I'm guessing that by 'slope' you are talking about an experimental site that is on the slope of a hill?  In that case, what I'm envisioning is that you have an area in which you are running the experiment and in this area you have a number of plants, each of which is assigned to a treatment.  What are you measuring?  That can make a difference as to the independence of the replicates.

In general though, here's my answer.  Having just one experimental site is fine; many field studies do so, and virtually all laboratory studies do (i.e. they are all done in one lab).  That means your data has limits; it only absolutely applies to the site at which and time during which the experiment was conducted.  However, we generally infer that if it happens on one slope or lab, a similar pattern will occur at the next.  So, if I understand the design aright, you will not be pseudoreplicating.

This is provided that 1) the treatments are randomly distributed within the experimental area (this helps to avoid bias) and 2) as you've implied, the replicates are distributed far enough apart that they won't interfere with each other.  How far is far enough will depend on the biology of the system and on the measurements you're making. You'll have to make that determination based on what you know about the biology of the plants, what you're measuring, and what other studies have done. 

What would be pseudoreplcation would be having sub-blocks on the slope (e.g., high and low elevation), or having multiple slopes (several experimental areas) and then treating each of the plants within each of those blocks/slopes as independent of each other.  In that case you'd need another factor in your model; either elevation or slope. 

Hi Justin -

It's a little hard to say without knowing a bit more about your experiment. In general, if it smells like pseudoreplication, it often is... but I'm not convinced in this case.

I assume that a slope is an experimental area? Is it an experimental unit? If it is an experimental unit, then yes, this is probably pseudoreplication. If instead the slope is your "laboratory" and you have distinct experimental units (plots?), this may not be pseudoreplication. You do run into issues of homogeneity in conditions - you mentioned unique microhabitat conditions. If you're looking for the effect of treatment, these conditions may confound your results. You will have to work to reduce the effect of these conditions (if you won't be considering them as factors), and potentially randomize or nest your experimental plots. If you end up using a split-plot design, I strongly recommend looking up doing nested analyses, as they are not always straightforward, and you may need more replicates than you're used to.

Good luck!

-Dan

I'm guessing that by 'slope' you are talking about an experimental site that is on the slope of a hill?  In that case, what I'm envisioning is that you have an area in which you are running the experiment and in this area you have a number of plants, each of which is assigned to a treatment.  What are you measuring?  That can make a difference as to the independence of the replicates.

In general though, here's my answer.  Having just one experimental site is fine; many field studies do so, and virtually all laboratory studies do (i.e. they are all done in one lab).  That means your data has limits; it only absolutely applies to the site at which and time during which the experiment was conducted.  However, we generally infer that if it happens on one slope or lab, a similar pattern will occur at the next.  So, if I understand the design aright, you will not be pseudoreplicating.

This is provided that 1) the treatments are randomly distributed within the experimental area (this helps to avoid bias) and 2) as you've implied, the replicates are distributed far enough apart that they won't interfere with each other.  How far is far enough will depend on the biology of the system and on the measurements you're making. You'll have to make that determination based on what you know about the biology of the plants, what you're measuring, and what other studies have done. 

What would be pseudoreplcation would be having sub-blocks on the slope (e.g., high and low elevation), or having multiple slopes (several experimental areas) and then treating each of the plants within each of those blocks/slopes as independent of each other.  In that case you'd need another factor in your model; either elevation or slope. 

Justin, your title about testing 'topographical effects' seems to imply measurement of some abiotic factor intrinsic to the landscape, but you also mention 'treatments' which implies some kind of manipulation which is being tested, perhaps micro-topographic manipulation? At any rate, your experiment sounds like many small-scale studies in ecology or geography which are restricted in scale- constrained to a marine cove, a ridge, or slope as in your case. Part of avoiding pseudo-replication is making sure your inference (and hypotheses) do not extend beyond the bounds of your study. You cannot infer anything about the response of lupine to your treatment type across "California", or "western facing slopes, for example." Rather, your hypothesis is testing your treatment on a particular slope, which is fine. In the future, time and funding permitting, you or others can replicate the experiment in another location and compare results. Since you mentioned micro-climatic variation (and there will certainly be other variation you can and cannot easily detect), you should consider mapping your slope into a grid and randomizing selection of your treatment quadrants). Hierarchical/mixed models are also a way of teasing out effects that may indicate interesting experimental unit level differences apart from, or which are interacting with your treatment. At any rate, don't let being stuck on one slope put a brake on your science- that fact alone is not enough to put that ominous pseudo-label on your work.   

Hi 

pls consider the following.

Consider the slope direction/orientation

Set your experimental design, including selection of it's type based on your treatment and replicates. then you will find out the 

Hi, 

Sorry I should have been more clear.  We have 3 different topographical treatments - 

1 on a steep slope

1 on a gentle slope

1 in a swale

Each of these 'areas' have 3 replicates spaced out within the area

We are monitoring for germination and reproduction rates

Other variables are:

Seed treatment (scarified or not)

Caging treatment (herbivory)

Topography

Overall it is at one reserve however we are limited to a certain area.  Therefore all the treatments are on the same topographical treatment, but they are spaced far apart in terms of the plants biology.

A ranked plot design for sampling attributes in low vegetation can be found in attached. Hope it helps.

Article Nitrogen and phosphorus limited production of cereals and se...

Hello again Justin,

Thanks for an update on your design. So here's my impression:

This is a pretty complex design, as you have three main factors: Topography (3 levels), Seed (2 levels) and Caging (2 levels). First and foremost, you must randomize the physical arrangement of the nested treatments (Seed and Caging) within your Topography treatment. 

You are dealing with a nested design, which can make analysis difficult, depending on the software package you are using. In R, the lm() and aov() functions can be difficult to use with nested designs (especially if you have any random factors). Just a heads up! There are some tutorials online that should help.

In terms of the original question - are replicates pseudoreplicates if they occur in the same slope treatment? In this case, with some caution, I think NOT, and that you are safe, assuming you take the randomization precautions above. Again, pseudoreplication depends on your experimental unit. If your unit is "plant", you are safe. If you take multiple measurements from each plant (for example, 10 measurements of leaf length for one plant), and treat them as independent, that would be pseudoreplication.

Hello Justin,

You have already received some great advice from the above contributors. I am a little cautious of the interpretation of this design as I have understood it because it sounds to me like it might be spatially confounded  at the level of topography.

If each of your types of topography are also a specific area, with all other treatments within this then any difference at the Topography level could also be simply a location effect (i.e. they are different because of the topography, or because of some other difference among  locations that is not related to the specific topography). Without replication at this level I cannot see how one would falsify the null hypothesis regardless of how much replication is done within each of these areas. Apologies if I have misunderstood your experimental design. What I think you are saying is that you have three areas that also have different topography and are treating it as a level in your experiment. If so then that is spatially confounded. If on the other hand what you are saying is you have different topography withing each of the three areas  (steep slope, gentle slope, swale) then that would not necessarily be so as long as you interspersed your replicate treatments.

This would not invalidate the interpretation of any other factors in the experiment from how you describe it and it would not be pseudoreplicated at these levels, it just may be at the level of topography if they each exist within discrete areas.

You could use a Latin Square Design and have replication by having three slopes at the site and have the test plots repeated in each slope site. See https://onlinecourses.science.psu.edu/stat503/node/21

Justin- One area that could become problematic for you might be differentiating slope effects from site effects. If I understand your design correctly, you are testing three topographies on the same slope. When you run your analyses, you are likely to discover any number of significant correlations in your data. So for example, herbivory might show a positive or negative correlation with the angle of slope. But I think even though your experimental design is very good, you might run into trouble if you attempt to extend your results from correlation to cause & effect. I say this because there could be something inherent to this slope that drives the outcomes that does not exist on other slopes.