that informative

-means and SDs are parameters

-the parameter describes the population, but we only measure a sample from the population

**mean or SD of our sample is called a statistic... we use this to estimate the population parameter

see table 1. in lab manual(p14)

-artificially increasing sample size

done by:

-counting same organism more than once

-taking measurements that are not independent of each other (how genetically related are individuals? etc)

-every member of population has equal chance of ending up in the sample

-this leads to a more representative sample

-also need to know variation within and between (i.e. a cherry tree) if applicable

-helps us to quantify how much confidence we should have in our estimate of the mean of a population (this is the standard error of the mean)

- the smaller the SE associated with the mean, the more confidence we can have in the mean

calculated by dividing standard deviation by the square root of sample size

 Factors that limit distributions

-what limits organism's geographical range?

-why is it more abundant in some parts of it's range than in others? (not yet dispersed, or limited survival and reproduction)

-

dispersal can be explained in a habitat by biotic and abiotic factors

-these questions exist on many different spatial scales.. from global to local

-a good way to get a sample representative of entire area

-it is a line running through the population to be sampled.... measurements are taken at regular/irregulat intervals along the transect

-to answer specific questions

-looking for a difference b/w 2+ populations or a correlation b/w 2+variables

-observational study... which uses natural variation in the factor we want to test

-generally cheaper and more practical

-manipulated experiment

-more control over factors

-field experimetns tend to be observational... they are generally cheaper and yield more realistic results

-the lab provides more control over those other factors that may influence outcome

independent variable - the factor that we think is the cause

dependent variable - is the factor that we believe is the effect

manipulated variable - this is the independent variable

response variable - this is the dependent variable

-controlled variable - we want to control every other factor that might influencethe outcome of the experiment

***when a ariable other than our manipulated variable could potentially explain our results, we call it a confounding factor

-sometimes, the control is a treatment in which the independent variable is not manipulated... used as a baseline

-controls can also be used to rule out the influence of experimental technique on the outcome

-we test a hypothesis by making a prediction of it... hypotheses are more general, and to run a specific experiment you need a prediction

-if our measurements are different from our prediction, we say that hypothesis is falsified

Marginal Value Theorum

-developed by economists - useful in understanding how animals maximize the amount of energy they gain from each unit of time spent foraging

"When should an animal leave a patch of food and search for a new patch?"... (answer to this would be a prediction, MVT is a hypothesis)

***trying to maximize E/t (energy per unit time) of foraging

Central Place Foraging

-same curve as MVT of depleting success in foraging over time (DIMINISHING RETURN)

-designed for foraging back and forth to certain area ... i.e. maternal bird and chicks... how much is it worth to carry back for how long you have to travel?

mathematical tool is identical...

-trends are general patterns examined in data

-The trends of most interest in ecology are those of DIFFERENCES or CORRELATIONS

-of course, other patterns are also important

-We want to summarize all measures in some brief and understandable way.

-most often we use statistics, such as mean and standard deviation, to help us describe our samples, so these are called descriptive statistics

-descriptive statistics are not useful for some data, such as nominal.

-descriptive statistics

-graphs

-graphs are helpful when descriptive statistics do not illustrate the trends

-used to help interpret data

-most common ones are bar graphs and scatterplots

***Generally, if you are looking for a difference you will use a bar graph, and if you are looking for a correlation, use a scatterplot

-**almost never plot raw data

-how many of any different kinds do we have?

-we do this by using a histogram (a special type of bar graph, with data ranges called bins on the x-axis, and the frequency on the Y-axis

NORMAL DISTRIBUTION

-we see lots of measurements that fall close to the centre of the range, and fewer and fewer as we move away from the centre in either direction

 -also known as a bell curve

***about 68% will fall within +/- 1 SD of mean

**about 95% within 2 SD

-should be included whenever you plot means (or medians)

-either standard deviation or standart error can be used for your error bars, and the graph should clearly indicate in the caption which is being used

-in excel, must use custom error bars, as built in ones don't work (for business)

The alternatieve hypothesis (H_A) will be that the expected difference or correlation does exist

-The null Hypothesis (H₀) will be that there is no difference or correlation

*** they are not opposites of each other**

-there are actually two alternative hypotheses for each null hypothesis - one in each direction

-When doing our statistical tests we can usually lump these two alternatives together and consider only the general H_A that a difference exist

***This is known as a "two-tailed test"

****We set up our tests with these 2 kinds of questions because statistical tests do not allow us to prove anythin... only to disprove

TYPE 1 ERROR

-when we conclude that the null hypothesis is false, and it is really true

TYPE 2 ERROR

-conclude the null hypothesis is true, and it is really false

-most inferential statistical tests only tell us the probability of making a type 1 error

-a Power Analysis tell us the probability of making a type 2 error

-Final result of most tests is a number called "P-Value"

-this numberi s the probability of getting the results we did in our samples, if the null hypothesis is true.

-it is the probability that our results can be explained purely by random chance

-it is our chance of making a type 1 error

- by convention, we use 0.05 as our cutoff

1)What question am I trying to answer?

-Are we looking for a difference or a correlation?

(if looking for a difference, can compare central tendency, variance, or distribution)

2)What type of data do I have?

-ratio/interval?

-nominal? ordinal?

-two samples? more?

-pairs?

-parametric? non-parametric?

-

-said to occur when organisms A and B BOTH do worse when together than apart

-typically, due to limited resources

INTERFERENCE COMPETITION

-competition that is direct and physical, in which one organisms interferes with the other in collecting the resource

EXPLOITATION COMPETITION

-one organism uses a resource, making it unavailable to another

***competition may be interspecific or intraspecific

 **When the degree of competition depends on the density of individuals in the habitat, competition is said to be DENSITY-DEPENDENT

1)Alternate Hypothesis is true, samples are different

2)Sample difference represents random chance. Null is true.

3)Sample differene represents bias in study

** Inferential statistical tests tell us the probability of explanation 2

Tests whether or not variances are equal (null is that they are ie. no difference)

-used to decide which T-test to use

-formulates to calculate a test statistic and degrees of freedom (related to sample size).250

********* If calculated value is less than the critical value,, out P-value will be greater than 0.05******

*****Because, as F increases, P-value decreases

If P<0.05, then there is a difference, and we reject null, otherwise, fail to reject null.

when reporting the outcome of a test, include:

-test statistic(t)

-degrees of freedom

-Pvalue

Presenting Results

-Six pieces of information are normally needed for each result being described

1)alternative hypothesis (prediction) being tested

2)Statistical Test being used

3)The test statistic calculated

4)The degrees of freedom calculated

5)The P-value estimated

6)The conclusion drawn

Presenting results-

Conclusions/trends

-The statement of hypothesis can be combined with the statement of conclusion

-A conclusion generally can also be caled a trend

-ultimately, looking for trends in the data is what research is all abut

-Note also that if we looked for a correlation or difference and failed to find one, this should also be reported, and is considered a trend

-We need to indicate this formal conclusion to the reader, but we can do it more conceisely than by aying formally that the alternate hypothesis has been rejected. Instead we simply say that the corelation is significant

significant is used in a results section only to indicate that a P-value<0.05 has been obtained, and the null hypothesis can therefore be rejected.

-define how the sexes interact during mating, reroduction, and parental care

-is influenced by internal and external factors

MONOGAMY-on male and one female form a bond which lasts for at least one breeding season

-usually associated with some degree of parental care by the male

POLYGAMY

POLYGYNY- most commonly, one male attracts a large number of females

POLYANDRY- in some cases, one female may form a long-term bond with several males

PROMISCUOUS-o long term bonds formed,and either sex may mate with more than one partner during a single breeding season

(typically, males are promiscuous)

-ultimately, the benefit is the offspring produces

CONFLICT BETWEEN THE SEXES arises due to the fact that the best strategy may be different for males than for females, and vice versa.

-Females are generally choosier (must invest more time/energy than males, therefore reproductive success of the males depends on the decision of females)

-choose males that provide either resources or better genes

-males are less choosy, especially those who provide little to no parental care

-parent must decide how much of its resources to invest in offspring

-less investment = more offspring

-more investment = less offspring

R-Selected - organisms which tend to produce many offspring, but provide little resources to each

 -tends to be found where population densities are low

-offspring have high probability of dying, even if time is invested

K-Selected - those which produce fewer offspring bu provide more resources to each

-high population densities, offspring will face a great deal of competition

extra-pair-copulations

-mating received by a female from a male who is not her mate.... 

-father ends up raising not his children

-led to evolution of mate guarding

-polygyny arises when a female can obtain greater reproductive success by sharing a male with one or amore other females than she can by forming a monogamous relationship

-polygyny threshold is the difference in territory quality at which polygynous and monogamous females do equally well

-according to this model, polygyny should occur only when the quality of male territories varies so much that some females will have higher reproductive success mated to a polygynous male o a high-quality territory than they would mated monogamously to a male on a poor quality territory.

Sexual Dimorphism-a difference in the outward appearnance of male and emale individuals of the same species.... this is a result of sexual selection

Secondary Sexual Characteristics- traits which distinguish sex over and above the primary sexual organs

(usually in the form of body size, ornamentation, coloration, and courtship behavior)

-elaborate male secondary sexual characteristics act as handicaps

-that a male can survive while bearing such a handicap indicates to a female that he has an otherwise superior genotype