Using line equations to calculate a difference in rates of development

[jakerm1995]

I have two line equations representing two temperatures:

Temperature 25C: y= 0.7479x + 0.6586
Temperature 33C: y= 1.050x + 1.601

I am tasked with using these to work out the difference in development rates of a particular species under each temperature. Y= development time and x=Time. I am confused with how to use these two equations to calculate the difference in growth rate. As when I apply a percentage increase calculation to temperature 33, I calculate an 87% increase over 10 hours, and with the 25C i see a 92% increase over 10 hours. It should be that the 33C has a higher development rate and so my calculations must be wrong :/ I am very confused. I will post the graph here so you can understand better. Any suggestions are much appreciated (bare in mind, I am a noob at maths).

 

[BigBeachBanana]

Not sure if I understand your question correctly.
At 25C, the growth rate is .7479, and at 33C, the growth rate is 1.050. Then, (1.050-.7479)/.7479= 40.4%. Meaning the growth rate of 33C is 40.4% faster than 25C.

 

[jakerm1995]

Thanks for your response! Ah okay, I see. And what if I had to represent that value as 'standard developmental hours per degree per day (h/°C/day)?

 

[Dr.Peterson]

Thanks for your response! Ah okay, I see. And what if I had to represent that value as 'standard developmental hours per degree per day (h/°C/day)?

What was the actual statement of the assignment? Before, you said,

I am tasked with using these to work out the difference in development rates of a particular species under each temperature.

What you evidently tried to work out yourself (wrongly), and BBB found for you, is the percent increase in development rate between two temperatures.

What you actually found yourself was the percent increase in age over some particular time intervals; since the growth is linear, not exponential, that is not a constant, and therefore is not an appropriate measurement.

It is not clear whether a percent increase is what you were asked for, or just the actual difference, 1.050 - 0.7479 = 0.3021 developmental hours per hour. (I don't know what "hpf" on the graph means, or why you mention days here.)

Now you appear to be looking for a linear increase in rate per degree, that is, "(developmental hours per day) per degree". But with only two temperatures, we have no evidence about the relationship between rate and temperature, so I would be reluctant to assume it is linear. And that is not what you originally appeared to need, which involved only the two specific temperatures.

I think we need to see the actual assignment.

 

[jakerm1995]

Hi, thanks for you reply. The question asks me to use my line equations from the graph to calculate the difference in the development rate of the species in question, between the temperatures (25c, 33c) And then I am asked to express the value as (h/°C/day). I have attached a photo of the question. I also included a photo of the plot above

 

[jakerm1995]

What was the actual statement of the assignment? Before, you said,

What you evidently tried to work out yourself (wrongly), and BBB found for you, is the percent increase in development rate between two temperatures.

What you actually found yourself was the percent increase in age over some particular time intervals; since the growth is linear, not exponential, that is not a constant, and therefore is not an appropriate measurement.

It is not clear whether a percent increase is what you were asked for, or just the actual difference, 1.050 - 0.7479 = 0.3021 developmental hours per hour. (I don't know what "hpf" on the graph means, or why you mention days here.)

Now you appear to be looking for a linear increase in rate per degree, that is, "(developmental hours per day) per degree". But with only two temperatures, we have no evidence about the relationship between rate and temperature, so I would be reluctant to assume it is linear. And that is not what you originally appeared to need, which involved only the two specific temperatures.

I think we need to see the actual assignment.

Hi, thanks for you reply. The question asks me to use my line equations from the graph to calculate the difference in the development rate of the species in question, between the temperatures (25c, 33c) And then I am asked to express the value as (h/°C/day). I have attached a photo of the question. I also included a photo of the plot above I have attached a screenshot above

 

[Dr.Peterson]

I'm a little confused. It appears that "hpf" means "hours post-fertilization", and is actual elapsed time, whereas "development age" is a set of standard times based on observation of development at a standard temperature. So it looks like the former should be on the vertical axis and the latter horizontal ("plot the actual age against the stage you observed").

It also sounds as if you are expected to assume the effect of temperature is linear, and to put the rate you determine in terms of days, and divide the change in rate by the temperature difference. The biology is all beyond my experience.

 

[jakerm1995]

Hi, sorry for the late response. This is what is asked of me:

"You should use your two line equations to work out the difference in development (in standard developmental hours) at a certain time (actual hours) between the two temperatures. If you do this for 24h (actual time = x value), then you already have a value of developmental hours/day. From then you just need to factor in the temperature difference as well to get a final value in h/°C/day."

Does this make any sense?

Thanks again for the help!